fractal dimension analysis of texture formation of whey...

Review ArticleFractal Dimension Analysis of Texture Formation of WheyProtein-Based Foods

Robi Andoyo Vania Dianti Lestari Efri Mardawati and Bambang Nurhadi

Department of Food Industrial Technology Faculty of Agro-Industrial Technology Universitas PadjadjaranJl Raya Bandung Sumedang Km 21 Jatinangor Sumedang 40600 Indonesia

Correspondence should be addressed to Robi Andoyo randoyounpadacid

Received 26 October 2017 Revised 21 March 2018 Accepted 15 April 2018 Published 21 May 2018

Academic Editor Salam A Ibrahim

Copyright copy 2018 Robi Andoyo et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Whey protein in the form of isolate or concentrate is widely used in food industries due to its functionality to form gel under certaincondition and its nutritive value Controlling or manipulating the formation of gel aggregates is used often to evaluate food textureMany researchers made use of fractal analysis that provides the quantitative data (ie fractal dimension) for fundamentally andrationally analyzing and designing whey protein-based food texture This quantitative analysis is also done to better understandhow the texture of whey protein-based food is formed Two methods for fractal analysis were discussed in this review imageanalysis (microscopy) and rheology These methods however have several limitations which greatly affect the accuracy of bothfractal dimension values and types of aggregation obtainedThis review therefore also discussed problem encountered and ways toreduce the potential errors during fractal analysis of each method

1 Introduction

The network system of proteins is often applied to foodone of which is whey protein This is because whey mayaffect the structure or texture as well as viscosity of foodsdepending on the processing applied [1] Whey protein isalso a high-quality protein that provides essential aminoacids and has a high bioavailability (protein efficiency ratioor PER) compared to the other sources of protein [2] Thisprotein functionality is influenced by the ability of wheyprotein to form an aggregated network that can act as gellingagent in protein-fortified foodThe textural properties of gel-type foods are principally determined by the combinationof structural properties of the gel matrix and filler particlesThe filler particles can be classified as ldquoactiverdquo or ldquoinactiverdquobased on the resulting effects of these particles in rheologicalproperties of gel The ldquoinactiverdquo filler has a low chemicalaffinity on the polymer matrix so it cannot strengthen theresulting gel The ldquoactiverdquo filler has a strong interaction withthe polymermatrix and therefore can strengthen the resultinggel structure [3] It is important to predict or manipulate theability of whey protein in forming gel in order to producefoods with desirable texture Gelling properties of wheyprotein are necessary in determining consumer acceptance

in many kinds of food products such as processed meatmilk bread and cakes and improving product appearanceby preventing surface moisture in yogurt [1 4]

The application of whey protein as both structure builderand structure breaker in food should therefore be conductedby manipulating the aggregation process of whey-basedparticles network to produce food products with controlledtexture This accounts for a fundamental and quantitativeunderstanding of the aggregation process Many studies hadobserved the kinetics and aggregation process of particlenetwork dispersions both theoretically and experimentallyWhey protein can theoretically form or alter the food texturebecause it can undergo conformational changes and formnetwork or gel aggregate under certain and continuoustreatmentWhey protein aggregation process consists of threestages that often occur subsequently including conforma-tional changes chemical reactions and physical interactions[5] and can be done through heat or cold gelation methodsThe rheological properties of protein gels produced from theprocess vary greatly depending on pH ionic strength tem-perature and heating rate and gelation methods used [6 7]

Whey protein gels under certain length scales wereproven to have self-similar structure this structure can bedescribed and quantified experimentally by fractal concept

HindawiInternational Journal of Food ScienceVolume 2018 Article ID 7673259 17 pageshttpsdoiorg10115520187673259

2 International Journal of Food Science

Cys106-Cys119

Cys66-Cys160

Figure 1 Structure of 120573-Lg Yellow lines represent disulfide bonds (adapted from Ikeguchi [89])

The fractal concept can be used to describe and quantify thestructure of aggregated particles by using fractal dimension119863 or 119863119891mdashthis shows the relationship between the numberof particles on aggregate and their size119873 sim 119877119863119863119891 values of17ndash18 represent diffusion-limited cluster-cluster aggregation(DLCA) while 119863119891 value of 20ndash22 represents reaction-limited cluster-cluster aggregation (RLCA)mdashthe higher 119863119891value also indicates a denser aggregate structure while lower119863119891 value indicates a more tenuous aggregate Observation ofthe fractal aggregation process can further be used to controlwhey protein-based aggregation so that foods with uniformand appropriate texture can be produced [8]

There are several techniques that can be used to analyzefractal structure in aggregates These experimental methodswere widely used to analyze and evaluate texture character-istics of whey protein-based foods which are carried out byforming a model of whey protein gel system that can be usedas medium The measurement of this physical quantity isrelated tomass distribution in space and can be done throughvarious techniques such as scattering settling microscopy(image analysis) and rheology [9 10] This paper willonly limit the discussion on two methods microscopy andrheology These methods however have several limitationswhich might affect the fractal dimension values and typeof aggregations obtained The review is therefore dividedinto three sections the first section discussed the structureof whey protein and its functionality the second section isabout fractal theories in relation to food structure methodsfor fractal analysis and their limitations the third sectionis a compilation on fractal dimension values and the typesof aggregation of whey protein aggregates gathered fromseveral researches This was done to finally understand howthe texture of whey protein-based food is formed despite thelimitations available on each method

2 Structure and Functionality ofWhey Protein

21 Composition and Structure Proteins provide variousfunctions in food and also maintain the stability of foodstructure Whey proteins can interact with each other andwith other types of protein to make networks associated withgels Whey protein comprises a globular structure as shown

in Figure 1 Globular proteins are usually curled up so that thehydrophobic R regions are centered in the molecule to avoidthe polar environment around them while the hydrophilic Rgroup is located on the surface of the molecule This makesglobular proteins (ie whey protein) soluble in water 120573-Lg as a major component in whey protein determines theproperties of the overall whey protein Each 120573-Lg moleculehas 5 cysteine (amino acid) residues Cys-66 Cys-106 Cys-119 Cys-121 and Cys-160 Cys-66Cys-160 and Cys-106Cys-119 are connected by disulfide bonds (-SS) to form oxidizedform of cysteine that is cystine while Cys-121 is availableas a free thiol (-SH) group One molecule of 120573-Lg (wheyprotein) therefore consists of one free thiol group and twodisulfide bonds [11 12] The free thiol group is entrapped inthe three-dimensional structure of native whey protein andexposed during denaturationThese structures are importantin terms of protein aggregation [13] Heat treatment highpressure mechanical stress and oil-in-water exposure to airduring food processing can cause changes in the tertiary(globular) structure of the whey protein so that the thiol andcystine groups become exposed to the solvent and becomechemically reactive [12]

22 Whey Protein as Gelling Agent Whey protein can en-hance texture formation in food due to one of its function-alities to form gelThis is an important functional attribute tomany food applications such as meat and milk processingand bakery and also to improving appearance of foodproducts such as yogurt [1 4 14]

Rheological properties of protein gel vary depending onthe type of protein pH ionic strength and rate of heatingGel of globular protein is classified into two distinct typesof morphology particulate and fine-stranded gels Extensivereviews on these morphologies were done by Bryant andJulian McClements [15] and Nicolai and Durand [6] Ingeneral particulate gels are turbid gels that can be formedby modifying the pH close to the isoelectric point or at highionic strength (low electrostatic repulsion force) while fine-stranded gels are transparent filamentous gels that can beformed at pH far from the isoelectric point in the absence ofsalt or low ionic strength (high electrostatic repulsion force)Figure 2 showed the microstructure on each type of gel

Verheul and Roefs [5] stated that there are three phenom-ena involved (often subsequently) in aggregation process of

International Journal of Food Science 3

UnaggregatedNative proteins

Particulate formation Aggregated particulates

Heat

+ salt

Increasing

Protein conc

Solution Viscous solution Filamentous gel


Filament formation Aggregated filaments

Heat

no salt

+ salt

Particulate gelViscous solutionSolution

Figure 2 Illustration of gel formation (adapted from Bryant and Julian McClements [15])

globular protein that is conformational changes chemicalreaction and physical interaction Conformational changesare related to denaturation process and consist of two stepsThe first step is unfolding of globular protein which is thenfollowed by the second step aggregation [1] Proteins inthe native form initially undergo a process of structuralconformation changes (denaturation) due to modificationof the external environment [16] The unfolding of globularwhey protein causes the exposure of hydrophobic free thioland disulfide groups which are initially present in the interiorof globular protein thus allowing inter- and intramolecularinteractions among whey proteins [15] This exposure leadsto chemical reactions and aggregation through covalent andnoncovalent bonds [5 7 8 11 15 17ndash19] The aggregationprocess itself is divided into two stages primary aggregationthat leads to the formation of spherical particles or flexiblestrands (filament) and secondary aggregation that occursas protein and salt concentration increase This secondaryaggregation finally leads to formation of gel precipitate orfractal clusters [6] A further stage of aggregate formation isphysical interaction or commonly noticed as cluster-clusteraggregation Particles in this stage diffuse and stick togetherrandomly in certain media with certain probability and formlarger clusters (gel network) [20]Theprocess of gel formationby whey protein itself can be done in two ways namely heatand cold gelation

Heat GelationHeat gelation is done by heating whey proteinsolution sample at gelation temperature until denaturationand aggregation occur The gel is prepared by heating thenative whey protein solution (119862119892 = 2ndash200 gL temperaturegt 60∘C) for 10 minutes to 24 hours at various pH (25ndash90)with certain salt concentration (sim20mMndash10MNaCl) [15 1821ndash28] followed by rapid cooling at room temperature [1]

McClements and Keogh [29] observed that the process ofgel formation in heat gelation is influenced by temperatureand heating time The gelation temperature of aggregatedwhey protein was 48∘C while for native whey protein it was77∘C This is because the aggregated whey protein has moreexposed hydrophobic groups to the whey protein solutionHydrophobic interactions that occur can therefore overcomethe electrostatic repulsion forces at lower temperature so thegelation temperature is also lowered On the other hand thegel will not form on native whey protein solution until thetemperature reaches a point where unfolding occurs Thiseffect of heating is also influenced by pH ionic strengthand the concentration of salt protein sugar and fat [114] Aggregation and gelation in heat gelation also occursimultaneously [13]

The formation of covalent bonds in the form of additionaldisulfide bonds from the oxidation of thiol groups or thiol-disulfide exchange reaction occurs in both gelation typesTheformation of additional disulfide bonds stabilizes some weakclusters and decreases the potential for restructuring duringgel formation [30] Hoffmann and van Mil [31] examinedthe role of free thiol groups and disulfide bonds in the heatgelation of 120573-Lg the result showed that 120573-Lg is dispersed atneutral pH and heating at 65∘C enhanced the formation ofaggregate mainly due to presence of intermolecular disulfidecrosslink

Cold Gelation Cold gelation consists of two stages thepreparation of heat-denatured whey protein solution andgelation at low (or ambient) temperature In contrast toVerheul and Roefs [5] research by Alting et al [32] indicatedthat the initial stage in cold gelation process was physicalinteraction This stage was then followed by an increase inhardness and stiffness of the gel due to a covalent reaction


between structural elements of the gel Aggregation andgelation process occur separately throughout this processThis causes the properties of the gel in cold gelation to bereadily adjusted in the early stages of aggregation before thegelation [13 15]

The aim of preparing a heat-denatured whey proteinsolution is to produce a solution containing filamentous typeof protein aggregate that does not gel [15] This is done byheating the native whey protein solution at low concentration(119862119892 = 6ndash10 (wv)) [29 32ndash38] at temperatures between 70and 90∘C for 5ndash60 minutes [29 30 35] at pH distant fromthe isoelectric point (sim2 units above the pI of protein) and atlow ionic strength (lt50mM NaCl or lt10mM CaCl2 at pH 7[29 35 36 39ndash43]) to form soluble aggregates The processof gel formation is influenced by a combination of proteinconcentration pH ionic strength temperature and heatingtime The gel is formed on a critical gel concentration (119862119892)where at a concentration higher than 119862119892 the gel network willnot flow if tilted but will flow at a lower concentration 119862119892will decrease with increasing salt concentration and decreasein pH while aggregate size will increase [30]The next step isto induce gelation at room temperature by adding salt (salt-induced) NaCl [8 38] or CaCl2 [8 35 38 42] Higher NaClconcentrations are needed to induce gel formation from coldgelation process than CaCl2 concentrations [44 45] this isbecause calcium has a specific ion bridge effect that con-tributes to gel formation The protein concentration which istypically used for salt-induced cold gelation is 100 gL wherethe rate of aggregation after salt addition increases sharplywith increasing salt and protein concentration The rate ofaggregation also increases with increasing temperature dueto exposure of hydrophobic groups that lead to hydrophobicinteractions [29 30 44] Kuhn et al [46] suggested that theuse of different types of salt encourages the formation ofdifferent gel structures Gelation with CaCl2 produced irreg-ular microstructure (particulate) resulting in stronger moreelastic and turbid gels whereas gelation with NaCl producedgel with a more-ordered microstructure but more brittle

Gelation also can be performed by adjusting pH of theheat-denatured solution to the isoelectric point of proteinThis is commonly called acid-induced cold gelation onetype of reagents which were used frequently is glucono-120575-lactone (GDL) [32ndash34 47ndash50] The addition of acid leadsto a decrease in electrostatic forces on proteins so thataggregates are formed Stronger gel is generally produced byacid gelation rather than by calcium gelation [48 49 51]where maximum strength is achieved at pH sim 5 which isthe isoelectric point of 120573-Lg [13 47 49] The morphologicalproperties of the initial gel network of acid-induced coldgelation are formed as a result of noncovalent bonding [52]The formation of additional disulfide bonds stabilizes someof the weak clusters and decreases the potential restructuringduring gel formation The formation of disulfide bonds inacid-induced cold gelation had also been studied by Altinget al [32 33 52] the formation of disulfide bonds inthis type of cold gelation was surprising since oxidation ofthiol groups or thiol-disulfide exchange reaction generallyoccurs under alkaline conditions [15] The results showed

that the formation of additional disulfide bonds may occurdepending on the pH used during the process in which thedisulfide bonds cannot form at pH 25ndash35 The rate of acidgelation also controls the level of structural rearrangementsduring gel formation and finally affects the properties ofthe gel The acid gel texture after gel formation tends tobe unstable and hardening gradually occurs due to thiol-disulfide exchange reaction during storage at a pH higherthan 39 [53]

There were different insights regarding the role of thiol-disulfide exchange reaction in acid-induced cold gelationFamelart et al [54] also stated that thiol-disulfide exchangereaction during acid-induced cold gelation also prevented theformation of large covalent structures during gelation of acidunder pH 5 the result also suggested that the role of thiol-disulfide exchange reaction during acid gelation at variouspH was almost insignificant This was demonstrated by theinsignificant difference of elastic modulus of milk gel formedby heating reconstituted milk with and without addition ofthiol-blocking agent (N-ethyl-maleimide or NEM) This wasin contrast with Vasbinder et al [55] Lucey et al [56] andLucey et al [57] that showed significant differences in elasticmodulus and gel hardness made with or without the additionof thiol-blocking agent in which the gel with the addition ofthiol-blocking agent has a slightly modulated (sim20) elasticmodulus and gel hardness (sim30) after gelation This clearlyshowed the presence of additional disulfide bonds duringand after gelation Relatively different results were shown byCavallieri et al [47] in which the disulfide bond is associatedwith the internal stabilization of whey protein aggregatesformed only during the initial heating in acid-induced coldgelation

3 Fractal Concept andQuantification Methods

Many foods like many other natural materials are inherentlyirregular in conformation Food has a complex geometryin which a large category of structural irregularities existsincluding pores (bread snack and cereals) protuberances(cauliflower) and replicating structures (broccoli) Suchattributes may exist over wide levels of magnification Fractalconcept was first introduced by Mandelbrot [58] to describedimensions between regular or conventional dimensions 12 and 3 Fractal dimension indicates the degree to whichan image or object deviates from regularity (Figure 3) Afeature of mathematically constructed fractal objects is self-similarity the attribute of having the same appearance atall magnifications or length scales Natural objects like foodtherefore can be characterized quantitatively in terms oftheir fractal dimension which may serve as an index ofirregularities [59] The fractal model may describe particleaggregation in a mixture of both particles from the pointwhen acidification renders the particles reactive [21] to thepoint when clusters have grown enough to come in closecontact interpenetrate and percolate The fractal dimension(119863119891) is used to describe the occupancy of the structure in thevolume of the gel while the scaling behavior can give insight


