Multiscale Modeling of Complex Formation and CD80 Depletion during Immune Synapse Development

Abstract

The mechanisms that discriminate self- and foreign antigen before T cell activation are unresolved. As part of the immune system’s adaptive response to specific infections or neoplasms, antigen-presenting cells (APC) and effector T cells form transcellular molecular complexes. CTLA4 expression on regulatory or effector T cells reduces T cell activation. The CTLA4 transendocytosis hypothesis proposes that CTLA4 depletes CD80 and CD86 proteins from the APC membrane, rendering the APC incapable of activating T cells. We developed a multiscale spatiotemporal model for the interaction of a T cell and APC. Formation of the immune complex between T cell and APC starts with formation of the transmembrane complexes between the major histocompatibility complex and the T cell receptor (Signal 1) and between CD80 or CD86 and CD28 (Signal 2) at the opposing membrane surfaces of the interacting cells. By 0.01 s after contact simulation, an increasing concentration gradient of the free membrane proteins develops between the opposing surfaces and spherical parts of each cell’s membrane, reaching a maximum at ∼30 s. Over several hours, diffusion across the gradient equalizes the free protein concentrations. During this phase, CTLA4 surface expression and its complexation with CD80/CD86 cause internalization and degradation of CD80/CD86. The simulation results show reasonable agreement with reported experimental data and indicate that key molecular processes take place over a very broad timescale, covering five orders of magnitude. Besides the fast complexation reactions, diffusion-limited processes, especially lateral diffusion in cell membranes and geometrical constraints, considerably slow down evolution of the synapse. Our results are consistent with the CTLA4 transendocytosis hypothesis and suggest the importance of lateral diffusion of surface proteins in contributing to a gradual increase in Signal 1 and Signal 2.

Introduction

The mechanisms involved in T cell activation and regulation are important for understanding immune homeostasis and for guiding the therapeutic modulation of immunity. After detecting foreign molecular structures or antigens that signal infection or malignancy, the immune system has the challenge of generating a specific antibody and cellular response of an appropriate intensity. If the immune system underreacts, the host may succumb to the foreign invasion. Overreaction may damage or kill the host, or precipitate autoimmune disease. A key aspect of this process is the discrimination of abundant self-antigens from rare foreign antigens. The interaction of T cell subtypes and antigen-presenting cells (APC), which form the immunological synapse, are critical for generating a specific response.

Activation of a naïve T cell by an APC requires independent signals that contribute to the specificity and appropriateness of the response. The primary signal, Signal 1, involves the recognition of a specific peptide antigen on the APC major histocompatibility protein (MHC) by the T cell receptor (TCR). This transcellular interaction alone is inadequate to activate the T cell. At a minimum, activation of the T cell also requires Signal 2, a costimulatory interaction between the receptor CD28 molecule on the T cell and the CD80 or CD86 ligand expressed on the surface of the APC.

Much of the work on elucidating mechanisms for discrimination of self- and foreign- antigens during immunological synapse formation have focused on Signal 1. Several mechanisms including kinetic proofreading (based on differing affinity) and complex microaggregation (reviewed in van der Merwe and Dushek (1)) have been proposed. Recent work on Signal 2 regulation by T lymphocyte antigen-4 (CTLA4) implicates mechanisms outside of Signal 1 in determining the discrimination of self- and foreign antigens (2).

CTLA4 is a key regulator of the immune system set point on the foreign and autoimmune response spectrum (3). Animals lacking CTLA4 die prematurely from T cell proliferation and autoimmunity (4, 5, 6). This negative regulatory immune response component has been successfully exploited therapeutically. Antibodies to CTLA4 that reduce its suppressive function (i.e., abatacept) are efficacious in the treatment of malignant melanoma (7, 8). Fusion antibodies that mimic the function of CTLA4 (i.e., ipilimumab) benefit patients with the autoimmune disease rheumatoid arthritis (9).

T cell membrane expression of CTLA4, which can be regulated, interferes with T cell activation and amplification. The mechanism responsible for CTLA4 suppression of T cell responses is controversial and several hypotheses for the suppressive effects of CTLA4 have been proposed (2, 10, 11, 12, 13, 14, 15). These hypotheses can be divided into two general categories: 1) cell intrinsic, in which the suppressive response is caused by activation of CTLA4 that leads to an inhibitory signaling cascade in the T cell; and 2) cell extrinsic, in which the effects of CTLA4 result from its action on other cells, such as the APC cells. One intriguing variant of the cell extrinsic hypothesis, proposed by Walker and Sansom (2) and Qureshi et al. (11), is that CTLA4 binds and removes the CD80/CD86 proteins from the APC membrane and degrades them in the T cell, rendering the APC unable to generate Signal 2 and activate T cells. This trans-endocytosis hypothesis has the advantage of providing a single mechanism to explain the suppressive role of CTLA4 when expressed on different types of T cells, both the effector T cells that are activated by APCs (T_eff) and the regulatory T_reg cells that suppress this process. CTLA4 expression on either cell is proposed to deplete APC CD80/CD86, thereby reducing T cell activation.

