Clustering of membrane proteins in the pre-stimulation stage is required for signal transduction: a computer analysis

Signal Transduction 2007, 7, 329 – 339 H. Kobayashi et al. 329

Research Paper

Clustering of membrane proteins in the pre-stimulation stage isrequired for signal transduction: a computer analysis

Hiroshi Kobayashi1,*, Ryuzo Azuma2, and Akihiko Konagaya2,3

1 Graduate School of Pharmaceutical Sciences, Chiba University, Chiba, Japan2 RIKEN Genomic Sciences Center, Yokohama, Japan3 Department of Mathematics and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan

The physiological significance of membrane protein clustering for signal transduction wasexamined theoretically using a Monte Carlo computer simulation. Simulation results revealedthat pre-stimulation clustering of membrane proteins enhanced signal transduction. Membraneprotein clustering induced by the binding of external stimuli provided no kinetic advantage interms of formation rate or maximum quantity of active membrane receptor complexes. Thesedata suggested that membrane proteins associate weakly in the clustering areas of non-stimu-lated cells, and that their association is strengthened upon binding of extracellular stimuli tothe membrane receptor. Additionally, the number of cytosolic proteins recruited to membranereceptor complexes was not increased by the membrane complex clustering, except when cyto-solic signal proteins were localized to a narrow area such as a tunnel that ran from the mem-brane cluster to the nucleus. Simulations were carried out on a conventional personal computerunder Windows XP or 2000 operating systems. Since neither special computing hardware norspecial training is required, our simulation procedure could be easily adapted for kinetic anal-ysis of any signal transduction pathway.

Keywords: signal transduction / cluster formation / kinetic analysis / computer simulation /

Received: December 7, 2006; accepted: April 10, 2007

DOI 10.1002/sita.200600126

Supporting Information for this article is available from the author or on the WWW underhttp://www.wiley-vch.de/contents/jc_2270/2007/2006-00126_s.pdf

Introduction

Protein-protein interactions on the cell surface arethought to be crucial for many cell functions. Lipid raftsconsisting of glycosphingolipids, cholesterol, and mem-brane proteins have been observed on the cell surface [1].Other membrane protein interactions have beenreported to involve the F-actin skeleton [2]. Both path-ways are involved in the intracellular signal transductioninduced by external stimuli. Raft formation upon thepresentation of an external stimulus has been proposed

to stimulate cell signaling [3]. In contrast, clustering ofligand-receptor complexes was suggested to downregu-late signal transduction after addition of excess ligand [4,5]. The receptors were shown to already be associatedwith other membrane proteins in non-stimulated cells[6–9]. Thus, important issues still remain unclear. Whendoes clustering occur, before or after the binding of exter-nal stimuli? Why is membrane protein clusteringrequired for signal transduction?

Kinetic analysis could be a useful way to dissect theseproblems. In the case of simple reactions such as thoseinvolving one enzyme, quantitative examination is notdifficult. In contrast, tools for kinetic analysis of complexphenomena such as signal transduction systems are stillrelatively unavailable. One method to facilitate suchexamination would be calculation with the aid of thecomputer.

Correspondence: Hiroshi Kobayashi, Graduate School of Pharmaceuti-cal Sciences, Chiba University, 1-8-1, Inohana, Chuo-ku, Chiba 260-8675, JapanE-mail: [email protected]: +81 43 226-2892

i 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.signaltrans.com

330 H. Kobayashi et al. Signal Transduction 2007, 7, 329 –339

Two methods for computer simulation of biologicalphenomena have been developed to date. The first is thenumerical integration of differential equations. The sec-ond is the Monte Carlo simulation. The former methodcan only be applied to simulations of the average behav-ior of a large number of molecules. Furthermore, theclustering of membrane receptors is difficult to simulateusing this technique. In contrast, the latter method cansimulate both single molecule dynamics and the averagebehavior of a small number of molecules. Monte Carlosimulations can also address the cell-to-cell populationheterogeneity of molecules in addition to time-depend-ent fluctuations involving noise.

In the present study, we have developed a Monte Carlocomputer simulation program for kinetic analysis ofligand-receptor complex formation on membranes,which is the first step of signal transduction. Calcula-tions can be performed on a conventional personal com-puter with a CPU running at approximately 2.5 GHzunder the Windows XP or 2000 operating systems, andeach simulation takes approximately 2 h. The presentstudy revealed that pre-stimulation clustering of mem-brane receptors and other proteins such as adaptor orlinker proteins was important for signal transduction,but membrane protein clustering after binding of exter-nal stimuli offered no kinetic advantage.

