6938 | Soft Matter, 2017, 13, 6938--6946 This journal is©The Royal Society of Chemistry 2017

Cite this: SoftMatter, 2017,

13, 6938

Interplay between membrane elasticity and activecytoskeleton forces regulates the aggregationdynamics of the immunological synapse†

Nadiv Dharana and Oded Farago *ab

Adhesion between a T cell and an antigen presenting cell is achieved by TCR–pMHC and LFA1–ICAM1

protein complexes. These segregate to form a special pattern, known as the immunological synapse (IS),

consisting of a central quasi-circular domain of TCR–pMHC bonds surrounded by a peripheral domain

of LFA1–ICAM1 complexes. Insights gained from imaging studies had led to the conclusion that the

formation of the central adhesion domain in the IS is driven by active (ATP-driven) mechanisms. Recent

studies, however, suggested that passive (thermodynamic) mechanisms may also play an important role

in this process. Here, we present a simple physical model, taking into account the membrane-mediated

thermodynamic attraction between the TCR–pMHC bonds and the effective forces that they experience

due to ATP-driven actin retrograde flow and transport by dynein motor proteins. Monte Carlo

simulations of the model exhibit a good spatio-temporal agreement with the experimentally observed

pattern evolution of the TCR–pMHC microclusters. The agreement is lost when one of the aggregation

mechanisms is ‘‘muted’’, which helps to identify their respective roles in the process. We conclude that

actin retrograde flow drives the centripetal motion of TCR–pMHC bonds, while the membrane-

mediated interactions facilitate microcluster formation and growth. In the absence of dynein motors, the

system evolves into a ring-shaped pattern, which highlights the role of dynein motors in the formation of

the final concentric pattern. The interplay between the passive and active mechanisms regulates the rate

of the accumulation process, which in the absence of one them proceeds either too quickly or slowly.

I. Introduction

The adaptive immune system heavily relies upon the ability ofT cells to properly interact with antigen presenting cells (APCs).The contact area between the two cells is established by specificreceptor–ligand bonds that crosslink the plasma membranes ofthe T cell and the APC. The key players in this cellular recognitionprocess are T cell receptor (TCR) and lymphocyte function-associated antigen 1 (LFA1) that respectively bind to peptidedisplaying major histocompatibility complex (pMHC) and inter-cellular adhesion molecule 1 (ICAM1) embedded in the APC’splasma membrane.1,2 During T cell activation, these two typesof bonds are redistributed and form a unique geometric patternof concentric supra-molecular activation centers (SMACs) withinapproximately 15–30 minutes of the initial contact.3,4 In thisspecial arrangement, which is commonly referred to as the

immunological synapse (IS), TCR–pMHC bonds are concentratedinto a central SMAC (cSMAC), while the LFA1–ICAM1 adhesionbonds form a surrounding ring termed the peripheral SMAC(pSMAC).5,6 This molecular redistribution is thought to play animportant role in signal regulation,7 T cell proliferation,8 andfocalized secretion of lytic granules and cytokines.9

Extensive research effort has been devoted to understandingthe mechanisms governing the formation of the special architectureof the IS. Mounting evidence from experimental studies point to theactin cytoskeleton as a vital element in controlling the centripetalmotion of TCR–pMHC and LFA1–ICAM1 bonds towards their finallocations.10 In the early stages of IS formation, the T cell’s actinmeshwork reorganizes such that actin-free and actin-rich zoneemerge that, later on, constitute the locations of the cSMAC andpSMAC of the IS, respectively.11 Moreover, actin polymerizationoccurring at the periphery of the contact area results in centripetalactin retrograde flow that is crucial for protein translocation.12,13 Ithas been hypothesized that actin retrograde flow produces viscousforces on the intracellular part of TCRs, which lead to theircentripetal motion.14–17 Furthermore, directed transport by dyneinmotor proteins along the cytoskeleton microtubules has beenidentified as another ATP-driven process contributing to protein

a Department of Biomedical Engineering, Ben Gurion University of the Negev,

Be’er Sheva 84105, Israel. E-mail: ofarago@bgu.ac.ilb Ilse Katz Institute for Nanoscale Science and Technology,

Ben Gurion University of the Negev, Be’er Sheva 84105, Israel

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7sm01064h

Received 29th May 2017,Accepted 14th August 2017

DOI: 10.1039/c7sm01064h

rsc.li/soft-matter-journal

Soft Matter

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localization in the IS.18,19 These experimental evidences have led tothe notion that IS formation is governed by active cellular processesrelated to the cytoskeleton activity.

Interestingly, several theoretical studies have suggested thatpassive (non-active) mechanisms may also be involved in theformation process of the IS.20–22 These include (i) receptor–ligandcooperative binding kinetics, and (ii) membrane-mediated attraction.The former is linked to the fact that receptor–ligand binding canonly occur when the inter-membrane separation matches the bondlength and, thus, new bonds are more likely to form in regions thatare already populated by other bonds.23 The latter is a mechanism ofattraction between distant bonds. It is linked to the reduction influctuation entropy and increase in curvature elasticity that themembranes experience due to their attachment by the adhesionbonds.24 The free energy cost is minimized when the adhesionbonds are localized in a single domain which is, therefore, thermo-dynamically favorable. Specifically to the IS, TCR–pMHC andLFA1–ICAM1 bonds are expected to segregate into two distinctdomains due to the marked difference in bond length betweenthem (C15 nm and C42 nm, respectively25), which causesstrong membrane deformation. The interplay between both ofthese passive mechanisms may result in patterns that are notonly extremely similar to those observed experimentally, butalso form on biologically relevant timescales.20–22

