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LocallyEstablished by Inhibitory Receptors ActingReveal that Activation Thresholds Can Be Simulations of the NK Cell Immune Synapse

Petter Höglund, Daniel M. Davis and Ramit MehrKohen, Gilad Halpert, Mali Salmon-Divon, Karsten Köhler, Asya Kaplan, Shulamit Kotzer, Catarina R. Almeida, Refael

http://www.jimmunol.org/content/187/2/760doi: 10.4049/jimmunol.10022082011;

2011; 187:760-773; Prepublished online 20 JuneJ Immunol 

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8.DC1http://www.jimmunol.org/content/suppl/2011/06/20/jimmunol.100220

Referenceshttp://www.jimmunol.org/content/187/2/760.full#ref-list-1

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Print ISSN: 0022-1767 Online ISSN: 1550-6606. Immunologists, Inc. All rights reserved.Copyright © 2011 by The American Association of1451 Rockville Pike, Suite 650, Rockville, MD 20852The American Association of Immunologists, Inc.,

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The Journal of Immunology

Simulations of the NK Cell Immune Synapse Reveal thatActivation Thresholds Can Be Established by InhibitoryReceptors Acting Locally

Asya Kaplan,*,1 Shulamit Kotzer,*,1 Catarina R. Almeida,†,1,2 Refael Kohen,*

Gilad Halpert,* Mali Salmon-Divon,*,3 Karsten Kohler,†,4 Petter Hoglund,‡

Daniel M. Davis,† and Ramit Mehr*

NK cell activation is regulated by a balance between activating and inhibitory signals. To address the question of how these signals

are spatially integrated, we created a computer simulation of activating and inhibitory NK cell immunological synapse (NKIS)

assembly, implementing either a “quantity-based” inhibition model or a “distance-based” inhibition model. The simulations

mimicked the observed molecule distributions in inhibitory and activating NKIS and yielded several new insights. First, the total

signal is highly influenced by activating complex dissociation rates but not by adhesion and inhibitory complex dissociation rates.

Second, concerted motion of receptors in clusters significantly accelerates NKIS maturation. Third, when the potential of a cis

interaction between Ly49 receptors and MHC class I on murine NK cells was added to the model, the integrated signal as

a function of receptor and ligand numbers was only slightly increased, at least up to the level of 50% cis-bound Ly49 receptors

reached in the model. Fourth, and perhaps most importantly, the integrated signal behavior obtained when using the distance-

based inhibition signal model was closer to the experimentally observed behavior, with an inhibition radius of the order 3–10

molecules. Microscopy to visualize Vav activation in NK cells on micropatterned surfaces of activating and inhibitory strips

revealed that Vav is only locally activated where activating receptors are ligated within a single NK cell contact. Taken together,

these data are consistent with a model in which inhibitory receptors act locally; that is, that every bound inhibitory receptor acts

on activating receptors within a certain radius around it. The Journal of Immunology, 2011, 187: 760–773.

Natural killer cells are lymphocytes that are able to lysea variety of tumor targets and cells infected with in-tracellular bacteria, parasites, or several types of viruses.

The cytolytic capability of NK cells is enabled after ligation of NKcell activating receptors such as NKG2D, which binds the stress-inducible ligands such as MICA (1, 2). The activation of an NKcell is tightly regulated by inhibitory receptors (including Ly49receptors in mice and killer cell Ig-like receptor [KIR] in humans)that limit and potentially terminate the response (3, 4). Inhibitoryreceptors mostly bind self MHC class I (MHC-I) molecules, suchthat target cells that do not express or have downregulated selfMHC-I expression are more likely to be killed by NK cells [the“missing self” hypothesis (5)]. Inhibitory receptors carry ITIMs intheir cytoplasmic domain. After ligand binding, ITIMs are tyro-

sine phosphorylated and then recruit and activate protein tyrosinephosphatases that lead to dephosphorylation of key componentsfor NK cell activation, such as Vav-1, and block signaling fromactivating receptors (3, 6–12). The mechanism(s) by which signalsare integrated in NK cells and how exactly the balance betweenthe two types of receptors determines NK cell function are,however, unclear.NK cell recognition of target cells can be either cytolytic or non-

cytolytic. Based on this distinction, two different NK cell immu-nological synapses (NKIS) can be defined: the inhibitory NKIS andthe cytolytic NKIS (10, 13). The main molecules that participate inthe formation of the NKIS are inhibitory and activating receptorsand adhesion molecules. Lipid microdomains (also known asrafts) are membrane regions enriched in specific lipids, which are

*The Mina and Everard Goodman Faculty of Life Sciences, Bar-Ilan University,Ramat-Gan 52900, Israel; †Division of Cell and Molecular Biology, Imperial CollegeLondon, South Kensington Campus, London SW7 2AZ, United Kingdom; and‡Department of Microbiology, Tumor and Cell Biology, Karolinska Institute, 171-77 Stockholm, Sweden

1A.K., S.K., and C.R.A. contributed equally to this work.

2Current address: Instituto de Engenharia Biomedica, Divisao de Biomateriais, Uni-versidade do Porto, Porto, Portugal.

3Current address: Cancer Research Center, Chaim Sheba Medical Center, Tel-Hashomer, Israel.

4Current address: Cambridge Institute for Medical Research, Addenbrooke’s Hospi-tal, Cambridge, United Kingdom; and Department of Pathology, Cambridge Univer-sity, Cambridge, United Kingdom.

Received for publication July 6, 2010. Accepted for publication May 9, 2011.

This work was supported in part by grants from the Swedish Cancer Society andthe Swedish Research Council (to P.H.); grants from the Medical Research Council(U.K.) and the Biotechnology and Biological Research Council; a Wolfram RoyalSociety Research Merit award (to D.M.D.); a Human Frontiers Science Program

Young Investigator grant (to P.H., D.M.D., and R.M.); a Swedish Foundation forStrategic Research grant funding the Strategic Research Center for studies on In-tegrative Recognition in the Immune System, Karolinska Institute, Stockholm, Swe-den (supporting P.H. and R.M.); an Israel Science Foundation Bikura program grant;and indirectly by Israel Science Foundation Grants 759/01-1 and 546; an IsraelCancer Research Fund project grant; a Human Frontiers Science Program projectgrant; and a Systems Biology prize grant from Teva Pharmaceuticals (to R.M.). C.R.A.was supported by Fundacao para a Ciencia e a Tecnologia. This work was part ofA.K.’s studies toward an M.Sc. degree and S.K.’s studies toward a Ph.D. degree atBar-Ilan University.

Address correspondence and reprint requests to Prof. Ramit Mehr, The Mina andEverard Goodman Faculty of Life Sciences, Bar-Ilan University, Ramat-Gan 52900,Israel. E-mail address: ramit.mehr@biu.ac.il

The online version of this article contains supplemental material.

Abbreviations used in this article: IS, immunological synapse; KIR, killer cell Ig-likereceptor; MHC-I, MHC class I; NKIS, NK cell immunological synapse.

