comparison between denaturant- and temperature-induced unfolding pathways of protein: a lattice...

Comparison between Denaturant- and Temperature-InducedUnfolding Pathways of Protein: A Lattice Monte Carlo

Simulation

Ho Sup Choi, June Huh, and Won Ho Jo*

Hyperstructured Organic Materials Research Center, School of Material Science and Engineering,Seoul National University, Seoul 151-744, Korea

Received June 8, 2004; Revised Manuscript Received August 26, 2004

Denaturant-induced unfolding of protein is simulated by using a Monte Carlo simulation with a latticemodel for protein and denaturant. Following the binding theory for denaturant-induced unfolding, thedenaturant molecules are modeled to interact with protein by nearest-neighbor interactions. By analyzingthe conformational states on the unfolding pathway of protein, the denaturant-induced unfolding pathway iscompared with the temperature-induced unfolding pathway under the same condition; that is, the free energiesof unfolding under two different pathways are equal. The two unfoldings show markedly differentconformational distributions in unfolded states. From the calculation of the free energy of protein as afunction of the number fraction (Q0) of native contacts relative to the total number of contacts, it is foundthat the free energy of the largely unfolded state corresponding to lowQ0 (0.1< Q0 < 0.5) under temperature-induced unfolding is lower than that under denaturant-induced unfolding, whereas the free energy of theunfolded state close to the native state (Q0 > 0.5) is lower in denaturant-induced unfolding than in temperature-induced unfolding. A comparison of two unfolding pathways reveals that the denaturant-induced unfoldingshows a wider conformational distribution than the temperature-induced unfolding, while the temperature-induced unfolding shows a more compact unfolded state than the denaturant-induced unfolding especiallyin the low Q0 region (0.1< Q0 < 0.5).

Introduction

Denaturant refers to a reagent that decreases the stabilityof protein and leads to a structural change from its specific,compact, and three-dimensional structure to an unfoldedstate. Examples of denaturant are urea and guanidiniumchloride, both of which have very similar chemical structuresbut differ in their efficiency to denature proteins. In contrast,sugars, glycerol, and poly(ethylene glycol) stabilize proteins.1-3

It is known that the protein stabilizers are excluded fromthe protein surface, and, therefore, the protein is preferentiallyhydrated in the presence of stabilizing solutes, whereasdenaturant increases the solubility of protein and interactspreferentially with the protein surface.4

Earlier studies have suggested that urea and guanidiniumchloride interact with both nonpolar and polar surfaces ofprotein more favorably than does water.4 A recent moleculardynamics simulation on the unfolding of barnase in aqueousurea has shown that most of the urea molecules in the firstsolvation shell of the protein form at least one hydrogen bondwith the protein.5 It has also been reported experimentallythat urea denatures proteins by reducing hydrophobic interac-tions and by directly binding to the amide units via hydrogenbonds.6

The conformational transition in the presence of denaturantis highly cooperative and reversible. Interestingly, it has been

observed experimentally for a large number of differentproteins that the free energy of unfolding∆FD-N is a linearfunction of denaturant concentration in a relatively narrowrange of the denaturant concentration. Accordingly, thedependence of the free energy of unfolding on the denaturantconcentrationC can be generally described as

where ∆FD-NH2O is the free energy of unfolding at zero

denaturant concentration andm is the constant slope of aplot of ∆FD-N(C) versusC. Using the linear relationship ofeq 1,∆FD-N

H2O can be obtained by extrapolatingFD-N(C) tozero denaturant concentration.

Some theoretical methods have been developed to explainthe interaction of denaturant with protein.7-11 Among them,the binding model of denaturant has widely been usedbecause of its simplicity. The binding model assumes thatthe denaturant interacts with solvent-exposed groups on aprotein molecule via direct binding and, hence, denaturesthe protein by reducing hydrophobic interactions in theprotein. In the binding model, if all the binding sites ofprotein are identical, the free energy of unfolding in thepresence of denaturant is defined as

where∆n is the difference in the number of binding sitesbetween denatured (D) and native (N) states andKb is an

* To whom correspondence should be addressed. E-mail: [email protected]. Fax:+82-2-885-1748. Tel:+82-2-880-7192.