Materials and methods

In the present study, we simulated the following threereactions.

L + R Ee LR, LR + A Ee LRA and LRA + S Ee LRAS,

where L, R, A and S are an extracellular ligand, a mem-brane receptor, a membrane protein such as an adaptoror a linker, and a cytosolic signal transfer protein, respec-tively. LR, LRA and LRAS are binary, ternary and quater-nary complexes, respectively. In the present simulation,we assumed a simplified model in which the cellular sur-face was present as a 2-dimensional plane between 3-dimensional extracellular and cytosolic simulationspaces, as illustrated in Fig. 1A. The cell surface(7206720 nm2), extracellular (7206720636.0 nm3), andcytosolic (7206720672.0 nm3) spaces were divided into360,000 (600660061), 10,800,000 (6006600630), and21,600,000 (6006600660) subspaces, respectively.

Real-type pseudo uniform random numbers N withrange (0 f N a 1) were generated as previously reported[10]. Each molecule was assumed to undergo randommotion with a diffusion rate t. We also assumed that t

had a normal probability distribution with mean V = 0and variance rv = t2

X, where tX stands for the average dif-fusion rate and X stands for a molecular species. To savecalculation time, unsigned integer-type random num-bers were used instead of real-type ones, as shown inTable 1. The average value of the diffusion rate (tX) was13.1. A molecule having t moved to its neighboring sub-space when s a t, where s was a uniform random number(0 f s a 100). Molecules whose t = 0 continuallyremained in the same subspace. Each molecule had itsown movement direction (positive or negative on eachaxis), and moved to the opposite side based on periodicboundary conditions when it reached the simulation boxboundary, except for at the membrane surface and itsopposite boundary, at which molecules were reflected inthe mirror-direction. The diffusion rates and directionsfor 1% of all molecules were updated at every step, andthese molecules were randomly selected. t was used asthe diffusion rate of L and S, and 0.1 t was used for R andA under standard simulation conditions. The distribu-tion of t and membrane protein trajectories are shownin Fig. 1B to 1D.

Two molecules of different species may bind to eachother when the two molecules occupy the same subspace.The binding probability was defined to be exp(–DE1/RT),where DE1, R and T are the activation energy, the gas con-stant and the absolute temperature, respectively. In ourMonte Carlo procedure, the binding of two moleculeswas accepted when a uniform random number f

(0 f f a1) was less than exp(–DE1/RT). Correspondingly,the bound complex could dissociate with the dissocia-tion probability exp(–DE2/RT). Based on these definitions,the dissociation constant Kd was calculated to beexp(–(DE2–DE1)/RT). The fixed value of 1.12 kilojou-les N mole–1 was used for DE1 in all reactions under stand-ard conditions.


Table 1. List of integral random numbers.

Used for Range Equations

Diffusion rate (t) 0–99 absolute value of (S/6-100),

where S =X12

i¼1

(Ni6100)*

Selection of movingstep (s)

0–99 N6100*

Pseudo uniform random numbers N from 0 to (1-1610–15) withrange (0 f N a 1) were generated as described in the Materialsand methods.* The integer parts of values obtained using the indicated equa-

tions were used.

Signal Transduction 2007, 7, 329 – 339 Computer analysis of membrane protein clustering 331

On the cell surface, clustering areas were assumed forboth membrane and cytosolic proteins as illustrated inFig. 1A. We carried out simulations using various modelswith different spatial localizations of proteins and com-plexes as listed in Table 2. The trapping energy of theclustering areas for these proteins was defined to be

25.8 kilojoules N mole–1. This meant that the probabilityof molecules escaping the clustering area was 0.01%. Toavoid bias, candidate molecules for all trials were ran-domly selected. All other molecules were reflected in themirror-direction at the boundaries of the clusteringareas. All molecules were initially distributed within


Figure 1. Cell model for simulation, diffusion rates and movement of membrane proteins. (A) The cell model used in the presentsimulations is illustrated. For details see text. (B) Distribution of diffusion rates (t). (C) Movement of R was plotted for 16105 steps atintervals of 10 steps. The diffusion rate of R was t. The number of subspaces was 30006300061. (D) Movement of R was plottedfor 16105 steps at intervals of 10 steps. The diffusion rate of R was 0.1t. The number of subspaces was 600660061.


their own compartments with equal probability. Inmodel 1, over 90% of membrane proteins were clusteredwithin 26106 steps under standard conditions (Fig. 2A).