From a physical perspective, domain formation induced bymembrane-mediated attraction can be viewed as a demixing phasetransition.26–28 In a previous study, we analyzed the membrane-mediated interactions between adhesion bonds and demonstratedthat TCR–pMHC can phase separate from LFA1–ICAM1 and formdomains with similar densities to those in the IS.29 However,conventional phase separation theories are insufficient to explainthe bullseye pattern of the IS, i.e., the aggregation of TCR–pMHCbonds at the central contact area and the accumulation ofLFA1–ICAM1 bonds at the periphery. This very particular structureseems to be directly linked to the activity of the actin cytoskeleton,especially to directed transport of TCR–pMHC by dynein motorsalong microtubules, and the actin retrograde flow which induces acentripetal force on the TCR–pMHC bonds.30,31 It may also berelated to the depletion of actin from the center of the contact area,which occurs at the very beginning of the IS formation process.The cytoskeleton is also expected to have a direct influence on themembrane-mediated interactions between the TCR–pMHC bonds.This follows from the attachment of the T cell’s membrane to theactin cytoskeleton by various molecules, such as proteins from theezrin–mesoin–radixin (ERM) family,32 phosphatidylinositol 4,5-bisphosphate (PIP2)33,34 and coronin 1.35 This coupling betweenthe membrane and the cytoskeleton may modify the shape of themembrane. Here, we extend our previous analysis of the role playedby membrane-mediated interactions in formation of TCR–pMHCdomains, by including the aforementioned cytoskeleton-relatedeffects, and studying the interplay between the passive and activemechanisms.

A schematic picture of the contact area between the APC andthe T cell is depicted in Fig. 1a, showing the two types ofadhesion bonds that connect them (the longer LFA1–ICAM1and shorter TCR–pMHC bonds), the actin cytoskeleton of the T

cell including the actin-depleted circular area of radius B2 mm,and the proteins that connect the actin cytoskeleton to theT cell membrane. In order to follow aggregation of the TCR–pMHC central domain, we develop a simple lattice model thatconstitutes a discrete representation of the system. The latticemodel is shown schematically in Fig. 1b. It includes three typesof sites: (i) empty (represented by � in Fig. 1b), or singly occupiedby either (ii) a mobile point representing a TCR–pMHC bond(black circles in Fig. 1b), or by (iii) an immobile point representingan attachment protein between the membrane and the cytoskeleton(red circles in Fig. 1b). The latter are absent from the actin-depletedcentral region of the contact area (marked by the dashed circle inFig. 1b). The membrane-mediated potential of mean force(PMF) between the TCR–pMHC bonds is accounted for via anearest-neighbor attraction between the mobile points. The cellcytoskeleton is not modeled explicitly in our coarse-grainedsimulations, but is implicitly introduced via an effective potential

Fig. 1 (a) Schematic of the contact area between the membranes of the Tcell and the APC. The two membranes are connected by two types ofadhesion proteins: LFA1–ICAM1 and TCR–pMHC with bond lengths of41 nm and 14 nm, respectively. The T cell’s membrane is attached to thecytoskeleton by a set of actin pinning proteins. A central region in thecontact area of radius B2 mm is devoid of actin. (b) The lattice model of thecontact area depicted in (a). The lattice sites are either empty (in whichcase they are marked by the� symbols), or occupied by a single TCR–pMHCbond (black circles) or by a single actin pinning point (red circles). The latterare immobile and are excluded from the actin-depleted central region of thesystem. The inner dashed circle marks the edge of the central actin-depletedregion with radius RC = 2 mm, while the outer dotted circle marks the edge ofthe pSMAC, and has a radius RP = 4 mm. The black and blue arrows representeffective centripetal forces arising from the actin retrograde flow anddirected transport by dynein motors, respectively. For r o RP, the magnitudeof the active centripetal force is set to f0 = 0.1 pN (small arrows), while forr 4 RP the force is set to a twice larger value of 2f0 = 0.2 pN, and isindicated by large arrows.

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that generates the active cytoskeleton forces. These centripetalforces are represented in Fig. 1b by arrows, and their magnitudesare evaluated in Section II C. Since we focus on the aggregationdynamics of TCR–pMHC bonds, we do not study the very rapidremodeling process of the actin cytoskeleton (which is completedwithin less than a minute from the initial contact between theT cell and the APC11), but consider a system where a central actin-depleted region has already been formed.