To further our understanding of the mechanisms underlying immune synapse formation leading to T cell activation, we study a model based on trans-endocytosis and compare this to models based on other hypotheses for the inhibitory mechanism of surface CTLA4. We are interested in elucidating the overall timescale of these processes and the role of short- and longer timescale events in the generation of the immune synapse. Ordinary differential equation modeling previously used to study T cell-APC interaction (15) cannot resolve the effects of these events occurring at widely different timescales or the role of local spatial and geometric constraints. To provide a framework to study processes not accessible experimentally, in particular lateral diffusion in the membrane, and the role of events occurring over different timescales, we develop a multiscale spatial model using the Simmune platform (16), a user-friendly program providing numerical solution of a set of partial differential equations. As we show in our model simulations, immediately after interaction of a T cell and APC, spatial inhomogeneity develops in the concentration of interacting proteins due to the much slower rate of lateral diffusion in the membrane in comparison with that of intracellular diffusion.

Materials and Methods

Model assumptions and parameter selection

We specify the geometry of the interacting cells, the location of each component (membrane associated or intracellular), the diffusion coefficients and the initial concentrations of each component, and the reactions in which the components are involved. The available values and sources of model parameters are listed in Table S1 in the Supporting Material. The interacting T cell and APC are modeled by two spheres (see Fig. 1 A). At the opposing surfaces of the interacting cells, the membranes are flat circles.

Figure 1.

Interacting T cell and AP cell simulations. (A) The T cell (blue) and APC (green) are represented by spheres of radius 3.31 ± 10⁻⁶ m (17). The contact of the cells is a flat circle of radius 2.45 × 10⁻⁶ m. Concentrations are calculated along the horizontal plane through the centers of both cells. Each of (B)–(D) contains first an illustration of certain part of the intercept between the horizontal plane and the interacting cells where the calculated concentrations are color-coded, and then a curve of the concentration along the considered part of the intercept. (B) MHC:TCR complex concentrations along the 4.9 × 10⁻⁶ m long diameter of the opposing membranes (indicated by white line) after 300 s of simulation after cell contact. The upper limit of the scale bar is X = 162.5 molecules/μ². The figure shows twice the concentration of the transmembrane complex. (C) MHC concentration along the intercept of the horizontal plane and the APC membrane (indicated by white line). Calculated concentration is plotted along an ∼11 × 10⁻⁶ m long segment of the intercept (starting from the midpoint of the flat segment to the farthest point of the spherical part of the cell membrane) after 300 s of simulation after cell contact. The vertical dashes at 2.45 × 10⁻⁶ m are at the intercept of the flat and spherical membrane segments. The upper limit of the scale bar is X = 200 molecules/μ². (D) Intracellular CTLA4 concentrations in the T cell after 0.01 s contact with APC. CTLA4 concentration is plotted along the white diameter line in the figure starting at the point of APC contact. The upper limit of the scale bar is X = 10⁻⁵ molecules/μ². To see this figure in color, go online.

Model construction

The model includes three receptors of the T cell, which are TCR, CD28, and CTLA4; and two proteins of the APC, which are MHC and CD80. In the model, we represent the functionally related proteins CD80 and CD86 as the single species CD80. Table S2 lists the components of the model.

The characteristics and binding site localization data of each component in the model are shown in Table S2. CTLA4 has two locations—intracellular (CTLA4) and membrane-associated (CTLA4M). The model represents five groups of processes: 1) Signal 1 or MHC:TCR complex formation; 2) Signal 2 or CD80:CD28 complex formation; 3) CTLA4 membrane expression from membrane fusion of intracellular vesicles; 4) CTLA4 internalization; and 5) CD80:CTLA4 complex formation and internalization. We include in the model complexes to account for known regulatory or degradation effects. For example, the effect of Signal 1 on increasing membrane CTLA4 levels is modeled via an interaction complex. Alternative mechanisms, such as intracellular signaling, could account for this regulation. The use of complexes was chosen for simplicity within this modeling framework. The respective reactions of each group are listed in Table 1.

Table 1.