Copyright� 2011 by TheAmerican Association of Immunologists, Inc. 0022-1767/11/$16.00

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postulated to be relatively ordered compared with the rest of theplasma membrane. These microdomains accumulate at the NK–target cell contact site, and there is evidence that many signalingmolecules are recruited to these microdomains during cytolyticNKIS, as also described for T cells interacting with APCs (14).Despite much research, it remains controversial whether lipid do-mains themselves are important in directing the organization of animmune synapse.The scenario of NKIS assembly has been observed experi-

mentally in detail (15–17). Activating signals lead to directedmovement of molecules (14, 18, 19), and of several types ofmembrane microdomains (20–29), toward the center of the con-tact area. LFA-1 molecules segregate into a ring surrounding thecenter of the contact area, due to the inward movement of mem-brane microdomains, with which nonactivated LFA-1 moleculesdo not associate, and possibly also due to membrane stress causedbetween the short bonds of NK cell receptors and ligands and thelonger LFA-1–ICAM-1 bonds (30). If, in contrast, enough in-hibitory receptors are bound to inhibit the signaling from acti-vating receptors, then the directed movements are stopped, actin-dependent recruitment of lipid rafts is prevented, and the synapsedoes not become an activating synapse (31, 32).The immune system exhibits highly complex dynamics in-

volving many cells and factors, whereas laboratory experimentstend to isolate and study one or two molecular or cellular inter-actions at a time. Simulation models of T cell IS (33, 34) helpedintegrate the data from experiments and test hypotheses. In thecurrent study, we established a computer simulation for the as-sembly of the NK cell immune synapse to elucidate whichmechanisms of signal integration may effectively control NK celleffector functions. Specifically, we assessed a “quantity-based”inhibition model, in which the number of bound inhibitoryreceptors is simply subtracted from the number of bound acti-vating receptors, and a “distance-based” inhibition model, inwhich every bound inhibitory receptor inhibits signals from allbound activating receptors within a certain radius around it. Thelatter hypothesis was suggested by the observation that inhibitoryreceptors can stop the response while being gradually integratedinto the synapse as the cell spreads (35) and that phosphorylationof KIR occurs in microclusters (36).The simulations presented below successfully mimic the ex-

perimentally observed molecule distributions in inhibitory andactivating NKIS. The results of simulations of the two signal in-tegration models differ not in NKIS images but in the dependenceof steady-state signal levels on receptor and ligand numbers. Weobserved a saturation of signal levels as a function of receptor andligand numbers, which was more similar to the experimentallyobserved behavior when simulating the distance-based inhibitionsignal integration model than when using the quantity-based in-hibition signal integration model. Thus, we suggest that measuringNK receptor signals during NKIS, as function of NK cell receptorand ligand numbers, will discriminate between different models ofhow an NK cell integrates the signals received and decides whetherto kill the target cell. In addition, model parameter investigationshowed that the total signal is highly influenced by activatingreceptor–ligand dissociation rates but not by adhesion and in-hibitory receptor–ligand dissociation rates, and that concertedmotion of receptors in clusters—in this case, by their associationwith membrane microdomains—significantly accelerates NKISmaturation.For mouse cells, just as Ly49 on an NK cell can be bound to its

MHC ligand on the target cell (a trans interaction), it can also bindMHC-I proteins on the NK cell itself (a cis interaction) (37–42).These interactions have to date only been found on NK cells in

mice and not on human NK cells, that is, with Ly49 but not withKIR. We have addressed the question of how cis interactionscontribute to NK cell function by also simulating the murine NKISand show here how including the cis interaction in the simulationincreases the activating signals during NKIS formation.

Materials and MethodsGrid model of the NKIS

Our model of the NKIS contains two parallel two-dimensional grids rep-resenting the contact areas on the membranes of the two interacting cells—the NK and the target cell grids (Fig. 1A, 1B). The grids contain some ofthe different cell surface molecules and membrane microdomains presentin the NKIS. The initial contact area is defined as a circle with a fixedradius (default value = 30 positions) around the grid’s center. The ringsurrounding the initial contact area is defined as the rest of a contact area,which grows after contact by one position per time step until reachinga maximum diameter of 0.95 of the grid’s dimension, to represent theflattening of the two cells against each other. The maximum diameter ofthe contact area is 95% of the grid length, so we can observe the behaviorat the margins of the contact area. Each grid position may be occupied bya molecule or not and may also be included within a membrane micro-domain or not. Some molecules prefer to associate with membranemicrodomains and move with them, whereas other molecules avoid them.

The general algorithm is presented in Fig. 1C. In each time step, thealgorithm performs a sweep over the grid; the sweep is divided to a de-cision phase and an action phase. After each time step, the locations of allmolecules in the two grids are stored as an image, and the followingvariables are counted: numbers of molecules on NK and target cell grids;the total number of complexes formed between NK cell receptors and theirligands; and the sum of all positive, negative, and total signals according toeach model.

The assumptions regarding each molecule’s behavior are described inthe following sections and summarized in Table I.

Molecules

In our simulation, we use only one representative inhibitory and onerepresentative activating receptor and their corresponding ligands. Thesimulations presented in this article included KIR2DL or Ly49 receptors,MHC-I, NKG2D, MICA, or Rae, and the integrin LFA-1 interacting withICAM-1 on the target cell. Each molecule is characterized at any given timeby its properties, such as its location, whether it is free or bound to its ligand,and whether it prefers or avoids association with membrane microdomains(see later). The latter preference is expressed as a “lipid microdomainpreference factor,” which indicates by how much a molecule is more likelyto be found on a lipid microdomain, or move into it, than a molecule thatdoes not prefer to be on lipid microdomains. There is considerably moreinformation on T cell synapses than NK cell synapses, but for the sake ofmodeling we assumed that the same molecules will behave similarly in Tand NK cell synapses when specific information on their behavior on NKcell synapses is missing. Molecules are additionally characterized by theprobabilities for each action they may perform in each time step (Table II,Supplemental Table I). These properties may change with time based onthe current state of each molecule and the interactions with its neighbors.For simplicity, at each time step, each molecule can perform only oneaction. A molecule can bind its ligand only when it is located in thecomplementary position on the parallel grid. The rules of motion for eachmolecule are as follows.

The probability to move to either direction for an unbound molecule islikely to be limited by other molecules around and also by actin [e.g., uponKIR binding, Vav-1 becomes dephosphorylated, which affects actin po-lymerization (11)]. However, for the sake of simplicity, it was assumed tobe equal for moving into any free neighboring position. That is, given thatthe probability of molecule of type i on grid g to move at all is Dg,i, thenthe probability to move to any direction is 0.25 3 Dg,i 3 (0 if desiredposition is occupied; 1 if free). Adding to the model the corrals created byan actin mesh or other protein–protein interactions such as tetraspaninprotein networks would have complicated the model and would be unlikelyto limit molecule movements much further, as in the simulation, molecularmovements are already quite limited by the density of packing of othermolecules and by lipid microdomains. The probability of movement intoa position containing a lipid microdomain is multiplied by the preferencefactor Kg,i_MM of the moving molecule, thus taking into considerationwhether the molecule favors lipid microdomains or not. Bound moleculescannot move out of the contact area, and their probability of movement issmaller than that of free molecules. We assigned this difference a factor of

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2 (i.e., the bound molecule movement probability is Dg,i/2) based on theStokes–Einstein equation (43).

When there are two bound molecules in neighboring positions, whichdiffer in size of the extracellular domain by more than 10 nm, the membraneis assumed to be in stress, as has been suggested by previous models of theT cell IS (33, 44–46) and recently in experimental studies of NK cellsynapses (47). To model the effect of the stress, the probability for themolecule to move away from the other molecule is multiplied by a stressfactor. The stress factor default value, for which there is no experimentalmeasurements, was varied at the range from 1 (no stress) to 50.

The binding decisions, and decisions of bound complexes, are performedby themolecules in the NK cell grid. For simplicity, we neglect arrival of newmolecules into the contact area and its vicinity and the internalization ofmolecules. Molecules that move out of the grid at its edges are recycled backto the grid in the next step, in randomly chosen locations at the grid edges.