Point

Fractal dust

Line

Fractal curve Plane Fractal surfaceSolid volume

0 1 2 3Dimension

Figure 3 Illustration for conventional (Euclidean) and fractal dimensions

(a)

500 nm

(b)

Figure 4 DLCA (a) dan RLCA (b) (adapted fromWeitz et al [61])

into the mechanism of assembly of the particles Fractalanalysis explains the quantitative analytical method thatcharacterized disorder shape of particles network of colloidalsystem [58] The fractal concept has led to considerableadvances of our understanding of colloid aggregation processincluding the structure and size distribution of the aggregatesas well as the kinetics [60]

31 Fractal Dimension in relation to Types of AggregationGel is an elastic network formed by collection of crosslinkedmacromolecular chains that interact with each other Physi-cal interaction processes (cluster-cluster aggregation) whichoccur in gel formation are greatly affected by one of themain characteristics of particle namely Brownian motionThis motion occurs since the small size of particles causesunequal collisions As a result the particles change directionand produce a zigzag randommotionThe Brownian motionallows particles to overcome the effect of gravity so that theparticles do not settle out or separate from the dispersingmedium

The growth model or ideal aggregate formation of parti-cles network based on Brownian motion is divided into twolimiting regimes diffusion-limited (DLCA) and reaction-limited cluster-cluster aggregation (RLCA) (Figure 4) [8]The fractal concept can be used to explain the fractalaggregation regimes of DLCA and RLCA by quantifyingthe structure of aggregated particles by using a parameternamely fractal dimension (119863119891) Aggregation on DLCAregime is very rapid and the collisions among particles arelimited only by Brownian motion The aggregate formed onthis regime is indicated by 119863119891 value of 17ndash18 Meanwhileaggregation in RLCA regime occurs more slowly due tothe electrostatic repulsions between approaching particles

Aggregates formed under these conditions are marked withslightly higher 119863119891 (20ndash22) Weitz et al [61] also stated thataggregate formation with119863119891 value above 20 was irreversibleso that it could be best described as in RLCA regimeThe119863119891values represented in both regimes were also proven to haveimportant effects on the mechanical properties of aggregatednetwork [8 10 61ndash63]

32 Scaling Theory The macroscopic nature of gel is some-how affected by hierarchical level of various factors whichcan be attributed to the properties of each individual proteinmoleculeThe importance of this structural hierarchy cannotbe ignored (Figure 5) They physicochemical propertiesof individual protein molecules as well as environmentalconditions (pH temperature ionic strength etc) will affectthe type of primary particles formed interactions betweenparticles and ultimately the final three-dimensional networkstructureThe observedmacroscopic properties of the systemare influenced by various levels of structure in the hierarchythe most influencinglevel is definitely the one closest to themacroscopic level that is themicrostructure level Predictionand manipulation of the macroscopic nature of the geltherefore require an understanding of the effect of propertiespresent at the microstructure level on the macroscopicproperties of gel Not involving the microstructure level willundoubtedly lead to failure in predicting and manipulatingmacroscopic properties of gels [38]

There are several developing methods for determiningfractal dimension values of complex material such as wheyprotein gels namely scattering settling image analysis andrheology This review will only limit its discussion to twomethods image analysis and rheology This is also based on


Primary Colloidal Particles (sub-micron)

Microstructural Elements (micron)

Microstructures (sub-millimeter)

Macroscopic (gel)

Heat Mass Momentum Transfer and Molecular Thermodynamicskinetic

Heat Mass Momentum Transfer



Molecules (Primary Secondary Tertiary Quaternary structure)

Figure 5Mechanism of protein gel formation (adapted fromMarangoni et al [38])

the fact that the gel aggregate is a quantifiable fractal structurefrom rheological and optical measurements [38]

33 Fractal Structure Measurement

331 Microscopy (Image Analysis) Interpretation of rheo-logical and mechanical properties depends on the structuralinformation derived primarily from microscopic methodsimage analysis and the use of computer simulations to testthe model of food structure in which rheological techniquescannot provide direct information about the underlying foodstructure at molecular level This is because most of theimportant elements affecting physical and rheological prop-erties as well as texture and sensory properties are availablein sizes below 100 120583m The development of the first (optical)microscope opens a new way to visualize and describe mate-rial structure at the molecular level Microscopic techniqueshave the same significance as rheology techniques and areavailable for analyzing food structure at different hierarchicallevels The use of microscopic methods to study food canreveal additional structural information and new insights andapplications in food science and technology [9 64 65]

Image analysis works well for large particles with highcontrast and low dimensionality High contrast and largeparticles are the attributes needed to produce a good andclear image so that the important structural information canbe extracted from the image The whey protein aggregateof 2D images is obtained from several types of microscopetransition electron microscope (TEM) [34 38] scanningelectronmicroscope (SEM) [46] and confocal scanning lasermicroscope (CSLM) [21 32 34 60 66ndash69] Image taken fromCSLM should be in 2D format meaning that the Z-stackshould not be appliedThe imageswill further be processed byusing image processing software (ImageJ Fiji etc) Throughthe software images with certain resolution are converted tograyscale format and then to binary color (black and white)Determination of threshold value (119879119871) is therefore importantas a first step before the image is converted to binary colorThresholding is performed to determine whether a pixel of agiven intensity (0ndash255 0 = black 255 = white) in the imageis considered as an object or background For the image

taken from CSLM the concentration of protein label thatis Rhodamine B should be added by considering the totalprotein concentration in the sample otherwise the unboundRhodamine B will appear as an artefact

Several methods to determine 119879119871 of aggregate imageswere proposed by Kuhn et al (2010) Pugnaloni et al (2005)and Thill et al (1998) [46 70 71] After conversion to binaryimage the119863119891 value from the image is then obtained by usingbox counting method (BCM) in which various sizes of gridsare placed on the image and the number of boxes containingthe pixels of object (119873) is calculated on each grid size (119871)The log-log graph between119873 as ordinate and 119871 as abscissa isthen plotted and the slope of the graph is a fractal dimensionvalue in two-dimensional space (119863BCM) The 119863119891 value inthree-dimensional space which represents the gel aggregatestructure is determined as follows119863119891 = 119863BCM + 1 [9 72]

Limitations on Image Analysis Technique Andoyo et al [34]observed the microstructure of mixture of whey proteinaggregates and native micellar casein by using both CSLMand TEM The results showed that the 119863119891 value from CSLMimage is slightly lower (264) than the TEM image (269)although both results were still in the same aggregationregime (RLCA) Hagiwara et al [60] observed images of 120573-Lgand BSA gels made by heat gelation method in the absenceof salt at pH 70 by using CSLM The resulting aggregateimage is not clear the researchers proposed that it occurredbecause the size of the aggregate was too small to be observedby microscope This also happened in the research doneby Andoyo et al [34] which used TEM to observe acid-induced cold-set gel in whey protein aggregate systemmdashthe119863119891 value cannot be extracted from the image since the flocwas so small that the image had a low contrast and 119879119871cannot be determined The advantages and disadvantagesof image analysis from different types of microscope fordairy gels had been explicitly described by Ercili-Cura [73]In general CSLM which was widely used to analyze thewhey protein aggregate images is capable of projecting three-dimensional structure of gel unto two-dimensional plane(image) The initial sample handling for CSLM is also easiercompared to the other microscope so it does not trigger


the structural changes of the gel CSLM can also provide amore homogeneous luminous flux on each observed imageso that the intensity of the background and object colors canbe clearly distinguished On the other hand SEM and TEMproduced a higher resolution image compared to CSLM butinitial sample preparation is so rough and complicated thatit might trigger structural and morphological changes of gelaggregates

In addition determination of 119879119871 also affects the119863119891 valueobtained from an image Ako et al [66] applied differentmethods of image analysis Various gray level intensities as119879119871 in 120573-Lg gel image higher 119879119871 resulted in lower 119863119891 valueand vice versa In higher 119879119871 more pixels of the image areconsidered as part of the background The effect of changingthresholding led to a change in the contrast and thus changeof the 119863119891 value The 119863119891 value was also determined by therhodamine concentration it should be sufficient to give aproper signal However too much rhodamine added couldchange the structure Furthermore it was not satisfied withthe self-similar concept The exact 119879119871 value therefore greatlydetermines the accuracy of119863119891 value and aggregation regimeobtained In addition to taking a long time and inconsistencydifferent results are likely to be obtained on different timeor by different operators Manual thresholding errors causemore problems during analysis compared to the other causes[74] This was also supported by Andoyo et al [34] who usedthree different manual thresholding methods [46 70 71] onmixture of whey protein aggregates and nativemicellar caseinimage in which the result showed that different proposedmanual thresholding methods resulted in relatively distinctvalues of 119879119871 and 119863119891 Russ [74] suggested that the use ofautomated thresholdingmethods is thereforemore advisableThese automated thresholding methods are readily availablein the image processing software based on several algorithmsproposed by many image processing researchers [75 76]These algorithms are based on the information or knowledgeabout the subject and images and how the images areacquired However the different types of automated thresh-olding algorithms that were previously proposed by manyresearchers also provide different binary images Furtherobjective and quantitative evaluation is needed to determinethe exact algorithm for each type of image Sezgin andSankur [77] performed a quantitative evaluation based on theaverage value of 5 criteria against 40 algorithms for automatedthresholding These algorithms were applied to documentimages and also to the nondestructive testing images (NDT)inwhich therewere 6 images produced from lightmicroscopewith bimodal histogram distribution [78] The result showedthat the minimum error method algorithm proposed byKittler and Illingworth [75] produced the most uniform andaccurate binary image among other methods This resultwas also supported by previous evaluation done by Glasbey[79] To the authorsrsquo knowledge this automated thresholdingalgorithm has been applied to images of whey protein gelbut it should be optimized furthermore the use of this algo-rithm for whey protein aggregate image with bimodal andmultimodal [80] histogram distributions is quite promisingfor certain type of gels For images with unimodal histogramdistribution statistical analysis of geometric parameters can

be done prior to image processing as stated in Chu et al[81] or Silva et al [82] Thresholding of the images can beoptimized by using automated methods for certain typesof gel For a certain type of gel the calculation of 119863119891 issensitive to the threshold value This is the reason why anoptimized method was used Variations were also observedwhen manual thresholding of images with a wide rangeof threshold values was applied Nevertheless changing thethreshold level or using different thresholding method doesnot really change the message

332 Rheology Determination of119863119891 value using rheologicalproperties of gel requires a model that covers the relationshipbetween the structure of the gel with its rheological proper-ties the most appropriate model for gel aggregate structureswith self-similar pattern is based on scaling theory Theearly development of scaling theory to explain the elasticityof gel was proposed by Buscall et al [83] who proposedthat aggregates network is fractal on a scale greater thantheir primary particle size and formulated the power-lawrelationship of elastic modulus (119864) to solid volume fractionsThe value of 119864 is equal to particle concentration of 120593119860 andthe value of strain at limit of linearity (1205740) is equal to particleconcentration of 120593119861 which are then linearized to

log119864 = 119860 log120593

log 1205740 = 119861 log120593(1)

where 119860 and 119861 are the slopes of log-log plot between rheo-logical parameters and particle concentration Exponents 119860and119861will vary with different gel systems [32]The calculationof fractal dimensions by means of rheological method isgenerally applicable to various rheological parameters of amaterial including strain at limit of linearity (1205740) [20 32 3438 60 68] storage modulus (1198661015840) [8 21 32 34 84] elasticity(119864) [38 60 68] and shear stress (120590) [8] These variousrheological properties of gel aggregate can be determined byusing rheometer or texture analyzer The power-law theorywas further verified by many researchers so three modelsof scaling theory were presented Bremer [85] Shih et al[63] Wu andMorbidelli [10]mdashthese three scaling models arebasically used to find the relationship between rheologicalproperties of a gel and its network structure Bremer [85]classified the particles of gel network into two types straightstrands and curved strands (Table 1) Shih et al [63] classi-fied the gel network into strong-link and weak-link regime(strong-link the extent of viscoelastic linear region decreasedas increasing protein concentration and vice versa (Table 1))based on the strength of inter- and intrafloc interactionswhile Wu and Morbidelli [10] added another regime thatis transition regime to describe the intermediate situationwhere both inter- and intrafloc interactions give similar effectto the gel elasticity Furthermore Narine and Marangoni[86] proposed themechanical models for colloidal aggregatesthat relate the fractal dimension of a colloidal aggregate tomechanical properties as follows

1198661015840 sim119898119860

611988812058712059012058511988930Φ1(119889minus119863) (2)


Table 1 Scaling models for determining fractal dimension

119860 119861 References Gel classification2(3 minus 119863119891) Bremer [85] (Straight strands)3(3 minus 119863119891) 1(119863119891 minus 3) Bremer [85] (Curved strands)(3 + 119909)(3 minus 119863119891) minus1(1 + 119909)(3 minus 119863119891) Shih et al [63] (Strong-link regime)1(3 minus 119863119891) 1(119863119891 minus 3) Shih et al [63] (Weak-link regime)

120573(3 minus 119863119891) (3 minus 120573 minus 1)(3 minus 119863119891) Wu ampMorbidelli [10]

120573 = 1 + (2 + 119909)(1ndash120572)120572 = 0rarr strong-link regime120572 = 1rarr weak-link regime

0 lt 120572 lt 1rarr transition regime(Adapted from Alting et al [32] and Wu and Morbidelli [10])

where 1198661015840 is elastic modulus 119898 is spring constant 119888 is pro-portionality constant 119860 is Hamakerrsquos constant 120585 is diameterof the microstructure 120590 is the diameter of a microstructuralelement assumed to be spherical Φ is the volume fraction119889 is the Euclidean dimension of the network usually 3and 119863 is the fractal dimension of the network They foundthat the model successfully identifies key parameters thatare important in determining the fractal dimension valueThe model relates the values of Hamakerrsquos constants andsize of microstructural elements with the composition of theparticles network Furthermore this model follows the weak-link theory inwhich the rheological parameter of the networkis dependent on the nature of the link betweenmicrostructureas opposed to the strength of the microstructures themselvesand only valid for the relatively high percentages of solidcontent (60ndash100)

Mellema et al [87] proposed five types of gel structuresnamely random curved hinged straight and rigid whichcould be derived using the framework of Kantor and Web-man This model is generalized by introducing a scalingparameter 120585 as percolation length 120575 as a measure of thenumber of deformable links in a strand and a parameter 120576 asa measure of the bendability of the link The model is shownas follows

1198661015840 prop 120585minus(1+2120576+120575)

1205740 prop 1205852120576+120575minus1

120590 prop 120585minus2

(3)

This model can at least cover a wide range of gel types byusing three rheological parameters the storage modulus theyield stress and the maximum linear strain as a function ofthe volume fraction Table 1 summarizes these three scalingmodels

Limitations on Rheological Technique Ikeda et al [20] usedthe scaling model of Shih et al [63] that showed that thevalue of 119863119891 for heat-induced WPI gel produced at 25mM100mM and 500mM NaCl decreased except at 100mMNaCl This suggested that WPI gel at given NaCl concen-tration (100mM NaCl) cannot be predicted appropriatelyby the fractal model The study also showed that limit oflinearity cannot be used to determine the value of 119863119891 sinceit produced unreasonable value (119863119891 between 02 and 07)