∆FD-N(C) ) ∆FD-NH2O - mC (1)

∆FD-N(C) ) ∆FD-NH2O - ∆nRTln(1 + KbC) (2)

2289Biomacromolecules 2004,5, 2289-2296

10.1021/bm049663p CCC: $27.50 © 2004 American Chemical SocietyPublished on Web 10/05/2004

equilibrium binding constant. IfKbC , 1, eq 2 can beapproximated as

where∆nRTKb corresponds to them value of eq 1.Although the theoretical models provide fairly reasonable

explanations particularly for the dependence of the freeenergy of unfolding on the concentration of denaturant, thepathway of denaturant-induced unfolding is not clearlyunderstood. Monitoring the unfolding pathway of proteinsis very difficult, if not impossible, because the conformationalspectrum of a protein is formidably wide. Therefore, it isvery important to develop a simplified model that neverthe-less implies the essence of folding/unfolding phenomena,rendering an investigation of the unfolding pathway com-putationally tractable. Another important question on theunfolding of proteins is whether different unfolding methodsyield different pathways of unfolding. For instance, it maybe very informative to examine the similarity or differencebetween the pathway of denaturant-induced unfolding andthe pathway of temperature-induced unfolding.

The present work is concerned with the comparisonbetween two different protein-unfolding methods: denatur-ant-induced unfolding and temperature-induced unfolding.For this purpose, a lattice Monte Carlo method is employedto simplify the conformational states of a protein, whichenables us to systematically analyze the conformational stateon the unfolding pathway. This paper is organized as follows.We begin in the next section with describing the lattice modelfor a 27-bead protein molecule and denaturant molecules andthe calculation method of thermodynamic quantities used inthis study. In Results and Discussion, the free energy profilesfor both denaturant-induced unfolding and temperature-induced unfolding are presented and compared to each other.Finally, the conclusions are summarized in the last section.

Model and Simulation Methods

Three-Dimensional Lattice Model for Protein andDenaturant. The lattice-based model has been widely usedto study the thermodynamic and kinetic properties of proteinfolding because of its simplicity. Although the model largelysimplifies the molecular complexity of real proteins, itcontains basic features of protein folding in both thermo-dynamic and kinetic aspects: the unique native structure (i.e.,only one conformation with the global energy minimum); alarge number of conformations (the Levinthal paradox); acooperative folding transition occurring at the level ofdomains; and fast folding to the native state at conditionsunder which the native state is thermodynamically stable.Of course, the geometric simplification of the lattice modelloses some detailed features of a real protein molecule suchas lack of the notion of secondary structure, nonphysicalbalance between the number of buried and the number ofexposed residues, and lack of proteinlike interplay betweenshort and long-range interactions. Nevertheless, the latticemodel often becomes more advantageous for prediction of

thermodynamic features of protein folding, because thesacrifice of geometric accuracy in the lattice model allowsus to characterize the collection of all possible sequencesand the collection of all possible chain conformations, whichis not possible in the full atomistic model. Here, a briefdescription of the lattice protein model used in this study isprovided as follows.

A protein molecule is modeled as a cubic lattice het-eropolymer consisting of 27 beads, each of which representsan amino acid residue.12-14 In this model, a contact is madeonly when two nonbonded residues are located at a unitdistance from each other. Therefore, a fully compact self-avoiding chain in a 3× 3 × 3 cube has 28 contacts, and thetotal number of compact conformations unrelated by sym-metry in the 3× 3 × 3 cube is 103 346.15

The total energy of the proteinE is given as

whereBij is the interaction energy between residuesi and jlocated at positionsri andrj. Here,∆(ri - rj) becomes unityif beadsi and j are in contact and becomes 0 otherwise.Bij

values, elements of the 27× 27 contact energy matrix, areobtained by the following procedure. First, a 20× 20sequence matrix whose elements represent the contactenergies between 20 different residues is generated, wherethe values of energies are determined from a Gaussiandistribution with a meanB0 ) -2 and the standard deviationof 1. Then, the random numbers between 1 and 20, witheach corresponding to an amino acid residue in a protein,are randomly encoded into the 27 beads of a compact chainpicked from the list of 103 346 compact structures. Therefore,the Bij value corresponds to the energy between a residuetype of beadi and a residue type of beadj in the 20× 20sequence matrix. The sequence optimization is then per-formed by a sequence swapping algorithm proposed byShakhnovich and Gutin.14 This method efficiently yields asequence that meets the folding requirement, that is, non-degenerate ground state with large energy gap from the firstexcited state. Figure 1 shows the native conformation andthe energy spectrum of the protein with an optimizedsequence used in this study. The energy of the nativestructure with the optimized sequence is-87.106, and theenergy gap between the lowest energy state and the firstexcited state is 8.719. TheZ score17 is estimated as-38.921.