Reactions during the Interaction of T Cell and AP Cell

Group	Reaction	Types of Reactions a: association; d: dissociation; t: transformation	Parameters
			[ka] = (Ms)−1
			[kd] = 1/s
			[kt] = 1/s
SIGNAL 1	$\left[MHC\right]+\left[TCR\right]\leftrightarrow \left[MHC:TCR\right]$	Trans-a/d (1,1)	$\begin{array}{l}{k}_a={10}^5\\ k_d=0.5\end{array}$
SIGNAL 2	$\left[CD80\right]+\left[CD28\right]\leftrightarrow \left[CD80:CD28\right]$	Trans-a/d (1,2)	$\begin{array}{l}{k}_a=5\times {10}^5\\ k_d=2\end{array}$
CTLA4 expression when Signal 1 is present	$\begin{array}{l}\left[MHC:TCR\right]+\left[CTLA4\right]\to \left[MHC:TCR\right]+\left[CTLA4\right]\\ \\ \left[MHC:TCR\right]:\left[CTLA4\right]+\lfloor \overline{\overline{CTLA4M}}\rfloor \to \end{array}$	Trans-a (1–3)	$k_a^{\text{tr}}=9\times {10}^4$a
	$\left[MHC:TCR\right]:\left[\overline{\overline{CTLA4M}}\right]:\left[CTLA4\right]\to$	Cis-a (2,3)	$k_a^{\text{cis}}={10}^7$b
	$\left[MHC:TCR\right]:\left[CTLA4M\right]:\left[\overline{\overline{CTLA4}}\right]\to$	t	$k_t=100$b
	$\left[MHC:TCR\right]:\left[CTLA4M\right]+\left[\overline{\overline{CTLA4}}\right]$	Trans-d (1–3)	$k_d=100$b
	$\left[MHC:TCR\right]:\left[CTLA4M\right]\to$
	$\left[MHC:TCR\right]+\left[CTLA4M\right]$	Cis-d (2,3)	$k_d=100$b
CTLA4 expression when Signal 2 is present	$\begin{array}{l}\left[CD80:CD28\right]+\left[CTLA4\right]\to \left[CD80:CD28\right]:\left[CTLA4\right]\\ \\ \end{array}$	Trans-a (1,1)	$k_{\text{a}}^{\text{tr}}=9\times {10}^4$a
	$\left[CD80:CD28\right]:\left[CTLA4\right]+\lfloor \overline{\overline{CTLA4M}}\rfloor \to$	Cis-a (3,3)	$k_a^{\text{cis}}={10}^7$b
	$\left[CD80:CD28\right]:\left[\overline{\overline{CTLA4M}}\right]:\left[CTLA4\right]\to$	t	$k_t=100$b
	$\begin{array}{l}\left[CD80:CD28\right]:\left[CTLA4M\right]:\left[\overline{\overline{CTLA4}}\right]\to \\ \left[CD80:CD28\right]:\left[CTLA4M\right]+\left[\overline{\overline{CTLA4}}\right]\end{array}$	Trans-d (1,1)	$k_d=100$b
	$\begin{array}{l}\left[CD80:CD28\right]:\left[CTLA4M\right]\to \\ \left[CD80:CD28\right]+\left[CTLA4M\right]\end{array}$	Cis-d (3,3)	$k_d=100$b
CTLA4 internalization	$\begin{array}{l}\left[CTLA4M\right]+\lfloor \overline{\overline{CTLA4}}\rfloor \to \\ \left[CTLA4M\right]:\lfloor \overline{\overline{CTLA4}}\rfloor \to \left[\overline{\overline{CTLA4M}}\right]:\left[CTLA4\right]\to \\ \left[\overline{\overline{CTLA4M}}\right]+\left[CTLA4\right]\end{array}$	Trans-a (1,1)	$k_a^{\text{tr}}=9\times {10}^4$a
		t	$k_t=100$b$k_d=100$b
		Trans-d (1,1)
CD80:CTLA4 internalization	$\left[CD80\right]+\left[CTLA4M\right]\leftrightarrow \left[CD80:CTLA4M\right]$	Trans-a/d (1,2)	$k_a^{\text{tr}}=3\times {10}^4$a$k_d=0.6$
	$\left[CD80:CTLA4M\right]+\left[\overline{\overline{CTLA4}}\right]\to$
	$\left[CD80:CTLA4M\right]:\left[\overline{\overline{CTLA4}}\right]\to$	Trans-a (1,1)	$k_a^{\text{tr}}=9\times {10}^4$a
	$\left[\overline{\overline{CD80}}:\overline{\overline{CTLA4M}}\right]:\left[CTLA4\right]\to$	t	$k_t=100$b
	$\left[\overline{\overline{CD80}}:\overline{\overline{CTLA4M}}\right]+\left[CTLA4\right]$	Trans-d (1,1)	$k_d=100$b
	$\left[\overline{\overline{CD80}}:\overline{\overline{CTLA4M}}\right]\to \left[\overline{\overline{CD80}}\right]+\left[\overline{\overline{CTLA4M}}\right]$	Trans-d (1,2)	$k_d=100$b

Kinetic parameters are listed in Table S1, except as noted below. The association/dissociation is called Cis-a/Cis-d, respectively, if the reacting components are located in the membrane of the same cell; otherwise it is Trans.

^aDefault values in Simmune.

^bValues chosen much higher than the respective default values in Simmune (see explanation in the text).