Lipid microdomains

Lipid microdomains are a type of membrane domain that is relativelyordered compared with the rest of the plasma membrane (48, 49); theyoccupy between 10 and ∼50% of the cell’s surface (24, 49) and wereobserved to diffuse faster than molecules (50). There are various types oflipid microdomains; in our work we use the term “lipid microdomains” or“lipid rafts” to refer only to the type with which there is a preferential

association of TCRs (21, 51–57) or NK cell activating receptors or theirligands (14, 18, 23). Whereas the precise type of microdomain remains tobe elucidated, we consider that our model applies to any domain-mediatedmechanism of receptor aggregation, and it is clear that most if not allimmunoreceptors are not uniformly distributed at cell surfaces. Althoughlipid rafts may or may not be the only or the most important mechanismfor receptor clustering at the NKIS, the specific reference to lipid rafts hereserves to focus on one specific example for parameterization. We assumethat, as in T cells, in NK cells signaling molecules are localized in thesedomains, in particular the Src-family kinases (54, 57–59), and suggest thatNK activating receptors, like TCRs, move with the microdomains (60).Moreover, MHC class II molecules are also associated with microdomains(61–63), even if there is no interaction with T cells (29, 64, 65). We assumethe same is true for MHC-I, based on their clustering along with MHCclass II molecules (66). After initial signaling events, lipid microdomainscan accumulate in the T cell2APC contact area (24, 60, 67–70) or theNK cell–target cell area (14, 18, 23), possibly aiding accumulation ofmicrodomain-associated receptors and Src-family kinases (71, 72). Over-all, it is clear that some selection of lipid domains occurs at the immunesynapse, but the extent to which such domains directly organize the syn-apse remains controversial.

In the model presented in this article, the decision to move is made by thefirst lipid microdomain position encountered by the algorithm. The prob-abilities to move to either direction are initially equal but may further be

Table I. Model assumptions regarding molecule behavior

Assumptions References

The initial contact area is defined as a circle with a fixed radius around the grid’s center, which grows aftercontact by one position per time step until reaching a maximum diameter of 0.95 of the grid’s dimension.

The probability to move to either direction for an unbound molecule is equal to that for moving intoany free neighboring position.

The probability of movement into a position containing a lipid microdomain is multiplied by Kg,i_MM of themoving molecule, thus taking into consideration whether the molecule favors lipid microdomains or not.

Bound molecules cannot move out of the contact area, and their probability of movement is smaller thanthat of free molecules.

To model the effect of the stress, the probability for the molecule to move away from the other moleculeis multiplied by a stress factor.

Lee et al., 2002 (30)

Lipid microdomains occupy between 10 and ∼50% of the cell’s surface and diffuse faster than molecules. Pike, 2003 (24)Horejsi, 2003 (49)Fujiwara et al., 2002 (50)

NK cells signaling molecules are localized in lipid microdomains, and NK activating receptors movewith the microdomains.

Eleme et al., 2004 (18)Endt et al., 2007 (77)

MHC-I molecules are also associated with microdomains. Hiltbold et al., 2003 (61)Wulfing et al., 2002 (62)Poloso et al., 2004 (63)Szollosi et al., 1996 (66)

Directed movement applies only to the movement of microdomains and activating receptors and their ligands. Vyas et al., 2001 (15)Lou et al., 2000 (23)

At the beginning of the contact, for the NK cell grid, LFA-1 molecules have a higher probability to beat the center of the contact area. In the target cell grid, all molecules are randomly and uniformly distributedover the grid.

Cmin is the minimal number of bound adhesion molecules that have to be bound before interactionsbetween NK cell receptors and HLA can start, based on the assumption that the first binding betweencells can only be through adhesion molecules.

Orange, 2008 (17)

The cell’s behavior is influenced by signals received in the last t time steps, and S is the amount ofsignal received in this time period.

Smin is the minimum value of positive integrated signal S, above which LFA-1, ICAM-1, and NKG2Dconvert from microdomains avoiding state to the microdomains favoring state and microdomain,activating receptor, and ligand movements become directed.

Endt et al., 2007 (77)

“Simple sum” model: the cell sums over all positive signals (number of bound activating receptors),subtracts the inhibited signals (number of bound inhibitory receptors), and acts according tothe net total signal.

Distance-based inhibition: signals transduced by activating receptors were counted, and for each boundactivating receptor, its signal was not counted at all if there were bound inhibitory receptors in itslocal environment, defined by a local inhibition radius.

Murine NKIS: similar assumptions but with new parameters (see Tables II, III), MHC molecules addedto the NK cell, and cis interactions (as below).

Back et al., 2007 (37)Back et al., 2010 (38)Chalifour et al., 2009 (39)Doucey et al., 2004 (40)Held et al., 2008 (41)Scarpellino et al., 2007 (42)Back et al., 2007 (37)Molecules that are bound in cis are not able to bind simultaneously in trans.

The cis complexes have a slower diffusion rate in comparison with that of single molecules.MHC is the larger molecule in the Ly49–MHC complex, thus the MHC is given the decision of where

to move the complex and pulls the Ly49 along.

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influenced by several situations, as follows. If there is no lipid microdomainor lipid microdomain-avoiding molecule in the desired position, the lipidmicrodomain moves to the desired position. If the desired position happensto be outside of the grid boundary, then the lipid microdomain positionmoves out of the grid. If the current lipid microdomain position is occupiedby a molecule, and there is a lipid microdomain in the desired position(which may be occupied or not), then neither the lipid microdomain nor themolecule move. If there is only a molecule in the desired position and itfavors lipid microdomains, then only the lipid microdomain moves to thedesired position without moving the molecule in the original position. Incase the lipid microdomain position is occupied by a bound molecule, onlythe lipid microdomain moves.

Lipid microdomains have the following characteristic parameters. KgR is

the rate of the lipid microdomain growth: if a grid position is at the edge ofthe lipid microdomain, then its neighbors have a probability (per time step)proportional to Kg

R to also become a lipid microdomain. Kg2R is the rate

of lipid microdomain diminishing: if a grid position is on the edge ofa lipid microdomain, then it has a probability (per time step) proportionalto Kg

2R to become “non-lipid microdomain.” The expansion and dimin-ishing probabilities further depend on the number of neighbors that are onmicrodomains, and in any case are very small compared with the rate oflipid microdomain movement. Dg

R is the basic movement probability ofwhole microdomains. Microdomains on different grids may differ in theirmovement probabilities, but in the same grid the basic movement proba-bility of microdomains is constant in time.

Directed movement of activating molecules and lipidmicrodomains

The molecule movement probabilities may further change when the overallintegrated signal received by the cell from all receptors (see later the modelsfor signal integration) exceeds a certain threshold, Smin. At this point, themovement of activating molecules and lipid microdomains becomes di-rected toward the center of the contact area. This is modeled by multi-plying their movement probabilities by a factor greater than 1. Because nodata are available on exactly how much microdomain and molecule di-rected movement toward the center is accelerated during an activatingsynapse, we chose the wide range of 1215 for the molecule directedmovement factor. In contrast, adhesion molecule directed movement wasnot necessary for synapse inversion; hence, the default value was 1.Microdomains were observed to diffuse faster than molecules (50), and wetherefore assumed that microdomain movements are more influenced bysignaling than are single molecules. We thus used a minimal defaultmovement probability and examined a wider range of values for micro-domains. Similarly, for the values of the lipid microdomain preference ofthe molecules in the model, we took the same range of values for thepreference factor (1–5) that has worked well in our T cell simulations.

In the current study, directed movement applies only to the movement ofmicrodomains and activating receptors and their ligands, as both signalingmolecules and lipid microdomains accumulate at the contact area of ac-tivating synapses but not at inhibitory synapses (15, 23). When micro-domains move, the decision to move is made by the central membranemicrodomain position in the group.

Parameters and initial conditions

The simulation starts when the two cells are opposite each other and thedistance between them permits molecule binding. The initial numbers ofmolecules on the grids are activating and inhibitory receptors, 1000–2000;activating and inhibitory ligands, 0–5000 (73); and LFA-1 and ICAM-1,500 (based on T cell synapse data). Molecules are distributed randomly.We assume that in NK cells, as in T cells (14, 31, 74–76), LFA-1 moleculesare in the center of the initial contact with the target cell, and that bindingof LFA-1 molecules to their ligands maintains cell conjugation longenough for activating receptors to bind their ligands (if present). Hence, forthe NK cell grid, we use the “central” initial conditions, in which LFA-1molecules have a higher probability to be at the center of the contact area.For the target cell grid, we use uniform initial conditions; that is, allmolecules are randomly and uniformly distributed over the grid.