To model denaturant-induced unfolding, the model proteinand denaturant molecules with a given concentration areplaced inside a 30× 30 × 30 cubic box with the periodicboundary condition. Here, a denaturant molecule is assumedto occupy a lattice site. The box size guarantees that theprotein molecule does not interact with its image. Theinteraction energy between a protein bead (an amino acidresidue) and a denaturant is given asεp-d ) -2.0, whichequals the average contact energy between amino acidresiduesB0, and the interaction energy between denaturantsis set to be null.

The explicit treatment of denaturant in the present studyis different from the previous lattice simulation18 in whichan additional term that measures the exposure of the core

∆FD-N(C) ≈ ∆FD-NH2O - ∆nRTKbC (3)

E ) ∑1ei<je27

Bij∆(ri - rj) (4)

2290 Biomacromolecules, Vol. 5, No. 6, 2004 Choi et al.

monomer was added to the energy function to accommodatethe effect of denaturant. In an implicit denaturant model,18

the denaturant concentration was adjusted by varying thestrength of the additional energy term. Although the implicitmodel is computationally efficient, the binding effect ofdenaturant on the distribution of the conformational ensemblemay not be properly simulated.

Before performing a simulation, the protein is initiallylocated at the center of the box and denaturant moleculesare randomly distributed in the simulation box without doubleoccupancy. The protein molecule moves according to theVerdier-Stockmayer algorithm19 (VSA), and denaturantmolecules can move to vacant sites. The move is acceptedor rejected according to the Metropolis criterion. All simula-tions start from the native state and are performed for 108

Monte Carlo steps, and the trajectories are saved every 100Monte Carlo steps.

Here, it is noteworthy to mention the ergodicity of VSA.Strictly, this algorithm is not ergodic, because certainconformational states are neither accessible from any con-formational states nor movable to any conformational states.Such conformational states giving rise to breaking theergodicity in VSA have a common geometric feature: theyare highly knotted conformations.20 For instance, a confor-mation that both ends are buried in a compact structure formsknots and cannot be unknotted by VSA. However, as longas the target structure chosen for the native state is accessible,the nonergodicity of VSA does not become a problem forfolding/unfolding simulation for the following reasons. It isknown that real proteins do not have tight knots,21 and, hence,we do not really need to choose such a knotted structure as

a target native structure. In the kinetic viewpoint, it is alsovery unlikely that a protein during folding passes through aknotted state, because proteins are known to fold rapidlydespite their structural complexity. Therefore, such knottedstates will not have an effect on the folding/unfoldingkinetics, because the probability that a knotted state isencountered during folding/unfolding simulation is almostzero. Of course, a thermodynamic viewpoint poses anotherquestion on whether such inaccessible states affect thethermodynamic average of interest. The answer depends onhow much the statistical weight of the inaccessible statescontributes to the thermodynamic average. Indeed, thestatistical weight of the inaccessible states in VSA isnegligibly small, particularly for a small chain such as a 27-mer. Therefore, nonergodicity of VSA is not a problempractically in the calculation of thermodynamic propertiesof protein folding as long as the target structure chosen forthe native state is accessible.

All simulations are performed at constant volume andtemperature (NVT), instead of at constant pressure andtemperature (NPT), which is more relevant to real experi-ments. However, such a constant pressure condition (NPT)cannot be properly incorporated into a lattice Monte Carlomethod. Although the constant-volume condition is not thebest constraint for describing the real situation, it is veryunlikely that the two different conditions (NVT and NPT)lead to a different result on the conformational distributionof the unfolded state.