From the simulation results we conclude that the combinationof membrane-mediated attraction, actin retrograde flow, andtransport by dynein motors is essential for proper spatio-temporal evolution of the TCR–pMHC bonds. We arrive at thisconclusion by performing simulations of systems subjected toonly one or two of these driving forces. When only the activecytoskeleton forces are present, the TCR–pMHC bonds individuallynavigate their way through the immobile pinning points towardsthe central actin-depleted area. The accumulation process,however, is completed within an extremely short time of severalseconds, and does not exhibit formation of peripheral TCRmicroclusters at early stage. TCR microclusters play a vital rolein the T cell response prior to the formation of the cSMAC thattriggers TCR down-regulation and signal termination.36–38 TCRmicroclusters are observed in simulations taking into accountthe membrane-induced attraction but neglecting the actinretrograde flow and dynein activity; however, in this case, theaggregation process becomes very slow and proceeds over manyhours. In simulations including the membrane-mediated effectand actin retrograde flow but missing the dynein motors,the system evolves into a ring-shaped pattern at the edge ofthe actin-depleted area. Similar patterns have indeed beenobserved in a recent experimental study where dynein activitywas impaired.19 Thus, our results corroborate the conclusionthat actin retrograde flow drives the centripetal motion of TCRmicroclusters from the periphery to the center, while dyneinmotor proteins govern their translocation at the actin-depletedcentral zone and, therefore, play an essential role in theformation of the final circular bullseye pattern of the IS. Whenall three mechanisms are present, the central accumulation ofthe TCR–pMHC bonds occurs within about half an hour, whichis indeed the correct biological timescale. The simulations donot only reproduce the experimentally observed values for thetimescale of IS formation, but are also able to capture twocritical features of this process, namely, (i) the peripheralcoarsening of TCR–pMHC into microclusters, and (ii) theirsubsequent transport towards the center of the contact region.From the simulations we conclude that membrane elasticityand active cytoskeleton forces act as complementary mechanismsthat balance each other in a manner that assures an adequateT cell response.

II. Model and simulationsA. Lattice-gas model

The accumulation of TCR–MHC bonds at the center of thecontact area between a T cell and an APC is studied using alattice-gas model. In this coarse-grained physical framework,

the cell membranes are implicitly accounted for by nearestneighbor interactions that represent the PMF originating fromthe membrane deformation energy. We consider a triangularlattice with lattice spacing x = 100 nm, which is the range of themembrane-mediated interactions in the system under considerationhere (see ESI†). This sets the spatial resolution of out model,and allows us to ignore direct (e.g., van der Waals and dipolar39)and lipid-mediated40 interactions between the various proteinsin the system since, typically, the range of these interactionsdoes not extend beyond t10 nm. The linear size of the systemis roughly L = 10 mm (we simulate a lattice of 99 � 114 sites withan aspect ratio close to unity), which is representative of thedimensions of the contact area. The model includes two types oflattice points representing the TCR–pMHC bonds (type A) andthe membrane–cytoskeleton pinning proteins (type B). Theformer are mobile, while the latter are located at fixed latticesites. Both A–A and A–B interactions are purely repulsive atshort separations (see ESI†), and this feature is accounted for byprohibiting multiple occupancy of a lattice site. At a distance x,the A–A interactions are attractive (ESI†), and this is representedin the model via a nearest neighbor interaction energy ofstrength e = �4.5 kBT. The value of e is derived from astatistical-mechanical calculation for the membrane-mediatedPMF between two TCR–pMHC bonds (ESI†). The model doesnot include explicit representation of the LFA1–ICAM1 bonds.The effect of these bonds is incorporated in the statistical-mechanical calculations of the PMFs through the parameterh0 = 27 nm (ESI†), which is the bond length mismatch betweenLFA1–ICAM1 and TCR–pMHC bonds.41

The densities of the TCR–pMHC bonds (type A lattice points)and the membrane–cytoskeleton pinning proteins (type B)greatly vary between different experimental works (if reportedat all). We therefore set their values in the simulations based onthe following considerations: type A points aggregate to formthe cSMAC, which is a circular domain of radius B2 mm thatalmost fills (at the end of the process) the actin-depleted centralregion. The latter includes about 1200 lattice sites, and thenumber of type A points is set to a slightly smaller valueNA = 1000. We note that since the lattice spacing x = 100 nm,the density of the TCR–pMHC bonds in a cluster is C80 bondsper mm2, which is indeed above the threshold density requiredfor full T cell activation.3,6 A reasonable estimate to the spacing, l,between membrane–cytoskeleton pinning proteins is a distance ofa few hundred nm.42 In what follows, we show results for systemswhere the average spacing between type B points is set tol = 300 nm. To avoid further complication of our model, weneglect the binding/unbinding kinetics of the membrane–cytoskeleton linkers and assume that the number of type Bpoints is fixed. Nevertheless, we note here that results ofsimulations with l = 500 nm (i.e., with fewer type B points)exhibit negligible differences. The type B points can be foundeverywhere on the lattice, except for the central actin-depletedregion. They are randomly distributed to account for localvariations in l, but we do not allow two type B points to occupynearest-neighbor lattice sites in order to ensure a fairly uniformdistribution and avoid type B clusters.

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B. Monte Carlo simulations

We perform Monte Carlo (MC) simulations to study the evolutionof the lattice model. While MC simulations are designed forstatistical ensemble sampling at equilibrium, they can be alsoused to effectively generate Brownian dynamics in lattice models.The simulations consist of move attempts of a randomly chosentype A point to a nearest lattice site, which is accepted accordingto the standard Metropolis criterion.43 During a single MC timeunit, tMC, each type A point experiences (on average) one moveattempt. Mapping the MC time unit to real time, t, can beachieved by considering the two-dimensional diffusion relationhr2i = 4Dt, where hr2i denotes the mean square displacement andD is the diffusion coefficient. For the MC simulations, each pointmoves a distances of the lattice spacing x = 100 nm and, there-fore, tMC = x2/4D. This can be compared to typical values for thediffusion coefficient of T cell membrane proteins D C 0.1 mm2 s�1,44

which yields tMC C 25 ms.