The values of all the relevant parameters are calculated from experi-mental data or were varied in the simulation (Table II, Supplemental TableI). The association and dissociation rates, Kon and Koff, of each complexwere calculated in a similar way to that used in our T cell IS simulation(34). Briefly, the experimentally observed three-dimensional kinetic ratesof each interaction were first converted to two-dimensional rates based onpreviously established methods (33) and then translated to probabilities,keeping the ratios between them fixed. That is, we took the highest value tobe 1 and normalized the other rates accordingly.

In the simulations, we defined several thresholds. Cmin is the minimalnumber of bound adhesion molecules that have to be bound before inter-actions between NK cell receptors and HLA can start, based on the as-sumption that the first binding between cells can only be through adhesionmolecules. We also assume that the cell’s behavior is influenced by signalsreceived in the last t time steps, and define the integrated signal S as theamount of signals received in this time period. Accordingly, Smin denotesthe minimum value of net positive integrated signal S, above which thefollowing actions are allowed: LFA-1, ICAM-1, and NKG2D convert fromthe membrane microdomain-avoiding state to the membrane microdomain-favoring state when S . Smin (77), and microdomain, activating receptor,and ligand movements become directed. The value ranges of t and Smin

were chosen such that activating synapses can be formed, based on ourT cell synapse simulations (34) and on preliminary runs of the NKISsimulations.

Models for receptor signal integration

We assume that when an activating receptor binds its ligand, it transducesa positive signal, which may be cancelled by the inhibitory receptors. Theinhibitory receptors recruit phosphatases that interfere with the signalingfrom activating receptors. If the phosphatase cannot diffuse very fast, theeffect will be “distance-based” inhibition. To model such inhibition, wecount signals transduced by activating receptors. For each bound activatingreceptor, we do not count its signal at all if there are bound inhibitoryreceptors in its local environment, defined by a local inhibition radius,which was varied in the simulation. In contrast, if inhibition extends overthe whole contact area because of diffusion of the phosphatase, then in-hibition may be regarded as “quantity-based” and described by a “simplesum” model: the cell sums over all positive signals (number of boundactivating receptors), subtracts the inhibited signals (number of boundinhibitory receptors), and acts according to the net total signal. Theseeffects are limited to the contact area.

Modeling murine NKIS and Ly49–H-2 cis interactions

The model of the murine NKIS is similar to the model of the human NKIS,with the following differences. First, the activating ligands here are themurine NKG2D ligands (78), and the inhibitory receptors are Ly49 and notKIR. The association/dissociation rates were changed accordingly, and allparameters were rescaled (Table III, Supplemental Table II). Second, MHCmolecules were added to the NK cell grid as well as the target cell grid.Third, the possibility of Ly49–H-2 cis interaction was added on the NKcell grid, with the same association/dissociation rates as for the trans in-teraction. Fourth, the following assumptions were made in the algorithm.Molecules that are bound in cis are not able to bind simultaneously in trans(as the binding site of the Ly49 to the MHC is identical in both types ofinteraction). We also decided to assign the cis-bound complex a slowerdiffusion rate in comparison with that of single molecules, which wouldappear likely given the larger mass of the proteins complex relative to thesingle proteins, as well as the potential effects of two adjacent membraneanchors on membrane mobility. MHC is the larger molecule in the Ly49–MHC complex, thus the MHC is given the decision of where to move thecomplex and pulls the Ly49 along. It is also possible for the MHC to movein the direction of the Ly49, even though this position seems to have beenalready occupied. In this case, the MHC pushes the Ly49 along. The Ly49receptor is responsible for deciding on binding in cis or dissociating fromthe MHC. If one of the molecules in a cis complex moves outside of thegrid, both molecules are removed together. To keep a balanced number ofmolecules, the molecules that exit may be recycled back into the gridduring the next time step of the program, not as cis complexes but as singlemolecules. If the position that one of cis complex molecules has decided tomove into is taken by another molecule, the whole complex is not able tomove. Conflicts are resolved as in the human NKIS simulation. If a Ly49 ison a lipid microdomain and binds in cis to an MHC that is not on a lipidmicrodomain, in case the lipid microdomain moves, the Ly49 that is on itdoes not move with it, as the MHC decides the movement for a cis typecomplex. In the opposite circumstances, where the MHC is on the lipidmicrodomain and is bound in cis to a Ly49 that is not on the lipidmicrodomain, if the lipid microdomain moves, it does move with it thewhole Ly49–MHC complex, unless the desired position for the Ly49 isoccupied.

Quantification of Vav phosphorylation at NK cell contacts withmicropatterned substrates

To visualize and compare the phosphorylation of Vav at different regions ofa single-cell contact, microcontact printing was performed as previouslydescribed (35) using polydimethylsiloxane stamps with a striped pattern.Stamps were coated with anti-NKG2D (100 mg/ml in PBS; clone 149810;

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R&D Systems) plus 15 mg/ml Alexa Fluor 568 anti-rat IgG (Invitrogen) for1 h at room temperature, washed with DD H2O, and dried with an airduster, then stamped onto poly-L-lysine–coated slides. Stamped areas wereoverlayed with a mixture of 5 mg/ml each anti-NKG2A (clone 131411;R&D Systems) plus anti-CD94 (clone HP3D9; Pharmingen) in PBS for 60min at room temperature, followed by blocking with PBS/1% BSA for 30min. NKL cells were added to microstructured surfaces and incubated for 6min at 37˚C. Then, cells were fixed for 15 min with Cytofix/Cytoperm (BDPharmingen) containing 1 mM sodium vanadate, followed by blockingwith Cytoperm (Pharmingen) containing 5% horse serum and 3% BSA for1 h, staining with 5 mg/ml anti-Vav (pY160; Abcam) for 1 h at roomtemperature, and Alexa 488-labeled anti-rabbit Ab (2 mg/ml) secondarystaining. To quantify the intensity of phospho-Vav staining on anti-NKG2D versus anti-NKG2A/anti-CD94 strips, two binary masks wereproduced using the Alexa 568 fluorescence from the stamped area andmultiplied by the channel containing the phospho-Vav staining (ImageJ).Microscopy was performed in the light microscopy facility (FILM) ofImperial College.

ResultsMicrodomain association accelerates molecule redistributionin activating NKIS simulations

We first verified that our simulations capture the molecule dis-tributions observed in activating and inhibitory synapses. In ourfirst simulations, the difference between inhibitory and activatingsynapses is that activating ligands (MICA) were only included inthe activating synapse simulations. All other initial conditions werethe same in both cases. When the total integrated signal is higherthan Smin, NKG2D, MICA, and microdomains have undergonedirected movement toward the initial contact area of the grids,yielding an activating synapse. After 10,000 time steps of thesesimulations, due to the directed movement, NKG2D and MICAmolecules, as well as microdomains, have accumulated in theinitial contact area (Fig. 1D).We plotted the changes in molecule placement as inhibitory or

activating synapses develop (Fig. 2A). In the activating synapse,after several thousand time steps, LFA-1 molecules have movedtoward the ring surrounding the initial contact area. In addition tothe random diffusion (as in the inhibitory synapse), in the acti-vating synapse LFA-1 molecules segregate away from the initialcontact area as a result of stress caused by bound receptors ofdifferent sizes (33) and, more often, because the center becomesoccupied by NKG2D molecules and membrane microdomains.The numbers of HLA molecules have, by this time, increased inthe center of the contact area, because they have a relatively highpreference to be on microdomains (79), and, therefore, havemoved with the microdomains to the center. KIR molecules alsoaccumulate in the center of the contact area due to binding theHLA molecules. KIR and HLA molecule numbers are still largerin the surrounding ring because the activating molecules clusterin the initial contact area and crowd them out. However, becausethe center area is smaller than the surrounding ring, KIR,HLA, NKG2D, and MICA concentrations in the center are muchhigher than in the surrounding ring (Fig. 2B), as observed inthe experiments (80). ICAM-1 molecules were distributed almostevenly over the target grid, although those bound to LFA-1 werepushed to the margins.When the total integrated signal is lower than Smin during the