The limit of linearity parameter in this study was only usedto determine the regime classification of the resulting gelin this study Research done by Alting et al [32] on acid-induced cold-set WPI gel using scaling model of Shih etal [63] and Bremer [85] also yielded ambiguous 119863119891 valuesThis ambiguity also occurred in heat-induced 120573-Lg gel atvarious NaCl concentrations in the research done by deKruif et al [21] The use of different scaling models can alsoresult in different 119863119891 values This significantly affects theinterpretation of the resulting aggregation regime Althoughrheological technique is relatively easy to apply and canbe performed at higher range of particle concentrationthis method has limitation in terms of appropriate scalingmodel and rheological parametersThe use of scaling modelsand rheological parameters under different gel conditionsdetermines the accuracy and consistency of the resulting 119863119891values

Another limitation includes the following rheologicaldata from various instruments such as rheometer or textureanalyzer cannot directly generate strain values at limit oflinearity this leads to the need for further processing of datamanually to determine the value Hagiwara et al [60 67 68]defined limit of linearity as the value of strain in which therewas a deviation of 5 (see (2)) between the ordinate value(120590) of stress-strain curve with 120574 (strain) times 119864 (elasticity) Theelasticity value itself was the slope value of linear part ofstress-strain curve at 120574 lt 001 Andoyo et al [34] also definedlimit of linearity the same way but formulated the calculationfor deviation (see (5)) in a relatively different way in whichthere was a deviation of 5 between slope at the end of linearpart of stress-strain curve (1198772 sim 099) (119904119897119900119901119890119900) with slope atcertain point (119904119897119900119901119890119899) after the end of linear point of stress-strain curve

Deviation119867 =120590 minus (120574 times 119864)

(120574 times 119864)times 100 (4)

Deviation119860 =slope119900 minus slope119899

slope119900times 100 (5)

Limit of linearity

= strain (120574) value at 5 deviation(6)

Each method used to determine the value of deviationand limit of linearity is relatively subjective therefore each


produces different value of limit of linearity The use of5 deviation value is also determined subjectively by theresearchers so that different percentages of deviation will alsoresult in different limit of linearity valuesThis was supportedby Andoyo et al [34] where the use of 5 and 10 deviationsin determining the strain at limit of linearity yielded relativelydifferent values Hagiwara et al [67] also indicated that theslope value of log 1205740 and log120593 could not be used to find119863119891 values of the observed gel system this might due to thenongenerality of method used to determine the value of limitof linearity or the 5 deviation value used was less accurateto determine the value In some cases the fractal assemblyof whey protein gels only occurred in the suspensions at theearly stages of the acid gelationaggregation until the flocsstarted to come in contact interpenetrate and eventuallypercolate into a gel [34 88] Therefore the range of lengthscales where acid gelation self-similarity investigated wasranging fromsim01 tosim10120583mFractalitymay also exist inwheyprotein-containing samples below the 01 120583m length scaleand it is possible that the flocculation mechanism somewhatdiffered among different samples tested [88] In another caseacid cold gelation probably starts off as a fractal process butis rapidly taken over by another mechanism at larger lengthscales (gt100 nm) [32]

4 119863119865 Value of Whey Protein Aggregates

41 119863119891 from Microscopy This section will explain all the119863119891 value compilations from various researchers by usingmicroscopymethod deKruif et al [21] examined the gel fromthe same solution but with addition of 01M and 05M NaClheated at 685∘C Hagiwara et al [60 67 68] analyzed gelsmade from BSA solution with the addition of 01M NaCl(pH 51) 30mM CaCl2 (pH 70) and 5mM CaCl2 (pH 70)which were heated at 50∘C for 60 minutes followed by 95∘Cfor 10 minutes In addition observations were also made onthe gel made from the 120573-Lg solution with the addition of10M NaCl at pH 70 and 30mM CaCl2 at pH 70 which wereheated at 40∘C for 60 minutes and then 95∘C for 10 minutesAll gels formed from those various researches were thenobserved by microscopy method The 119863119891 values generatedfrom this method for heat gelation of whey protein and itscomponents are in the range of 22ndash281 The addition ofsalt and adjustment of pH of the protein solution prior toheating process to regulate the ionic strength of the solutionalso affected the value of 119863119891 where 119863119891 decreased withincreasing ionic strength Higher119863119891 values may occur due torestructuring and micro-phase separation process occurredin the protein gel during aging (storage) [6 32 68]The imagefrom CSLM also showed that the gel structure tended to bemore homogeneous at NaCl concentrations below 02M andmore heterogeneous at higher ionic strengths Gel formedfrom whey protein solution with salt concentrations higherthan 02M had a more heat-sensitive structure whereas atlower ionic strength the heating temperature only affected thekinetics of gelation [21 66] The 119863119891 value derived from themicroscopy method for whey protein gel made from the heatgelation method lay between 22 and 27 in various types ofconditions so that it could be ideal for reaction controlled gel

formation However such high range of119863119891 values could leadto a different structure formation mechanism as it is not fullycomplying with well-defined RLCA model

Marangoni et al [38] studied salt-induced cold-set WPIgels with 10 (wv) protein concentration induced by CaCl2(10 30 and 120mM) and 9 10 11 and 12 (wv) protein con-centration induced by 300mMNaClThe heating was carriedout at temperature of 80∘C for 30 minutes before gelation atroom temperature Kuhn et al [46] also studied gel with thesame gelation process in 10 (ww)WPI concentrationwhichwas heated at 90∘C for 30 minutes and then diluted to 5 6 78 and 9 (ww) WPI concentrations These solutions werethen induced by 150mMNaCl or 150mM CaCl2 to form gelThe 119863119891 values for these salt-induced cold-set whey proteingels were in the range of 245 and 281 for NaCl-induced and263 and 282 for CaCl2-induced gelsThe difference in valuesresulting from both studies can be due to differences in rate ofaggregation time required to achieve equilibrium conditionsor heating temperatures [46]Marangoni et al [38] also statedthat microscopy method yielded 119863119891 values similar to rhe-ological technique at NaCl and CaCl2 concentrations above30mMThe119863119891 values obtained forwhey protein gel preparedby the salt-induced cold gelationmethod fromvarious studiesunder various conditions were between 225 and 282

The images from SEM showed that the cold-set gelinduced by CaCl2 had a thinner more compact microstruc-ture with a less porous network As WPI concentrationincreased the number of pores decreased and the gel networkformed had a denser structure this could be associatedwith an increase in water-holding capacity (WHC) Cold-set WPI gels induced by NaCl represented a more porousnetwork but had a higher WHC than gels induced by CaCl2this might be because the WHC depended not only on theporosity of the gel but also was influenced by the polymercharacteristics (its availability in water binding) which washighly dependent on the types of salt added NaCl-inducedgels were transparent (fine-stranded) while CaCl2-inducedgels were turbid (particulate) Fine-stranded gels tended tohave higher WHC since they contained smaller and morehomogeneous pore sizes that can bind water more strongly[15 46 47] The increased salt concentration also causedthe gel to become more turbid this suggested an increasein the size of the particle diameter as the salt concentrationincreased at constant119863119891 value Increased protein concentra-tions led to more transparent gels this indicated a decreasein particle size as the concentration of protein increased atconstant119863119891 value [38 50]

Alting et al [32] compared gels formed from 9 (ww)WPI heated at 685∘C and induced by GDL with and withoutaddition of thiol-blocking agent NEM Andoyo et al [34]observed119863119891 values in WPA (whey protein aggregates) madefrom 90 g proteinkg WPI solution heated at 685∘C pH75 for 2 hours and then standardized to 70 g proteinkg119863119891 observations were also performed on mixture of WPAand NMC (native micellar casein) with a ratio of 20 80Both types of solution were then set to achieve certainconcentrations (14ndash62 g proteinkg for WPA and 15ndash90 gproteinkg for WPA and NMC mixtures) The gel formation


Table 2 Fractal dimension (119863119891) values of different types of gels measured by using microscopic method

Reference Gel type 119863119891de Kruif et al (1995) Salt-induced cold gelation 120573-Lg [NaCl] = 01 or 05M 22Hagiwara et al (1997a) Heat-induced 120573-Lg pH = 70 [CaCl2] = 30mM 27Hagiwara et al (1997b) Heat induced 120573-Lg pH = 70 [NaCl] = 10M 268

Hagiwara et al (1998)Heat-induced BSA I = 50mM buffer pH 51 01MNaCl II = 50mM buffer pH 70 30mM CaCl2 III =

50mM buffer pH 70 5mM CaCl2

I = 281II = 281III = 268

Marangoni et al (2000) Heat-inducedWPI (5 wv) salt-induced cold gelationsim245 for 300mMNaCl at different

protein concentrationAlting et al (2003) Acid-induced cold gelationWPI 9 23

Kuhn et al (2010) Heat-inducedWPI + 150mM NaCl or CaCl2CaCl2 = 282NaCl = 281

Torres et al (2012) Yogurt with substituted microparticulate whey protein(MWP) 14ndash26

Andoyo et al (2015) Acid-induced cold gelation whey protein aggregates(WPA) ampWPA + native micellar casein (NMC) pH 45

CSLMWPA = 215

WPA + NMC = 264TEM

WPA + NMC = 269

Eissa Khan (2005)Whey protein solution 3 and 75 (heat withwithouttransglutaminase TG) low pH cold-set whey protein gel

final pH 40

CSLM 196ndash198Rheology 205ndash209

was then induced by using GDL The 119863119891 values generatedfrommicroscopy method for acid-induced cold-set gels werein the range of 215ndash269 The results were consistent withother studies that suggested that 119863119891 values for gels inducedby using GDL ormicroorganisms were in the range of 23ndash24[85] Eissa and Khan [90] compared119863119891 values obtained fromgels made from transglutaminase-modified WPI and WPIwithoutmodificationWPI solution at various concentrationsand pH 70 was initially heated at 80∘C for 1 hour and transg-lutaminase enzyme was added at 50∘C while cooling stirredfor 20 minutes and incubated at the same temperature for 10hours The gel formation was then induced by using GDL atroom temperature until pH increased to 40The resulting gelbased on the CSLM image showed that both types of gel hadfine-stranded morphology with119863119891 values of 196ndash198

The microscopy method has even been used not onlyfor whey protein-based gel models but also for comparingthe structure of protein-based food products Torres et al[69] substituted the use of fats in yogurt by using severaltypes ofmicroparticulate whey protein (MWP)with differentnutrient compositions (including different amount of nativeand denatured whey protein)The results showed that the119863119891values were in the range of 14ndash26 in which lower amount ofnative whey protein would form less interconnected networkwith low self-similarity MWP with higher amount of nativewhey protein produced yogurt with characteristics similarto that of high-fat yogurt This suggested that the denaturedwhey protein might act as a structure breaker because of itsinability to form a cohesive network The appropriate MWPtypes therefore could substitute the use of fats in yogurtproduction Detailed data presented above was collected inTable 2

42 119863119891 from Rheology This section will discuss all the 119863119891value compilations from various researchers by using rheol-ogymethod Stading et al [84] conducted a study of120573-Lg gelsmade by heat gelationmethodThe 120573-Lg solution at pH 53 or75 was heated at a rate of 01∘Cminute or 5∘Cminute from30 to 90∘C and was held constant for an hour Microstruc-tures formed on rapid-heated gels were more open andinhomogeneous and had a higher fracture stress meanwhilethe slow-heated gels had more homogeneous and compactmicrostructure This was also supported by 119863119891 value gener-ated from the same study by using scaling model of Bremer[85] with rheological parameter 1198661015840 where gels formed at pH53 had a particulate morphology with 119863119891 value of 246 for01∘Cminute heating rate and 246 for 5∘Cminute Gels at pH75 were fine-stranded with119863119891 value of 294 for 01

∘Cminuteand 291 for 5∘Cminute Hagiwara et al [60 67 68] alsoexamined the 120573-Lg and BSA gels made by heat gelation byusing scaling model of Shih et al [63] and elasticity as rheo-logical parameter to determine 119863119891 BSA and 120573-Lg solutionswith various protein concentrations were initially added with50mM buffer pH 70 or 50mM acetate buffer pH 51 andthen varied with or without salt addition (01MNaCl or 5 and30mMCaCl2)The solutionswere then heated at 40ndash50∘C for60minutes followed by a temperature of 95∘C for 10minutesand cooled to 25∘C and stored for 24 hours The addition ofNaCl and CaCl2 salts to the protein solution prior to heatingcaused the gel to be classified in the weak-link regime with119863119891 values between 261 and 282 whereas the gel formedwithout the addition of salt at pH 70 fell into the classificationof strong-link regime with 119863119891 values between 200 and 220Hagiwara et al [67] also more specifically suggested that the


119863119891 values resulting from BSA gel aggregates were greaterthan119863119891 values of aggregates in the aqueous solution (resultsgathered from scattering method) [91] This might be due tothe interpenetration effect between aggregates at high proteinconcentration to form a compact gel (higher 119863119891 value) deKruif et al [21] examined the gel from WPI at various con-centrations added with 01 and 05M NaCl prior to heating(heat gelation) Heating was done at a temperature of 685∘Cfor 20 hours The log-log graph between the concentrationsof WPI and 1198661015840 showed that the value of slope decreasedwith increasing NaCl concentration therefore the 119863119891 valuealso decreased as NaCl concentration increased This was incontrast to the observations done using permeabilitymethodwhere the119863119891 value increased along with the increase of NaClconcentrationThese statements differed from those of Ikedaet al [20] and Vreeker et al [8] who stated that the increaseof NaCl concentration added in heat gelation method causedthe decrease in119863119891 value Despite the ambiguity authors triedto extract the 119863119891 value from the study We observed that thegel belonged to the weak-link regime based on Shih et al[63] with119863119891 281 for the gel with addition of 01M NaCl and278 for 05M NaCl The result was in line with microscopymethod (119863119891 = 220) Ikeda et al [20] also examined WPIgel made by heat gelation method The WPI solution wasinitially stirred for 1 hour in 25ndash1000mM NaCl adjusted topH 70 diluted to the desired protein concentration thenheated from 25 to 90∘C at a rate of 25∘Cminute and heldfor 1 hour Gel produced based on Shih et al [63] and strainas rheological parameter belonged to the strong-link regimewhile based on stress and storage modulus the gel underthis study was included in the weak-link regime The 119863119891values determined in this study were based on the strong-linkregime with 119863119891 22 (25mM NaCl) 15 (100mM NaCl) and18 (500mM NaCl) The difference of regime classificationon some rheological parameters was then clarified by Wuand Morbidelli [10] who proposed that the gels were onthe transition regime with 119863119891 values of 256 (25mM NaCl)222 (100mM NaCl) and 220 (500mM NaCl) The resultsmade more sense because the increase of NaCl concentrationshould accelerate the aggregation process causing a decreasein119863119891 value [8] This was also supported by research done byFoegeding et al [92]which showed thatmicrostructure imageof gel at 100mMNaCl comprised a mixture of gel with a fine-stranded and particulate morphologies therefore indicatingthat at 100mMNaCl a transition of microstructural changesof gel occurred Verheul and Roefs [93] also showed thatWPI gel formed with NaCl concentration of 04ndash30Mresulted in 119863119891 value of 220 by using permeability methodnevertheless the fractal concept cannot simply be applied toWPI gels The type of aggregation on heat gelation by usingrheology method in general followed the reaction controlledaggregationwith some limitations as already explained aboveThe resulting aggregation type was similar to microscopymethod and even other methods

Marangoni et al [38] and Kuhn et al [46] also conducteda comparison of119863119891 values resulting from themicroscopy andrheology method in salt-induced cold gelation system Theresulting 119863119891 values were 245 and 262 for the NaCl-inducedgels and 263 and 266 for the CaCl2-induced gels It was

also observable that the gel produced by salt-induced coldgelation of whey protein followed the weak-link regimealthough both researchers used different scaling models andrheological parameters to determine the regime and 119863119891values of gelsThe119863119891 values generated from the salt-inducedcold gelation method lied between 262 and 266 the resultswere similar to those observed using themicroscopymethod