The source code of the computing program was imple-mented using the C-language with Visual Studio C++.net(Microsoft Co.), and the program was run on a personalcomputer under Windows XP or 2000 (Microsoft Co.).Source codes are attached as supporting information.

Results

Validation of our simulation models and methodsTo validate our methods, the dissociation constant (Kd) ofthe following equation was first calculated and thencompared with the theoretical constants.

A + B Ee AB

A single subspace was postulated to be a cubic box witha volume of 1.73 (1.23) nm3 as described above. When onestep was defined as 0.25 microsecond and the diffusionrate was t, the diffusion coefficient of the molecules wascalculated to be 9.2 lm2 N second–1 (Table 3). As shown inTable 4, the simulated dissociation constants were inagreement with the theoretical values. When DE1 was setto 6.72 kilojoule N mole–1, the simulated dissociation con-stants were again in agreement with the theoretical val-ues (Table 4).

The numbers of membrane proteins R and A were setto 100 and 100, respectively, and the cell surface

(7206720 nm2) was divided into 360,000 (600660061)subspaces as shown in Fig 1. Over 90% of membrane pro-teins were clustered within 26106 steps in model 1(Fig. 2A) under the standard conditions described inMethods. The diffusion coefficient of the membrane pro-teins was approximately 0.17 lm2 N second–1 (Table 3).These data suggested that our procedure was adequate toachieve our purpose.

Simulation IThe numbers of L, R, and A were set to 200, 100, and 100,respectively, and three clustering models (1, 2 and 3,


Table 2. Clustering models for simulation.

Models L R A S LR LRA LRAS

1 o,F m,T m,T – m,T m,T –2 o,F m,F m,F – m,F m,T –3 o,F m,F m,F – m,F m,F –4 o,F m,T m,T c,F m,T m,T m,T5 o,F m,F m,F c,F m,F m,T m,T6 o,F m,F m,F c,F m,F m,F m,F7 o,F m,T m,T c,T m,T m,T m,T8 o,F m,F m,F c,T m,F m,T m,T9 o,F m,T – – m,T – –10 o,F m,F – – m,T – –11 o,F m,F – – m,F – –

Models L R A S LR LRA LRS

12 o,F m,T – c,F m,T – m,T13 o,F m,F – c,F m,T – m,T14 o,F m,F – c,F m,F – m,F

Location: o, extracellular space; m, membrane; c, cytosol.Moving area: T, within the clustering area; F, whole area.–: absent.

Table 3. Diffusion coefficients.

Calculationsteps

Diffusionrates

Diffusion coefficients(lm2 N second–1)*

3D 2D

1000 t 8.99 € 1.06 8.80 € 1.022000 t 9.42 € 0.62 8.52 € 0.97

60000 0.1t 0.191 € 0.017 0.176 € 0.015100000 0.1t 0.194 € 0.015 0.168 € 0.010200000 0.01t 0.0538 € 0.0032 0.0509 € 0.0062300000 0.01t 0.0521 € 0.0053 0.0426 € 0.0021

Numbers of subspaces for extracellular space and cell surfacewere set at 60066006600 and 600660061, respectively.Number of molecules was set at 100. One calculation step waspostulated to be 0.25 microsecond.* Diffusion coefficients in 3- (3D) and 2- (2D) dimensional spaces

were calculated. Average values and standard deviations of 6data are represented.



Figure 2. Simulation of the formation of LRA complexes in the absence of S. The quantities of L, R and A were set to 200, 100 and100, respectively. The number of S was zero. The numbers of the subspaces for the membrane proteins (R and A) and L were600660061 and 6006600630, respectively. The diffusion rates were set as described in the Methods. (A) Positions of R and A atthe 26106th step in model 1 are depicted. Symbols: blue, R; red, A; large circle, clustered R and A. (B) to (T) The dissociation con-stants of LR (Kd1) and LRA (Kd2) are indicated in the figure. The ligand L was added immediately before the 26106th (B to P) or56106th (Q to T) step, as indicated with arrows. Molecules were not allowed to move outside the clustering area (J). DE1 was set to1.12 (B to J and P to T), 0.14 (K and L) and 6.72 (M to O) kilojoule N mole–1. The number of subspaces in the clustering area was 565(A to P), 463 (Q and R) or 263 (S and T). Clustering models: black, model 1; blue, model 2; red, model 3.