whole simulation run, there is no directed movement of NKG2D/MICA molecules and microdomains, and inhibition dominatesthe outcome of signal integration. After 10,000 time steps, due torandom diffusion, most molecules and membrane microdomainsare uniformly distributed over each grid. LFA-1 molecules are stilllocated mostly in the center, but less concentrated than at thebeginning of the simulation (Fig. 2A). In these inhibitory synapsesimulations, the numbers of KIR2DL and HLA in the surroundingring quickly increase and stabilize approximately from the point

of 4000 time steps, whereas in the initial contact area, KIR2DLnumbers increase slowly, during almost the whole simulation, andstabilize only at the end. This increase of KIR2DL numbers inthe initial contact area is probably due to random diffusion andbinding to HLA molecules because we do not assume here a di-rected movement of inhibitory molecules. This is consistent withthe observations on SH2 domain-containing phosphatase 1 mol-ecules, which associate with the inhibitory receptors and are moreconcentrated in the initial contact area than in the periphery in theinhibitory NKIS (3, 16). NKG2D molecule numbers increase inthe surrounding ring, probably due to random diffusion fromoutside this area, whereas in the initial contact area the number ofNKG2D remains constant during the simulation, as there is nobinding of activating ligands. The dissipation of LFA-1 moleculeswith time, from the initial contact area to the surrounding ring, isclearly evident. ICAM-1 molecule numbers slightly increase inthe initial contact area due to binding to LFA-1, also stabilizingaround 4000 time steps. The above observations were similarwhen we assumed that HLA molecules do not favor membranemicrodomains, although molecule numbers have stabilized ona longer time scale (data not shown).In simulations in which membrane microdomains are not in-

cluded at all, the mature synapse (with NKG2D and MICA in thecenter) is created at a very late stage, and LFA-1 molecules do notmove to the periphery of the synapse (Fig. 2C). The variability inthese runs is lower than in the runs with microdomains becausemicrodomains introduce additional noise into the system.

Inhibition acts locally rather than over the whole contact area

To compare the different signal integration models, we ran thesimulation with various initial NK cell receptor–ligand numbersand plotted the net number of signals integrated by the NK cell(“integrated signal”) at the steady state reached by quantity-basedand distance-based inhibition model simulations. In the quantity-based inhibition model simulations (Fig. 3), as HLA or KIRnumbers increase and/or MICA or NKG2D numbers decrease, thesteady-state integrated signal decreases, as expected. The simu-lations, however, yield additional nontrivial insights on the precisebehavior of the signal under each model, as follows. For highnumbers of MICA, the steady-state signal decreases more or lesslinearly with the increase in HLA numbers. For lower MICAnumbers, this decrease is faster than linear, but at the points with0 MICA, where the steady-state integrated signal reflects only thenumbers of bound inhibitory receptors and hence takes negativevalues, the signal decline becomes linear again. This suggests aneffect of saturation: when there are many activating ligands, mostof the activating receptors are bound, and the signals are lesssensitive to the addition of inhibitory ligands. However, as MICAnumbers decrease, the overall signal becomes much more sensi-tive to the addition of inhibitory ligands. The influence of KIRnumbers is more clearly seen with high HLA numbers and lowMICA numbers (compare Fig. 3Awith 3C or 3B with 3D), but forhigher MICA numbers, the effect of KIR numbers becomes lesspronounced again.In the distance-based inhibition model, in addition to molecule

numbers, the “local environment radius” also influences the in-tegrated signal (Fig. 4). In this model, in contrast to the quantity-based inhibition model, the minimal possible value of the steady-state integrated signal is zero. When the local inhibition radiusequals 1, each bound inhibitory receptor may cancel the signals ofup to four activating receptors (Fig. 4A), as bound inhibitoryreceptors have to be adjacent to bound activating receptors toinhibit the signal, and a radius of 1 in a square grid implies fournearest neighbors. Because having activating receptors in all four

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neighboring positions is relatively rare, the level of steady-stateintegrated signals is only slightly decreased as HLA numbers in-crease. As the radius increases (Fig. 4B–E), inhibition increasesand the signal depends more strongly (and nonlinearly) on mol-ecule numbers. Unlike in the quantity-based model, the effect ofdecreasing MICA numbers is not seen, but there is a very clearsaturation effect as a function of HLA numbers: at some point,increasing HLA numbers does not lead to more inhibition, as most

KIRs are already bound to their ligands. Similar effects wereobserved by Brodin et al. (81).This latter saturation effect is similar to the experimental ob-

servations by Almeida et al. (73, 81), where specific thresholdsin the level of target cell HLA-C had to be exceeded to inhibitcytotoxicity and to cause segregation of HLA-C from ICAM-1 atthe synapse; beyond that HLA-C level, however, inhibition alwaysoccurred to the same extent. In contrast to the quantity-based

FIGURE 1. The simulation. A and B, Illustration of the NK cell (A) and target cell (B) grids. The program runs in parallel on both grids (simultaneously

checking a position on the NK cell grid and the parallel position on the target cell grid, proceeding row by row). Each molecule takes up one grid position,

representing the typical width of one molecule, taken to be ∼10 nm. The cell–cell contact area diameter is of the order ∼3 mm. For computational

simplicity, we use a grid size of 1503 150 positions (half of the actual contact area diameter; this speeds up computation without qualitatively changing the

results). C, The general algorithm scheme. One time step consists of one sweep over the whole double grid, row by row, and represents a real time interval

of the order 10 ms. Indeed, as shown below, in our simulations activating synapses can be distinguished from inhibitory synapses after a few thousand time

steps, corresponding with the order of a few minutes, as observed experimentally. To prevent artifacts resulting from sweeping over the grid sequentially

(row by row), we have taken the following steps. First, the sweep is divided to a decision phase and an action phase. In the decision phase, the algorithm

goes over all positions, and for each molecule or lipid microdomain found, it 1) calculates the probabilities for each action this molecule or lipid

microdomain can take, based on its immediate environment and interactions, as explained in the text; and 2) based on the calculated probabilities, it makes

a random decision regarding which action will actually be taken in this step. Second, before the action phase, there is also a conflict resolution phase. This

phase deals with all the conflicts between decisions made by different molecules, for example in case two or more molecules have decided to move into the

same grid position—a situation that occurs in higher probabilities once molecules start crowding into the center of the NKIS. Conflicts are resolved by yet

another random decision between the competing actions, with equal probabilities. Finally, in the action phase, all the decisions are performed, and the grid

is updated. D, Demonstration of the activating NKIS simulation. The initial numbers of molecules on the NK cell grid are 500 LFA-1, 1000 KIR2DL, 1000

NKG2D, and on the target cell grid 500 ICAM-1, 1000 HLA, and 1000 MICA. The NK cell grid (left) and target cell grid (right) molecule and membrane

microdomain distributions from time step 0 and time step 10,000 are shown. The accumulation of NKG2D/MICA along the diagonals of the grid is an

artifact of the use of a square grid, which appears only when molecule movement is strongly directed by the integrated signal. MM, membrane micro-

domains.

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inhibition model, in the distance-based inhibition model simu-lations, the saturation effect is also observed in the highest num-bers of MICA. With a radius of 50 (Fig. 4E), in all molecule

number combinations except with zero HLA, the steady-state in-tegrated signals are zero because this radius enables very few KIRmolecules to inhibit all activating receptor signals in the contact

FIGURE 2. NK and target cell molecule placement inside and outside the initial contact area. A, The average numbers of molecules from five different

runs, in the initial contact area (gray lines) and in the ring surrounding the contact area (black lines). Averages are displayed by continuous lines; dashed

lines represent standard deviations. The initial molecule numbers in inhibitory synapse simulations were 500 LFA-1, 1000 KIR2DL, and 1000 NKG2D on

the NK cell grid and 500 ICAM-1, 1000 HLA, and 0 MICA on the target cell grid; in activating synapse simulations these numbers were the same except

for taking 1000 MICA on the target cell grid. B, The same simulation as in A, with the graphs showing molecule concentrations rather than numbers. C, A

simulation of the activating synapse, where no membrane microdomains were included.