Vreeker et al [8] examined acid-induced cold-set gelprepared fromWPI solution with 1 and 10 protein (ww) atpH 67 which was then heated at 70 and 90∘C for 60 minutesThe solution was then cooled to 20∘C and gel formation wasinduced by using 01MHCl to a pH of 54The results showedthat the gel belonged to the weak-link regime with 119863119891 value20ndash25 Alting et al [32] also examined the WPI gel by samegelation method but using aWPI concentration of 9 (ww)which was heated at 685∘C and diluted to 05ndash9 (ww)Thesolution was then stored at 40∘C and GDL was added to apH of 5119863119891 values from various methods and scaling modelswere not obtained this might be because gel made by acid-induced cold gelation process at a certain level (gt100 nm) didnot generate fractal structure although the aggregate imagegenerated from CSLM could give a 119863119891 value of 22 on thesame gel system Andoyo et al [34] observed the 119863119891 valueby using rheology method on the same acid-induced coldgelation systemwith observation bymicroscopymethodThescaling model used was that of Shih et al [63] with storagemodulus and limit of linearity as rheological parametersBoth rheological parameters produced similar 119863119891 valuesalthough for WPA system 119863119891 values from rheology method(115ndash17) were slightly different compared to the microscopymethod (215) WPA gel belonged to strong-link regime andgel made frommixture ofWPA and NMC belonged to weak-link regime with 119863119891 value 229ndash26 The values were not ofmuch difference with microscopy method (119863119891 264ndash269)Eissa and Khan [90] also examined acid-induced cold-setgels made from WPI with or without enzyme modificationThe results showed that the119863119891 value obtained from rheology(205ndash209 for strong-link regime) did not vary much withthe microscopy method (196ndash198) Based on log-log graphfrom limit of linearity the resulting gel belonged to strong-link regime but based on log-log graph of elastic modulusthe resulting gel belonged to weak-link regime Authorsattempted to obtain 119863119891 values of gels based on weak-linkregime results obtained were relatively larger (119863119891 277ndash278)The observations also showed that microstructure and 119863119891values for both gels were similar but the fracture stress andstrain values were relatively different this might be becauseseveral factors that affect the fracture properties of gel werenot observable atmicrostructure levelThe rate of aggregationresulting from acid-induced cold gelation method by usingrheology method in general was varied among differentresearchers ranging from 115 to 285 However we couldconclude that the gelation process was not ideal RLCA Thepretreatment of whey proteins can be done to modify theaggregation process so as to alter the119863119891 value thus changingthe type of aggregation [34 94] Detailed data presentedabove was collected in Table 3

The values of 119863119891 obtained from rheology method frommost of the studies were not of much difference with the


Table3Fractald

imensio

n(119863119891)v

alueso

fdifferenttypes

ofgels

measuredby

usingrheologicalm

etho

d

Reference

Geltype

119863119891

Hagiwarae

tal(19

97a)

Heatind

uced

BSA

I=pH

70II=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

120573-Lg

IV=pH

70V=pH

70+30

mM

CaCl2

I=strong

-link

200ndash

207

II=weak-lin

k282

III=

weak-lin

k261

IV=str

ong-lin

k214ndash220

V=weak-lin

k269

Hagiwarae

tal(19

97b)

Heatind

uced

120573-Lg

pH=70

[NaC

l]=10

MWeak-lin

k262

Hagiwarae

tal(19

98)

Heat-indu

cedBS

AI=

50mM

bufferp

H5101M

NaC

lII=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

I=weak-lin

k282

II=weak-lin

k282

III=

weak-lin

k261

Vreekere

tal(19

92)

Acid-in

ducedcoldgelatio

nWPI

(1or

10ww

)+01M

NaC

lorC

aCl 2atpH

54

1198661015840

Shih

etal(1990)=

20

Brem

er(19

92)=

23

120590B

remer

(1992)=

24ndash

25

Ikedae

tal(1999)

Heat-indu

cedWPI

pH70

+25ndash100

0mM

NaC

l

25mM

NaC

l=22

100m

MNaC

l=15

(incorrectly

predicted)

500m

MNaC

l=18

5080500and1000

mM

NaC

l=DLC

A

Alting

etal(2003)

Acid-in

ducedcoldgelatio

nWPI

9

11986311989123acid-in

duced

cold

gelatio

nprob

ablysta

rtso

ffas

afractalprocessb

utisrapidlytakenover

byanotherm

echanism

atlarger

leng

thscales

(gt100n

m)

deKr

uifetal(19

95)

Salt-indu

cedcoldgelatio

n120573-Lg

[NaC

l]=01o

r05M

Afterp

assin

gtheg

elatio

nthresholdgelw

ithmoreo

rlessfractal-likes

tructure

was

form

edanditcoarsens

with

increasin

gsaltconcentration

Neverthelessgels

prop

ertie

scou

ldno

tcom

pletely

bedescrib

edusingthe

scalinglawsa

sexplained

bymanyauthors

Marangoni

etal(2000)

Heat-indu

cedWPI

(5wv)

Salt-indu

cedcoldgelatio

nCa

Cl2=weak-lin

k263

NaC

l=weak-lin

k245

Stadingetal(1993)

Heat-indu

ced120573-LgatpH

53with

different

heatingrate

Microstructureo

fgels

show

edstraight-strandtype

pH53=246

ndash247

pH57=291ndash294


Table3Con

tinued

Reference

Geltype

119863119891

Kuhn

etal(2010)

Heat-indu

cedWPI

+150m

MNaC

lorC

aCl 2

CaCl2=weak-lin

k266

NaC

l=weak-lin

k262

And

oyoetal(2015)

Acid-in

ducedcoldgelatio

nWPA

ampWPA

+NMC

pH45

WPA

gels

strong

-link

1198661015840=16

ndash17

120574 0=115

WPA

+NMCgels

weak-lin

k1198661015840=26

120574 0=229

Hagiwarae

tal(19

96)

BSAdissolvedin

HEP

ESbu

ffero

fpH70

andacetateb

uffer

ofpH

51to01

and

0001

solutio

nsheatedat95∘ Cvarying

theh

eatin

gtim

eBS

AatpH

70werea

bout

21and

15119863119891of

heat-in

ducedaggregates

atpH

51w

asabou

t18

Foegedingetal(1995)

Afin

e-strand

edmatrix

form

edin

proteinsuspensio

nscontainedmon

ovalentcation

(Li+K+R

b+and

Cs+)chloridessod

ium

sulfateorsod

ium

phosph

atea

tion

icstr

engths

le01m

oldm3Th

ismatrix

varie

sinstressandstr

ainatfracture

atdifferent

saltconcentrations

Protein-specificfactorscanaffectthe

dispersib

ilityof

proteins

andtherebydeterm

inethe

microstructurea

ndfracture

prop

ertie

sofglobu

larp

rotein

gels

Verheulamp

Roefs(1998)

Gels

werem

adea

tnear-neutralp

HP

rotein

concentration(35ndash89

gl)andNaC

lconcentration(01ndash

3moldm3)w

eres

ystematicallyvarie

d

Gelstr

ucture

didno

tchangem

uchaft

ergelformation

whilegelrigidity

continuedto

increaseand

attheg

elpo

into

nlypartof

thep

rotein

inthed

ispersio

ncontrib

utes

totheg

elnetworkTh

efractalconcept

cann

otsim

plybe

appliedto

WPI

gels

EissaKhan(2005)

Wheyproteinsolutio

n3

and75

(heatw

ithw

ithou

ttransglutam

inaseTG

)low

pHcold-se

twheyp

rotein

gelfin

alpH

40

CSLM

196ndash

198

Rheology205ndash209


values of119863119891 obtained frommicroscopy or even other meth-ods This indicated that the various rheological propertiesof gel aggregates were reflection of the fractal structure ofgel aggregate [34 38 46 60 68] The salt-induced coldgelation process generally resulted in weak-link gels [38 4651] whereas acid-induced cold gelation generally producedstrong-link gel when the initial pH of protein solution wasabove 70 andweak-link gel when pH is below 70 [8 32 34 5190 95]The strong-link gels were generally transparent (fine-stranded gel formed at low ionic strength and pH far frompI) while weak-link gels were turbid (particulate gel formedat high ionic strength and pH close to pI) Hagiwara et al [60]therefore suggested that the transparency and turbidity of gelaggregates were universal characteristics for gels with bothstrong- and weak-link regime respectively Aggregation forall three types of gelation was reaction limited but additionof other components or pretreatment of the protein prior toprocessing could be done to modify the aggregation processso as to produce structure 119863119891 values regime classificationand different aggregation types

From the above description regarding 119863119891 value bymicroscopy and rheology in general there were a variationof 119863119891 values among researchers and differences of 119863119891values within the same gel system These may occur dueto several reasons for example different length scale usedamong researcher means that different resolution of themeasurements and dynamic changes inside the gel make thescaling laws not able to be applied completely as explainedby several authors The fractal gel model assumes that the gelconsists of crosslinked flocs that fill up the space The flocsare supposed to be fractal structures formed by aggregatedparticles The model allows for the possibility that differenttypes of bonds are formed between particles within the flocsand between particles of different flocs One way to obtainsuch a structure is by random aggregation of particles whichleads to fractal aggregates (flocs) that grow until they fillup the space and interconnect into a space filling networkFurthermore the volume fraction of the particles used byauthors was small so that the fractal character of the flocscan be expressed before they fill up the space Differentthresholdingmethods used for119863119891 values by microscopy leadto varied values of119863119891This is one of the critical steps in usingdigital imaging for fractal analysis and different thresholdingvalue can lead to different fractal dimensions Thresholdingis not straightforward and changing the threshold valuecan slightly change the fractal dimension This is probablythe reason why fractal dimensions calculated using differentrheological and microscopy parameter are varied Howeverthe results are still on the same correspondence aggregationregime

5 Conclusion

Results confirmed the applicability of fractal analysis bymacroscopic or microscopic methods in describing wheyprotein-based gels in which viscoelastic measurements cor-relatedwell with themicrostructure of gelsThis can be shownby the values of 119863119891 obtained from rheological measurement

which agreed to some extent with those from image analysisan indication that the rheological behavior of the aggregategels is a reflection of fractal structure of the aggregates ingels Both methods tended to produce 119863119891 values with sameaggregation types for similar gel systems and even yielded119863119891 values similar to other methods Results from numerousstudies confirmed that fractal analysis from macroscopicand microscopic methods were applicable to quantify wheyprotein-based gels despite the presence of several limitationsin both methods

Conflicts of Interest

The authors declare that there are no conflicts of interest

References

[1] S Jovanovic M Barac and O Macej ldquoWhey Proteins-Properties And Possibility of Applicationrdquo Journal for DairyProduction and Processing Improvement vol 55 pp 215ndash2332005

[2] C I Onwulata and P J Huth Whey Processing Functionalityand Health Benefits Wiley-Blackwell Oxford UK 2008

[3] J Chen and E Dickinson ldquoViscoelastic properties of heat-setwhey protein emulsion gelsrdquo Journal of Texture Studies vol 29no 3 pp 285ndash304 1998

[4] L M Huffman and L De Barros Ferreira ldquoWhey-BasedIngredientsrdquo Dairy Ingredients for Food Processing pp 179ndash1982011

[5] M Verheul and S P F M Roefs ldquoStructure of particulatewhey protein gels effect of NaCl concentration pH heatingtemperature and protein compositionrdquo Journal of Agriculturaland Food Chemistry vol 46 no 12 pp 4909ndash4916 1998

[6] T Nicolai andD Durand ldquoControlled food protein aggregationfor new functionalityrdquo Current Opinion in Colloid amp InterfaceScience vol 18 no 4 pp 249ndash256 2013

[7] P Walstra ldquoDispersed Systems Basic Considerationsrdquo in FoodChemistry pp 95ndash155Marcel Dekker Inc NewYork NY USA3rd edition 1996

[8] R Vreeker L L Hoekstra D C den Boer andWGMAgterofldquoFractal aggregation of whey proteinsrdquo Topics in Catalysis vol6 no 5 pp 423ndash435 1992

[9] G C Bushell Y D Yan D Woodfield J Raper and RAmal ldquoOn techniques for the measurement of the mass fractaldimension of aggregatesrdquo Advances in Colloid and InterfaceScience vol 95 no 1 pp 1ndash50 2002

[10] HWu andMMorbidelli ldquoModel relating structure of colloidalgels to their elastic propertiesrdquo Langmuir vol 17 no 4 pp 1030ndash1036 2001

[11] T Croguennec S Bouhallab D Molle B T OrsquoKennedy andR Mehra ldquoStable monomeric intermediate with exposed Cys-119 is formed during heat denaturation of 120573-lactoglobulinrdquoBiochemical and Biophysical Research Communications vol 301no 2 pp 465ndash471 2003

[12] R W Visschers and H H J De Jongh ldquoBisulphide bond for-mation in food protein aggregation and gelationrdquo BiotechnologyAdvances vol 23 no 1 pp 75ndash80 2005

[13] A C Alting M Weijers E H de Hoog et al ldquoAcid-inducedcold gelation of globular proteins effects of protein aggregatecharacteristics anddisulfide bonding on rheological propertiesrdquo


Journal of Agricultural and Food Chemistry vol 52 no 3 pp623ndash631 2004

[14] J E Kinsella and D M Whitehead ldquoProteins in WheyChemical Physical and Functional Propertiesrdquo Advances inFood and Nutrition Research vol 33 no C pp 343ndash438 1989

[15] C M Bryant and D Julian McClements ldquoMolecular basis ofprotein functionality with special consideration of cold-set gelsderived from hat-denatured wheyrdquo Trends in Food Science ampTechnology vol 9 no 4 pp 143ndash151 1998

[16] H H J de Jongh ldquoProteins in food microstructure formationrdquoin Understanding and Controlling Microstructure of ComplexFoods pp 40ndash66 Woodhead Publishing Limited ampCRC PressLLC FLorida Fla USA 2007

[17] A Brodkorb T Croguennec S Bouhallab and J J KehoeldquoHeat-Induced Denaturation Aggregation and Gelation ofWhey Proteinsrdquo in Advanced Dairy Chemistry P L HMcSweeney and J A OrsquoMahony Eds pp 155ndash178 SpringerNew York NY USA 2016

[18] K Katsuta D Rector and J e Kinsella ldquoViscoelastic propertiesof whey protein gels mechanical model and effects of proteinconcentration on creeprdquo Journal of Food Science vol 55 pp 516ndash521 1990

[19] R N W Zeiler and P G Bolhuis ldquoNumerical study of theeffect of thiol-disulfide exchange in the cluster phase of 120573-lactoglobulin aggregationrdquo Faraday Discussions vol 158 pp461ndash477 2012

[20] S Ikeda E A Foegeding and T Hagiwara ldquoRheological studyon the fractal nature of the protein gel structurerdquo Langmuir vol15 no 25 pp 8584ndash8589 1999

[21] K G de Kruif M A M Hoffmann M E Van Marle et alldquoGelation of proteins from milkrdquo Faraday Discussions vol 101pp 185ndash200 1995

[22] L Donato C Schmitt L Bovetto and M Rouvet ldquoMechanismof formation of stable heat-induced 120573-lactoglobulin microgelsrdquoInternational Dairy Journal vol 19 no 5 pp 295ndash306 2009

[23] C Le Bon T Nicolai and D Durand ldquoKinetics of aggregationand gelation of globular proteins after heat-induced denatura-tionrdquoMacromolecules vol 32 no 19 pp 6120ndash6127 1999

[24] M McSwiney H Singh O Campanella and L K CreamerldquoThermal gelation and denaturation of bovine 120573-lactoglobulinsA and Brdquo Journal of Dairy Research vol 61 no 2 pp 221ndash2321994

[25] M Paulsson P Dejmek and T Van Vliet ldquoRheological Prop-erties of Heat-Induced 120573-Lactoglobulin Gelsrdquo Journal of DairyScience vol 73 no 1 pp 45ndash53 1990

[26] M Paulsson P-O Hegg and H B Castberg ldquoHeat-inducedgelation of individual whey proteins a dynamic rheologicalstudyrdquo Journal of Food Science pp 87ndash90 1986

[27] M Stading and A-M Hermansson ldquoViscoelastic behaviour of120573-lactoglobulin gel structuresrdquo Topics in Catalysis vol 4 no 2pp 121ndash135 1990

[28] M Verheul S P F M Roefs and K G De Kruif ldquoKineticsof Heat-Induced Aggregation of 120573Lactoglobulinrdquo Journal ofAgricultural and Food Chemistry vol 46 no 3 pp 896ndash9031998