Because the Simmune modeling framework does not have a direct way to represent the translocation of components between intracellular and membrane-associated compartments, this type of process is modeled through the use of virtual intermediates. For example, MHC:TCR formation (i.e., Signal 1) promotes translocation of intracellular CTLA4 from the intracellular vesicle (CTLA4) to the membrane (CTLA4M). To achieve this, we include virtual intermediate states of CTLA4 and CTLA4M. Thus, MHC:TCR stimulation of CTLA4 moving from the intracellular to the membrane compartment to become CTLA4M is modeled as follows: 1) intracellular CTLA4 binds to the membrane-associated two-component complex (MHC:TCR) to form MHC:TCR:CTLA4; 2) a virtual membrane-associated component $\overline{\overline{CTLA4M}}$ laterally binds to the previously formed three-component complex; 3) $\overline{\overline{CTLA4M}}$ and CTLA4 in this four-component complex each change their state (transformation in Simmune terminology) to become CTLA4M and $\overline{\overline{CTLA4}}$); 4) the virtual intermediate $\overline{\overline{CTLA4}}$ dissociates from the complex; and 5) CTLA4M dissociates from the complex leaving MHC:TCR in the membrane and, in effect, intracellular CTLA4 being transformed into membrane-associated CTLA4M (see also Fig. S15, which illustrates the use of virtual complexes).

When Signal 2 is present (i.e., CD28:CD80 is formed), a similar set of virtual intermediate processes also results in transforming intracellular CTLA4 into membrane-associated CTLA4M. CD80 also has a virtual intermediate state to allow modeling of internalization and degradation. The effects of these virtual components and reactions on the simulations were minimized by using arbitrarily high values for the relevant rate constants and initial values (see values marked by “b” and “#” in Tables 1 and S2, respectively). In other words, these virtual intermediates, which are used merely as a bookkeeping approach to allow proteins to move into different compartments, transform instantaneously in the model.

The modeling of CTLA4 internalization and CD80:CTLA4 internalization requires three and five processes, respectively (see details in Table 1). We classify the various processes as association (a), dissociation (d), or transformation (t), and indicate the binding sites involved (Table 1). Finally, the binding is called cis if the reacting components are in the membrane of the same cell, otherwise it is trans binding. Table 1 also contains the reaction constants of the reactions.

Results and Discussion

As described in the Materials and Methods, we develop a model of T cell-APC interaction based on the CTLA4 transendocytosis hypothesis. The model consists of 23 coupled chemical reactions, six components, and 13 complexes. The model is used to study the spatiotemporal change of components and complexes involved in this interaction. The model is parameterized using values obtained from the literature and no optimization of parameters is performed. Based on the quantitative results of the model (see Figs. 1, 2, 3, 4, 5 and S1–S13), we present here a qualitative discussion of the level and localization of the Signal 1 and Signal 2 complexes, as well as CTLA4 and CD80 during the initial seconds of interaction and extending to many hours. The model simulations are compared to experimental data. Most of our simulations are based on modeling the APC interaction with the T effector (T_eff) cell, which, for simplicity, we refer to as “T cell”. The mechanism for induction of CTLA4 expression differs in the T_reg cell; we also present the modeling and results of simulation of the interaction of T_reg cells and APC in a separate section.

Figure 2.

Spatial and temporal variations in the amount of membrane component MHC and transmembrane complex MHC:TCR during APC-T cell interaction. (A) Spatial-temporal change of MHC concentration along the entire membrane (corresponding to Fig. 1C). Each curve represents a different time after initial APC-T cell interaction: red (0.01 s), blue (0.1 s), green (1 s), black (30 s), purple (300 s), light blue (1500 s), and yellow (35,000 s). (B) Change over time in total uncomplexed MHC to 300 s. (C) Change over time in total uncomplexed MHC to 35,000 s. (Inset) Change during the first second. (D) Spatial-temporal change of MHC:TCR concentration, with color codes as in (A), along the diameter of the opposing cells (corresponding to Fig. 1B). (E) Change over time of total MHC:TCR complex to 300 s. (F) Change over time of total MHC:TCR complex to 35,000 s. (Inset) Change during the first second. To see this figure in color, go online.

Figure 3.

Calculated spatial and temporal variations in the amount of membrane components CD28 and CD80. (A) Spatial change of uncomplexed CD28 concentration along the membrane as illustrated in Fig. 1C. (Curves) Red (0.01 s), blue (0.1 s), green (1 s), black (30 s), purple (300 s), light blue (1500 s), and yellow (35,000 s). (B) Uncomplexed CD28 levels from 0 to 300 s. (C) Uncomplexed CD28 levels from 0 to 35,000 s. (Inset) Levels in the first second. (D) Spatial change of uncomplexed CD80 concentration along the membrane, with the curve colors indicating the same time points as in (A). (E) Uncomplexed CD80 from 0 to 300 s. (F) Uncomplexed CD80 from 0 to 10,000 s. (Green markers) Experimentally assayed levels of CD86 reported in Qureshi et al. (11). To see this figure in color, go online.

Figure 4.