Table 2) were used without including the cytosolic pro-tein S. In model 1, R and A were gathered in 9 clusteringareas before the addition of L, and each area contained565 subspaces. Since over 90% of membrane proteinswere clustered within 26106 steps under these condi-tions as described above, the ligand L was added immedi-ately before the 26106th step (arrows in Fig. 2). After theaddition of L, LR and LRA complexes were generated andkept within the clustering areas. In model 2, only LRAcomplex was assumed to localize to the clustering areas;LRA was formed at random positions on the cell surfaceand then clustered. In model 3, neither protein nor com-plex was assumed to cluster.

Figure 2 shows the time evolution of LRA complexesnormalized by the total number of receptors R with sev-eral combinations of dissociation constants for LR (Kd1)and LRA (Kd2). The difference between these three modelswas small when Kd1 and Kd2 were set to 1.0 and 10.0 lmo-le N l–1 (Fig. 2B and C). Next, Kd1 and Kd2 were set to 100and 1000 lmole N l–1 (Fig. 2D and E), respectively. The for-mation speed of LRA complexes and its saturation levelwere higher in model 1 than models 2 or 3. There was nosignificant difference between models 2 and 3. In thesesimulations, the concentration of L was calculated to be17.8 lmole N l–1. The surface density of R and A were each193 molecules/lm2, which corresponded to approxi-mately 60,000 molecules/cell since the surface area of aspherical cell with diameter of 10 lm is 314 lm2.

When Kd1 and Kd2 were set to 10.0 and 100, respec-tively, the amount of LRA at equilibrium was higher inmodel 1 than models 2 or 3 (Fig. 2F). A similar result wasobserved when Kd1 and Kd2 were set to 100 and 10.0,

respectively (Fig. 2G). Rapid formation of LRA complexeswas observed in model 1 when Kd1 and Kd2 were set to100 and 1000 or 1000 and 100, respectively, but no com-plexes were formed in models 2 or 3 (Fig. 2H and I).

Similar results were obtained with decreased (Fig. 2Kand L) and increased (Fig. 2M to O) activation energies,although the complex formation rates varied. When mol-ecules were not allowed to move outside the clusteringarea, similar results were obtained at Kd values of100 lmole N l–1 (Fig. 2J).

In our simulation procedure, the number of moleculesoccupying the same subspace was not restricted. However,it is unlikely that multiple molecules of the same specieswould be present in the same subspace, because the totalnumber of molecules is much smaller than the number ofsubspaces. In fact, the pattern of results was essentiallyunchanged when only one molecule of the same specieswas allowed to occupy each subspace (Fig. 2P). In this sim-ulation, each clustering area contained 25 subspaces.Even when the number of subspaces was decreased to 12in order to increase the likelihood of R and A colocaliza-tion, similar results were still obtained (Fig. 2Q and R).Since membrane protein clustering took more stepsunder these conditions, L was now added immediatelybefore the 56106th step. The rate and maximum quantityof LRA formation were not significantly affected by thepresence of two molecules of the same species in the samesubspace (Fig. 2S and T), probably because the rate of LRAformation mainly depends on the ligand diffusion ratewhen membrane proteins are clustered.

In the above simulations, the concentration of L was17.8 lmole N l–1. However, much lower ligand concentra-


Table 4. Kd at equilibrium stage.

Number ofsubspaces

–DG/RT Dissociation constant (Kd)

Theoretical Simulated* Ratio**

DE1=1.12 kilojoule N mole–1

20062006200 8.0 3.35610–4 3.23610–4 € 0.15610–4 0.9620062006200 10.0 4.54610–5 4.36610–5 € 0.16610–5 0.9620062006200 12.0 6.14610–6 5.92610–6 € 0.18610–6 0.9660066006600 12.0 6.14610–6 6.10610–6 € 0.17610–6 0.99

DE1=6.72 kilojoule N mole–1

20062006200 8.0 3.35610–4 3.35610–4 € 0.16610–4 1.0020062006200 10.0 4.54610–5 4.58610–5 € 0.14610–5 1.0120062006200 12.0 6.14610–6 6.19610–6 € 0.40610–6 1.0160066006600 12.0 6.14610–6 6.19610–6 € 0.33610–6 1.01

Average 0.98

Number of AB was set at 600.* Average values and standard deviations of 5 data.

