LoD PLI: Level of Detail for Visualizing Time-Dependent, Protein-LipidInteraction

Naif Alharbi1, Michael Krone2, Matthieu Chavent3 and Robert S. Laramee1

1Swansea University, UK2University of Tbingen, Germany

3IPBS, Toulouse, France

Keywords: Scientific visualization, Molecular Dynamics, Protein-lipid Interaction

Abstract: In Molecular Dynamics (MD) Visualization, representative surfaces of varying resolution are commonly usedto depict protein molecules while a variety of geometric shapes, ribbons, and spheres are used to representresidues and atoms at different levels of detail (LoD). The focus of the visualization is usually on individ-ual atoms or molecules themselves and less often on the interaction space between them. Here we focus onLoD interaction between lipids and proteins and the space in which this occurs in the context of a membranesimulation. With naive approaches, particles may overlap and significant interaction details can be obscureddue to clutter. Furthermore, the spatial complexity of the protein-lipid interaction (PLI) increases over time.Co-developed with an MD domain expert, we address the challenge of visualizing complex, time-dependentinteractions between lipids and proteins by introducing two abstract LoD representations with six levels ofdetail for lipid molecules and protein interaction. We also propose a fast GPU-based projection that mapslipid-constituents involved in the interaction onto the abstract LoD protein interaction space. The tool pro-vides fast LoD, the imagery of PLI for 336,260 particles over almost 2,000 time-steps. The result is a greatsimplification in both perception and cognition of this complex interaction that reveals new patterns and insightfor computational biologists. We also report feedback from the domain expert to our visualization.

1 INTRODUCTION ANDMOTIVATION

Visualization of Molecular Dynamics (MD) has re-ceived a great amount of attention over the past twodecades. Numerous MD visualization tools are usedfor visualizing MD data from simple to complexmolecules [Kozlıkova et al. (2017) and Alharbi et al.(2017)]. With recent advances in computer graphics,most of the MD visualization research focuses on op-timal rendering quality and performance.

Proteins perform an array of functions such asdrug and neurotransmitter transport. Lipids inti-mately influence the structure and function of mem-brane proteins by extensive protein-lipid interaction(PLI) Antonny (2011). Here the PLI plays a sig-nificant role in understanding the interdependenceof membrane proteins with their surrounding lipids.Simulations facilitate structural understanding in thecontext of a lipid bi-layer. This is the application wefocus on here.

In an MD visualization, a number of models areused to depict molecules at the molecular and atom-istic scale. Protein molecules, for example, are of-ten represented by surfaces. This representation pro-

vides an overview of the protein shape at the molecu-lar scale. At the atomistic scale, small molecules in-cluding atoms’ bounds are often represented by mod-els such as ball-and-stick. These representations arecommonly used to visualize the MD data at the de-sired scale. However, depending on the intended anal-ysis task, these same representations might also be-come part of the challenge due to their complexity.

The visualization of PLIs in time-dependent sys-tems involves a number of challenges. Complex pro-tein surfaces might not be an ideal solution in thiscase. The dynamics of the system may cause manyparticles to be occluded or to overlap. The PLI oc-curs at the atomistic level which presents computationand visualization challenges. Every single interactionholds information that might explain the lipid’s influ-ence on a protein’s functions. At the very beginningof the simulation, a lipid might interact with one pro-tein at most. Over time, the complexity of the systemincreases due to the evolution of the system particles.Figure 1 illustrates the motivation behind this workwhere lipid particles interact with more than one pro-tein. Special techniques we can use to enable usersto investigate the PLI at different levels of abstrac-

Figure 1: A snapshot of a naive Protein-Lipid interactionrepresentation. Protein particles are yellow, and lipid par-ticles are green initially and turn red after an interaction.Perceptual difficulties stem from complexity and occlusion.

tion. We extend Alharbi et al. (2018) by design andimplement a LoD PLI in close cooperation with do-main experts to help computational biology scientiststo obtain insight into PLI for time-dependent systems.Our contributions are:

• Six levels of detail for the protein-lipid interactionand an enhanced implementation of the PLI spaceutilizing a tree-structure.

• A smooth transition between the six LoDs uti-lizing lipid-scale and particle-scale effects. Thelipid-scale effect provides a smooth transition forparticle positions between levels. The particle-scale effect provides a smooth change of the ra-dius of the particles between levels.