Calculated spatial and temporal variations in the amount of transmembrane complex CTLA4: $\overline{\overline{CTLA4M}}$ :MHC:TCR and expressed CTLA4. (A) Spatial change of CTLA4: $\overline{\overline{CTLA4M}}$ :MHC:TCR concentration along the white line shown in Fig. 1B. (B and C) Time dependence of the amount of CTLA4: $\overline{\overline{CTLA4M}}$ :MHC:TCR from 0 to 300 s and from 0 to 35,000 s, respectively. (D) Spatial change of CTLA4M concentration along the white line shown in Fig. 1 C. (E and F) Time dependence of the amount of CTLA4M from 0 to 300 s and from 0 to 35,000 s, respectively. In (A) and (D), each curve belongs to different time with the following color code: red (0.01 s), blue (0.1 s), green (1 s), black (30 s), purple (300 s), light blue (1500 s), and yellow (35,000 s). (Insets in C and F show the time dependence of the amount of CTLA4: $\overline{\overline{CTLA4M}}$ :MHC:TCR and CTLA4M in the first second, respectively.) To see this figure in color, go online.

Figure 5.

Calculated spatial and temporal variations in the amount of transmembrane complex CD80:CTLA4M and degraded CD80. (A) Spatial change of CD80:CTLA4M concentration along the white line shown in Fig. 1B. (B and C) Time dependence of the amount of CD80:CTLA4M from 0 to 300 s and from 0 to 35,000 s, respectively. (D) Spatial change of $\overline{\overline{CD80}}$ (i.e., degraded CD80) concentration along the white line shown in Fig. 1C. (E and F) Time dependence of the amount of $\overline{\overline{CD80}}$ from 0 to 300 s and from 0 to 35,000 s, respectively. In Fig. 5, A and D, each curve belongs to different time with the following color code: red (0.01 s), blue (0.1 s), green (1 s), black (30 s), purple (300 s), light blue (1500 s), and yellow (35,000 s). (Insets in C and F show the time dependence of the amount of CD80:CTLA4M and $\overline{\overline{CD80}}$ in the first second, respectively.) To see this figure in color, go online.

Signal 1

As a consequence of MHC interaction with TCR (Signal 1), the simulation shows that the concentration of MHC decreases at the flat, circular contact region of the cells until ∼30 s (Fig. 2 A). After 30 s, the decrease of MHC concentration in the spherical part of the APC becomes apparent. This is the result of MHC diffusion from the spherical part of the APC membrane toward the flat part opposed with the T cell, and after several hours the concentrations are equalized everywhere in the membrane. The total amount of uncomplexed MHC (Fig. 2, B and C) decreases continuously; after a rapid decrease in the first second, the rate of decrease slows down considerably. Finally, beginning at ∼14,000 s, the amount of MHC levels off.

Experimental studies of T cell-APC activation have shown that these cells can remain in contact for periods exceeding 1 h (17). In simulations over this longer timescale, lateral diffusion provides an important contribution to the levels of MHC and TCR in the opposing membrane regions. As a consequence of the lateral diffusion of MHC, the content of total (complexed and uncomplexed) MHC increases by 56% in this flat contact region. The spatial and temporal variation in the amount of TCR is very similar for MHC (see Fig. S11); its total content in the flat contact region increases by 86%. The transmembrane complex, MHC:TCR, forms only in contact regions. Its concentration increases throughout the simulation, while nearly leveling off after 12,000 s at ∼175 molecules/μm² (Fig. 2, D–F). Within the 30–300 s time interval, the complex concentration is maximal at the edge of the contact region; otherwise, at any other time, it is nearly constant along the contact region. The total amount of the complex increases rapidly in the first s and then it slowly increases up to a level of ∼12,000 molecules (Fig. 2, E and F).

Signal 2

Signal 2 results from the formation of the transmembrane complex CD28:CD80. Fig. 3, A and D shows the change in the concentration of CD28 and CD80 while these components interact in the flat circular sections of the cell membranes. As shown in Fig. 3 A, uncomplexed CD28 concentration in the T cell membrane contacting the APC decreases rapidly, reaching a minimum at 0.1 s. By 30 s, uncomplexed CD28 has rapidly increased in the opposed membrane region, nearly regaining its initial concentration. The increase in uncomplexed CD28 in the opposed T cell membrane is achieved much more rapidly than that of MHC in the APC (see Fig. 2 A) and TCR in the T cell (see Fig. S11). The increase in MHC and TCR are both due to lateral diffusion of the free proteins in the unopposed membrane regions. All three proteins have the same diffusion parameters in the model, and the behavior of CD28 results from a different mechanism. As shown below, the rapid increase in CD28 in the opposed membrane is accompanied by a similarly rapid membrane translocation of CTLA4, complexing of this CTLA4M with CD80, and internalization and degradation of CD80. Because the association rate of CD80 to CTLA4M is approximately five times higher than that of to CD28 (see Table 1), and with the appearance of CTLA4M, the amount of uncomplexed CD28 starts to increase in the opposed membrane.