Calculation of Thermodynamic Quantities. Thermo-dynamic quantities such as the free energy of unfolding andthe heat capacity have been calculated from the trajectoriesof Monte Carlo simulation. First, the partition function isobtained from the simulation trajectory.12 The partitionfunction of the protein can be described as

whereQ0 is the number fraction of the native contacts,E isthe energy of the protein, andω(Q0, E) is the density ofstate withQ0 andE. The Boltzman constant is set to be unity.The density of stateω(Q0, E) is calculated as follows. First,the average occupancy of the bin,ν(Q0, E), is obtained fromthe simulation trajectory. The size of each bin is 1/28 inQ0

and 1 inE. Then, the density of the state can be calculatedusing the following relation:12

where E0 is the energy of the native state. Because it isknown from enumeration of all possible conformations in a3 × 3 × 3 cube that the degeneracy of the native stateω(Q0

) 1, E ) E0) is unity, the above equation can be expressedas

Figure 1. Native structure of the protein lattice model used in thepresent study. The native structure has the lowest value (0.275) ofcontact order among 103 336 compact structures. The contact order(CO) is the average sequence distance between all pairs of contactingresidues normalized by the total sequence length, CO ) 1/(LN)∑N∆Si,j,where N is the total number of contacts, L is the total number ofresidues, and ∆Si,j is the sequence separation between contactingresidues i and j.16 The energy is calculated for all 103 346 compactstructures using the optimized sequence, and the energy spectrumfor the 400 lowest conformations is shown. The lowest energy of-87.11 corresponds to the native state and the energy gap (8.72)between the native state and the first excited state is indicated by anarrow.

Z(Q0) ) ∑E

ω(Q0, E) exp(-E/kBT) (5)

V(Q0, E)

V(Q0 ) 1, E ) E0))

ω(Q0, E) exp(-E/kBT)

ω(Q0 ) 1, E ) E0) exp(-E0/kBT)(6)

ω(Q0, E) )V(Q0, E) exp[-(E0 - E)/kBT]

V(Q0 ) 1, E ) E0)(7)

Monte Carlo Simulation of Protein Unfolding Biomacromolecules, Vol. 5, No. 6, 2004 2291

The free energy of protein is, therefore, written as

It should be pointed out that the free energy expressed in eq8 does not account for the contributions arising from thepresence of denaturant molecules. The presence of denaturantgives an additional term to the free energy, which containsboth the energetic contribution due to the binding betweendenaturant and protein and the translational entropy ofdenaturant molecules. As will be shown below, this ad-ditional term, however, is independent ofQ0 and, thus, shiftsF(Q0) only vertically in the plot ofF versusQ0. To avoidsome confusion, we denote the free energy containing suchan additional term byFd. In the presence of denaturant, thepartition functionZd is given as

where Epd is the total binding energy between residuesand denaturant molecules. Because the density of statesω(Q0, E, Epd) can be expressed as

the free energyFd is written as

Note that the additional term is independent ofQ0, and, thus,Fd(Q0) - Fd(1) ) F(Q0) - F(1). Because the property ofinterest in this study is the relative stability between the nativestate (Qo ) 1) and the denatured state (Q0 * 1), the additionalterm is omitted in the calculation of the free energy.

Results and Discussion

First, dynamic Monte Carlo simulations are performed inthe absence of denaturant molecules at various temperatures,to obtain the free energy profile of folding/unfolding ofprotein itself. Figure 2a shows the free energy of proteinplotted against the fraction of native contactQ0 at varioustemperatures. The free energy curves show that there existtwo distinct minima of free energy corresponding to theunfolded (Q0 ) 0.286) and the native states (Q0 ) 1). Asthe temperature increases, the free energy of the unfoldedstate becomes lowered. When the heat capacity of protein

Cv and the probability of native statePN ) exp(-E0/kBT)/Zare plotted against temperature by using the histogramreweighting method,22 as shown in Figure 2b, it shows thatboth Cv and PN show a cooperative transition atT = 1.5.

The simulations in the presence of denaturant moleculesare then performed at constant temperatureT ) 1.0, wherethe probability of the native statePN is 0.986 in the absenceof denaturant. Figure 3a shows the free energy profiles ofprotein in the presence of denaturant. As the concentrationof denaturant increases, the free energy of unfolded state islowered. The free energy profile also shows that the twominima of the free energy corresponding to the unfolded stateat Q0 ) 0.286 and the native state atQ0 ) 1.0 are separatedby the barrier at 0.893. When bothPN and Cv are plottedagainst the denaturant concentration, as shown in Figure 3b,it is realized that the denaturant-induced unfolding also showsa cooperative transition atC = 0.04. To monitor theunfolding pathway along the reaction coordinate defined asQ0, we calculate the ensemble averaged density profile ofdenaturant and the ensemble averaged structure of unfoldedstate at eachQ0. As shown in Figure 4, when the proteinreaches the barrier atQ0 ) 0.893, the protein still retains acompact structure and the denaturant molecules do notpenetrate into the protein molecule, while the density of thefirst hydration shell (2< r < 3) is almost two times higherthan the given concentration of denaturantC ) 0.04. As theunfolding proceeds further over the transition state, thedensity of denaturant inside the protein becomes higher thanthe given concentration of denaturantC ) 0.04, indicating