• While the previous work harnesses the GPU to ac-celerate the computation of PLI here we propose afast GPU-based approach to accelerate represent-ing the PLI LoD in the abstract interaction space.

• A number of PLI filtering and selecting tech-niques as well as a custom color-map feature toenhance the visualization.

The paper is organized as follows: In Section 2, wediscuss related work. In Section 3, we describe thesimulation data. Section 4 discusses the visual-designaspects. In Section 5 we present the results of ourmethod and discuss the reaction of a domain expertin computational biology to our novel LoD PLI repre-sentation. Conclusions and directions for future workare given in Section 6. The implementation is de-scribed in the supplementary file.

2 RELATED WORKThere has been a fair amount of recent as well as use-ful review papers on the theme of molecular visual-ization. Readers can be referred to O’Donoghue et al.(2010). The report covers web-based and stand-alonetools and discusses the advantages and disadvantagesof the most common molecular structure acquisitiontechniques for biological data. Kozlıkova et al. (2017)in another of their state-of-the-art review, classify re-cent advances in visualization undertaken within thearea of molecular simulation particularly focussed onstructural biology applications. Alharbi et al. (2017)present the first survey of surveys on molecular dy-namics visualization involving survey papers from thecomputational biology community as well as com-puter graphics. The chosen surveys (in total 11 sur-veys) discuss a diverse range of research topics inmolecular visualization spanning the long history ofadvances in molecular dynamics visualization (MDV)spanning 1980 to 2017.

In the molecular visualization literature, metaphorand levels of detail (LoD) are often used to enhancesoftware performance or reduce visual complexity,and enhance perception. Table 1 classifies relatedwork into LoD for performance and perception andtheir complexity.LoD for Performance And Computational Com-plexity Preceding literature often cites spatial datastructures which rely on 1) the assembly of atomswithin a molecule, or 2) modifying the surface resolu-tion of a molecule concerning the LoD. The aim is toallow a user to interactively visualize larger moleculardatasets by minimizing the computational complexityneeded for data representation.

Sharma et al. (2004) implement a hierarchicalfrustum-culling algorithm on the basis of an octreedata structure. This algorithm is efficient for remov-ing atoms which are outside the field-of-view win-dow. This is through the application of probabilisticand depth-based occlusion culling as well as the uti-lization of a multi-resolution algorithm for renderingthe chosen subset of visible atoms at different levelsof detail.

Bajaj et al. (2004) introduce a biochemically sen-sitive level-of-detail hierarchy for molecular repre-sentations. The hierarchy is constructed from the baseupwards in such a manner that each member of this hi-erarchy includes all members which are related to thelevel immediately preceding it. For example, an atomis the lowest level of the hierarchy. A residue con-tains all constituent atoms, while a secondary struc-ture contains all constituent residues. Each level ofthe hierarchy is associated with a geometric repre-sentation. A single sphere represents an atom with

Table 1: A classification of the related work with respect to: performance and perception and their complexity. The fourthcolumn presents the focus elements. (S= Surfaces, P= Protein, M= Molecules, R= Residues, A= Atoms, Ast= Astrocytes, N=Neurites).

Paper Performance andComputational Complexity

Perception andPerceptual Complexity Focus Objects

Bajaj et al. (2004) 3 7 SSharma et al. (2004) 3 7 ALee et al. (2006) 3 7 SLampe et al. (2007) 3 7 PWeber (2009) 7 3 MVan Der Zwan et al. (2011) 7 3 M, ALindow et al. (2012) 3 7 M, AKrone et al. (2012) 3 7 SFalk et al. (2013) 3 7 M, AParulek et al. (2014) 7 3 M, A, SLe Muzic et al. (2014) 3 7 M, AMohammed et al. (2018) 7 3 N, AstAlharbi et al. (2018) 3 7 M, A

a Van der Waal radius, while a residue is depicted bya minimal single bounding sphere which includes allits constituent atoms. This approach considerably re-duces visual clutter by presenting the suitable volumeoccupancy and shape. Additionally, the hierarchicalimage-based rendering enables the mapping of de-rived physical characteristics onto the molecular sur-faces.