The spatial and temporal behavior of uncomplexed CD80 is qualitatively different from that of CD28. Because its initial concentration is higher than CD28, it is reduced by <50% in the opposed membrane region during the first second of complex formation with CD28 (Fig. 3 D). Its level in this membrane region falls to nearly zero by 30 s, due to rapid recruitment of CTLA4 to the membrane (see Fig. 4) and complex formation of the resulting CTLA4M with CD80. The effects of diffusion of uncomplexed CD80 from the unopposed membrane into the opposed membrane can be seen by 30 s, in the slight reduction in CD80 concentration in the unopposed membrane near the opposed membrane segment (Fig. 3 D). This diffusion leads over time to progress in reduction of uncomplexed CD80 at increasing distances from the opposed segment. However, unlike MHC (Fig. 2 A) and TCR (Fig. S11), the uncomplexed CD80 in the opposed membrane remains low due to complexation with CD28 and CTLA4M as well as CD80 internalization and degradation. The time dependence of the amount of CD28:CD80 (Fig. S4, B and C) is similar to the inverse of the time dependence of CD28.

Shown in Fig. 3 F is the comparison of experimental data reported for the levels of membrane GFP-labeled CD86 (11) to the simulated levels of CD80 in the model. In the model, CD80 represents both CD80 and CD86, which are not distinguished. The number of the CD80 molecules determined from model simulation and the measured fluorescence intensity of membrane-associated GFP labeled CD86 are proportional. In Fig. 3 F, we choose a proportionality constant of 9.08 × 10³ [number of CD80 per GFP intensity of CD86]. It is important to note that the measured and calculated half time (40.5 ± 7.5 and 33.3 min, respectively), which are obtained without using a proportionality constant, are in good agreement.

CTLA4 expression

In T_eff, either Signal 1 or Signal 2 complex formation leads to translocation of intracellular CTLA4 to the membrane. As described in Materials and Methods, intracellular CTLA4 is represented in the model by CTLA4, membrane CTLA4 is represented in the model by CTLA4M, and the transformation of CTLA4 into CTLA4M (that results from Signal 1 or 2 complexes) is modeled through the use of $\overline{\overline{CTLA4}}$ and $\overline{\overline{CTLA4M}}$ virtual intermediates. When Signal 1 or Signal 2 is present, complex CTLA4: $\overline{\overline{CTLA4M}}$ :MHC:TCR or CTLA4: $\overline{\overline{CTLA4M}}$ :CD28:CD80 can form, respectively, and rapidly lead to CTLA4M expression. Fig. 4 shows the spatial and temporal changes in CTLA4: $\overline{\overline{CTLA4M}}$ :MHC:TCR transmembrane complex and CTLA4M, respectively.

CD80 degradation

The formation of the CD80:CTLA4M complex initiates the internalization and then the degradation of CD80. Fig. 5, A–C show the spatial and temporal variation of the complex CD80:CTLA4M. The amount of the complex reaches its maximum at 0.7 s, while at 10.7 s the amount of the complex reaches 1/10th of its maximum. The amount of the degraded CD80 (represented by $\overline{\overline{CD80}}$) continuously increases in time (Fig. 5, D–F). Initially the amount of $\overline{\overline{CD80}}$ slightly increases while at ∼0.09 s, the increase becomes much faster (see inset to Fig. 5 F) and by 14,000 s, 90% of the CD80 degrades (Fig. 5 F).

On the maximum concentrations at the edge of the contact region

In many cases, within the 30–300 s time interval, we see a maximum of the concentration close to the edge of the flat region, i.e., a ring of high concentration of different compounds appears for a short time next to the edge of the flat contact region (e.g., see Figs. 2 D and 4 A). The primary reason for this is the formation of transmembrane complexes (MHC:TCR and CD28:CD80) at the flat region just after the T cell-APC contact is established. As a consequence, the concentration of either one or both of the components of these complexes decreases in the flat region, resulting in a concentration gradient at the edge of the flat region. (A concentration decrease for CD28 does not develop because it is released from the complex before CD80 degradation.) The concentration gradient becomes particularly high within the 30–300 s time interval and, consequently, the diffusion of the components becomes fastest toward the flat region of cell to cell contact. Once the components reach the contact region, complexes form rapidly near the edge of this region, resulting in a local maximum of the concentration of the transmembrane complexes (MHC:TCR and CD28:CD80; see Figs. 2 D, S4 A, S16 A, and S17 A). Next higher-order complexes start to form from these two-component complexes. Because the concentration of the two-component complexes is highest close to the edge of the flat region, the concentration of the higher-order complexes also shows a maximum at the same place and same time interval (see Figs. 4 A, S1 A, S2 A, and S12 A). Finally, from the high order complexes, lower order complexes are forming. Because the concentration of the high order complexes is highest close to the edge of the flat region, the concentration of the forming lower order complexes also shows a maximum at the same place and same time interval (see Figs. 4 D, S3 A, S8 A, S9 A, and S13 A). Note that the higher order complexes usually contain a virtual component and thus the formation/dissociation constants of these higher order complexes were chosen to be much higher than the default values. The ring of maximum concentration of the above mentioned low- and high ordered complexes almost disappears by 1500 s as a consequence of the diffusion of these complexes toward the center of the flat contact region.