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area. The same effects were seen for other initial KIR and NKG2Dnumbers and parameter values (Supplemental Figs. 1–4).The distance-based inhibition model with a high local inhibition

radius is not exactly the same as the quantity-based inhibitionmodel because in the former model, we assume that one inhibitoryreceptor can inhibit many activating receptors, whereas the lattermodel simply deducts the number of inhibitory bonds from that ofactivating bonds. The question may be raised whether the distance-based inhibition model is equivalent to the quantity-based in-hibition model, if we allow—in the latter model—each inhibitoryreceptor to inhibit several activating receptors. To check this, weran the quantity-based inhibition model while multiplying thenumber of bound inhibitory molecules by a factor representing theapproximate number of activating receptors that can be simul-taneously inhibited by one inhibitory receptor (Fig. 4F). Theresulting curves of the steady-state integrated signals did not re-semble the curves of the steady-state integrated signals obtained inthe distance-based inhibition model simulation, even when theaverage numbers of inhibited activating receptors per bound in-hibitory receptor were equivalent. An example equivalent to thedistance-based inhibition model, with radius = 5, is shown in Fig.4F, (compare with Fig. 4C). In Fig. 4F, the graphs become morelinear, rather than less linear, as MICA numbers are increased. Thesame differences hold for other molecule number and radiusvalues (data not shown). Therefore, our model predicts that thedistance-based inhibition model is qualitatively different from thequantity-based inhibition model and that signal integration dy-namics depend on local interactions between activating and in-hibitory signaling pathways and not just on the average numbersof each type of receptor in the whole contact area.To test experimentally whether inhibitory receptors act locally

within a given intercellular contact, we allowed NK cells to bestimulated by coverslips coated with strips of Abs against theactivating receptor NKG2D or inhibitory NKG2A/CD94, using anapproach recently described (35). The level of phosphorylated Vavwas then imaged and quantified (Fig. 5). It is interesting to notethat the cells tend to spread along the NKG2D strips but not alongthe NKG2A/CD94 strips (Fig. 5A, 5C). Additionally, in regionscontaining activating Ab anti-NKG2D only, clusters of phos-phorylated Vav are most common. These bright signaling clusters

are concentrated on the edge of the spreading cell, which is oftenwhere the anti-NKG2D regions border the anti-NKG2A/CD94regions (yellow ellipses in Fig. 5C), but are not seen deeper intothe NKG2A/CD94 strips. Most importantly, the overall intensityof phosphorylated Vav was significantly higher where there is anactivating ligand (Fig. 5F), indicating that phosphorylation istriggered only locally where activating receptors are bound.

Signal integration is insensitive to the inhibitory complexdissociation rate

The most critical parameters in the simulation are the moleculedissociation rates, as they determine the duration of receptor andligand binding and hence the amount of signal transduced. Wevaried the dissociation rate of each type of complex in the distance-based inhibition model simulations (Table II, Supplemental TableI) and recorded the steady-state integrated signals as a function ofthese rates (Fig. 4G). The results show a very fast nonlinear de-crease of the steady-state integrated signals as a function of theNKG2D–MICA Koff, as expected. Surprisingly, we observed onlya very slight increase of the signals as KIR–HLA Koff increases,and this only in the lower values of NKG2D–MICA Koff. Thereason for this low dependence may be that in the distance-basedinhibition model, each bound inhibitory molecule can inhibitseveral bound activating molecules, so each bound activating re-ceptor may be “covered” by more than one inhibitory receptor. Thedependence is negligible in the higher values of NKG2D–MICAKoff, because when the dissociation rate of activating molecules isvery high, they probably dissociate before supplying much signal;beyond a certain value of Koff, even the possibility of quick re-binding of the complex is not sufficient because receptors have tobe bound for some time to contribute significantly to the signal.The adhesion molecule dissociation rate also had no influence on

the total signal. The number of bound LFA-1–ICAM-1 is importantfor initial cell–cell binding (34), but because a small number ofbound adhesion molecules is sufficient for synapse stabilization,signaling continues even with a very high LFA-1–ICAM-1 Koff

value. The directed movement factors also influence synapse dy-namics, as expected; the results of our parameter value effectinvestigation are given in Supplemental Fig. 4.

The influence of Ly49–H-2 cis interactions on NKIS assembly

To investigate the influence of Ly49–H-2 cis interactions on NKISassembly, we added the cis interaction into the model by allowingneighboring Ly49 and MHC-I molecules to bind with the sameassociation and dissociation rates of the trans interaction andcompared the simulations that included the cis interaction withthose that did not. All these simulations were done with theparameters of the murine system (Table III, Supplemental TableII). As expected, there was about twice as much integrated acti-vating signal with cis interactions as without cis interactions (Fig.6A, 6B) because, in this case, fewer inhibitory receptors areavailable for trans binding, in both cSMAC and pSMAC (Fig. 6C,6D). However, the simulations again yield additional quantitativeinsights on the precise behavior of the signal with and without cisinteractions, as follows. Unexpectedly, the Smin threshold was notreached earlier while running the simulation with cis interactionsthan while running without cis interactions, and thus the dynamicsof molecule placement changes were similar in both cases (Fig.6E–P). However, we still see a small increase in the number ofNKG2D molecules in the cSMAC at the expense of the pSMACwhile running with cis interactions as opposed to without cisinteractions. This may be because with cis interactions, fewerLy49 molecules reach the cSMAC (Fig. 6I–L) and thus physicallyoccupy less space in the center and leave more room for NKG2D

FIGURE 3. A–D, Steady-state integrated signal as a function of HLA

and MICA molecule numbers. Quantity-based inhibition model. The av-

erage integrated signal in the last 1000 time steps is shown. Values of KIR

and NKG2D for each run series are shown within each graph. Points

represent the averages of five different runs and bars represent the corre-

sponding SDs. :, 0 MICA; n, 1000 MICA; ♦, 3000 MICA; d, 5000

MICA.

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molecules to enter. This small decrease in the number of Ly49molecules in cSMAC and their corresponding increase in thepSMAC most probably occurs because we assigned Ly49 mol-ecules in cis to diffuse more slowly toward the cSMAC. This ef-fect makes it important, in future experiments, to test criticallywhether cis interaction actually does slow down the movement ofLy49 molecules toward the synapse center or not and whether thishas a role in modifying NK cell inhibition.No significant difference was seen in the number of Rae mol-

ecules on the target cell between the two runs. The effects ofdirected movement factors were similar to those observed withoutcis interaction (Supplemental Figs. 5, 6). Thus, the overall effectof the cis interaction was not so much to accelerate synapse for-

mation but to increase the overall signal. That is, cis interactionscan change the quantitative aspects of signaling at the synapse, butthey do not qualitatively alter synapse dynamics, which depend onthe mechanisms for signal integration.