Lee et al. (2006) propose an algorithm for real-time surface visualization on the basis of a view-dependent LoD method. This technique comprisestwo stages: a pre-processing stage and a real-timerendering stage. This technique offers high-qualityrendering and also displays critical components ofmolecular models. In the preprocessing stage, themesh of the molecular surface is simplified and clas-sified by different levels of detail. In the real-timerendering stage, hierarchical LoD models are con-structed which result in accelerating the renderingperformance. Lampe et al. (2007) introduce a two-stage approach for visualizing large as well as time-dependent protein complexes. In the first stage, eachresidue is substituted with a single vertex based onthe residue’s rigid transformation. In the second level,the atoms which are contained in the residues are dy-namically generated within the geometry shader onthe basis of the initial simulation vector and the trans-formation matrix.

Lindow et al. (2012) introduce a 3D voxel gridbased on the GPU, for storing the atomic data and uti-lizing a fast ray-voxel traversal through which just thespheres within the existing voxel are tested for inter-section. This algorithm enables for the interactive rev-

elation of biological structures comprising of billionsof atoms. Comparable to results obtained by Lindowet al. (2012), Falk et al. (2013) store every moleculein its own supportive grid, which is further traversedin detail via a ray. Here the grid is constructed on thebasis of each atom’s size while in Lindow et al. (2012)the grid is constructed based on the number of atoms.Krone et al. (2012) propose a novel fast approach formolecular surface extraction that can be used for de-picting structural details on a constant scale. By mod-ifying the resolution of the grid as well as the densitykernel function the scale may vary from atomic detailto lower resolution detail in visual representations.

Le Muzic et al. (2014) present a LoD approachwhich envelopes adjacent atoms within a singlesphere dependent on the distance from the camera.They utilize texture for storing the atomic positionsof the whole molecule. Tessellation and geometryshaders are used for constructing the atom’s positionbased on a rotational quaternion which represents themolecule’s present orientation. Their approach is sim-ilar to Lampe et al. (2007) but uses the tessellationshader instead of the geometry shader. Alharbi et al.(2018) introduce a novel abstract protein space andprovide a solution to address PLI computations andvisualizations challenges. They focus on the spacebetween lipids and proteins and visualize the PLI atthe atomistic level. The PLI details are maintained viaa uniform cylindrical grid. The paper mainly focuseson the abstract protein space as a proposed solutionfor PLIs in complex MD systems.LoD for Perception and Perceptual ComplexityIn the context of molecular visualization, abstraction

typically refers to structural abstraction. The struc-ture of a molecule is commonly depicted via variousrepresentations. e.g., a space-filling diagram, the balland sticks model, and the ribbon model.Generally, every representation is associated with aparticular molecular structure, and several LoD tech-niques are applied for the provision of a smooth tran-sition within the structures.

Van Der Zwan et al. (2011) propose a novelcontinuous abstraction space for illustrative molec-ular visualization. This approach is GPU-basedfor depicting continuous transitions between variousstages of structural abstraction of a molecular sys-tem (i.e. space-filling, licorice, ball-and-stick, rib-bon, and backbone). A seamless structural transi-tion is applied from space-filling to ribbon. Paruleket al. (2014) propose a novel LoD approach for vi-sualizing larger protein complexes. Its applicationto individual levels is based on the distance to thecamera. They utilize three distinct surface represen-tations (such as solvent-excluded surface (SES), Vander Waals spheres and Gaussian kernels). Shading ab-stractions, as well as hierarchical representations, areused for creating smooth transitions between the threerepresentations. Mohammed et al. (2018) present anovel tool for visualization of astrocytes and neuronsat varied levels of abstraction. This tool employs anovel abstraction space to provide a set of visualiza-tions ranging from detailed 3D surface images of seg-mented structures (realistic images) to simplified ab-stractions (like skeletons and graphs). Previous work,in general, does not focus on the interaction space be-tween lipids and proteins.

In this work we extend Alharbi et al. (2018) byproviding six dynamic, levels of detail to address vi-sual complexity and perception. We provide a simpli-fied representation of the PLI at different levels. Here,the protein’s interaction space is also used to enhanceperformance during detection of protein-lipid inter-sections on-the-fly. The LoD is computed based onthe zoom value. Each level represents the moleculeby increasing the number and the size of its parti-cles. Our approach enables the user to smoothly zoombetween the levels of detail without losing the over-all structure of the molecule. Also, our visualiza-tion conveys historical information about the dynamicprotein-lipid interaction overall simulation time steps.It differs from the previous one in three significantways. First, Alharbi et al. (2018) focus on the PLIspace at the atomistic level while we here introduce 1)six LoD representations for an abstract protein spaceand 2) six LoD representations for lipid molecules.Second, Alharbi et al. (2018) utilize a uniform 2Dgrid to maintain the PLI detail. We employ a custom

quad-tree structure to exploit the properties of a treestructure in the PLI LoD representations. We also im-plement a fast GPU-based method to accelerate rep-resenting the PLI on the PLI space. Thirdly, this workintroduces a number of additional features which en-able the user to 1) filter the frequency of the PLI, 2)filter the PLI based on the participating molecule type,3) map the PLI frequency to different color maps uti-lizing a custom color map method that provide an en-hanced color mapping with respect to the distributionof the PLI along the color scale.