C. Active cytoskeleton forces

Similarly to the approach taken in ref. 31, active cytoskeletonprocesses are not modeled explicitly in our simulations but areinstead represented by the effective forces that they induce onthe TCR–pMHC bonds. Two active processes are considered,namely (i) actin retrograde flow, and (ii) dynein minus-enddirected transport toward the microtubule organizing center(MTOC). These may be viewed as complementary mechanismssince they produce the same net effect of transport toward thecenter, while operating at different regions of the system.Explicitly, dynein-driven transport governs the dynamics atthe central actin-depleted area, while actin-retrograde flow isbelieved to predominate at the periphery of the system.

Experimental studies reveal that the velocity of the actinretrograde flow towards the center of the contact area achievesa maximal value vmax C 0.1 mm s�1 at the periphery of thecontact area. As the flow proceeds toward the center of thecontact area, it decreases to approximately 0.5vmax, and finallyvanishes at the edge of the central actin-depleted region.12,45

The flow generates a centripetal force on the TCR–pMHC bondswith magnitude proportional to the flow velocity. Inside theactin-depleted region, the centripetal motion of the TCR–pMHCbonds continues, but is now driven by the activity of dyneinmotors. This has been concluded by experiments showing thatin the absence of dynein motor activity, the TCR–pMHC bondsdo not penetrate into the actin-depleted region, but insteadaccumulate around it. Modeling the dynein-induced forces is ahighly challenging task since the motor activity depends onmany factors, including the concentration of available ATP, thedensity of dynein motors, and the load opposing the motorswhich may depend on the size of the transported microcluster.To bypass this issue, we clump all of these factors togetherinto an effective dynein-driven force that acts on individualTCR–pMHC bonds inside the actin-depleted zone, and pullsthem towards the center of the system (where the MTOC islocated). Experiments suggest that the centripetal velocity ofTCR–pMHC bonds transported by both actin retrograde flow

and dynein motors is roughly twice larger than the velocity inthe absence of motor activity, which suggests that the effectivecentripetal force induced by both mechanisms is of the sameorder of magnitude.19 Taking these various considerations intoaccount, the combined active cytoskeleton forces are introducedto the model via the following effective potential that dependson the distance r from the center of the system

FactiveðrÞ ¼f0r r � RP

2f0 r� RPð Þ þ f0RP r4RP

;

((1)

where RP is the outer radius of the pSMAC, which is the regionwhere the flow of actin becomes weaker.45 This potentialgenerates a centripetal force of magnitude f0 for r r RP and2f0 for r 4 RP. The former region includes the actin-depletedregion (0 o r o RC) and the pSMAC (RC o r o RP), where a forceof magnitude f0 is induced by dynein motor activity and actinretrograde flow, respectively. The latter region corresponds tothe periphery of the cell, where actin retrograde flow is strongerand produces an effective force of magnitude 2f0. A schematicdepicting the forces associated with the potential Factive atdifferent regions of the contact area is shown in Fig. 1b. Basedon confocal images, we set RC = 2 mm and RP = 4 mm.14 In orderto determine the value of f0, we use the observation that theactin retrograde flow causes a small peripheral microcluster(a few hundred nanometers in size) to move toward the cell’scenter at a velocity of vc C 20 nm s�1.46 We, thus, performedshort MC simulations for a single microcluster composed of10 TCR–pMHC bonds, which is located at the outer region of thesystem. We measured the velocity of the centripetal movementof the microcluster as a function of f0, and found that it attainsthe value of vc for f0 = 0.1 pN. Comparable forces have beenmeasured in experiments of optically trapped microbeadscoupled to actin retrograde flow of similar velocity.47

III. Results

The spatio-temporal evolution of the system has been analyzedfrom 10 independent MC runs starting with different randomdistribution of both type A and B points. Typical snapshotsfrom different stages of the process are shown in Fig. 2, withthe type A and B points presented by black and red dots,respectively. At t = 0, the type A points are randomly distributedoutside of the inner actin-depleted regime (Fig. 2a). Within lessthan one minute, the type A points coalesce and form smallperipheral microclusters consisting of t20 points (Fig. 2b),which begin to move centripetally. Several type A points havealready reached the center system at this stage. The peripheralmicroclusters are believed to play a vital role in initiating andsustaining TCR signaling.36,48 As time proceeds, the clustersfurther coarsen, which decreases their mobility and slows downtheir centripetal motion (Fig. 2c–e). The increase in the size ofthe clusters also causes them to be more affected by thepresence of the type B points which act as repelling obstacles.This further restrains the centripetal movement of the micro-clusters, which have to ‘‘navigate’’ their way through the

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‘‘curvature corrals’’ that the type B points form. We also observein Fig. 2c–e the gradual increase in the size of the central domain,which is the destination where the microclusters accumulate. After45 minutes (Fig. 2f), almost all type A points reside in the centraldomain. The dynamics of the MC simulations, as depicted inFig. 2a–f, closely resembles epifluorescence and total internal reflec-tion fluorescence (TIRF) microscopy images of the IS formationprocess. Specifically, the microscopy images show the generation ofsimilar microclusters, their drift to the center of the contact area,and their accumulation at the center of the contact area.17,49 Thesimulations exhibit a very good agreement with the experimentalobservations not only with regard to spatial evolution of the system,but also with respect to the time scales of the different stages of theprocess. Fig. 2g depicts the percentage of type A points located in thecentral domain at the actin-depleted area. About 90% of thelattice points have been accumulated at the center after roughly40 minutes, which agrees very well with the times reported inthe literature for cSMAC formation.