F(Q0) ) -kBT ln Z(Q0)

) E0 + kBT(ln ν(1, E0)

∑E

ν(Q0, E)) (8)

Zd(Q0) ) ∑E,Epd

ω(Q0, E, Epd) exp[-(E + Epd)/kBT] (9)

ω(Q0, E, Epd) )ω(Q0 ) 1, E ) E0, Epd ) 0)

ν(Q0 ) 1, E ) E0, Epd ) 0)ν(Q0, E, Epd)

exp[-(E0 - E - Epd)/kBT] (10)

Fd(Q0) ) E0 + kBT(ln ν(1, E0, 0)

ω(1, E0, 0)∑E

ν(Q0, E))) F(Q0) + kBT(ln ν(1, E0, 0)

ω(1, E0, 0) ν(1, E0)) (11)

Figure 2. (a) Free energy of the protein as a function of the fractionof native contact Q0. The results are obtained from the average ofsimulations at four different temperatures in the absence of denatur-ant. (b) Plots of heat capacity Cv and the probability of native statePN versus temperature. The histogram reweighting method is usedby using the data collected at T ) 1.5.


that denaturant molecules penetrate into the protein moleculeand are bound to the unfolded state of the protein. Whenthe unfolding reaches the state atQ0 ) 0.286 correspondingto the lowest free energy of unfolded state, the inside of theprotein is nearly occupied by denaturant molecules, and thedensity of the denaturant shows a maximum atr ) 2.0.

The free energy change upon unfolding has been calculatedas a function of the denaturant concentration. The free energyof unfolding ∆FD-N is defined as

where PN ) exp(-E0/kBT)/Z. When the free energy ofunfolding∆FD-N is plotted against the denaturant concentra-tion, as shown in Figure 5, it reveals that the free energydecreases linearly with increasing the concentration ofdenaturant. This linearity has often been observed in previousexperiments on the denaturant-induced unfolding of pro-teins.7,10,11The value of the binding constantKb of urea wasestimated to be 0.06( 0.01 M-1 from calorimetric experi-ment.11 However, Schellman7 indicated that the bindingconstant with an order of 0.01 is not large enough to explainthe interaction of a urea molecule with protein sites and,

therefore, the ordinary binding theory may not be correctfor the interaction between denaturant and protein. Hesuggested that the binding of a denaturant molecule to aprotein site is an exchange of water for denaturant at thesite. Therefore, for two solvent components of water and

Figure 3. (a) Free energy of the protein as a function of the fractionof native contact Q0 in the presence of denaturant. The denaturantconcentration C is expressed as the number density of denaturant inthe simulation box. The number density of denaturant is defined asthe number of denaturant divided by the total lattice sites 27 000.Monte Carlo simulations were performed at different concentrationsof denaturant (0.005 e C e 0.07) for 108 Monte Carlo steps. Allsimulations were carried out at T ) 1.0, where PN is 0.986 in theabsence of denaturant. (b) Plots of the probability of native state PN

(open circles) and heat capacity Cv (filled circles) versus denaturantconcentration C. The solid line is plotted by using a regressionmethod.

∆FD-N ) -kBT lnPD

PN) -kBT ln

1 - PN

PN(12)

Figure 4. Averaged density profiles of denaturant and protein atunfolded states corresponding to each Q0, where r is the distancefrom the center of mass of protein, and Nd(r) and Np(r) are the numberof denaturant molecules and protein segments, respectively, locatedat the shell of radius r. The radius of gyration of the native state is1.414, and the denaturant concentration C is 0.04.