3 SIMULATION DATADESCRIPTION

Data-sets characterize biological dynamics of lipidsand proteins within the perspective of a membranemodel. The simulation domain’s dimensions are 116× 116 × 10 nanometers (x, y, and z respectively). In-dividual trajectories reflect the evolution of 336,260particles over 1,980 nanoseconds (ns). The systemcomprises three molecule types: one protein, and twolipid types (POPE and POPG). The protein type simu-lates 256 protein molecules while the collective lipidPOPE and the POPG types comprise of 14,354 and4,738 molecules respectively. The collection of thestructures is described below:

1- Each protein has 171 residues. Each residueconsists of 1 to 3 particles. A single protein consistsof 344 particles which result in (256 × 344) 88,064particles in total.

2- The lipid collection consists of 19,092 lipids.Each lipid contains 3 groups: i) a head group (2 par-ticles), ii) a tail group (6 particles), and iii) a secondtail group (5 particles). Each lipid molecule has 13particles which result in (19,092 × 13) 248,196 lipidparticles in total.The models discussed are on the basis of the MAR-TINI coarse-grained forcefield Marrink and Tieleman

Figure 2: Representation of molecules: Protein, POPE andPOPG types (left to right). The Protein and the Lipid typeimages are generated with our tool.

(2013) which does not signify all the atoms, how-ever, simplifies four heavy atoms through one coarse-grained particle. Figure 2 provides a depiction of thestructure of a protein, lipid POPE type, and POPGtype. Regarding the size of the simulation, the data-set contains more than 666 million space-time posi-tions that occupy 8 Gigabytes of memory.

4 VISUALIZATION OFPROTEIN-LIPIDINTERACTION

This section discusses the main aspects of the visu-alization of protein-lipid interaction. It describes theLoD representation of lipids and discusses the rela-tion between lipid LoD representations and the PLIdetail at different levels. It also discusses the proteininteraction space and describes the LoD representa-tions of the protein-lipid interaction space. The lasttwo subsections discuss the construction of our IBQT(index-based quad-tree) and the projection of the PLIonto the protein LoD space.

4.1 Lipid LoD Representation

The hierarchy for lipid is simplified based on theMARTINI coarse-grained forcefield Marrink andTieleman (2013). Generally, lipids are represented ei-ther by an abstraction such as Van der Waals spheres,CPC, licorice Humphrey et al. (1996) and hyperballsChavent et al. (2011) or by atomistic representationswhere every individual particle is depicted by a sin-gle sphere (sticks might be used to represent bondsbetween atoms). We choose the atomistic represen-tation over the abstract representations as the latterlends itself to a smooth LoD representation, espe-cially with dynamic systems. We depict the lipidparticles as spheres and cylinders representing bondsbetween particles. The rendering is accelerated byGPU-based ray-casting techniques for both spheresand cylinders.

Lipid Base-Structure: Our lipid LoD representa-tion starts with the lipid base-structure. As describedin section 3 lipids have a well-defined structure: ahead group and two tails. The three groups are con-nected via a linker particle in such a way that theirfinal representation reflects the Lipid model in Figure2. We employ the geometry of the base-structure tobuild five derivative structures such that each extendsthe previous one and represents the lipid at the givenLoD.

Derived Structure: The first derived structure con-sists of only one relatively large particle, i.e., the

Figure 3: Six levels of detail for Lipids. A smooth transition(ST) is applied between the six levels. The size of the sphereshrinks between level as well. The yellow spheres representthe transition stage. The LoD is calculated based on thezoom value.

linker particle which is the representative of the lipidat LoD 1. The second derived structure involves thelinker and its closest neighbors which represent thelipid at LoD 2. New structures for LoD 3, 4 and 5 arederived by smoothly extending neighbors of existingparticles until a lipid reaches the most detailed rep-resentation and smallest particle size at LoD 6. SeeFigure 3.