Fig. 2h–j show snapshots from simulations in which dyneinactivity is turned off. This is done by modifying the effectivepotential (1) such that Factive(r o RC) = f0RC = constant, andthus, the associated force vanishes at the actin-depleted areawhere the dynein motors operate. For this model system, weobserve formation of peripheral microclusters that move cen-tripetally, but do not enter the actin-depleted area. Instead offorming a central quasi-circular domain, the type A points nowaccumulate in a ring-shaped domain at the edge of the actin-depleted region. Interestingly, very similar ring-like structureshave been observed in experiments where dynein activity wasinhibited by dynein heavy chain ablation.19 From the agreementwith the experimental results we conclude that cSMAC formationrequires that centripetal forces act on the TCR–pMHC bonds inthe actin-depleted area, and that the origin of these forces is theaction of the dynein motors.

The results displayed in Fig. 2 appears to be in agreementwith the widely-held view that the active cytoskeleton forces dueto actin retrograde flow and the dynein motors determine thefinal destination of the TCR–pMHC bonds, which is the centerof the cell when dynein activity is enabled and the inner edge ofthe actin-rich zone when it is disabled. The results also demon-strate that while a central domain located inside the actin-depletedarea constitutes the equilibrium state of the system from a purethermodynamic perspective, membrane-mediated interactions donot contribute significantly to the centripetal accumulation of theTCR microclusters over the biologically relevant time scales. This isdemonstrated in Fig. 3a–d showing snapshots from simulationswhere Factive is completely turned off, leaving the system to evolveonly under the influence of the passive membrane-mediatedinteractions. Neither centripetal motion nor central accumulationof TCR–pMHC bonds are observed in this set of simulations.However, the data seems to indicate that the membrane-mediatedinteractions play an important role in facilitating the formationand coarsening of peripheral TCR microclusters, which areknown to be essential for adequate T-cell immune response.The importance of the passive interactions in inducing theformation of the TCR microclusters is illustrated in Fig. 4,showing snapshots from yet another set of simulations. Here,the nearest-neighbor membrane-mediated attraction betweenthe type A points is muted by setting e = 0, while the effectivecentripetal potential Factive (1) is retained. The simulationsreveal that, in this case, the type A points do not form micro-clusters but instead move individually and quickly accumulateat the center of the system. Since the mobility of a single point ishigher than that of a cluster, it is expected that the aggregationprocess is completed in a shorter time than required in thepresence of membrane-mediated attractions. Our computationalresults show that, indeed, 100% of the points arrive at the centralarea in less than 6 seconds (see Fig. 4g). We note here that therate of the accumulation process depicted in Fig. 4 may beexaggerated, since it implies that individual (non-clustered)TCR–pMHC move centrally at a velocity which is about 5 timeslarger than the velocity of the actin retrograde flow. This proble-matic dynamic feature is an artifact of the lattice MC dynamicsthat we employ. Since the focus of interest is the evolution of the

Fig. 2 Simulation snapshots depicting the aggregation process of theTCR–pMHC bonds (type A, black dots) at different times: (a) the randominitial distribution, (b–d) early stage formation, coarsening, and centripetaldrift of microclusters, and (e and f) late stage accumulation of microclustersand cSMAC formation. The red dots represent the cytoskeleton pinningproteins (type B). (g) The percentage of type A bonds located at the centralactin-depleted area as a function of time. (h–j) The evolution of the system inthe absence of dynein forces at the center.

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system over durations of minutes and hours, the actin retrogradeflow force has been calibrated to produce correctly the centripetalvelocity of small clusters on these temporal scales – see detaileddiscussion in Section II C. The consequence of this choice is that

the velocity of the individual TCR–pMHC bonds turns out to betoo high. A reasonable estimation for the centripetal velocity ofindividual bonds at the periphery of the system is 20 o v o100 nm s�1, i.e., higher than the velocity of a single smallmicrocluster but lower than the actin retrograde flow velocity.The accumulation time of bonds moving at such speeds is0.5–2 minutes, which is still more than an order of magnitudesmaller than the IS formation time. Comparing the results of Fig. 4from simulations that miss the membrane-mediated attraction withFig. 2 highlights two important aspects of membrane elasticity:First, it facilitates early microcluster formation that play a vital rolein T cell activation. Second, they lead to coarsening dynamics thatresult in a decrease in the mobility of the clusters and, thereby,regulates the duration of the aggregation process.