[29] D JMcClements andMKKeogh ldquoPhysical properties of cold-setting gels formed from heat-denatured whey protein isolaterdquoJournal of the Science of Food and Agriculture vol 69 no 1 pp7ndash14 1995

[30] T Nicolai M Britten and C Schmitt ldquo120573-Lactoglobulin andWPI aggregates Formation structure and applicationsrdquo FoodHydrocolloids vol 25 no 8 pp 1945ndash1962 2011

[31] M A Hoffmann and P J van Mil ldquoHeat-Induced Aggregationof 120573-Lactoglobulin Role of the Free Thiol Group and DisulfideBondsrdquo Journal of Agricultural and Food Chemistry vol 45 no8 pp 2942ndash2948 1997

[32] A C Alting R J Hamer C G De Kruif and R W VisschersldquoCold-set globular protein gels Interactions structure andrheology as a function of protein concentrationrdquo Journal ofAgricultural and Food Chemistry vol 51 no 10 pp 3150ndash31562003

[33] A C Alting H H J De Jongh R W Visschers and J-W F ASimons ldquoPhysical and chemical interactions in cold gelation offood proteinsrdquo Journal of Agricultural and Food Chemistry vol50 no 16 pp 4682ndash4689 2002

[34] R Andoyo F Guyomarcrsquoh A Burel andM-H Famelart ldquoSpa-tial arrangement of casein micelles and whey protein aggregateinacid gels Insight onmechanismsrdquo Food Hydrocolloids vol 51pp 118ndash128 2015

[35] S Barbut and E A Foegeding ldquoCa2+-Induced Gelation of Pre-heated Whey Protein Isolaterdquo Journal of Food Science vol 58pp 867ndash871 1993

[36] C Elofsson P Dejmek M Paulsson and H Burling ldquoCharac-terization of a cold-gelling whey protein concentraterdquo Interna-tional Dairy Journal vol 7 no 8-9 pp 601ndash608 1997

[37] P Hongsprabhas and S Barbut ldquoCa2+-induced gelation ofwhey protein isolate Effects of pre-heatingrdquo Food ResearchInternational vol 29 no 2 pp 135ndash139 1996

[38] A GMarangoni S Barbut S EMcGauley MMarcone and SS Narine ldquoOn the structure of particulate gels -The case of salt-induced cold gelation of heat-denatured whey protein isolaterdquoFood Hydrocolloids vol 14 no 1 pp 61ndash74 2000

[39] S Barbut ldquoEffects of calcium level on the structure of pre-heatedwhey protein isolate gelsrdquo LWT- Food Science and Technologyvol 28 no 6 pp 598ndash603 1995

[40] E Doi ldquoGels and gelling of globular proteinsrdquo Trends in FoodScience amp Technology vol 4 no 1 pp 1ndash5 1993

[41] P Hongsprabhas and S Barbut ldquoEffect of gelation temperatureon Ca2+-induced gelation of whey protein isolaterdquo LWT- FoodScience and Technology vol 30 no 1 pp 45ndash49 1997

[42] P Hongsprabhas and S Barbut ldquoProtein and salt effects onCa2+-induced cold gelation of whey protein isolaterdquo Journal ofFood Science vol 62 no 2 pp 382ndash385 1997

[43] S P Roefs and K G De Kruif ldquoA Model for the Denaturationand Aggregation of beta-Lactoglobulinrdquo European Journal ofBiochemistry vol 226 no 3 pp 883ndash889 1994

[44] K Ako T Nicolai and D Durand ldquoSalt-induced gelation ofglobular protein aggregates Structure and kineticsrdquo Biomacro-molecules vol 11 no 4 pp 864ndash871 2010

[45] C M Bryant and D J McClements ldquoInfluence of NaCl andCaCl2 on cold-set gelation of heat-denatured whey proteinrdquoJournal of Food Science vol 65 no 5 pp 801ndash804 2000

[46] K R Kuhn A L F Cavallieri and R L da Cunha ldquoCold-setwhey protein gels induced by calcium or sodium salt additionrdquoInternational Journal of Food Science amp Technology vol 45 no2 pp 348ndash357 2010

[47] A L F Cavallieri A P Costa-Netto M Menossi and R LDa Cunha ldquoWhey protein interactions in acidic cold-set gelsat different pH valuesrdquo Dairy Science amp Technology vol 87 no6 pp 535ndash554 2007

[48] Z Y Ju and A Kilara ldquoGelation of pH-Aggregated WheyProtein Isolate Solution Induced by Heat Protease CalciumSalt andAcidulantrdquo Journal of Agricultural and FoodChemistryvol 46 no 5 pp 1830ndash1835 1998


[49] Z Y Ju and A Kilara ldquoTextural properties of cold-set gelsinduced from heat-denatured whey protein isolatesrdquo Journal ofFood Science vol 63 no 2 pp 288ndash292 1998

[50] Z Y Ju and A Kilara ldquoProperties of Gels Induced by HeatProtease Calcium Salt and Acidulant from Calcium Ion-AggregatedWhey Protein Isolaterdquo Journal of Dairy Science vol81 no 5 pp 1236ndash1243 1998

[51] Z Y Ju and A Kilara ldquoEffects of Preheating on Propertiesof Aggregates and of Cold-Set Gels of Whey Protein IsolaterdquoJournal of Agricultural and Food Chemistry vol 46 no 9 pp3604ndash3608 1998

[52] A C Alting R J Hamer C G De Kruif and R W VisschersldquoFormation of disulfide bonds in acid-induced gels of preheatedwhey protein isolaterdquo Journal of Agricultural and Food Chem-istry vol 48 no 10 pp 5001ndash5007 2000

[53] A C Alting E T Van Der Meulena J Hugenholtz and RW Visschers ldquoControl of texture of cold-set gels through pro-grammed bacterial acidificationrdquo International Dairy Journalvol 14 no 4 pp 323ndash329 2004

[54] M-H Famelart N H T Le T Croguennec and F RousseauldquoAre disulphide bonds formed during acid gelation of preheatedmilkrdquo International Journal of Food Science amp Technology vol48 no 9 pp 1940ndash1948 2013

[55] A J Vasbinder ACAlting RWVisschers andCGDeKruifldquoTexture of acid milk gels Formation of disulfide cross-linksduring acidificationrdquo International Dairy Journal vol 13 no 1pp 29ndash38 2003

[56] J A Lucey M Tamehana H Singh and P A Munro ldquoEffectof interactions between denatured whey proteins and caseinmicelles on the formation and rheological properties of acidskimmilk gelsrdquo Journal of Dairy Research vol 65 no 4 pp 555ndash567 1998

[57] J A Lucey C T Teo P A Munro and H Singh ldquoRheologicalproperties at small (dynamic) and large (yield) deformations ofacid gelsmade fromheatedmilkrdquo Journal of Dairy Research vol64 no 4 pp 591ndash600 1997

[58] B Mandelbrot The Fractal Geometry of Nature Times BooksNew York NY USA 1982

[59] A H Barrett and M Peleg ldquoApplications of fractal analysis tofood structurerdquo LWT- Food Science and Technology vol 28 no6 pp 553ndash563 1995

[60] T Hagiwara H Kumagai and T Matsunaga ldquoFractal Analysisof the Elasticity of BSA and 120573-Lactoglobulin Gelsrdquo Journal ofAgricultural and Food Chemistry vol 45 no 10 pp 3807ndash38121997

[61] D A Weitz J S Huang M Y Lin and J Sung ldquoLimits of thefractal dimension for irreversible kinetic aggregation of goldcolloidsrdquo Physical Review Letters vol 54 no 13 pp 1416ndash14191985

[62] L G B Bremer B H Bijsterbosch P Walstra and T van VlietldquoFormation properties and fractal structure of particle gelsrdquoAdvances in Colloid and Interface Science vol 46 no C pp 117ndash128 1993

[63] W-H ShihW Y Shih S-I Kim J Liu and I A Aksay ldquoScalingbehavior of the elastic properties of colloidal gelsrdquo PhysicalReview A Atomic Molecular and Optical Physics vol 42 no 8pp 4772ndash4779 1990

[64] J M Aguilera ldquoWhy food micro structurerdquo Journal of FoodEngineering vol 67 no 1-2 pp 3ndash11 2005

[65] V J Morris and K Groves ldquoFood microstructures Microscopymeasurement and modellingrdquo Food MicrostructuresMicroscopy Measurement and Modelling pp 1ndash438 2013

[66] K Ako D Durand T Nicolai and L Becu ldquoQuantitativeanalysis of confocal laser scanning microscopy images of heat-set globular protein gelsrdquo Food Hydrocolloids vol 23 no 4 pp1111ndash1119 2009

[67] THagiwara H Kumagai andKNakamura ldquoFractal analysis ofaggregates in heat-induced BSA gelsrdquo Food Hydrocolloids vol12 no 1 pp 29ndash36 1998

[68] T Hagiwara H Kumagai T Matsunaga and K NakamuraldquoAnalysis of aggregate structure in food protein gels with theconcept of fractalrdquo Bioscience Biotechnology and Biochemistryvol 61 no 10 pp 1663ndash1667 1997

[69] I C Torres J M Amigo Rubio and R Ipsen ldquoUsing fractalimage analysis to characterize microstructure of low-fat stirredyoghurt manufactured with microparticulated whey proteinrdquoJournal of Food Engineering vol 109 no 4 pp 721ndash729 2012

[70] L A Pugnaloni L Matia-Merino and E DickinsonldquoMicrostructure of acid-induced caseinate gels containingsucrose Quantification from confocal microscopy and imageanalysisrdquo Colloids and Surfaces B Biointerfaces vol 42 no 3-4pp 211ndash217 2005

[71] A Thill S Veerapaneni B Simon M Wiesner J Y Botteroand D Snidaro ldquoDetermination of structure of aggregates byconfocal scanning laser microscopyrdquo Journal of Colloid andInterface Science vol 204 no 2 pp 357ndash362 1998

[72] R Quevedo L-G Carlos J M Aguilera and L CadocheldquoDescription of food surfaces and microstructural changesusing fractal image texture analysisrdquo Journal of Food Engineer-ing vol 53 no 4 pp 361ndash371 2002

[73] D Ercili-Cura ldquoImaging of Fermented Dairy Productsrdquo inImaging Technologies and Data Processing for Food EngineersN Sozer Ed Food Engineering Series pp 99ndash128 SpringerInternational Publishing 2016

[74] J C Russ The Image Processing Handbook CRC Press 7thedition 2016

[75] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[76] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo IEEE Transactions on Systems Man and Cyberneticsvol 9 no 1 pp 62ndash66 1979

[77] M Sezgin and B Sankur ldquoSurvey over image thresholdingtechniques and quantitative performance evaluationrdquo Journal ofElectronic Imaging vol 13 no 1 pp 146ndash168 2004

[78] Z-K Huang and K-W Chau ldquoA new image thresholdingmethod based on Gaussianmixture modelrdquoAppliedMathemat-ics and Computation vol 205 no 2 pp 899ndash907 2008

[79] C A Glasbey ldquoAn analysis of histogram-based thresholdingalgorithmsrdquo CVGIP Graphical Models and Image Processingvol 55 no 6 pp 532ndash537 1993

[80] J H Xue and Y-J Zhang ldquoRidler and Calvardrsquos Kittlerand Illingworthrsquos and Otsursquos methods for image thresholdingrdquoPattern Recognition Letters vol 33 no 6 pp 793ndash797 2012

[81] C P Chu D J Lee and J H Tay ldquoBilevel thresholding of flocimagesrdquo Journal of Colloid and Interface Science vol 273 no 2pp 483ndash489 2004

[82] J V C Silva D Legland C Cauty I Kolotuev and J FlouryldquoCharacterization of the microstructure of dairy systems usingautomated image analysisrdquo FoodHydrocolloids vol 44 pp 360ndash371 2015

[83] R Buscall P D A Mills J W Goodwin and D W LawsonldquoScaling behaviour of the rheology of aggregate networksformed from colloidal particlesrdquo Journal of the Chemical Society


FaradayTransactions 1 Physical Chemistry inCondensed Phasesvol 84 no 12 pp 4249ndash4260 1988

[84] M Stading M Langton and A-M Hermansson ldquoMicrostruc-ture and rheological behaviour of particulate 120573-lactoglobulingelsrdquo Topics in Catalysis vol 7 no 3 pp 195ndash212 1993

[85] L G B Bremer Fractal Aggregation in Relation to Formationand Properties of Particle Gels Wageningen University 1992

[86] S S Narine and A G Marangoni ldquoMechanical and structuralmodel of fractal networks of fat crystals at low deformationsrdquoPhysical Review E Statistical Nonlinear and SoftMatter Physicsvol 60 no 6 pp 6991ndash7000 1999

[87] M Mellema J H J Van Opheusden and T Van VlietldquoCategorization of rheological scaling models for particle gelsapplied to casein gelsrdquo Journal of Rheology vol 46 no 1 pp 11ndash29 2002

[88] N Mahmoudi S Mehalebi T Nicolai D Durand and ARiaublanc ldquoLight-scattering study of the structure of aggregatesand gels formed by heat-denatured whey protein isolate and 120573-lactoglobulin at neutral pHrdquo Journal of Agricultural and FoodChemistry vol 55 no 8 pp 3104ndash3111 2007

[89] M Ikeguchi ldquoTransient non-native helix formation during thefolding of 120573-lactoglobulinrdquo Biomolecules vol 4 no 1 pp 202ndash216 2014

[90] A S Eissa and S A Khan ldquoAcid-induced gelation of enzymati-callymodified preheatedwhey proteinsrdquo Journal of Agriculturaland Food Chemistry vol 53 no 12 pp 5010ndash5017 2005

[91] T Hagiwara H Kumagai and K Nakamura ldquoFractal analysisof aggregates formed by heating dilute bsa solutions using lightscattering methodsrdquo Bioscience Biotechnology and Biochem-istry vol 60 no 11 pp 1757ndash1763 1996

[92] E A Foegeding E L Bowland and C C Hardin ldquoFactorsthat determine the fracture properties and microstructure ofglobular protein gelsrdquo Topics in Catalysis vol 9 no 4 pp 237ndash249 1995

[93] M Verheul and S P F M Roefs ldquoStructure of whey proteingels studied by permeability scanning electronmicroscopy andrheologyrdquo Food Hydrocolloids vol 12 no 1 pp 17ndash24 1998

[94] E A Foegeding J P Davis D Doucet and M K McGuffeyldquoAdvances in modifying and understanding whey protein func-tionalityrdquo Trends in Food Science amp Technology vol 13 no 5 pp151ndash159 2002

[95] F Li X Kong C Zhang and Y Hua ldquoGelation behaviour andrheological properties of acid-induced soy protein-stabilizedemulsion gelsrdquo Food Hydrocolloids vol 29 no 2 pp 347ndash3552012

Hindawiwwwhindawicom

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MicrobiologyHindawiwwwhindawicom

Nucleic AcidsJournal of

Volume 2018

Submit your manuscripts atwwwhindawicom


Cys106-Cys119

Cys66-Cys160

Figure 1 Structure of 120573-Lg Yellow lines represent disulfide bonds (adapted from Ikeguchi [89])

The fractal concept can be used to describe and quantify thestructure of aggregated particles by using fractal dimension119863 or 119863119891mdashthis shows the relationship between the numberof particles on aggregate and their size119873 sim 119877119863119863119891 values of17ndash18 represent diffusion-limited cluster-cluster aggregation(DLCA) while 119863119891 value of 20ndash22 represents reaction-limited cluster-cluster aggregation (RLCA)mdashthe higher 119863119891value also indicates a denser aggregate structure while lower119863119891 value indicates a more tenuous aggregate Observation ofthe fractal aggregation process can further be used to controlwhey protein-based aggregation so that foods with uniformand appropriate texture can be produced [8]