Smooth LoD Transition: By convention we usethe term ”terminal particle” to describe relativelysmall particles that occupy leaf nodes of the givenstructure. We utilize a smooth dynamic transitionbetween levels to avoid flickering caused by suddentransitions. The smooth transition is achieved byapplying two continuous effects, a lipid-scale, anda particle-scale effect. The lipid-scale effect is re-sponsible for providing a smooth, forward/backwardtranslation for terminal particles between levels. Theparticle-scale effect is responsible for providing asmooth increasing/decreasing of each terminal parti-cles’ radius during the transition. The speed of thetransition is a user option, and it can be configuredby increasing or decreasing the transition time. Thelonger the time, the smoother the transition. Figure 3shows the transition between levels.

4.2 LoD Lipid InteractionOne of the properties of the PLI is that it occurs at theatomistic level. This property poses a LoD computa-tional and visualization challenge. The property im-plies that for every lipid molecule each of its particlesneeds to be included in the PLI proximity test. Forexample, if the interaction test is performed at LoD1 then, for every lipid, only one particle is involved

in the interaction test while some of its other particlesmight pass the interaction test if they were involved.On the other hand, not all the particles of the givenlipid necessarily pass the interaction test at the max-imum LoD. For example, if the interaction is causedby a particle p that exists only at LoD n we will notbe able to reveal its interaction detail at LoD n−1 asparticle p is not represented at this level downward.These challenges might result in unexpected approxi-mations at all the LoDs except LoD 6 as all the lipidparticles are included in the structure. Hence the PLItest is performed on the GPU for LoD 6 as the lipidstructure in this level involves all the lipid particles.The result is maintained in full detail. For every LoD,we inherit the interaction details from the upper levelin such way the visualization reveals the interactiondetail for the present LoD and higher approximations.It is clear from Figure 4 that adding lipid LoD helpsreduce occlusion and clutter. However further inno-vation is required for protein LoD.

4.3 Protein Interaction Space

Cylindrical PLI Representation: The description ofthe cylindrical PLI representation is given by Alharbiet al. (2018). See Section 4.

4.4 LoD Protein-Lipid Interaction spacePLIs can occur at any position within a protein space.By utilizing an abstract cylinder to represent a proteinspace, a PLI can be directly depicted on the surfaceof the abstract protein space using a tile. Essentially,the surface of the abstract protein space is dividedinto 1024 tiles. Each tile is associated with an IBQT(index-based quad-tree) node (see Section 4.5). TheIBQT nodes are responsible for maintaining the PLIdetail while tiles are used to depict the nodes’ infor-mation. We exploit the properties of IBQT to applyLoD techniques to a PLI space. The root of the IBQTrepresents the first LoD. The PLI frequency is accu-mulated from the nested levels before it is projectedon the cylinder. The LoD level 1 helps the user obtainan overview of the PLI. The leaf nodes of level 6 rep-resent the sixth LoD. Each node is mapped to a tileon the cylinder. LoD 6 provides the user with the PLIat the highest resolution where each tile depicts thesmallest interaction area on the abstract surface. Theuser can investigate the PLI at different resolutions inbetween LoD 1 and LoD 6. The LoD is calculatedbased on the camera zoom level. The zoom intervalbetween levels is parametrized enabling the user tocontrol the switching time between levels. The useralso is provided with a manual LoD slider. The man-ual LoD slider helps the user to focus on the PLI atparticular LoD while zooming in and out or at a fixed

Figure 4: An overview of protein-lipid interaction. Thetop image shows the default representation of the lipidmolecules (no level of detail). The middle and bottom im-ages show the representation of the same lipid after enablingthe level of detail (level 4 and 1 respectively). Protein par-ticles are yellow, and lipid particles are green initially andturn red after an interaction. In the first image, more in-teraction details are occluded, due to overlapping particles.

camera position. Figure 5 illustrates six LoDs for asingle PLI.