IV. Discussion and summary

The formation of the immunological synapse (IS) is a complexbiological process involving multiple molecular components,including several adhesion proteins, motor proteins, the actincytoskeleton, and the membranes of both the T cell and theantigen presenting cell. Adhesion between the two cell membranesis established by two types of receptor–ligand bonds, namely,TCR–pMHC and LFA1–ICAM1. At the onset of the process, theT cell’s cytoskeleton remodels and an actin-depleted region isformed at the center of the contact area between the cells. Withinseveral tens of minutes, the adhesion bonds segregate such thatthe TCR–pMHC bonds aggregate into a quasi-circular domainlocated at the actin-depleted region. The macroscopic timeevolution of such a complex system can be only addressedthrough coarse-grained models employing simplified molecularrepresentation and focusing on the most dominant biophysicalmechanisms. Here, we present a minimal computational latticemodel aiming to study the dynamics of the TCR–pMHC bonds(represented as lattice points). The model takes into accountseveral forces that emerge in the literature as key factors inTCR–pMHC localization. One is a passive thermodynamic forceassociated with the membrane curvature energy, which inducesattraction between the TCR–pMHC bonds, and provides repulsionbetween the TCR–pMHC bonds and the proteins connecting theactin cytoskeleton to the membrane. The others are centripetalforces exerted on the TCR–pMHC bonds due to the actinretrograde flow and directed transport by dynein motors alongmicrotubules. These are active (non-equilibrium) forces becausethe processes that they originate from are driven by consumptionof ATP chemical energy.

Our coarse-grained model and MC simulations producecorrect evolution dynamics of the IS formation process at theexperimentally observed time scales. They thus provide a clearand intuitive picture for the roles played by the main drivingforces, and into the intricate interplay between them. Membrane-mediated attraction facilitates the formation of TCR–pMHCmicroclusters. These microclusters, which initiate biological cuesnecessary for T cell activation, are rapidly formed and continueto grow by coarsening dynamics over a period of approximately

Fig. 3 Simulation snapshots depicting the aggregation process in theabsence of active cytoskeleton forces. The type A points form micro-clusters that, on time scales of hours, barely grow and do not exhibit a drifttoward the central area. Color coding as in Fig. 2.

Fig. 4 (a–f) Simulation snapshots depicting the aggregation process inthe absence of membrane-mediated attraction. The type A points do notform microclusters, and accumulate at the central area within a fewseconds. Color coding as in Fig. 2. (g) The percentage of type A bondslocated at the central actin-depleted area as a function of time.

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10 minutes. The TCR–pMHC microclusters are corralled by themembrane–cytoskeleton binding proteins of the T cell, withwhich they have repulsive membrane-mediated interactions. Asthe microclusters grow in size, the corralling effect becomes moresignificant and their diffusivity decreases. This inhibits theiraccumulation in a central quasi-circular domain, despite the factthat this configuration represents the equilibrium state of thesystem. What speeds up the dynamics of the microclusters anddirects their movement toward the center of the contact area is acentripetal active force induced by actin retrograde flow at theperiphery of the synapse. This observation corroborates thelargely consensual view about the importance of actin remodelingand retrograde flow for the centripetal translocation of TCR–pMHC bonds at the IS. It is, however, important to emphasizethat in simulations without membrane-mediated attraction, acentral domain forms very rapidly without exhibiting intermediatemicroclusters. This observation highlights the, rather overlooked,important role played by the membrane-mediated interactionsin regulating the rate of the IS formation process. This novelconclusion drawn from our model and simulations has notbeen addressed experimentally thus far. A possible setup bywhich it can be tested is a model system consisting of all themolecular ingredients of the system, except for the LFA1–ICAM1bonds. This would shut down the membrane-mediated inter-actions whose origin is the mismatch in bond length betweenthe TCR–pMHC and the LFA1–ICAM1 bonds.

At the central actin-depleted region, a centripetal force (ofmagnitude similar to the actin retrograde flow induced force) iseffectively generated by dynein motors that walk toward theminus-end of the microtubules. An interesting observation isthe formation of a ring-shaped domain at the edge of the actin-depleted region in simulations where this force is turned off.This result is in line with a recent study, in which similarstructures were observed when dynein activity was geneticallyimpaired, but actin retrograde flow was maintained. Theinability of the system to produce a central circular domainin the absence of dynein activity highlights the role played bythe motors at the final stage of the process, where they enablethe TCR microclusters to enter the actin-depleted region.Furthermore, the agreement between our simulation resultsand the experimental data supports the notion presented hereof considering two different concentric regions for the activeforces, namely a central area dominated by the dynein motors,and a more distant one where the actin retrograde flow is theorigin of the centripetal movement of the microclusters.

To conclude, we explored the role played by passive andactive forces in the process of IS, and demonstrated how theinterplay between them regulates the spatio-temporal patternformation. Only in simulations where all the driving forceswere present, the signature features of the IS formation processwere observed. These include microclusters formation andcoarsening dynamics, their transport to the central actin-depletedarea, and their aggregation into a single quasi-circular domain(the cSMAC). Moreover, the simulated system evolves at theexperimentally observed rates: Microclusters are formed withinroughly a minute from the beginning of the process, and the

final bullseye structure is formed within 15–30 minutes. Ourresults point to an interesting role of membrane elasticity inregulating the IS formation process in a manner that providesT cells with an appropriate time window to allow biologicalsignaling via the peripheral TCR microclusters, which is vital fora proper immune response.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Israel Science Foundation (ISF)through grant 1087/13.

References

1 B. Alberts, A. Jhonson, J. Lewis, M. Raff, K. Roberts andP. Walker, Molecular Biology of the Cell, Garland, New York,4th edn, 2002.

2 J. B. Huppa and M. M. Davis, T-cell-antigen recognition andthe immunological synapse, Nat. Rev. Immunol., 2003, 3(12),973–983.