There are several techniques that can be used to analyzefractal structure in aggregates These experimental methodswere widely used to analyze and evaluate texture character-istics of whey protein-based foods which are carried out byforming a model of whey protein gel system that can be usedas medium The measurement of this physical quantity isrelated tomass distribution in space and can be done throughvarious techniques such as scattering settling microscopy(image analysis) and rheology [9 10] This paper willonly limit the discussion on two methods microscopy andrheology These methods however have several limitationswhich might affect the fractal dimension values and typeof aggregations obtained The review is therefore dividedinto three sections the first section discussed the structureof whey protein and its functionality the second section isabout fractal theories in relation to food structure methodsfor fractal analysis and their limitations the third sectionis a compilation on fractal dimension values and the typesof aggregation of whey protein aggregates gathered fromseveral researches This was done to finally understand howthe texture of whey protein-based food is formed despite thelimitations available on each method

2 Structure and Functionality ofWhey Protein

21 Composition and Structure Proteins provide variousfunctions in food and also maintain the stability of foodstructure Whey proteins can interact with each other andwith other types of protein to make networks associated withgels Whey protein comprises a globular structure as shown

in Figure 1 Globular proteins are usually curled up so that thehydrophobic R regions are centered in the molecule to avoidthe polar environment around them while the hydrophilic Rgroup is located on the surface of the molecule This makesglobular proteins (ie whey protein) soluble in water 120573-Lg as a major component in whey protein determines theproperties of the overall whey protein Each 120573-Lg moleculehas 5 cysteine (amino acid) residues Cys-66 Cys-106 Cys-119 Cys-121 and Cys-160 Cys-66Cys-160 and Cys-106Cys-119 are connected by disulfide bonds (-SS) to form oxidizedform of cysteine that is cystine while Cys-121 is availableas a free thiol (-SH) group One molecule of 120573-Lg (wheyprotein) therefore consists of one free thiol group and twodisulfide bonds [11 12] The free thiol group is entrapped inthe three-dimensional structure of native whey protein andexposed during denaturationThese structures are importantin terms of protein aggregation [13] Heat treatment highpressure mechanical stress and oil-in-water exposure to airduring food processing can cause changes in the tertiary(globular) structure of the whey protein so that the thiol andcystine groups become exposed to the solvent and becomechemically reactive [12]

22 Whey Protein as Gelling Agent Whey protein can en-hance texture formation in food due to one of its function-alities to form gelThis is an important functional attribute tomany food applications such as meat and milk processingand bakery and also to improving appearance of foodproducts such as yogurt [1 4 14]

Rheological properties of protein gel vary depending onthe type of protein pH ionic strength and rate of heatingGel of globular protein is classified into two distinct typesof morphology particulate and fine-stranded gels Extensivereviews on these morphologies were done by Bryant andJulian McClements [15] and Nicolai and Durand [6] Ingeneral particulate gels are turbid gels that can be formedby modifying the pH close to the isoelectric point or at highionic strength (low electrostatic repulsion force) while fine-stranded gels are transparent filamentous gels that can beformed at pH far from the isoelectric point in the absence ofsalt or low ionic strength (high electrostatic repulsion force)Figure 2 showed the microstructure on each type of gel

Verheul and Roefs [5] stated that there are three phenom-ena involved (often subsequently) in aggregation process of




Heat

+ salt

Increasing

Protein conc




Heat

no salt

+ salt

















Point

Fractal dust

Line


0 1 2 3Dimension


(a)

500 nm

(b)












Macroscopic (gel)



















log119864 = 119860 log120593

log 1205740 = 119861 log120593(1)


1198661015840 sim119898119860

611988812058712059012058511988930Φ1(119889minus119863) (2)









1198661015840 prop 120585minus(1+2120576+120575)

1205740 prop 1205852120576+120575minus1

120590 prop 120585minus2

(3)






(120574 times 119864)times 100 (4)



Limit of linearity
















I = 281II = 281III = 268






CSLMWPA = 215

WPA + NMC = 264TEM

WPA + NMC = 269


final pH 40













Table3Fractald

imensio

n(119863119891)v

alueso

fdifferenttypes

ofgels

measuredby

usingrheologicalm

etho

d

Reference

Geltype

119863119891

Hagiwarae

tal(19

97a)

Heatind

uced

BSA

I=pH

70II=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

120573-Lg

IV=pH

70V=pH

70+30

mM

CaCl2

I=strong

-link

200ndash

207

II=weak-lin

k282

III=

weak-lin

k261

IV=str

ong-lin

k214ndash220

V=weak-lin

k269

Hagiwarae

tal(19

97b)

Heatind

uced

120573-Lg

pH=70

[NaC

l]=10

MWeak-lin

k262

Hagiwarae

tal(19

98)

Heat-indu

cedBS

AI=

50mM

bufferp

H5101M

NaC

lII=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

I=weak-lin

k282

II=weak-lin

k282

III=

weak-lin

k261

Vreekere

tal(19

92)

Acid-in

ducedcoldgelatio

nWPI

(1or

10ww

)+01M

NaC

lorC

aCl 2atpH

54

1198661015840

Shih

etal(1990)=

20

Brem

er(19

92)=

23

120590B

remer

(1992)=

24ndash

25

Ikedae

tal(1999)

Heat-indu

cedWPI

pH70

+25ndash100

0mM

NaC

l

25mM

NaC

l=22

100m

MNaC

l=15

(incorrectly

predicted)

500m

MNaC

l=18

5080500and1000

mM

NaC

l=DLC

A

Alting

etal(2003)

Acid-in

ducedcoldgelatio

nWPI

9

11986311989123acid-in

duced

cold

gelatio

nprob

ablysta

rtso

ffas

afractalprocessb


byanotherm

echanism

atlarger

leng

thscales

(gt100n

m)

deKr

uifetal(19

95)

Salt-indu

cedcoldgelatio

n120573-Lg

[NaC

l]=01o

r05M

Afterp

assin

gtheg

elatio

nthresholdgelw

ithmoreo

rlessfractal-likes

tructure

was

form

edanditcoarsens

with

increasin

gsaltconcentration

Neverthelessgels

prop

ertie

scou

ldno

tcom

pletely

bedescrib

edusingthe

scalinglawsa

sexplained

bymanyauthors

Marangoni

etal(2000)

Heat-indu

cedWPI

(5wv)

Salt-indu

cedcoldgelatio

nCa

Cl2=weak-lin

k263

NaC

l=weak-lin

k245

Stadingetal(1993)

Heat-indu

ced120573-LgatpH

53with

different

heatingrate

Microstructureo

fgels

show


pH53=246

ndash247

pH57=291ndash294


Table3Con

tinued

Reference

Geltype

119863119891

Kuhn

etal(2010)

Heat-indu

cedWPI

+150m

MNaC

lorC

aCl 2

CaCl2=weak-lin

k266

NaC

l=weak-lin

k262

And

oyoetal(2015)

Acid-in

ducedcoldgelatio

nWPA

ampWPA

+NMC

pH45

WPA

gels

strong

-link

1198661015840=16

ndash17

120574 0=115

WPA

+NMCgels

weak-lin

k1198661015840=26

120574 0=229

Hagiwarae

tal(19

96)

BSAdissolvedin

HEP

ESbu

ffero

fpH70

andacetateb

uffer

ofpH

51to01

and

0001

solutio


theh

eatin

gtim

eBS

AatpH

70werea

bout

21and

15119863119891of

heat-in

ducedaggregates

atpH

51w

asabou

t18

Foegedingetal(1995)

Afin

e-strand

edmatrix

form

edin

proteinsuspensio

nscontainedmon

ovalentcation

(Li+K+R

b+and

Cs+)chloridessod

ium

sulfateorsod

ium

phosph

atea

tion

icstr

engths

le01m

oldm3Th

ismatrix

varie

sinstressandstr

ainatfracture

atdifferent

saltconcentrations


dispersib

ilityof

proteins

andtherebydeterm

inethe

microstructurea

ndfracture

prop

ertie

sofglobu

larp

rotein

gels

Verheulamp

Roefs(1998)

Gels

werem

adea

tnear-neutralp

HP

rotein


gl)andNaC


3moldm3)w

eres

ystematicallyvarie

d

Gelstr

ucture

didno

tchangem

uchaft

ergelformation

whilegelrigidity

continuedto

increaseand

attheg

elpo

into

nlypartof

thep

rotein

inthed

ispersio

ncontrib

utes

totheg

elnetworkTh

efractalconcept

cann

otsim

plybe

appliedto

WPI

gels

EissaKhan(2005)

Wheyproteinsolutio

n3

and75

(heatw

ithw

ithou

ttransglutam

inaseTG

)low

pHcold-se

twheyp

rotein

gelfin

alpH

40

CSLM

196ndash

198

Rheology205ndash209




5 Conclusion





References







































































































Volume 2018

Zoology











Volume 2018

















Advances in




Enzyme Research





Volume 2018





Heat

+ salt

Increasing

Protein conc




Heat

no salt

+ salt

















Point

Fractal dust

Line


0 1 2 3Dimension


(a)

500 nm

(b)












Macroscopic (gel)



















log119864 = 119860 log120593

log 1205740 = 119861 log120593(1)


1198661015840 sim119898119860

611988812058712059012058511988930Φ1(119889minus119863) (2)









1198661015840 prop 120585minus(1+2120576+120575)

1205740 prop 1205852120576+120575minus1

120590 prop 120585minus2

(3)






(120574 times 119864)times 100 (4)



Limit of linearity
















I = 281II = 281III = 268






CSLMWPA = 215

WPA + NMC = 264TEM

WPA + NMC = 269


final pH 40













Table3Fractald

imensio

n(119863119891)v

alueso

fdifferenttypes

ofgels

measuredby

usingrheologicalm

etho

d

Reference

Geltype

119863119891

Hagiwarae

tal(19

97a)

Heatind

uced

BSA

I=pH

70II=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

120573-Lg

IV=pH

70V=pH

70+30

mM

CaCl2

I=strong

-link

200ndash

207

II=weak-lin

k282

III=

weak-lin

k261

IV=str

ong-lin

k214ndash220

V=weak-lin

k269

Hagiwarae

tal(19

97b)

Heatind

uced

120573-Lg

pH=70

[NaC

l]=10

MWeak-lin

k262

Hagiwarae

tal(19

98)

Heat-indu

cedBS

AI=

50mM

bufferp

H5101M

NaC

lII=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

I=weak-lin

k282

II=weak-lin

k282

III=

weak-lin

k261

Vreekere

tal(19

92)

Acid-in

ducedcoldgelatio

nWPI

(1or

10ww

)+01M

NaC

lorC

aCl 2atpH

54

1198661015840

Shih

etal(1990)=

20

Brem

er(19

92)=

23

120590B

remer

(1992)=

24ndash

25

Ikedae

tal(1999)

Heat-indu

cedWPI

pH70

+25ndash100

0mM

NaC

l

25mM

NaC

l=22

100m

MNaC

l=15

(incorrectly

predicted)

500m

MNaC

l=18

5080500and1000

mM

NaC

l=DLC

A

Alting

etal(2003)

Acid-in

ducedcoldgelatio

nWPI

9

11986311989123acid-in

duced

cold

gelatio

nprob

ablysta

rtso

ffas

afractalprocessb


byanotherm

echanism

atlarger

leng

thscales

(gt100n

m)

deKr

uifetal(19

95)

Salt-indu

cedcoldgelatio

n120573-Lg

[NaC

l]=01o

r05M

Afterp

assin

gtheg

elatio

nthresholdgelw

ithmoreo

rlessfractal-likes

tructure

was

form

edanditcoarsens

with

increasin

gsaltconcentration

Neverthelessgels

prop

ertie

scou

ldno

tcom

pletely

bedescrib

edusingthe

scalinglawsa

sexplained

bymanyauthors

Marangoni

etal(2000)

Heat-indu

cedWPI

(5wv)

Salt-indu

cedcoldgelatio

nCa

Cl2=weak-lin

k263

NaC

l=weak-lin

k245

Stadingetal(1993)

Heat-indu

ced120573-LgatpH

53with

different

heatingrate

Microstructureo

fgels

show


pH53=246

ndash247

pH57=291ndash294


Table3Con

tinued

Reference

Geltype

119863119891

Kuhn

etal(2010)

Heat-indu

cedWPI

+150m

MNaC

lorC

aCl 2

CaCl2=weak-lin

k266

NaC

l=weak-lin

k262

And

oyoetal(2015)

Acid-in

ducedcoldgelatio

nWPA

ampWPA

+NMC

pH45

WPA

gels

strong

-link

1198661015840=16

ndash17

120574 0=115

WPA

+NMCgels

weak-lin

k1198661015840=26

120574 0=229

Hagiwarae

tal(19

96)

BSAdissolvedin

HEP

ESbu

ffero

fpH70

andacetateb

uffer

ofpH

51to01

and

0001

solutio


theh

eatin

gtim

eBS

AatpH

70werea

bout

21and

15119863119891of

heat-in

ducedaggregates

atpH

51w

asabou

t18

Foegedingetal(1995)

Afin

e-strand

edmatrix

form

edin

proteinsuspensio

nscontainedmon

ovalentcation

(Li+K+R

b+and

Cs+)chloridessod

ium

sulfateorsod

ium

phosph

atea

tion

icstr

engths

le01m

oldm3Th

ismatrix

varie

sinstressandstr

ainatfracture

atdifferent

saltconcentrations


dispersib

ilityof

proteins

andtherebydeterm

inethe

microstructurea

ndfracture

prop

ertie

sofglobu

larp

rotein

gels

Verheulamp

Roefs(1998)

Gels

werem

adea

tnear-neutralp

HP

rotein


gl)andNaC


3moldm3)w

eres

ystematicallyvarie

d

Gelstr

ucture

didno

tchangem

uchaft

ergelformation

whilegelrigidity

continuedto

increaseand

attheg

elpo

into

nlypartof

thep

rotein

inthed

ispersio

ncontrib

utes

totheg

elnetworkTh

efractalconcept

cann

otsim

plybe

appliedto

WPI

gels

EissaKhan(2005)

Wheyproteinsolutio

n3

and75

(heatw

ithw

ithou

ttransglutam

inaseTG

)low

pHcold-se

twheyp

rotein

gelfin

alpH

40

CSLM

196ndash

198

Rheology205ndash209




5 Conclusion





References







































































































Volume 2018

Zoology











Volume 2018

















Advances in




Enzyme Research





Volume 2018











Point

Fractal dust

Line


0 1 2 3Dimension


(a)

500 nm

(b)












Macroscopic (gel)



















log119864 = 119860 log120593

log 1205740 = 119861 log120593(1)


1198661015840 sim119898119860

611988812058712059012058511988930Φ1(119889minus119863) (2)









1198661015840 prop 120585minus(1+2120576+120575)

1205740 prop 1205852120576+120575minus1

120590 prop 120585minus2

(3)






(120574 times 119864)times 100 (4)



Limit of linearity
















I = 281II = 281III = 268






CSLMWPA = 215

WPA + NMC = 264TEM

WPA + NMC = 269


final pH 40













Table3Fractald

imensio

n(119863119891)v

alueso

fdifferenttypes

ofgels

measuredby

usingrheologicalm

etho

d

Reference

Geltype

119863119891

Hagiwarae

tal(19

97a)

Heatind

uced

BSA

I=pH

70II=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

120573-Lg

IV=pH

70V=pH

70+30

mM

CaCl2

I=strong

-link

200ndash

207

II=weak-lin

k282

III=

weak-lin

k261

IV=str

ong-lin

k214ndash220

V=weak-lin

k269

Hagiwarae

tal(19

97b)

Heatind

uced

120573-Lg

pH=70

[NaC

l]=10

MWeak-lin

k262

Hagiwarae

tal(19

98)

Heat-indu

cedBS

AI=

50mM

bufferp

H5101M

NaC

lII=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

I=weak-lin

k282

II=weak-lin

k282

III=

weak-lin

k261

Vreekere

tal(19

92)

Acid-in

ducedcoldgelatio

nWPI

(1or

10ww

)+01M

NaC

lorC

aCl 2atpH

54

1198661015840

Shih

etal(1990)=

20

Brem

er(19

92)=

23

120590B

remer

(1992)=

24ndash

25

Ikedae

tal(1999)