4.5 Constructing the InteractiveIndex-Based Quad-Tree (IBQT)

Taking into account 256 simulated proteins, we main-tain a dynamic LoD interaction representation i.e eachinteraction position, time and frequency over 1981time-steps. In terms of storing and retrieving the in-

Figure 5: Six levels of detail to represent protein interac-tion. The color of each tile is mapped to the number ofinteractions with each tile’s extent. The interaction detail ismaintained by passing the number of particle interactionsdown to the next level. The LoD is dynamically updatedbased on the camera zoom value.

teraction data in a spatial data structure, there are avariety of solutions discussed by Samet (2006). How-ever, the key challenge here is posed by the dynamicsof the simulation. The interaction position of every in-dividual particle needs to be identified, translated, androtated, per time step with the given protein. Anotherchallenge is that the PLI occurs in a three-dimensionalspace represented by an abstract cylinder. A naive so-lution might require conversion between a cylindricalcoordinate system to a 3D Cartesian system. The con-version is necessary to map the PLI from/to the cylin-drical space to a 3D Cartesian space which can be rep-resented by a quad-tree. We address these challengesby proposing a fast quadtree-based mapping approachusing the given protein’s local coordinate space. Ourapproach eliminates the need for storing the global in-teraction position of each individual particle or updat-ing its translation or rotation. Also, it eliminates anyexplicit conversion between cylindrical and Cartesiancoordinate systems. See Section 4.6.

We utilize a custom index-based quad-tree (IBQT)to capture and store the protein-lipid interactions. TheIBQT is designed to accommodate a GPU-based pro-jection onto each protein’s local cylinder. Because thePLI is represented with an abstract cylindrical shape,the local polar system of each protein can be exploitedin the IBQT design. The IBQT is inspired by theSamet’s sector tree Samet (2006). Samet (2006) dis-cusses a sector tree structure that utilizes a polar co-ordinate system to maintain an object’s spatial datain two dimensions. In the sector tree, the angle ofthe intersection between the boundary of the two re-gions participates in its construction. The commonfacet between the sector tree and the IBQT is that inboth angles play a key role in defining a tree structure.Our IBQT differs from the sector tree in two aspects.

First, our structure is a point-based quad-tree struc-ture while the sector tree is region-based. Second, ourIBQT encodes a three-dimensional position to repre-sent a PLI in 3D space. Each IBQT node has a key in-dex (called a base index). The base index of a node isused to identify the node with respect to a given LoD.The node index consists of two components; the firstcomponent encodes the interaction position along thez axis while the second component encodes the angleof the interaction. Every interaction node stores theinteraction frequency, a list of particles involved inthe interaction, and the interaction time-step. Figure6 depicts our IBQT and illustrates the PLI encoding.The index components are derived from the interac-tion position by applying the following:

u1 =h

2LoD−1 (1)

Where h indicates the height of the cylinder used torepresent a protein’s interaction space.

u2 =2π

2LoD−1 (2)

With respect to a given LoD, Equation 1 calculatesthe size of a unit scale that span the z axis while 2calculates the size of unit scale spanning 2π.

iz = f loor(z

u1) (3)

Equation 3 calculates iz which represents the PLIalong the z axis with respect to a given LoD. The fol-lowing calculates the angular value ixy of the PLI withrespect to a given LoD:

ixy = f loor(DoublePI(arctangent(y,x))

u2) (4)

Figure 6: This image illustrates the computation of theIBQT node’s index. An IBQT node index is encoded onthe GPU by applying Equations 1, 2, 3, 4 to an interactionposition.

The function DoublePI() returns a positive radian ∈[0,2π], arctangent returns an angle confined to the in-terval [−π,π] and positive for y > 0. Equations 3 and4 encode the PLI position into an IBQT node index.The index consists of two components. The first andsecond components are represented by iz and ixy re-spectively. Finally, we construct the IBQT by utiliz-ing the derived node index instead of the global in-teraction coordinates. Figure 6 illustrates process ofencoding the PLI position into IBQT node index. Thefollowing equation is used to find the index of the par-ent node index (PNIndex) of any given node:

d f =2LoDmax−1

2LoD−1 (5)

LoDmax indicates the maximum level of detail. Thed f is used to calculate the parent node’s index basedon the first and second components of the given nodeindex. It ensures that the node index ∈ [0,31].