Figure 5. Free energy of unfolding ∆FD-N is plotted as a function ofdenaturant concentration. ∆FD-N is defined in eq 9. The solid line isplotted by using a linear regression method, where the correlationcoefficient R is 0.98.


denaturant, the contribution of a protein sitej to the unfoldingfree energy∆FD-N

j can be described as

whereKjw and Kj

d are the binding constants for water anddenaturant, respectively, andφw andφd are the mole fractionsof water and denaturant, respectively. The first term of theright-hand side in eq 13,-kBT ln Kj

w, is the free energy ofhydration at the site.Kj

d/Kjw corresponds to the equilibrium

constant for the replacement of a water molecule by adenaturant molecule at the site. IfKj

d/Kjw and φw of eq 13

are put asKj and 1- φd, respectively, eq 2 for∆FD-N canbe rewritten as

in which Kj has the following meaning:

where [denaturant] and [water] are the averaged occupationof the site by denaturant and water, respectively. Becauseφd/φw corresponds to the ratio of the two occupations forthe random case where the binding energy is not applied,Kj

is a multiplicative factor that reflects nonrandom occupationwhen the binding energy is applied. WhenKj is much greaterthan 1, eq 13 reduces to the normal binding theory of eq 2.WhenKj is equal to 1, the protein site is randomly occupiedby denaturant or water and, therefore, the free energycontribution of the site becomes 0. WhenKj is less than 1,water molecules occupy the site preferentially, which cor-responds to preferential hydration in the presence of stabiliz-ing solutes. Therefore,Kb in eq 2 has a built-in subtractionfor random replacement of water.7 The averaged bindingconstant⟨Kj⟩ is calculated in our study as follows. First, theratio of the average occupations [denaturant]/[water] iscalculated from the unfolded ensembles sampled duringsimulation. Then, because the vacant lattice sites are regardedas the sites occupied by water molecules andφd/φw corre-sponds to the ratio of the number densities, the average valuesof ⟨Kj⟩ can be obtained from the average taken over allprotein sitesj and over all unfolded conformations (Q0 *1). The ⟨Kj⟩ obtained from the simulation is 7.69, whichdemonstrates that the denaturant molecules preferentiallyoccupy the protein surface.

Figure 6 shows the free energy profiles of denaturant- andtemperature-induced unfolding. The two free energy profilesare calculated under the same condition that the probabilityof the native statePN is equal to 0.03. Comparison of thetwo profiles shows that in the lowQ0 region (0.1< Q0 <0.5), the free energy of denaturant-induced unfolding ishigher than that of temperature-induced unfolding, whereasthe free energy profiles are reversed in the highQ0 region(Q0 > 0.5) where the protein retains more native contacts.Because the probabilities of the native statePN are the same,the free energy difference demonstrates that denaturant-induced unfolding shows a different conformational distribu-

tion of the unfolded state alongQ0 as compared withtemperature-induced unfolding.

When the free energy of proteinF is decomposed intothe contact energy (E) between amino acid residues and theconformational entropy of the protein (S), as shown in Figure7, it is realized that the averaged contact energy of proteinunder denaturant-induced unfolding is higher than that undertemperature-induced unfolding in the lowQ0 region (0.1<Q0 < 0.5), while there is no significant difference of contactenergy between the two unfoldings in the highQ0 region(Q0 > 0.5). This implies that the unfolded state of denaturant-induced unfolding loses more contacts than that of temper-ature-induced unfolding in lowQ0 region (0.1< Q0 < 0.5).

∆FD-Nj ) -kBT ln(Kj

wφw + Kj

dφd)

) -kBT ln Kjw - kBT ln[φw + (Kj

d/Kjw)φd] (13)

∆FD-N ) ∆FD-NH2O - kBT∑

j

ln[1 + (Kj - 1)φd] (14)

[denaturant]/[water]) Kjφd/φw (15)

Figure 6. Free energy profiles of denaturant-induced (solid line) andtemperature-induced (broken line) unfolding pathways. Temperature-induced unfolding simulation was performed at T ) 1.77 and C )0.00, and denaturant-induced unfolding simulation was performed atT ) 1.00 and C ) 0.05, where the values of PN for the two differentunfolding simulations are the same as 0.03.

Figure 7. Contribution of contact energy (a) and entropy (b) to thefree energy of the protein. The free energy of the protein isrepresented in Figure 5.


Because the magnitude of the binding energy between proteinand denaturant is equal to that of the average contact energybetween residues, the binding of denaturant to protein cancompete with the contact between residues. Therefore, acontact between residues can be replaced by a contactbetween a residue and a denaturant, leading to an unfoldedstructure that has fewer contacts between residues ascompared to that of temperature-induced unfolding. Conse-quently, the number of possible unfolded conformationsunder denaturant-induced unfolding becomes larger as aresult of the binding of denaturant to protein, resulting inthe denaturant-induced unfolding having a higher confor-mational entropy, as shown in Figure 7b.