Heat-indu

cedWPI

pH70

+25ndash100

0mM

NaC

l

25mM

NaC

l=22

100m

MNaC

l=15

(incorrectly

predicted)

500m

MNaC

l=18

5080500and1000

mM

NaC

l=DLC

A

Alting

etal(2003)

Acid-in

ducedcoldgelatio

nWPI

9

11986311989123acid-in

duced

cold

gelatio

nprob

ablysta

rtso

ffas

afractalprocessb


byanotherm

echanism

atlarger

leng

thscales

(gt100n

m)

deKr

uifetal(19

95)

Salt-indu

cedcoldgelatio

n120573-Lg

[NaC

l]=01o

r05M

Afterp

assin

gtheg

elatio

nthresholdgelw

ithmoreo

rlessfractal-likes

tructure

was

form

edanditcoarsens

with

increasin

gsaltconcentration

Neverthelessgels

prop

ertie

scou

ldno

tcom

pletely

bedescrib

edusingthe

scalinglawsa

sexplained

bymanyauthors

Marangoni

etal(2000)

Heat-indu

cedWPI

(5wv)

Salt-indu

cedcoldgelatio

nCa

Cl2=weak-lin

k263

NaC

l=weak-lin

k245

Stadingetal(1993)

Heat-indu

ced120573-LgatpH

53with

different

heatingrate

Microstructureo

fgels

show


pH53=246

ndash247

pH57=291ndash294


Table3Con

tinued

Reference

Geltype

119863119891

Kuhn

etal(2010)

Heat-indu

cedWPI

+150m

MNaC

lorC

aCl 2

CaCl2=weak-lin

k266

NaC

l=weak-lin

k262

And

oyoetal(2015)

Acid-in

ducedcoldgelatio

nWPA

ampWPA

+NMC

pH45

WPA

gels

strong

-link

1198661015840=16

ndash17

120574 0=115

WPA

+NMCgels

weak-lin

k1198661015840=26

120574 0=229

Hagiwarae

tal(19

96)

BSAdissolvedin

HEP

ESbu

ffero

fpH70

andacetateb

uffer

ofpH

51to01

and

0001

solutio


theh

eatin

gtim

eBS

AatpH

70werea

bout

21and

15119863119891of

heat-in

ducedaggregates

atpH

51w

asabou

t18

Foegedingetal(1995)

Afin

e-strand

edmatrix

form

edin

proteinsuspensio

nscontainedmon

ovalentcation

(Li+K+R

b+and

Cs+)chloridessod

ium

sulfateorsod

ium

phosph

atea

tion

icstr

engths

le01m

oldm3Th

ismatrix

varie

sinstressandstr

ainatfracture

atdifferent

saltconcentrations


dispersib

ilityof

proteins

andtherebydeterm

inethe

microstructurea

ndfracture

prop

ertie

sofglobu

larp

rotein

gels

Verheulamp

Roefs(1998)

Gels

werem

adea

tnear-neutralp

HP

rotein


gl)andNaC


3moldm3)w

eres

ystematicallyvarie

d

Gelstr

ucture

didno

tchangem

uchaft

ergelformation

whilegelrigidity

continuedto

increaseand

attheg

elpo

into

nlypartof

thep

rotein

inthed

ispersio

ncontrib

utes

totheg

elnetworkTh

efractalconcept

cann

otsim

plybe

appliedto

WPI

gels

EissaKhan(2005)

Wheyproteinsolutio

n3

and75

(heatw

ithw

ithou

ttransglutam

inaseTG

)low

pHcold-se

twheyp

rotein

gelfin

alpH

40

CSLM

196ndash

198

Rheology205ndash209




5 Conclusion





References







































































































Volume 2018

Zoology











Volume 2018

















Advances in




Enzyme Research





Volume 2018






Macroscopic (gel)



















log119864 = 119860 log120593

log 1205740 = 119861 log120593(1)


1198661015840 sim119898119860

611988812058712059012058511988930Φ1(119889minus119863) (2)









1198661015840 prop 120585minus(1+2120576+120575)

1205740 prop 1205852120576+120575minus1

120590 prop 120585minus2

(3)






(120574 times 119864)times 100 (4)



Limit of linearity
















I = 281II = 281III = 268






CSLMWPA = 215

WPA + NMC = 264TEM

WPA + NMC = 269


final pH 40













Table3Fractald

imensio

n(119863119891)v

alueso

fdifferenttypes

ofgels

measuredby

usingrheologicalm

etho

d

Reference

Geltype

119863119891

Hagiwarae

tal(19

97a)

Heatind

uced

BSA

I=pH

70II=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

120573-Lg

IV=pH

70V=pH

70+30

mM

CaCl2

I=strong

-link

200ndash

207

II=weak-lin

k282

III=

weak-lin

k261

IV=str

ong-lin

k214ndash220

V=weak-lin

k269

Hagiwarae

tal(19

97b)

Heatind

uced

120573-Lg

pH=70

[NaC

l]=10

MWeak-lin

k262

Hagiwarae

tal(19

98)

Heat-indu

cedBS

AI=

50mM

bufferp

H5101M

NaC

lII=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

I=weak-lin

k282

II=weak-lin

k282

III=

weak-lin

k261

Vreekere

tal(19

92)

Acid-in

ducedcoldgelatio

nWPI

(1or

10ww

)+01M

NaC

lorC

aCl 2atpH

54

1198661015840

Shih

etal(1990)=

20

Brem

er(19

92)=

23

120590B

remer

(1992)=

24ndash

25

Ikedae

tal(1999)

Heat-indu

cedWPI

pH70

+25ndash100

0mM

NaC

l

25mM

NaC

l=22

100m

MNaC

l=15

(incorrectly

predicted)

500m

MNaC

l=18

5080500and1000

mM

NaC

l=DLC

A

Alting

etal(2003)

Acid-in

ducedcoldgelatio

nWPI

9

11986311989123acid-in

duced

cold

gelatio

nprob

ablysta

rtso

ffas

afractalprocessb


byanotherm

echanism

atlarger

leng

thscales

(gt100n

m)

deKr

uifetal(19

95)

Salt-indu

cedcoldgelatio

n120573-Lg

[NaC

l]=01o

r05M

Afterp

assin

gtheg

elatio

nthresholdgelw

ithmoreo

rlessfractal-likes

tructure

was

form

edanditcoarsens

with

increasin

gsaltconcentration

Neverthelessgels

prop

ertie

scou

ldno

tcom

pletely

bedescrib

edusingthe

scalinglawsa

sexplained

bymanyauthors

Marangoni

etal(2000)

Heat-indu

cedWPI

(5wv)

Salt-indu

cedcoldgelatio

nCa

Cl2=weak-lin

k263

NaC

l=weak-lin

k245

Stadingetal(1993)

Heat-indu

ced120573-LgatpH

53with

different

heatingrate

Microstructureo

fgels

show


pH53=246

ndash247

pH57=291ndash294


Table3Con

tinued

Reference

Geltype

119863119891

Kuhn

etal(2010)

Heat-indu

cedWPI

+150m

MNaC

lorC

aCl 2

CaCl2=weak-lin

k266

NaC

l=weak-lin

k262

And

oyoetal(2015)

Acid-in

ducedcoldgelatio

nWPA

ampWPA

+NMC

pH45

WPA

gels

strong

-link

1198661015840=16

ndash17

120574 0=115

WPA

+NMCgels

weak-lin

k1198661015840=26

120574 0=229

Hagiwarae

tal(19

96)

BSAdissolvedin

HEP

ESbu

ffero

fpH70

andacetateb

uffer

ofpH

51to01

and

0001

solutio


theh

eatin

gtim

eBS

AatpH

70werea

bout

21and

15119863119891of

heat-in

ducedaggregates

atpH

51w

asabou

t18

Foegedingetal(1995)

Afin

e-strand

edmatrix

form

edin

proteinsuspensio

nscontainedmon

ovalentcation

(Li+K+R

b+and

Cs+)chloridessod

ium

sulfateorsod

ium

phosph

atea

tion

icstr

engths

le01m

oldm3Th

ismatrix

varie

sinstressandstr

ainatfracture

atdifferent

saltconcentrations


dispersib

ilityof

proteins

andtherebydeterm

inethe

microstructurea

ndfracture

prop

ertie

sofglobu

larp

rotein

gels

Verheulamp

Roefs(1998)

Gels

werem

adea

tnear-neutralp

HP

rotein


gl)andNaC


3moldm3)w

eres

ystematicallyvarie

d

Gelstr

ucture

didno

tchangem

uchaft

ergelformation

whilegelrigidity

continuedto

increaseand

attheg

elpo

into

nlypartof

thep

rotein

inthed

ispersio

ncontrib

utes

totheg

elnetworkTh

efractalconcept

cann

otsim

plybe

appliedto

WPI

gels

EissaKhan(2005)

Wheyproteinsolutio

n3

and75

(heatw

ithw

ithou

ttransglutam

inaseTG

)low

pHcold-se

twheyp

rotein

gelfin

alpH

40

CSLM

196ndash

198

Rheology205ndash209




5 Conclusion





References







































































































Volume 2018

Zoology











Volume 2018

















Advances in




Enzyme Research





Volume 2018







log119864 = 119860 log120593

log 1205740 = 119861 log120593(1)


1198661015840 sim119898119860

611988812058712059012058511988930Φ1(119889minus119863) (2)









1198661015840 prop 120585minus(1+2120576+120575)

1205740 prop 1205852120576+120575minus1

120590 prop 120585minus2

(3)






(120574 times 119864)times 100 (4)



Limit of linearity
















I = 281II = 281III = 268






CSLMWPA = 215

WPA + NMC = 264TEM

WPA + NMC = 269


final pH 40













Table3Fractald

imensio

n(119863119891)v

alueso

fdifferenttypes

ofgels

measuredby

usingrheologicalm

etho

d

Reference

Geltype

119863119891

Hagiwarae

tal(19

97a)

Heatind

uced

BSA

I=pH

70II=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

120573-Lg

IV=pH

70V=pH

70+30

mM

CaCl2

I=strong

-link

200ndash

207

II=weak-lin

k282

III=

weak-lin

k261

IV=str

ong-lin

k214ndash220

V=weak-lin

k269

Hagiwarae

tal(19

97b)

Heatind

uced

120573-Lg

pH=70

[NaC

l]=10

MWeak-lin

k262

Hagiwarae

tal(19

98)

Heat-indu

cedBS

AI=

50mM

bufferp

H5101M

NaC

lII=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

I=weak-lin

k282

II=weak-lin

k282

III=

weak-lin

k261

Vreekere

tal(19

92)

Acid-in

ducedcoldgelatio

nWPI

(1or

10ww

)+01M

NaC

lorC

aCl 2atpH

54

1198661015840

Shih

etal(1990)=

20

Brem

er(19

92)=

23

120590B

remer

(1992)=

24ndash

25

Ikedae

tal(1999)

Heat-indu

cedWPI

pH70

+25ndash100

0mM

NaC

l

25mM

NaC

l=22

100m

MNaC

l=15

(incorrectly

predicted)

500m

MNaC

l=18

5080500and1000

mM

NaC

l=DLC

A

Alting

etal(2003)

Acid-in

ducedcoldgelatio

nWPI

9

11986311989123acid-in

duced

cold

gelatio

nprob

ablysta

rtso

ffas

afractalprocessb


byanotherm

echanism

atlarger

leng

thscales

(gt100n

m)

deKr

uifetal(19

95)

Salt-indu

cedcoldgelatio

n120573-Lg

[NaC

l]=01o

r05M

Afterp

assin

gtheg

elatio

nthresholdgelw

ithmoreo

rlessfractal-likes

tructure

was

form

edanditcoarsens

with

increasin

gsaltconcentration

Neverthelessgels

prop

ertie

scou

ldno

tcom

pletely

bedescrib

edusingthe

scalinglawsa

sexplained

bymanyauthors

Marangoni

etal(2000)

Heat-indu

cedWPI

(5wv)

Salt-indu

cedcoldgelatio

nCa

Cl2=weak-lin

k263

NaC

l=weak-lin

k245

Stadingetal(1993)

Heat-indu

ced120573-LgatpH

53with

different

heatingrate

Microstructureo

fgels

show


pH53=246

ndash247

pH57=291ndash294


Table3Con

tinued

Reference

Geltype

119863119891

Kuhn

etal(2010)

Heat-indu

cedWPI

+150m

MNaC

lorC

aCl 2

CaCl2=weak-lin

k266

NaC

l=weak-lin

k262

And

oyoetal(2015)

Acid-in

ducedcoldgelatio

nWPA

ampWPA

+NMC

pH45

WPA

gels

strong

-link

1198661015840=16

ndash17

120574 0=115

WPA

+NMCgels

weak-lin

k1198661015840=26

120574 0=229

Hagiwarae

tal(19

96)

BSAdissolvedin

HEP

ESbu

ffero

fpH70

andacetateb

uffer

ofpH

51to01

and

0001

solutio


theh

eatin

gtim

eBS

AatpH

70werea

bout

21and

15119863119891of

heat-in

ducedaggregates

atpH

51w

asabou

t18

Foegedingetal(1995)

Afin

e-strand

edmatrix

form

edin

proteinsuspensio

nscontainedmon

ovalentcation

(Li+K+R

b+and

Cs+)chloridessod

ium

sulfateorsod

ium

phosph

atea

tion

icstr

engths

le01m

oldm3Th

ismatrix

varie

sinstressandstr

ainatfracture

atdifferent

saltconcentrations


dispersib

ilityof

proteins

andtherebydeterm

inethe

microstructurea

ndfracture

prop

ertie

sofglobu

larp

rotein

gels

Verheulamp

Roefs(1998)

Gels

werem

adea

tnear-neutralp

HP

rotein


gl)andNaC


3moldm3)w

eres

ystematicallyvarie

d

Gelstr

ucture

didno

tchangem

uchaft

ergelformation

whilegelrigidity

continuedto

increaseand

attheg

elpo

into

nlypartof

thep

rotein

inthed

ispersio

ncontrib

utes

totheg

elnetworkTh

efractalconcept

cann

otsim

plybe

appliedto

WPI

gels

EissaKhan(2005)

Wheyproteinsolutio

n3

and75

(heatw

ithw

ithou

ttransglutam

inaseTG

)low

pHcold-se

twheyp

rotein

gelfin

alpH

40

CSLM

196ndash

198

Rheology205ndash209




5 Conclusion





References







































































































Volume 2018

Zoology











Volume 2018

















Advances in




Enzyme Research





Volume 2018










1198661015840 prop 120585minus(1+2120576+120575)

1205740 prop 1205852120576+120575minus1

120590 prop 120585minus2

(3)






(120574 times 119864)times 100 (4)



Limit of linearity
















I = 281II = 281III = 268






CSLMWPA = 215

WPA + NMC = 264TEM

WPA + NMC = 269


final pH 40













Table3Fractald

imensio

n(119863119891)v

alueso

fdifferenttypes

ofgels

measuredby

usingrheologicalm

etho

d

Reference

Geltype

119863119891

Hagiwarae

tal(19

97a)

Heatind

uced

BSA

I=pH

70II=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

120573-Lg

IV=pH

70V=pH

70+30

mM

CaCl2

I=strong

-link

200ndash

207

II=weak-lin

k282

III=

weak-lin

k261

IV=str

ong-lin

k214ndash220

V=weak-lin

k269

Hagiwarae

tal(19

97b)

Heatind

uced

120573-Lg

pH=70

[NaC

l]=10

MWeak-lin

k262

Hagiwarae

tal(19

98)

Heat-indu

cedBS

AI=

50mM

bufferp

H5101M

NaC

lII=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

I=weak-lin

k282

II=weak-lin

k282

III=

weak-lin

k261

Vreekere

tal(19

92)

Acid-in

ducedcoldgelatio

nWPI

(1or

10ww

)+01M

NaC

lorC

aCl 2atpH

54

1198661015840

Shih

etal(1990)=

20

Brem

er(19

92)=

23

120590B

remer

(1992)=

24ndash

25

Ikedae

tal(1999)

Heat-indu

cedWPI

pH70

+25ndash100

0mM

NaC

l

25mM

NaC

l=22

100m

MNaC

l=15

(incorrectly

predicted)