PNIndex = ( f loor(izd f

)×d f , f loor(ixy

d f)×d f ) (6)

For example, let us take a node n from level 6 and letus say its index is (17,23). We can compute the indexof the parent of node n at level 5 as follows:The node index at level 6 is given by iz =17 andixy =23. First, we compute d f =

25

24 = 2 via Equa-tion 5. Then Equation 6 can be used to compute theindex of the parent node:PNIndex= ( f loor( 17

2 )×2, f loor( 232 )×2) = (16,22)

4.6 Projecting the Interaction on to theLoD Protein Space

The interaction mapping process is performed on theGPU utilizing a geometry shader. The advantage ofthis approach is that it is no longer necessary to store,update, translate or rotate the interaction positions forevery time-step because they are based on the givenprotein’s local coordinate system. First we re-trieve the interaction data from the IBQT using threeparameters: the time step, the LoD and a vector of aTileData object. The time step and the LoD parame-ters are used to specify the IBQT query. The TileDatavector returns a list of TileData objects. Each Tile-Data contains an interaction node index, a moleculetype identifier and interaction frequency. Then, basedon the chosen level, every non-empty node is pro-jected and visualized by a tile on the surface of thecorresponding abstract protein space. The projectioninvolves three steps. The first step is to project the leftedge of the interaction node on the surface. The sec-ond step to identify the right edge of the interactionbefore finally forming a tile by constructing a curved,

Figure 7: This image illustrates our GPU-based LoD pro-jection. A protein interaction space and the index of a non-empty node are used to construct the associated tile on thesurface of the cylinder. The red and green segments rep-resent the left and right edges of the interaction node re-spectively. The blue dotted arrows represent two curves thatconnect the left and right edges to construct a tile.

triangular mesh between the two edges. To identifythe left edge, we derive two 3D points from the in-teraction node index. For a given LoD, we calculatethe zstart and the zend of the left edge of the interactionnode.

zstart = f loat(iz)×u1 (7)

zend =2Lodmax−1

2LoD ×u1 (8)

The interaction angle is computed and used to con-struct the interaction normal #»nnn i

iθ =ixy

2Lodmax−1×2π(9)

The interaction angle iθ of a node can be computedby utilizing the node index. For example, given thenode (17, 23). Its interaction angle can be computedas follows: iθ =

ixy2Lodmax−1×2π

= 2332×2π

= 0.11439 Rad.The #»nnn i components are computed as:

#»nnn i(x) = cos(iθ)× #»xxx x + sin(iθ)× #»yyy x (10)#»nnn i(y) = cos(iθ)× #»xxx y + sin(iθ)× #»yyy y (11)#»nnn i(z) = cos(iθ)× #»xxx z + sin(iθ)× #»yyy z (12)

Where #»xxx and #»yyy are the eigenvectors in the x-directionand y-direction of the protein interaction space re-spectively. The zstart , the zend and #»nnn i, then, can beused to find the left edge start and end points:

is = sCoM +(zmin× #»zzz )+(zstart × #»zzz )+ rrr× #»nnn i (13)

ie = sCoM +(zmin× #»zzz )+(zend× #»zzz )+ rrr× #»nnn i (14)

Where zmin is the min z value of the cylinder. Theterms sCoM and rrr are the center of mass and the radiusof the abstract protein space respectively and #»zzz is the

eigenvector in the z direction of the protein interactionspace.

Similarly, we can obtain the starting and endingpoints of right edge by adding the tile segment countto the second component and apply Equations 13 and14. See Figure 7.

5 EXPERIMENTAL RESULTSAND DOMAIN EXPERTFEEDBACK

The new visual design enables the user to investigatethe system and obtain insight into the PLI. See the ac-companying video for further visualization results at:https://youtu.be/VTh-IOk7hWoFigure 9 shows three different LoD representationsfor the PLI. The top image depicts lipid particles anda PLI space at high LoD (LoD 6). The visualization atthis resolution reveals more PLI detail. i.e., each tilerepresents the number of PLI that take place withinits extent. The middle image shows lipid particles andPLI at LoD 4. The PLI frequencies are spatially ag-gregated. The user can easily observe regions that re-ceive the highest number of interactions. The bottomimage shows lipid particle and PLI space at low LoD.This visualization is useful for an overview. It canguide users to identify proteins that receive the high-est frequency of interaction for further investigation.Color Map Schemes and Adjusting the Color MapLegend: We provide the user with two-color maps.A continuous color map based on Telea (2014) and acategorised color map using Color Brewer Harrowerand Brewer (2003). The PLI frequency is mappedto the selected color schema. However, the PLIhistogram shows an uneven distribution which leadssome colors to dominate. A naive approach to addressthis challenge is to clamp and rearrange the underly-ing data to obtain a better color distribution. However,

Figure 8: PLI filtering and color map steering. The left im-age shows no filtering and no modification to the color mapalgorithm. The middle image shows highest frequency PLIusing the filtering slider. The right image shows the effect ofsteering the underlying map to enhance color distribution.