3 A. Grakoui, et al., The immunological synapse: a molecularmachine controlling T cell activation, Science, 1999, 285(5425),221–227.

4 K. G. Johnson, S. K. Bromley, M. L. Dustin and M. L. Thomas,A supramolecular basis for CD45 tyrosine phosphatase regula-tion in sustained T cell activation, Proc. Natl. Acad. Sci. U. S. A.,2000, 97(18), 10138–10143.

5 C. R. F. Monks, B. A. Freiberg, H. Kupfer, N. Sciaky andA. Kupfer, Three-dimensional segregation of supramolecu-lar activation clusters in T cells, Nature, 1998, 395(6697),82–86.

6 S. K. Bromley, et al., The immunological synapse, Annu. Rev.Immunol., 2001, 19(1), 375–396.

7 K. D. Mossman, G. Campi, J. T. Groves and M. L. Dustin, AlteredTCR signaling from geometrically repatterned immunologicalsynapses, Science, 2005, 310(5751), 1191–1193.

8 J. Storim, E. B. Brocker and P. Friedl, A dynamic immunologicalsynapse mediates homeostatic TCR-dependent and -independentsignaling, Eur. J. Immunol., 2010, 40(10), 2741–2750.

9 G. M. Griffiths, A. Tsun and J. C. Stinchcombe, The immuno-logical synapse: a focal point for endocytosis and exocytosis,J. Cell Biol., 2010, 189(3), 399–406.

10 M. L. Dustin and J. A. Cooper, The immunological synapseand the actin cytoskeleton: molecular hardware for T cellsignaling, Nat. Immunol., 2000, 1(1), 23–29.

11 A. T. Ritter, et al., Actin depletion initiates events leading togranule secretion at the immunological synapse, Immunity,2015, 42(5), 864–876.

12 J. Yi, X. S. Wu, T. Crites and J. A. Hammer III, Actinretrograde flow and actomyosin II arc contraction drive receptorcluster dynamics at the immunological synapse in JurkatT cells, Mol. Biol. Cell, 2012, 23(5), 834–852.

Soft Matter Paper

Publ

ishe

d on

15

Aug

ust 2

017.

Dow

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ded

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en G

urio

n U

nive

rsity

of

Neg

ev o

n 04

/10/

2017

15:

29:1

8.

View Article Online

This journal is©The Royal Society of Chemistry 2017 Soft Matter, 2017, 13, 6938--6946 | 6945

13 A. Babich, et al., F-actin polymerization and retrograde flowdrive sustained PLCg1 signaling during T cell activation,J. Cell Biol., 2012, 197(6), 775–787.

14 Y. Kaizuka, A. D. Douglass, R. Varma, M. L. Dustin andR. D. Vale, Mechanisms for segregating T cell receptor andadhesion molecules during immunological synapse formationin Jurkat T cells, Proc. Natl. Acad. Sci. U. S. A., 2007, 104(51),20296–20301.

15 C. H. Yu, H. J. Wu, Y. Kaizuka, R. D. Vale and J. T. Groves,Altered actin centripetal retrograde flow in physicallyrestricted immunological synapses, PLoS One, 2010, 5(7),e11878.

16 I. Tskvitaria-Fuller, A. L. Rozelle, H. L. Yin and C. Wulfing,Regulation of sustained actin dynamics by the TCR andcostimulation as a mechanism of receptor localization,J. Immunol., 2003, 171(5), 2287–2295.

17 N. C. Hartman, J. A. Nye and J. T. Groves, Cluster sizeregulates protein sorting in the immunological synapse,Proc. Natl. Acad. Sci. U. S. A., 2009, 106(31), 12729–12734.

18 T. Schnyder, et al., B cell receptor-mediated antigen gather-ing requires ubiquitin ligase Cbl and adaptors Grb2 andDok-3 to recruit dynein to the signaling microcluster,Immunity, 2011, 34(6), 905–918.

19 A. Hashimoto-Tane, et al., Dynein-driven transport ofT cell receptor microclusters regulates immune synapseformation and T cell activation, Immunity, 2011, 34(6),919–931.

20 S. Y. Qi, J. T. Groves and A. K. Chakraborty, Synaptic patternformation during cellular recognition, Proc. Natl. Acad. Sci.U. S. A., 2001, 98(12), 6548–6553.

21 A. Carlson and L. Mahadevan, Elastohydrodynamics andkinetics of protein patterning in the immunological synapse,PLoS Comput. Biol., 2015, 11(12), e1004481.

22 M. T. Figge and M. Meyer-Hermann, Modeling receptor-ligand binding kinetics in immunological synapse formation,Eur. Phys. J. D, 2009, 51(1), 153–160.

23 H. Krobath, B. Rozycki, R. Lipowsky and T. R. Weikl, Bindingcooperativity of membrane adhesion receptors, Soft Matter,2009, 5(17), 3354–3361.

24 R. Bruinsma, M. Goulian and P. Pincus, Self-assembly ofmembrane junctions, Biophys. J., 1994, 67(2), 746–750.

25 S. J. E. Lee, Y. Hori, J. T. Groves, M. L. Dustin and A. K.Chakraborty, Correlation of a dynamic model for immuno-logical synapse formation with effector functions: two path-ways to synapse formation, Trends Immunol., 2002, 23(10),492–499.