DiscussionUsing computer simulations, we investigated how the NK cellintegrates signals from activating and inhibitory receptors anddecides whether to form a cytolytic or non-cytolytic synapse (3,82–84). We have been able to simulate the experimentally ob-served structures of NK cell activating and inhibitory synapses byvarying the numbers of activating and inhibitory receptors andtheir ligands. Inhibitory NKIS images showed a uniform dis-

FIGURE 4. Steady-state integrated signal as a function of model parameters. Steady-state integrated signals are shown here for the distance-based

inhibition model. A–F, Effects of molecule numbers. The initial number of KIR was 1000 and of NKG2D was 2000. Otherwise, the same parameter values

as in Fig. 3 were used. :, 0 MICA; n, 1000 MICA; ♦, 3000 MICA;d, 5000 MICA. A–E, Runs with five different values of local inhibition radius (radius:

A, = 1; B, = 3; C, = 5; D, = 10; E, = 50). F, Example of a simulation in which the quantity-based inhibition model was used with a factor representing the

number of activating receptors that can be simultaneously inhibited by one inhibitory receptor. The factor was taken to be the ratio of inhibited activating

receptors per bound inhibitory receptor in the steady state and was calculated for each initial molecule number combination and each radius, based on the

distance-based model. In these simulations, the signal was calculated as: Signal = #_Activating_complexes 2 Factor 3 #_ Bound_inhibitory_complexes.

G–I, Effect of molecule dissociation rates. The points represent the averages of five different runs and the bars represent the standard deviations. The Koff of

KIR–HLAvaries between graphs as indicated. The Koff of NKG2D–MICA complexes changes from 0.01 to 1 on the x-axis. LFA-1–ICAM-1 Koff values are

denoted by symbols: n, 0.001; ♦, 0.01; d, 0.1. Initial numbers of all molecules were 1000, except those of LFA-1 and ICAM-1, which were 500 each.

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tribution of almost all molecules and microdomains, thoughLFA-1 was mostly found in the initial contact area because of ourchoice of initial conditions. In addition, the molecules that preferbeing associated with membrane microdomains were arranged insmall patches because of their entrance to microdomains, which isconsistent with the observation that molecules in the inhibitoryNKIS are arranged in clusters (73). Activating synapse images

showed activating receptors and their ligands and membranemicrodomain cluster formation in the initial contact area due tothe directed movement included in the model. The inhibitoryreceptors and ligands, which were not subject to directed move-ment, also moved slightly toward the initial contact area becauseof ligand binding and membrane microdomain preference. LFA-1moved away from the center due to membrane stress, combined

FIGURE 5. Phosphorylation of Vav on tyrosine

160 in NKL cells (A) stimulated by micropatterned

inhibitory and activating Abs. Anti-NKG2D coated

surfaces are designated by the red strips (B), anti-

NKG2A/anti-CD94 by the black strips (B), and

phospho-Vav by staining in green (C). The yellow

ellipses in C denote the enrichment of phospho-

Vav at the edge of the spreading cell, often corre-

lating with a border region between anti-NKG2D

and anti-NKG2A/CD94 strips. Scale bar, 10 mm.

The binary mask generated from B was used to

quantify separately the amounts of phospho-Vav on

the anti-NKG2D strips (D) and the anti-NKG2A/

CD94 strips (E). The plot F shows phospho-Vav

quantities (arbitrary units) for individual cells on

anti-NKG2D versus anti-NKG2A/anti-CD94 areas

(n = 21). The differences are statistically signifi-

cant: ***p , 0.001, Wilcoxon test.

Table II. Human NKIS simulation parameters and default values used in the simulations and references

Parameter Default Value References

LFA-1–ICAM-1 bond length (nm) 40 McCann et al., 2002 (13)KIR–HLA-C bond length (nm) 15 McCann et al., 2002 (13)NKG2D–MICA bond length (nm) 8 McCann et al., 2002 (13)LFA-1–ICAM-1 Kon (pts) 0.03 Labadia et al., 1998 (87); Tominaga et al., 1998 (88)

Labadia et al., 1998 (87); Tominaga et al., 1998 (88)LFA-1–ICAM-1 Koff (pts) 0.01KIR–HLA Kon (pts) 0.03 Maenaka et al., 2001 (89)KIR–HLA Koff (pts) 0.1 Maenaka et al., 2001 (89)NKG2D–MICA Kon (pts) 0.03 Assumed to be the same as that of KIR–HLANKG2D–MICA Koff (pts) 0.1 Assumed to be the same as that of KIR–HLALFA-1 movement probability (pts) 0.02 Dustin et al., 1996 (90)KIR movement probability (pts) 0.01 Assumed to be the same as the TCR diffusion rate;

Sloan-Lancaster et al., 1998 (91)MICA movement probability (pts) 0.01 Assumed to be the same as the TCR diffusion rate;

Sloan-Lancaster et al., 1998 (91)NKG2D movement probability (pts) 0.01 Assumed to be the same as the TCR diffusion rate;

Sloan-Lancaster et al., 1998 (91)ICAM-1 movement probability (pts) 0.38 von Essen et al., 2004 (92)HLA movement probability (pts) 0.1 Groves et al., 1996 (93)LFA-1 microdomain preference (nd) 1 Increases with activationKIR microdomain preference (nd) 1 Standeven et al., 2004 (85)NKG2D microdomain preference (nd) 5 McCann et al., 2002 (13)ICAM-1 microdomain preference (nd) 1 Not known to prefer microdomainsHLA microdomain preference (nd) 5 Rubio et al., 2004 (79)MICA microdomain preference (nd) 5 Cebo et al., 2006 (19);

Eleme et al., 2004 (18)Microdomain growth and diminishing rates in the NK and target cell

grids (pts)0.00005 Varied in the simulations

Microdomain movement probability in the NK and target cell grids (pts) 0.4 Varied in the simulationsAdhesion molecules dmf (nd) 1 Varied in the simulationsInhibitory receptor and ligand dmf (nd) 1 Varied in the simulationsActivating receptors and their ligands dmf (nd) 3 Varied in the simulationsMembrane microdomains dmf (nd) 6 Fujiwara et al., 2002 (50)Membrane stress factor (nd) 5 Varied in the simulationsCmin (nd) 5 Varied in the simulationsSmin (nd) 8 Varied in the simulationst 5 Varied in the simulationsPercentage of membrane in microdomains 35 According to the T cell synapse

Krogsgaard et al., 2005 (94)Maximum initial microdomain radius (positions) 10 Varied in the simulationsMicrodomain total size (positions) 50 Pike, 2003 (24)

The ranges explored and more detailed explanations for various parameters are given in Supplemental Table I.dmf, directed movement factor; nd, non-dimensional; pts, per time step.

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with the fast entrance of NKG2D into the center. We have ach-ieved these results assuming that only activating receptor andmembrane microdomain movement becomes directed toward thecenter of the contact area when the activating signal levels aresufficient. Whether inhibitory receptors exhibit directed move-ment is still controversial (85), but our simulations predict that ifsuch movement exists, it will help reduce and even stop the di-rected movement of all molecules and thus prevent activatingsynapse formation (Supplemental Figs. 2, 3).In the inhibitory synapse, molecule density graphs (Fig. 2)

showed increasing KIR, HLA, and ICAM-1 numbers in the initialcontact area because of their binding to their ligands, whichretained these molecules in the center of the synapse. This isconsistent with the observation that in the inhibitory synapse, SH2

domain-containing phosphatase 1 molecules that associate withinhibitory receptors are more concentrated in the initial contactarea than in the periphery (3, 16). In the activating synapse, thesegraphs show the expected: activating receptors, ligands, andmembrane microdomains move to the center, and LFA-1 mole-cules move to the surrounding ring. We observed a similar timepoint for stabilization of these patterns in the activating and theinhibitory synapses for almost all molecule types. The increase ofKIR and HLA numbers in the initial contact area in the beginningof the activating as well as in the inhibitory synapses may beneeded to achieve the balance of the two types of receptors. Thesepredictions now await experimental testing. Additionally, whenthere are no membrane microdomains in the simulation, the courseof synapse formation is much slower.