** simulated value/theoretical value.


tions have been shown to trigger intracellular signaltransduction in experimental studies. Here, when wedecreased the simulated ligand concentration 8-fold, thepattern of results remained unchanged, although the sat-uration level and the rate of complex formation were low(Fig. 3A to C). Approximately 15% of receptors were occu-pied by ligands when L, Kd1 and Kd2 were set to 0.22 lmo-

le N l–1, 100 lmole N l–1, and 100 lmole N l–1, respectively(Fig. 3D). Next, the concentrations of R and A weredecreased 8-fold at a ligand concentration of 2.2 lmo-le N l–1. In this case, 66106 steps were required for mem-brane protein clustering, and more than 90% of mem-brane proteins were clustered (Fig. 3I). Approximatelyhalf of the receptors were occupied by ligands in model


Figure 3. Simulation of the formation of LRA complexes at a low concentration of L and at a low membrane protein diffusion rate inthe absence of S. The quantity of L was set to 100 (A to F and I) or 200 (G, H and J). R and A were set to 100 (A to D, G, H and J) or50 (E, F and I). The number of S was zero. The numbers of the subspaces for the membrane proteins were 600660061 (A to D, G,H and J) and 12006120061 (E, F and I). The numbers of the subspaces for L were 60066006120 (A to C), 600660061200 (D),120061200630 (E, F and I) and 6006600630 (G, H and J). The diffusion rate of L was set to t. The diffusion rates of R and Awere 0.1t (A to F and I) and 0.01t (G, H and J). The dissociation constants of LR (Kd1) and LRA (Kd2) are indicated in the figure. Theligand L was added immediately before the 26106th (A to D) or 66106th (E to H) step, as indicated with arrows. Clustering models:black, model 1; blue, model 2; red, model 3. Positions of R and A at 66106th step in model 1 are depicted (I and J). Symbols: blue, R;red, A; large circle, clustered R and A.


1, whereas LRA complex formation rarely occurred inmodels 2 and 3 (Fig. 3E).

The membrane molecule diffusion rate was postulatedto be 10% of the extracellular ligand diffusion rate in theabove simulations. However, the same pattern of resultswas obtained even when the membrane molecule diffu-sion rate was set to 1% of the extracellular ligand diffu-sion rate; pre-clustering still enhanced LRA complex for-mation (Fig. 3F to H). Under these conditions, the diffu-sion coefficient was calculated to be 0.047 lm2 N second–1.In this case, clustering of more than 90% of the mem-brane proteins required 66106 steps (Fig. 3J), so L wasadded immediately before the 66106th step.

Simulation IIThe binding of the cytosolic signal transfer protein S tothe membrane receptor complex LRA was simulated.When membrane receptor complexes were pre-clustered,the recruitment of S in model 4 was as low as in models 5and 6 (Fig. 4A to C). Notably, no LRAS complexes wereformed when all Kd values were 1000 lmole N l–1 (Fig. 4C).When S was localized to its respective clustering areas(Fig. 1A), its binding increased dramatically in model 7(Fig. 4D). The LRAS quantity was low at Kd values of 100and 1000 lmole N l–1 in model 8, which assumed that Swas localized to its clustering areas and LRA clusteringoccurred after ternary complex formation (Fig. 4E and F).

Simulation IIIIn the absence of A, the formation profile of LR com-plexes was identical for models 9 to 11; no advantage ofpre-clustering was observed (Fig. 4G to I). Theoreticallythe same results would be obtained when R binds Atightly, since R and A would always be present as the RAcomplex. To investigate the recruitment of S under theseconditions, in which the amounts of the membrane com-plex are the same in all models, the following reactionswere simulated.

L + R Ee LR, LR + S Ee LRS.

The dissociation constant of the latter reaction wasdenoted by Kd4. No significant difference in the recruit-ment of S was observed between models 12 to 14 (Fig. 4J).In the cell, after binding to the membrane complex, S isactivated and then released to the cytosol. Therefore, therate of recruitment is more important than the steady-state level of the ternary LRS complex. When the simu-lated diffusion rate of S was decreased 10-fold (the diffu-sion coefficient was 0.17 lm2 N second–1), the recruitmentof S in model 12 was less than that in model 14 (Fig. 4K).Next, the concentration of S was decreased 2-fold while

keeping the reduced diffusion rate. The difference in therate of ternary complex formation between model 12and 14 was increased (Fig, 4L).