Figure 9: Three LoD PLI representations. PLI frequency ismapped to color. From top to bottom, PLI at high resolu-tion, medium resolution, and low resolution. Lipid particlesare green and brown. Blue spheres indicate lipid interactionparticles.

this method might result in a mapping error for datathat lay outside the lower and upper boundaries. Weaddress this challenge by enabling the user to adjustthe color map’s underlying look-up table. The usercan control the color map’s look-up table through arange slider to obtain more color distribution. Theright image in Figure 8 shows an example of usingthe color map slider.PLI Frequency to Tile Height: A three-dimension

histogram can enhance the visualization. The heightof the histogram encodes a property to emphasize it.We enable the user to map the PLI frequency to thetile height. Figure 10 depicts the PLI by a simple his-togram by mapping the PLI frequency to tile height.PLI Space Cluttering Reduction: When two ormore protein spaces intersect each other, they causevisual cluttering. The user may reduce cluttering byeither omitting the back face of a protein cylinder orrendering the cylinder lids.Lipid Type and Protein Selection and Filtering:Three types of molecules are involved in the PLI. ThePLI molecule filter enables the user to focus on oneor more molecule types. Applying the PLI moleculefilter on one or more molecule types showing only thePLI of the selected types. The user also can filter thePLI based on the PLI frequency. The PLI frequencyfilter accepts a range of values between the PLI minand max of the current histogram data.Focus-and-Context: We apply the focus-and-contexttechnique to reduce visual complexity. It can re-sult in more detailed visualization, especially for anoverview. See the accompanying video for a demon-stration.

Domain Expert Feedback The following is feed-back from a domain expert in computational biologywith whom we have collaborated since 2014. “Thisnew representation is particularly useful to better un-derstand the fine interactions in between lipids andmembrane proteins in very large membrane models.These models are constituted by millions of particlescomposing thousands of lipids and hundreds of pro-teins. These systems are very complex to understandespecially if we only visualize them without filtering.Even with some filters (removing some molecules,changing the representation of the proteins), it is stillalmost impossible for a user to interactively under-stand how lipids may transiently interact with pro-teins. Thanks to the new visualization, the user canzoom on a protein and easily understand how (andwhich) lipids can create contact with this protein.This is possible thanks to the combination of LoD andthe new PLI visualization. Mapping the interactionsonto a cylinder also helps the user to identify areaswhere the lipid may preferentially interact with theprotein just by visualizing the trajectory. Without thisvisualization, lipid-protein interaction analysis neces-sitates long post-processing treatments which give,in general, only a final averaged view. The filter-ing based on the number of interactions is helpingthe user to focus on the important proteins. To thisexpert’s knowledge, this feature is unique and hasnever been available in any other molecular viewer

Figure 10: (Left) the number of protein-lipid interactions ismapped to color. (Right) the same data map to the height ofthe tiled interaction cylinder.

program. Thus, this new depiction helps considerablythe users to understand their models and gives newclues to better analyze them. This new representationis also clear enough to be used directly as a figure forpublications in a scientific article.”

6 CONCLUSIONS AND FUTUREWORK

We describe an abstract protein space in the contextof membrane protein-lipid interaction and we proposesix levels of detail for both lipid types and the PLI ab-stract space. The visual design of the abstract spacesimplifies the PLI challenge and helps users obtain in-sight into the PLI. The LoD lipid representations re-duce clutter caused by lipid particles. The LoD PLIspace representations enable users to investigate thePLI space at the desired LoD. We also introduce anumber of useful user options to aid the PLI visual-ization.

In future work, we aim to focus more on analysis.Discrete abstract rings can be employed to visualizeprotein deformation. Properties of cylinder shape canbe exploited to map the PLI from a cylinder onto a2D plane. Visual analytic techniques can be appliedto 2D PLI results to understand the relation betweenresidues and particles involved in the interaction.

ACKNOWLEDGEMENTS

This work was partially funded by the Ministry of Ed-ucation of Saudi Arabia, the Saudi Cultural Bureauin London, the Department of Computer Science atSwansea University, and the DFG as part of projectPROLINT. Finally, we would like to thank D. Reesand L. McNabb for proof-reading the paper.

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