The averaged number of contacts calculated from unfoldedstates corresponding to eachQ0 is shown in Figure 8, whichshows that the unfolded structure from denaturant-inducedunfolding has fewer contacts than that from temperature-induced unfolding. It is also realized from Figure 8 that thedifference of the number of contacts is greater in the lowQ0 region (0.1< Q0 < 0.5). Figure 9 shows the contourmap of the number of sampled conformations duringsimulation on the surface of the contact energy andQ0. Inthe high region (Q0 > 0.5), the number of sampledconformations under denaturant-induced unfolding is largerthan that under temperature-induced unfolding. This isobserved in all concentration ranges examined in this study.

Recently, the dependence of the urea-induced stability onthe size of the protein has been reported by Shimizu andChan.23 Using the free energy calculation for pairwisehydrophobic association in aqueous solutions of urea, theyreported that the denatured protein retains the nativelikecompactness. In addition, it has been reported that adenatured protein retains nativelike topology even under arelatively concentrated condition of 8 M urea.24 From theseresults, it is suggested that an increase in the concentrationof urea would not lead to further significant expansion ofthe urea-denatured chains. This result is also observed inour simulation. Our simulation results show that the unfoldedstructure even at relatively high concentration of denaturant(C ) 0.05-0.07) still retains 25-30% of native contacts(Figure 6) and roughly 70% of the number of contacts offully compact structure (Figure 8), indicating that denaturedprotein persists a nativelike semicompact structure rather than

a loosely expanded structure. Although there are somesimplifications in our denaturant model such as that the sizedependences of denaturant and side chain of amino acid areignored, the simple denaturant model based on the bindingtheory can reproduce the experimentally observed charac-teristics of denaturant-induced unfolding.

Concluding Remarks

The denaturant-induced unfolding has been investigatedby using a Monte Carlo simulation. When the denaturant-induced unfolding pathway is compared with the tempera-ture-induced unfolding pathway, the two unfolding pathwaysshow different conformational distributions at unfolded andtransition states. The free energy of unfolded states corre-sponding to lowQ0 (0.1 < Q0 < 0.5) under temperature-induced unfolding is lower than the case under denaturant-induced unfolding, whereas the free energy of the unfoldedstate close to the native state (Q0 > 0.5) is higher undertemperature-induced unfolding than under denaturant-inducedunfolding. It is realized that the denaturant-induced unfolding

Figure 8. Plots of the averaged number of contacts between residuesversus Q0. Temperature-induced unfolding simulation (broken line)was performed at T ) 1.77 and C ) 0.00, and denaturant-inducedunfolding simulation (solid line) was performed at T ) 1.00 and C )0.05.

Figure 9. Contour map of log v(Q0, ε), where v(Q0, ε) is the numberof conformations corresponding to the bin (Q0, ε). The size of eachbin is 1/28 in Q0 and 1 in ε (see the model and simulation method inthe text for details): (a) temperature-induced unfolding at T ) 1.77and C ) 0.00, (b) denaturant-induced unfolding T ) 1.00 andC ) 0.05.


shows a wider conformational distribution than the temper-ature-induced unfolding, because denaturant molecules boundto a protein molecule break contacts between amino acidresidues, resulting in higher conformational entropy. On theother hand, the temperature-induced unfolding passes throughmore compact unfolded states than the denaturant-inducedunfolding especially in the lowQ0 region (0.1< Q0 < 0.5).

It should be noted that our model has two importantsimplifications: one is an assumption that the size of adenaturant is equal to that of an amino acid residue, and theother one is that the effect of the water molecule ondenaturation is implicitly taken into account by introducingthe pairwise hydrophobic interactionBij, which is tempera-ture-independent. As a result, our model may not describethe cold denaturation25-27 but only shows the temperature-induced unfolding. Moreover, it has been reported that theprotein folding pathway can be affected by temperature.28

Hence, further refinement for our model is needed toaccommodate the effect of temperature on the state of waterfor studying temperature-dependent properties as well as thecold denaturation.

Acknowledgment. The authors thank the Korea Scienceand Engineering Foundation (KOSEF) for financial supportthrough the Hyperstructured Organic Materials ResearchCenter (HOMRC).

References and Notes

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BM049663P


comparison between denaturant- and temperature-induced unfolding pathways of protein: a lattice...

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