Simulation IVFinally, the dissociation of the receptor complex LRA afterthe removal of L from the extracellular space was exam-


Figure 4. Simulation of the formation of LRAS, LR and LRS. Thequantities of L and R were 200 and 100, respectively. A was 100(A to F) and zero (G to L). The quantity of S was set to 100 (A toF), zero (G to I), 200 (J and K) or 100 (L). The diffusion rates ofL, R and A were set as described in the Methods. The diffusionrate of S was t (A to F and J) or 0.1t (K and L). The numbers ofthe subspaces for ligands and membrane proteins were thesame as those of Fig. 2, and the number for S was6006600660. Dissociation constants Kd1 (LR), Kd2 (LRA), Kd3

(LRAS) and Kd4 (LRS) are described in the figure. The ligandwas added immediately before the 26106th step (arrow). In thesimulation of the LRS formation, A was used as S and A locatedin the cytosolic space in the simulation program. Clustering mod-els of A to C: black, model 4; blue, model 5; red, model 6. D to F:black, model 7; blue, model 8. G to I: black, model 9; blue,model 10; red, model 11. J to L: black, model 12; blue, model13; red, model 14.


ined. Ligands were allowed to pass through the bounda-ries of the simulation box, except on the cell surface, andwere removed when outside the box past the 1.06107thstep. When Kd1 and Kd2were both 10 lmole N l–1, no signifi-cant decrease in receptor complex concentration wasobserved (Fig. 5A). In contrast, complexes dissociated at aslow rate when Kd1 and Kd2 were both 100 lmole N l–1

(Fig. 5A). The dissociation rate increased when Kd1 and Kd2

were both 1000 lmole N l–1 (Fig. 5A). Decreasing the con-centration of A, which increased the LR complex concen-tration, did not accelerate dissociation after ligand clear-ance (data not shown). After ligand removal, the dissocia-tion of the receptor complex (LR) was observed when Kd1

was 1.00 lmole N l–1 (Fig. 5B).

Discussion

In the present simulation, we postulated that one sub-space and one calculation step were 1.73 (1.23) nm3 and0.25 microsecond, respectively. When the diffusion ratesof the 3-dimensional spaces (extracellular and cytosolicspaces) and the 2-dimensional cell surface were set to t

and 0.1t under standard conditions, their diffusion coef-ficients were 9.2 and 0.17 lm2 N second–1, respectively.When the diffusion rate of the membrane proteins wasset to be 0.01t, the diffusion coefficient was 0.047

lm2 N second–1. These values are close to experimentaldata previously reported in prokaryotes [11] and eukar-yotes [12, 13]. When DE1 values were set to 0.14 (Fig. 2K),1.12 (Fig. 2C) and 6.72 (Fig. 2M) kilojoule N mole–1, theapparent rate constants of ligand binding in model 1were calculated to be 2.56105, 2.06105, and 1.06105

mole–1 N l N second–1, respectively. These values were simi-lar to those obtained experimentally [14–16].

Receptor complex dissociation constants and mem-brane protein velocities may be different in differentcells. The reaction speed of complex formation may alsobe different for different receptors. Therefore, we useddifferent sets of Kd values, membrane protein diffusionrates, and reaction speeds for complex formation. In allcases, our simulations clearly demonstrated that cluster-ing of LR or LRA after the binding of external stimuli pro-vided no kinetic advantage for signal transduction, andthat pre-clustering of membrane receptors and associ-ated proteins increased the formation rate and quantityof LRA ternary complexes upon ligand addition.

When R and A were clustered, LRA complex formationwas generally enhanced because local concentrations ofR and A were high. However, this effect became negli-gible when the dissociation constant was low; when Kd1

and Kd2 were 1.00 or 10.0 lmole N l–1, no significantadvantage of pre-clustering was observed. Under thesame conditions, no dissociation of complexes afterligand release was observed for at least 1.56107 steps(3.75 seconds); no shutdown of signal transfer occurred,although activation was achieved within 26106 steps(0.5 seconds). Therefore, these conditions were physiolog-ically unrealistic, since signal shutdown is an importantand inherent cellular process. However, significant shut-down was observed when Kd1 and Kd2 were set to100 lmole N l–1 (Fig. 5A). Under these conditions, mem-brane protein clustering before stimulation was shownto be essential for cell activation (Fig. 2D).