Notably, experimental results similar to the ring formation we observe in model simulations were reported by Grakoui et al. (18). Thirty seconds after the immune synapse formation, they observed MHC-peptide engagement by the TCR only in the outer, closely apposed ring of the junction. Over the next 300 s, the engaged MHC-peptides moved to the center of the junction to form a central cluster.

On the effect of increasing initial concentration of CD28

Our model can make predictions that can be tested experimentally. Here, as an example, we calculate the effect of increasing initial concentration of CD28 on the strength of Signal 2, CD80 reduction, and CTLA4 expression. With increasing initial concentration of CD28, the overall amount of CD28:CD80 complex (i.e., the strength of Signal 2) increases (see Fig. S14 A). The character of the time dependence of the amount of CD28:CD80 remains the same, but the maximum became sharper and is reached earlier with increasing initial CD28 concentration. Fig. S14 B shows qualitatively similar CD80 reduction processes at different initial CD28 concentrations. Initially, CD80 reduces faster with increasing initial CD28 concentration. Similar to the time dependence of the amount of CD28:CD80 with increasing initial concentration of CD28, the overall amount of CTLA4M and the amount of CTLA4M complexes increases (see Fig. S14, C and D). The character of the time dependence of the amount of CTLA4M and the amount of CTLA4M complexes remains the same; however, the maximum became sharper and reached earlier with increasing initial CD28 concentration.

T_eff versus T_reg cell

T cells involved in AP cell regulation can be distinguished as cell classes that activate the immune response (effector, or T_eff) and cells that suppress the immune response (T_reg). During experimental studies of T_eff-AP cell interaction, membrane CTLA4 is detected when either Signal 1 or Signal 2 is present (12, 13, 14). In contrast, in the case of the T_reg cell-AP cell interaction, membrane CTLA4 is expressed only when both Signal 1 and Signal 2 are present (19, 20, 21). In the previous sections, the T cell model represents the T_eff. We now explore these differences in the requirements for CTLA4 membrane expression in T_eff- and T_reg-AP cell interactions.

After the interaction of AP cells with either T_eff or T_reg cells, the degradation of CD80 eliminates Signal 2. In the case of the T_eff cell-AP cell interaction, CTLA4 remains expressed because Signal 1 remains present. In contrast, in the case of T_reg cell-AP cell interaction, with the disappearance of Signal 2, CTLA4 ceases to be expressed. We model T_reg cell AP cell interaction by modifying the model of T cell-AP cell interaction (see Table S3). In the case of T_reg cell-AP cell interaction, CTLA4 surface expression is modeled by several processes as follows: 1) association of the two-component complexes originated from Signal 1 and Signal 2 to a four-component complex; 2) the intracellular CTLA4 binds to the membrane-associated four-component complex; 3) a virtual membrane-associated component called $\overline{\overline{CTLA4M}}$ laterally binds to the previously formed five-component complex; 4) in the newly formed six-component complex, a change of states (transformation) takes place (i.e., $\overline{\overline{CTLA4M}}$ becomes CTLA4M and CTLA4 becomes $\overline{\overline{CTLA4}}$, a virtual intracellular component); and 5) from the resulting six-component complex, $\overline{\overline{CTLA4}}$ first dissociates and then 6) CTLA4M dissociates. In summary, these six processes result in the appearance of a CTLA4 in the membrane and the disappearance of a CTLA4 from the intracellular space.

Both T_reg and T_eff models provide similar time courses for APC CD80 reduction before 0.07 s, while they differ after this time (Fig. 6). The fast decrease of CD80 in the initial 0.07 s can be attributed to the formation of the CD28:CD80 complex (i.e., Signal 2), which forms five times faster than Signal 1. In the case of T_eff–APC interaction, Signal 2 alone is sufficient for the expression of membrane CTLA4 and consequently to the formation of CTLA4M:CD80 complexes. Thus, the level of CD80 keeps decreasing after 0.07 s (see inset, Fig. 6 B, red curve). On the other hand, in the case of T_reg-APC interaction, Signal 2 alone is not sufficient for the expression of membrane CTLA4. Thus, the level of CD80 remains constant until 1 s (see inset, Fig. 6 B, blue curve). Then TCR:MHC complexes start to form (i.e., Signal 1 and Signal 2 become simultaneously present), triggering CTLA4 membrane expression and, with the formation of CTLA4M:CD80 complexes, CD80 starts to decline again. Note that the CD80 decline is faster in the case of T_eff-APC interaction because Signal 1 and Signal 2 separately trigger CTLA4 membrane expression, while in the case of T_reg-APC interaction only Signal 1 and Signal 2 together trigger CTLA4 membrane expression. In the case of T_eff-APC and T_reg-APC interaction, the CD80 level at the opposing membrane surfaces become low at 7.5 and 32 s, respectively. From this point, the lateral diffusion of CD80 from the spherical part of the APC membrane to the flat part of the membrane defines the rate of CD80 degradation. Fig. 6 C shows CTLA4 surface expression in the case of T_eff-APC (red curve) and T_reg-APC interaction (blue curve). In the case of T_eff-APC interaction, the amount of TCR:MHC complex (i.e., Signal 1), and consequently, the amount of CTLA4M, are increasing and leveling off. However, in the case of T_reg-APC interaction with CD80 degradation, Signal 2 becomes weaker and from 1200 s the level of CTLA4M declines.