26 T. R. Weikl, M. Asfaw, H. Krobath, B. Rozycki and R. Lipowsky,Adhesion of membranes via receptor–ligand complexes: domainformation, binding cooperativity, and active processes, SoftMatter, 2009, 5(17), 3213–3224.

27 N. Weil and O. Farago, Entropy-driven aggregation of adhesionsites of supported membranes, Eur. Phys. J. E: Soft Matter Biol.Phys., 2010, 33(1), 81–87.

28 T. Speck and R. L. C. Vink, Random pinning limits the sizeof membrane adhesion domains, Phys. Rev. E: Stat., Nonlinear,Soft Matter Phys., 2012, 86(3), 031923.

29 N. Dharan and O. Farago, Formation of semi-dilute adhesiondomains driven by weak elasticity-mediated interactions, SoftMatter, 2016, 12(31), 6649–6655.

30 N. J. Burroughs and C. Wulfing, Differential segregation in acell-cell contact interface: the dynamics of the immunologicalsynapse, Biophys. J., 2002, 83(4), 1784–1796.

31 T. R. Weikl and R. Lipowsky, Pattern formation duringT-cell adhesion, Biophys. J., 2004, 87(6), 3665–3678.

32 A. S. Shaw, FERMing up the synapse, Immunity, 2001, 15(5),683–686.

33 C. M. Johnson and W. Rodgers, Spatial segregation ofphosphatidylinositol 4,5-bisphosphate (PIP2) signaling inimmune cell functions, Immunol., Endocr. Metab. AgentsMed. Chem., 2008, 8(4), 349–357.

34 Y. Sun, R. D. Dandekar, Y. S. Mao, H. L. Yin and C. Wulfing,Phosphatidylinositol (4,5) bisphosphate controls T cell acti-vation by regulating T cell rigidity and organization, PLoSOne, 2011, 6(11), e27227.

35 J. Gatfield, I. Albrecht, B. Zanolari, M. O. Steinmet andJ. Pieters, Association of the leukocyte plasma membranewith the actin cytoskeleton through coiled coil-mediatedtrimeric coronin 1 molecules, Mol. Biol. Cell, 2005, 16(6),2786–2798.

36 R. Varma, G. Campi, T. Yokosuka, T. Saito and M. L. Dustin,T cell receptor-proximal signals are sustained in peripheralmicroclusters and terminated in the central supramolecularactivation cluster, Immunity, 2006, 25(1), 117–127.

37 E. Molnar, S. Deswal and W. W. A. Schamel, Pre-clusteredTCR complexes, FEBS Lett., 2010, 584(24), 4832–4837.

38 D. M. Davis and M. L. Dustin, What is the importance of theimmunological synapse?, Trends Immunol., 2004, 25(6),323–327.

39 J. Israelachvili, Intermolecular and Surface Forces, AcademicPress, San Diego, 2nd edn, 1991.

40 J. Gomez-Llobregat, J. Buceta and R. Reigada, Interplay ofcytoskeletal activity and lipid phase stability in dynamicprotein recruitment and clustering, Sci. Rep., 2013, 3, 2608.

41 The utility of this approach was demonstrated in ref. 29,where we employed a more fine-grained lattice model with amicroscopic spacing of 5nm and an explicit representationof the membrane that resulted in TCR–pMHC domains withsimilar densities to those observed in the IS.

42 A. Kusumi, et al., Dynamic organizing principles of theplasma membrane that regulate signal transduction: com-memorating the fortieth anniversary of Singer and Nicolson’sfluid-mosaic model, Annu. Rev. Cell Dev. Biol., 2012, 28,215–250.

43 N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Tellerand E. Teller, Equation of state calculations by fast computingmachines, J. Chem. Phys., 1953, 21(6), 1087–1092.

44 B. Favier, N. J. Burroughs, L. Wedderburn and S. Valitutti,TCR dynamics on the surface of living T cells, Int. Immunol.,2001, 13(12), 1525–1532.

45 S. Kumari, S. Curado, V. Mayya and M. L. Dustin, T cellantigen receptor activation and actin cytoskeleton remodeling,Biochim. Biophys. Acta, 2014, 1838(2), 546–556.

Paper Soft Matter

Publ

ishe

d on

15

Aug

ust 2

017.

Dow

nloa

ded

by B

en G

urio

n U

nive

rsity

of

Neg

ev o

n 04

/10/

2017

15:

29:1

8.

View Article Online

6946 | Soft Matter, 2017, 13, 6938--6946 This journal is©The Royal Society of Chemistry 2017

46 A. L. DeMond, K. D. Mossman, T. Starr, M. L. Dustin andJ. T. Groves, T cell receptor microcluster transport throughmolecular mazes reveals mechanism of translocation,Biophys. J., 2008, 94(8), 3286–3292.

47 C. O. Mejean, et al., Elastic coupling of nascent apCAMadhesions to flowing actin networks, PLoS One, 2013,8(9), e73389.

48 G. Campi, R. Varma and M. L. Dustin, Actin and agonistMHC–peptide complex-dependent T cell receptor micro-clusters as scaffolds for signaling, J. Exp. Med., 2005, 202(8),1031–1036.

49 T. Yokosuka, et al., Newly generated T cell receptor micro-clusters initiate and sustain T cell activation by recruitmentof Zap70 and SLP-76, Nat. Immunol., 2005, 6(12), 1253–1262.

Soft Matter Paper

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15

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