It has been shown that ligand concentrations of lessthan 1 lmole N l–1 are enough to initiate intracellular sig-nal transduction in many cases, and that cells can be acti-vated when only some receptors are occupied by ligands.For example, HeLa cells were found to contain approxi-mately 50.000 EGF receptors, but half of the cells wereactivated when only about 300 ligands were bound to thecell surface [17]. In our simulation, when the ligand con-centration was set to 0.22 lmole N l–1 and Kd1 and Kd2

were 100 lmole N l–1, approximately 15% of the receptorswere bound by ligands (Fig. 3D). Therefore, cells can beactivated with less than 1 lmole N l–1 of ligand even if Kd1

and Kd2 are 100 lmole N l–1.It has been proposed that rafts are formed by the move-

ment of receptor ligand complexes to regions containing


Figure 5. Simulation of the dissociation of the receptor complex.The quantities of L and R were 200 and 100, respectively. S wasset to zero. A was set to 100 (A) or zero (B). The numbers of thesubspaces and diffusion rates were the same as those of Fig. 2.Dissociation constants are described in the figure. The ligandwas added immediately before the 26106th step (down arrow).After the 16107th step (up arrow), the ligand was removed, asdescribed in the text. Models used were 1 (A) or 9 (B).


high amounts of lipids, such as glycosphingolipids andcholesterol [3]. It is now generally understood that thesedetergent-resistant rafts are formed after ligand binding.However, it remains unclear whether the membranecomponents are located at random positions or whetherthey cluster before cell activation. In the latter case, clus-tered complexes would be sensitive to the detergentbecause of weak binding forces. The present simulationresults lead us to predict that membrane proteins such asreceptors, linkers, and adaptors are already clusteredwithin microdomains of the cell surface by weak bindingforces, and that complexes of L, R and A with strong bind-ing forces are formed after the cells are activated. Clus-tered complexes of membrane proteins have beendetected in non-stimulated cells [6–9], supporting oursimulation results.

Time-dependent fluctuation was always small inmodel 1 (Fig. 2). No significant difference in fluctuationswas observed between models 2 and 3, making it lesslikely that signal transduction was stabilized by LRA com-plex clustering after formation.

The clustering of membrane proteins did not enhancethe binding of cytosolic proteins. Since many signaltransduction pathways involve signal transfer from thecell membrane to the nucleus, the binding of cytosolicsignal proteins to membrane receptor complexes is likelyan essential step. One possible strategy to overcome thedisadvantage posed by clustering could be movement ofcytosolic signal proteins from the cell surface to thenucleus through a special route constructed within thecellular matrix. When cytosolic proteins were localizedto the small channel shown in Fig 1A, their binding tomembrane protein complexes increased dramatically.Similar channels have been suggested experimentally[18].

Our simulation results led us to another predictionthat signal transduction could be kinetically downregu-lated by receptor complex clustering when cytosolic pro-teins are not clustered and present at a relatively low con-centration. These results may provide theoretical supportto previous experimental data showing that excessligand application decreases cell activation [4, 5]. Similarresults might also be obtained when R tightly binds othermembrane proteins such as adaptors or linkers. Signaltransduction might also be downregulated through thebinding of an inhibitory protein, as reported previously[4, 5].

Our simulations were carried out using a conventionalpersonal computer with a CPU running at 2.6 GHz underWindows XP or 2000 operating systems. The calculationof 16107 steps took approximately two hours. Our simu-lation program could readily be implemented for simula-

tions of other biological phenomena, and does notrequire special computing hardware or special training.

We greatly appreciate the valuable suggestions and commentsof Marc Daeron, Hannes Stockinger and Yasushi Sako.

References

[1] Horejsi, V. (2003) The roles of membrane microdomains(rafts) in T cell activation. Immunol. Rev. 191: 148–164.

[2] Luna, E.J., Hitt, A.L. (1992) Cytoskeleton-plasma mem-brane interactions. Science 258: 955 –964.

[3] Kusumi, A., Koyama-Honda, I., Suzuki, K. (2004) Molecu-lar dynamics and interactions for creation of stimula-tion-induced stabilized rafts from small unstable rafts.Traffic 5: 213–230.

[4] Gimborn, K., Lessmann, E., Kuppig, S., Krystal, G., Huber,M. (2005) SHIP down-regulates FcepsilonR1-induceddegranulation at supraoptimal IgE or antigen levels. J.Immunol. 174: 507–516.