500m

MNaC

l=18

5080500and1000

mM

NaC

l=DLC

A

Alting

etal(2003)

Acid-in

ducedcoldgelatio

nWPI

9

11986311989123acid-in

duced

cold

gelatio

nprob

ablysta

rtso

ffas

afractalprocessb


byanotherm

echanism

atlarger

leng

thscales

(gt100n

m)

deKr

uifetal(19

95)

Salt-indu

cedcoldgelatio

n120573-Lg

[NaC

l]=01o

r05M

Afterp

assin

gtheg

elatio

nthresholdgelw

ithmoreo

rlessfractal-likes

tructure

was

form

edanditcoarsens

with

increasin

gsaltconcentration

Neverthelessgels

prop

ertie

scou

ldno

tcom

pletely

bedescrib

edusingthe

scalinglawsa

sexplained

bymanyauthors

Marangoni

etal(2000)

Heat-indu

cedWPI

(5wv)

Salt-indu

cedcoldgelatio

nCa

Cl2=weak-lin

k263

NaC

l=weak-lin

k245

Stadingetal(1993)

Heat-indu

ced120573-LgatpH

53with

different

heatingrate

Microstructureo

fgels

show


pH53=246

ndash247

pH57=291ndash294


Table3Con

tinued

Reference

Geltype

119863119891

Kuhn

etal(2010)

Heat-indu

cedWPI

+150m

MNaC

lorC

aCl 2

CaCl2=weak-lin

k266

NaC

l=weak-lin

k262

And

oyoetal(2015)

Acid-in

ducedcoldgelatio

nWPA

ampWPA

+NMC

pH45

WPA

gels

strong

-link

1198661015840=16

ndash17

120574 0=115

WPA

+NMCgels

weak-lin

k1198661015840=26

120574 0=229

Hagiwarae

tal(19

96)

BSAdissolvedin

HEP

ESbu

ffero

fpH70

andacetateb

uffer

ofpH

51to01

and

0001

solutio


theh

eatin

gtim

eBS

AatpH

70werea

bout

21and

15119863119891of

heat-in

ducedaggregates

atpH

51w

asabou

t18

Foegedingetal(1995)

Afin

e-strand

edmatrix

form

edin

proteinsuspensio

nscontainedmon

ovalentcation

(Li+K+R

b+and

Cs+)chloridessod

ium

sulfateorsod

ium

phosph

atea

tion

icstr

engths

le01m

oldm3Th

ismatrix

varie

sinstressandstr

ainatfracture

atdifferent

saltconcentrations


dispersib

ilityof

proteins

andtherebydeterm

inethe

microstructurea

ndfracture

prop

ertie

sofglobu

larp

rotein

gels

Verheulamp

Roefs(1998)

Gels

werem

adea

tnear-neutralp

HP

rotein


gl)andNaC


3moldm3)w

eres

ystematicallyvarie

d

Gelstr

ucture

didno

tchangem

uchaft

ergelformation

whilegelrigidity

continuedto

increaseand

attheg

elpo

into

nlypartof

thep

rotein

inthed

ispersio

ncontrib

utes

totheg

elnetworkTh

efractalconcept

cann

otsim

plybe

appliedto

WPI

gels

EissaKhan(2005)

Wheyproteinsolutio

n3

and75

(heatw

ithw

ithou

ttransglutam

inaseTG

)low

pHcold-se

twheyp

rotein

gelfin

alpH

40

CSLM

196ndash

198

Rheology205ndash209




5 Conclusion





References







































































































Volume 2018

Zoology











Volume 2018

















Advances in




Enzyme Research





Volume 2018















I = 281II = 281III = 268






CSLMWPA = 215

WPA + NMC = 264TEM

WPA + NMC = 269


final pH 40













Table3Fractald

imensio

n(119863119891)v

alueso

fdifferenttypes

ofgels

measuredby

usingrheologicalm

etho

d

Reference

Geltype

119863119891

Hagiwarae

tal(19

97a)

Heatind

uced

BSA

I=pH

70II=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

120573-Lg

IV=pH

70V=pH

70+30

mM

CaCl2

I=strong

-link

200ndash

207

II=weak-lin

k282

III=

weak-lin

k261

IV=str

ong-lin

k214ndash220

V=weak-lin

k269

Hagiwarae

tal(19

97b)

Heatind

uced

120573-Lg

pH=70

[NaC

l]=10

MWeak-lin

k262

Hagiwarae

tal(19

98)

Heat-indu

cedBS

AI=

50mM

bufferp

H5101M

NaC

lII=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

I=weak-lin

k282

II=weak-lin

k282

III=

weak-lin

k261

Vreekere

tal(19

92)

Acid-in

ducedcoldgelatio

nWPI

(1or

10ww

)+01M

NaC

lorC

aCl 2atpH

54

1198661015840

Shih

etal(1990)=

20

Brem

er(19

92)=

23

120590B

remer

(1992)=

24ndash

25

Ikedae

tal(1999)

Heat-indu

cedWPI

pH70

+25ndash100

0mM

NaC

l

25mM

NaC

l=22

100m

MNaC

l=15

(incorrectly

predicted)

500m

MNaC

l=18

5080500and1000

mM

NaC

l=DLC

A

Alting

etal(2003)

Acid-in

ducedcoldgelatio

nWPI

9

11986311989123acid-in

duced

cold

gelatio

nprob

ablysta

rtso

ffas

afractalprocessb


byanotherm

echanism

atlarger

leng

thscales

(gt100n

m)

deKr

uifetal(19

95)

Salt-indu

cedcoldgelatio

n120573-Lg

[NaC

l]=01o

r05M

Afterp

assin

gtheg

elatio

nthresholdgelw

ithmoreo

rlessfractal-likes

tructure

was

form

edanditcoarsens

with

increasin

gsaltconcentration

Neverthelessgels

prop

ertie

scou

ldno

tcom

pletely

bedescrib

edusingthe

scalinglawsa

sexplained

bymanyauthors

Marangoni

etal(2000)

Heat-indu

cedWPI

(5wv)

Salt-indu

cedcoldgelatio

nCa

Cl2=weak-lin

k263

NaC

l=weak-lin

k245

Stadingetal(1993)

Heat-indu

ced120573-LgatpH

53with

different

heatingrate

Microstructureo

fgels

show


pH53=246

ndash247

pH57=291ndash294


Table3Con

tinued

Reference

Geltype

119863119891

Kuhn

etal(2010)

Heat-indu

cedWPI

+150m

MNaC

lorC

aCl 2

CaCl2=weak-lin

k266

NaC

l=weak-lin

k262

And

oyoetal(2015)

Acid-in

ducedcoldgelatio

nWPA

ampWPA

+NMC

pH45

WPA

gels

strong

-link

1198661015840=16

ndash17

120574 0=115

WPA

+NMCgels

weak-lin

k1198661015840=26

120574 0=229

Hagiwarae

tal(19

96)

BSAdissolvedin

HEP

ESbu

ffero

fpH70

andacetateb

uffer

ofpH

51to01

and

0001

solutio


theh

eatin

gtim

eBS

AatpH

70werea

bout

21and

15119863119891of

heat-in

ducedaggregates

atpH

51w

asabou

t18

Foegedingetal(1995)

Afin

e-strand

edmatrix

form

edin

proteinsuspensio

nscontainedmon

ovalentcation

(Li+K+R

b+and

Cs+)chloridessod

ium

sulfateorsod

ium

phosph

atea

tion

icstr

engths

le01m

oldm3Th

ismatrix

varie

sinstressandstr

ainatfracture

atdifferent

saltconcentrations


dispersib

ilityof

proteins

andtherebydeterm

inethe

microstructurea

ndfracture

prop

ertie

sofglobu

larp

rotein

gels

Verheulamp

Roefs(1998)

Gels

werem

adea

tnear-neutralp

HP

rotein


gl)andNaC


3moldm3)w

eres

ystematicallyvarie

d

Gelstr

ucture

didno

tchangem

uchaft

ergelformation

whilegelrigidity

continuedto

increaseand

attheg

elpo

into

nlypartof

thep

rotein

inthed

ispersio

ncontrib

utes

totheg

elnetworkTh

efractalconcept

cann

otsim

plybe

appliedto

WPI

gels

EissaKhan(2005)

Wheyproteinsolutio

n3

and75

(heatw

ithw

ithou

ttransglutam

inaseTG

)low

pHcold-se

twheyp

rotein

gelfin

alpH

40

CSLM

196ndash

198

Rheology205ndash209




5 Conclusion





References







































































































Volume 2018

Zoology











Volume 2018

















Advances in




Enzyme Research





Volume 2018









Table3Fractald

imensio

n(119863119891)v

alueso

fdifferenttypes

ofgels

measuredby

usingrheologicalm

etho

d

Reference

Geltype

119863119891

Hagiwarae

tal(19

97a)

Heatind

uced

BSA

I=pH

70II=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

120573-Lg

IV=pH

70V=pH

70+30

mM

CaCl2

I=strong

-link

200ndash

207

II=weak-lin

k282

III=

weak-lin

k261

IV=str

ong-lin

k214ndash220

V=weak-lin

k269

Hagiwarae

tal(19

97b)

Heatind

uced

120573-Lg

pH=70

[NaC

l]=10

MWeak-lin

k262

Hagiwarae

tal(19

98)

Heat-indu

cedBS

AI=

50mM

bufferp

H5101M

NaC

lII=50

mM

bufferp

H70

30m

MCa

Cl2

III=

50mM

bufferp

H70

5mM

CaCl2

I=weak-lin

k282

II=weak-lin

k282

III=

weak-lin

k261

Vreekere

tal(19

92)

Acid-in

ducedcoldgelatio

nWPI

(1or

10ww

)+01M

NaC

lorC

aCl 2atpH

54

1198661015840

Shih

etal(1990)=

20

Brem

er(19

92)=

23

120590B

remer

(1992)=

24ndash

25

Ikedae

tal(1999)

Heat-indu

cedWPI

pH70

+25ndash100

0mM

NaC

l

25mM

NaC

l=22

100m

MNaC

l=15

(incorrectly

predicted)

500m

MNaC

l=18

5080500and1000

mM

NaC

l=DLC

A

Alting

etal(2003)

Acid-in

ducedcoldgelatio

nWPI

9

11986311989123acid-in

duced

cold

gelatio

nprob

ablysta

rtso

ffas

afractalprocessb


byanotherm

echanism

atlarger

leng

thscales

(gt100n

m)

deKr

uifetal(19

95)

Salt-indu

cedcoldgelatio

n120573-Lg

[NaC

l]=01o

r05M

Afterp

assin

gtheg

elatio

nthresholdgelw

ithmoreo

rlessfractal-likes

tructure

was

form

edanditcoarsens

with

increasin

gsaltconcentration

Neverthelessgels

prop

ertie

scou

ldno

tcom

pletely

bedescrib

edusingthe

scalinglawsa

sexplained

bymanyauthors

Marangoni

etal(2000)

Heat-indu

cedWPI

(5wv)

Salt-indu

cedcoldgelatio

nCa

Cl2=weak-lin

k263

NaC

l=weak-lin

k245

Stadingetal(1993)

Heat-indu

ced120573-LgatpH

53with

different

heatingrate

Microstructureo

fgels

show


pH53=246

ndash247

pH57=291ndash294


Table3Con

tinued

Reference

Geltype

119863119891

Kuhn

etal(2010)

Heat-indu

cedWPI

+150m

MNaC

lorC

aCl 2

CaCl2=weak-lin

k266

NaC

l=weak-lin

k262

And

oyoetal(2015)

Acid-in

ducedcoldgelatio

nWPA

ampWPA

+NMC

pH45

WPA

gels

strong

-link

1198661015840=16

ndash17

120574 0=115

WPA

+NMCgels

weak-lin

k1198661015840=26

120574 0=229

Hagiwarae

tal(19

96)

BSAdissolvedin

HEP

ESbu

ffero

fpH70

andacetateb

uffer

ofpH

51to01

and

0001

solutio


theh

eatin

gtim

eBS

AatpH

70werea

bout

21and

15119863119891of

heat-in

ducedaggregates

atpH

51w

asabou

t18

Foegedingetal(1995)

Afin

e-strand

edmatrix

form

edin

proteinsuspensio

nscontainedmon

ovalentcation

(Li+K+R

b+and

Cs+)chloridessod

ium

sulfateorsod

ium

phosph

atea

tion

icstr

engths

le01m

oldm3Th

ismatrix

varie

sinstressandstr

ainatfracture

atdifferent

saltconcentrations


dispersib

ilityof

proteins

andtherebydeterm

inethe

microstructurea

ndfracture

prop

ertie

sofglobu

larp

rotein

gels

Verheulamp

Roefs(1998)

Gels

werem

adea

tnear-neutralp

HP

rotein


gl)andNaC


3moldm3)w

eres

ystematicallyvarie

d

Gelstr

ucture

didno

tchangem

uchaft

ergelformation

whilegelrigidity

continuedto

increaseand

attheg

elpo

into

nlypartof

thep

rotein

inthed

ispersio

ncontrib

utes

totheg

elnetworkTh

efractalconcept

cann

otsim

plybe

appliedto

WPI

gels

EissaKhan(2005)

Wheyproteinsolutio

n3

and75

(heatw

ithw

ithou

ttransglutam

inaseTG

)low

pHcold-se

twheyp

rotein

gelfin

alpH

40

CSLM

196ndash

198

Rheology205ndash209




5 Conclusion





References







































































































Volume 2018

Zoology











Volume 2018

















Advances in




Enzyme Research





Volume 2018



Table3Con

tinued

Reference

Geltype

119863119891

Kuhn

etal(2010)

Heat-indu

cedWPI

+150m

MNaC

lorC

aCl 2

CaCl2=weak-lin

k266

NaC

l=weak-lin

k262

And

oyoetal(2015)

Acid-in

ducedcoldgelatio

nWPA

ampWPA

+NMC

pH45

WPA

gels

strong

-link

1198661015840=16

ndash17

120574 0=115

WPA

+NMCgels

weak-lin

k1198661015840=26

120574 0=229

Hagiwarae

tal(19

96)

BSAdissolvedin

HEP

ESbu

ffero

fpH70

andacetateb

uffer

ofpH

51to01

and

0001

solutio


theh

eatin

gtim

eBS

AatpH

70werea

bout

21and

15119863119891of

heat-in

ducedaggregates

atpH

51w

asabou

t18

Foegedingetal(1995)

Afin

e-strand

edmatrix

form

edin

proteinsuspensio

nscontainedmon

ovalentcation

(Li+K+R

b+and

Cs+)chloridessod

ium

sulfateorsod

ium

phosph

atea

tion

icstr

engths

le01m

oldm3Th

ismatrix

varie

sinstressandstr

ainatfracture

atdifferent

saltconcentrations


dispersib

ilityof

proteins

andtherebydeterm

inethe

microstructurea

ndfracture

prop

ertie

sofglobu

larp

rotein

gels

Verheulamp

Roefs(1998)

Gels

werem

adea

tnear-neutralp

HP

rotein


gl)andNaC


3moldm3)w

eres

ystematicallyvarie

d

Gelstr

ucture

didno

tchangem

uchaft

ergelformation

whilegelrigidity

continuedto

increaseand

attheg

elpo

into

nlypartof

thep

rotein

inthed

ispersio

ncontrib

utes

totheg

elnetworkTh

efractalconcept

cann

otsim

plybe

appliedto

WPI

gels

EissaKhan(2005)

Wheyproteinsolutio

n3

and75

(heatw

ithw

ithou

ttransglutam

inaseTG

)low

pHcold-se

twheyp

rotein

gelfin

alpH

40

CSLM

196ndash

198

Rheology205ndash209




5 Conclusion





References







































































































Volume 2018

Zoology











Volume 2018

















Advances in




Enzyme Research





Volume 2018





5 Conclusion





References







































































































Volume 2018

Zoology











Volume 2018

















Advances in




Enzyme Research





Volume 2018



























































































Volume 2018

Zoology











Volume 2018

















Advances in




Enzyme Research





Volume 2018


fractal dimension analysis of texture formation of whey...

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