Table III. Murine NKIS simulation parameters and default values used in the simulations and references

ParameterDefaultValue References

Ly49–H-2 bond length (nm) 15 Dimasi et al., 2002 (95)NKG2D–Rae bond length (nm) 8 Assumed the same as NKG2D–ULBP; McCann et al., 2002 (13)Ly49–H-2 Kon (pts) 0.03 Natarajan et al., 1999 (96)Ly49–H-2 Koff (pts) 0.02 Natarajan et al., 1999 (96)NKG2D–Rae Kon (pts) 0.03 O’Callaghan et al., 2001 (97)NKG2D–Rae Koff (pts) 0.1 O’Callaghan et al., 2001 (97)Ly49 movement probability (pts) 0.067 Assumed the same as CD94/NKG2A

Borrego et al., 2006 (98)Rae movement probability (pts) 0.01 Assumed to be the same as the TCR diffusion rateNKG2D movement probability (pts) 0.01 Assumed to be the same as the TCR diffusion rateRae microdomain preference (nd) 5 Colocalizes with microdomains during the synapse, but less so than ULBP

The ranges explored and more detailed explanations for various parameters are given in Supplemental Table II.nd, non-dimensional; pts, per time step.

FIGURE 6. The effects of cis interactions on the NKIS, as shown in simulations using the default parameter values (Tables II, III, Supplemental Tables I,

II), in the initial contact area (gray lines) and the surrounding ring (black lines). A and B, Integrated signal without (A) and with (B) cis interaction. C and D,

The numbers of Ly49–MHC complexes bound in trans, without (C) and with (D) cis interaction. E–H, Activating molecule placements, without (E, G) and

with (F, H) cis interaction. I–L, Inhibitory molecule placements, without (I, K) and with (J, L) cis interaction.M–P, Adhesion molecule placements, without

(M, O) and with (N, P) cis interaction.

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Although it is established that inhibitory receptors act locallywithin a given intercellular contact, it is not known whether in-hibitory receptors act to inhibit all receptors within an individualsynapse or within an individual microcluster (containing hundreds ofproteins) or alternatively only on the few juxtaposed activatingreceptors. To understand how the NK cell integrates activatingsignals, which are inhibited by the inhibitory receptors, we im-plemented in the simulations either one of two different signal in-tegration models: the quantity-based inhibition model and thedistance-based inhibition model. These models were inspired bythe fact that both molecule numbers and their spatial distributions areimportant in IS, and we wanted to examine each factor separatelyto some extent. It is also possible to examine combinations ofthe quantity-based and the distance-based inhibition models, or tomake the inhibition decrease as the distance from the bound acti-vating molecules increase. However, these combined or interme-diate models would have resulted in the same observations as thoseof the distance-based inhibition model with some average localinhibition radius. Hence, we only focused on the two extreme cases.In the activating NKIS simulations using the quantity-based

inhibition model, the positive signals from bound activatingreceptors increase, whereas bound inhibitory receptor numbersundergo almost no change during the simulation and are relativelylow. Therefore, in activating synapses, the steady-state integratedsignals increase nonlinearly and stabilize at a certain time point.The slope of the increase and the maximal signal level depend onNK cell receptor and ligand numbers. In the inhibitory NKISsimulations using the quantity-based inhibition model, the steady-state integrated signal is negative, that is, the available inhibitionexceeds the activating signals, and the bound inhibitory receptornumber is low, as molecule movement in this case is affected onlyby movement probability. The steady-state total integrated signalsobserved in the quantity-based inhibition model simulations exhibitsaturation effects as a function of KIR and HLA numbers, whichare more significant in the lower MICA numbers—a qualitativeeffect that is not seen in the distance-based inhibition model.In the distance-based inhibition model, the signal’s decrease

with increasing HLA numbers, which is mostly nonlinear, be-comes much stronger as the local inhibition radius increases butincreases with MICA numbers (rather than decrease with highMICA numbers as in the quantity-based model). When the signalinhibition radius is small, the inhibition is more influenced by theprecise locations of bound molecules on the grids, but when theradius is very large, inhibition spreads over almost the whole grid,and the signal’s decrease with HLA numbers becomes faster thanlinear for all molecule numbers. A similar saturation effect wasobserved in measurements of NK cell cytotoxicity as a function ofHLA molecule numbers (73, 81). The strong experimentally ob-served saturation effect was more similar to the one observed hereunder the distance-based model than to the results from thequantity-based model. Thus, our simulations predict that signalintegration dynamics between activating and inhibitory signalingpathways depend on local interactions within the synapse and notjust on the average numbers of each type of receptor in the contactarea. Importantly, experiments with micropatterned substrateswith strips of activating ligands in between strips of inhibitoryligands indicate that activation of Vav, one of the most upstreamevents for integration of NK cell signals, is regulated locally (Fig.5). Moreover, it has recently been shown that KIR2DL2 micro-clusters that assemble at the synapse periphery upon inhibitorysignaling are associated with suppression of activating micro-clusters in the same area, but not microclusters that form in thecenter of the synapse, away from KIR2DL2 (86). Further ex-periments aimed at measuring NK cell signal levels during the

NKIS as a function of NK cell receptor and the ligand numberswill quantify, with the assistance of our simulations, how NK cellsintegrate the signals and their inhibition.The steady-state integrated signal showed a very fast nonlinear

decline with increasing NKG2D–MICA Koff for all values of KIR–HLA Koff. Adhesion molecule Koff had no influence on the totalsignals because of the small number of bound adhesion moleculesrequired for the NK cell receptors to start binding. Surprisingly,the signal’s dependence on the KIR–HLA Koff was small becausein the distance-based inhibition model, each bound inhibitory re-ceptor can inhibit several bound activating receptors.In the last series of simulations, our goal was to investigate the

influence of cis interactions in murine NK cells on the formationof the IS. Our results show that there is only a small influence ofcis interactions on the distribution of activation molecules in thesynapse—there is only a slight increase in the percentage of ac-tivation molecules in the center of the synapse. However, there isa significant increase in the level of integrated signal due to thedecrease in the level of inhibitory signal (because of the blockingof inhibition molecules by cis interactions without the possibilityof trans binding). It would be interesting to test experimentally theparameters of this interaction—such as the movement of ciscomplexes—and see which of these parameters has the mostsignificant effects on NKIS dynamics.In summary, we have presented here a computer simulation of

activating and inhibitory NK cell NKIS assembly and observed that1) the total signal is highly influenced by activating complexdissociation rates but not by adhesion and inhibitory complexdissociation rates; 2) the contribution of concerted motion ofreceptors in clusters (e.g., by their association with membranemicrodomains) significantly accelerates NKIS maturation; 3) thesaturation of signal levels, as a function of receptor and ligandnumbers, obtained when using the distance-based inhibition signalmodel was more similar to the experimentally observed behaviorthan when using the quantity-based inhibition signal model; and 4)in murine NKIS, the cis interaction between Ly49 and MHC-Imolecules on the target cell effectively decreases inhibition butonly slightly accelerates synapse formation.Probably the most significant and accessible finding is that our

model and data further indicate that inhibitory receptors act locally,that is, that every bound inhibitory receptor can only inhibit signalsfrom bound activating receptors within a certain radius around it, asopposed to balancing signals across the whole synapse. Although itis certainly already established that inhibitory receptors act locallywithin a given intercellular contact, it is not known whether in-hibitory receptors act to inhibit all receptors within an individualsynapse or within an individual microcluster (containing hundredsof proteins) or alternatively only on the few juxtaposed activatingreceptors. Our model directly addresses this important unknownand suggests that the data are consistent with inhibitory receptorsacting only at the level of immediately juxtaposed activatingreceptors. This is important in understanding how NK cell signalintegration works and may be tested in the near future by exploitingthe emerging superresolution imaging techniques.

AcknowledgmentsWe are indebted to Prof. Klas Karre and Dr. Mira Barda-Saad for helpful

discussions and critical reading of the manuscript, Hanna Edelman for help

in manuscript preparation, Dr. Neta Zuckerman and Helena Hazanov for

help with the figures, and Gunter Roth and Roland Brock for help in

developing the micropatterned surfaces.

DisclosuresThe authors have no financial conflicts of interest.

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