[5] Lesourne, R., Fridman, W.H., Daeron, M. (2005) Dynamicinteractions of Fc gamma receptor IIB with filamin-bound SHIP1 amplify filamentous actin-dependent nega-tive regulation of Fc epsilon receptor I signaling. J. Immu-nol. 174: 1365–1373.

[6] Varma, R., Mayor, S. (1998) GPI-anchored proteins areorganized in submicron domains at the cell surface.Nature 394: 798-801.

[7] Zacharias, D.A., Violin, J.D., Newton, A.C., Tsien, R.Y.(2002) Partitioning of lipid-modified monomeric GFPsinto membrane microdomains of live cells. Science 296:913–916.

[8] Sharma, P., Varma, R., Sarasij, R.C., Ira, Gousset, K., Krish-namoorthy, G.G., Rao, M., Mayor, S. (2004) Nanoscaleorganization of multiple GPI-anchored proteins in livingcell membranes. Cell 116: 577 –589.

[9] Leksa, V., Godar, S., Schiller, H.B., Fuertbauer, E., Muham-mad, A., Slezakova, K., Horejsi, V., Steinlein, P., Weidle,U.H., Binder, B.R., Stockinger, H. (2005) TGF-beta-inducedapoptosis in endothelial cells mediated by M6P/IGFII-Rand mini-plasminogen. J. Cell Sci. 118: 4577–4586.

[10] Matsumoto, M., Nishimura, T. (1998) Mersenne twister: A623-dimensionally equidistributed uniform pseudo-ran-dom number generator. ACM Transactions on Modelingand Computer Simulation 8: 3 –30.

[11] Mullineaux, C.W., Nenninger, A., Ray, N., Robinson, C.(2006) Diffusion of green fluorescent protein in threecell environments in Escherichia coli. J. Bacteriol. 188:3442–3448.

[12] Jacobson, K., O'Dell, D., August, J.T. (1984) Lateral diffu-sion of an 80,000-dalton glycoprotein in the plasmamembrane of murine fibroblasts: relationships to cellstructure and function. J. Cell Biol. 99: 1624–1633.



[13] Zhang, F., Crise, B., Su, B., Hou, Y., Rose, J.K., Bothwell, A.,Jacobson, K. (1991) Lateral diffusion of membrane-span-ning and glycosylphosphatidylinositol-linked proteins:toward establishing rules governing the lateral mobilityof membrane proteins. J. Cell Biol. 115: 75–84.

[14] Andrews, A.L., Holloway, J.W., Puddicombe, S.M., Hol-gate, S.T., Davies, D.E. (2002) Kinetic analysis of the inter-leukin-13 receptor complex. J. Biol. Chem. 277: 46073 –46078.

[15] Felder, S., LaVin, J., Ullrich, A., Schlessinger, J. (1992)Kinetics of binding, endocytosis, and recycling of EGFreceptor mutants. J. Cell Biol. 117: 203–212.

[16] Wilkinson, J.C., Stein, R.A., Guyer, C.A., Beechem, J.M.,Staros, J.V. (2001) Real-time kinetics of ligand/cell surfacereceptor interactions in living cells: binding of epider-mal growth factor to the epidermal growth factor recep-tor. Biochemistry 40: 10230–10242.

[17] Uyemura, T., Takagi, H., Yanagida, T., Sako, Y. (2005) Sin-gle-molecule analysis of epidermal growth factor signal-ing that leads to ultrasensitive calcium response. Biophys.J. 88: 3720–3730.

[18] Janmey, P.A. (1998) The cytoskeleton and cell signaling:component localization and mechanical coupling. Phys-iol. Rev. 78: 763 –781.


Correction

Signal Transduction 2007, 7, 329–339 DOI 10.1002/sita.200600126

Clustering of membrane proteins in the pre-stimulation stageis required for signal transduction: a computer analysis

Unfortunately, the legend to Figure 3 is incorrect in two places.

Line 5:Incorrect: 120061200630 (E, F and I) and 6006600630 (G, H and J).Correct: 120061200630 (E and I) and 6006600630 (F to H and J).

Line 6:Incorrect: were 0.1 t (A to F and I) and 0.01 t (G, H and J).Correct: were 0.1 t (A to E and I) and 0.01 t (F to H and J).

We apologise for these errors which were missed by the authors in the proof stage.

Documents

Clustering of membrane proteins in the pre-stimulation stage is required for signal transduction: a computer analysis