Figure 6.

Calculated CD80 depletion and CTLA4 expression in the case of T_eff cell and T_reg cell. (A) Time dependence of the amount of CD80 to 140 s. (B) Time dependence of the amount of CD80 to 35,000 s. (Inset) Change during the first second. (C) Time dependence of the amount of CTLA4M. (Red curve) T_eff cell model, (blue dashed line) T_reg cell model. To see this figure in color, go online.

Overall, the simulation of the T_reg-APC interaction shows a gradual and profound depletion of CD80 in the APC membrane, dependent on both Signal 1 and Signal 2, so that the APC is then rendered incapable of activating T_eff cells. The differing kinetics of the two models accommodate their differing roles. In the case of T_reg, this cell can only contribute to inactivation of a specific APC and the longer time involved in this process contributes to its specificity. In the case of the T_eff-APC interaction, a race is established between CD80 depletion and loss of Signal 2 and the activation and proliferation of the T_eff. The more rapid induction of CTLA4 and depletion of CD80 seen in the T_eff-APC simulation provides a rapid negative feedback so that a strong Signal 1 must be present for T cell activation to occur. Thus, low affinity self-antigens, for example, would be less likely to activate the T_eff before the Signal 2 CD80 component is depleted and the possibility for activation is eliminated. This formulation is consonant with the increased autoimmunity seen with reduced CTLA4 activity in animal models and human therapy and may complement other mechanisms such as kinetic proofreading (22) that improve the discrimination of self- from foreign antigens.

On the effect of specific peptides

The dissociation and association rate of MHC:TCR strongly depends on the type of the peptide associated with MHC (23). In our previous calculations, we simulated a high affinity Signal 1 interaction (dissociation and association rates of $0.5\left(1/\text{s}\right)$ and ${10}^5\left(1/\text{Ms}\right)$, respectively). Here we simulate the model for a low affinity Signal 1 interaction ($k_{\text{off}}=0.022\left(1/\text{s}\right)$ and $k_{\text{on}}=3720\left(1/\text{Ms}\right)$), to investigate the effects on the model results. These rates are characteristic to OVA/K^b peptide/MHC (23). The results for MHC:TCR, CD28:CD80, and CD80 from this simulation are shown in Figs. S16–S18. Comparing these results with the corresponding results of our original model, we found the following three differences in this model: 1) the MCT:TCR concentrations (shown in Fig. S16 A) increase more slowly in the first s, while later, the concentration distributions become similar to the concentration distributions shown in Fig. 2 D; 2) the amount of MHC:TCR increases quasi-linearly in the first s (see inset to Fig. S16 C), while in the original model there is considerable deviation from linearity even in the first s (see inset to Fig. 2 F); and 3) the equilibrium amount of MHC:TCR is slightly lower (11,000; see Fig. S16 C) than in our original model (12,000; see Fig. 2 F).

However, overall, we find that changing the Signal 1 affinity does not dramatically affect the behavior of the model (compare Fig. S17 with Fig. S4, and Fig. S18 with Fig. 3, D–F). In particular, Signal 2 formation is unaffected. In conclusion, the type of the peptide may affect the early kinetics and final concentration of Signal 1, but overall the model is robust to changes in Signal 1 affinity. The model output includes only the concentrations and locations of complexes, not the intracellular T cell activation signals and kinetics that would show more sensitivity to peptide affinity. These results suggest that the effects of CTLA4 on CD80 levels and signal 1 formation are independent of the strength of Signal 1 formation. This result is not inconsistent with the known effects of CTLA4 modulation in autoimmunity. CTLA4 sets the likelihood of T cell activation by altering the levels of CD80 and the likelihood of generating Signal 2. While this set point effect is independent of the strength of Signal 1, the T cell activation, which is not modeled, would depend on both this CTLA4-influenced set point and the strength of Signal 1.

Modeling the ligand-independent CTLA4 hypothesis

CTLA4 is an essential negative regulator of T cell immune responses whose mechanism of action is the subject of debate. Above we modeled a process called “transendocytosis”, i.e., expressed CTLA4 captures its ligands (CD80/CD86) from opposing APC. After removal, these costimulatory ligands are degraded inside the CTLA4-expressing T cell, resulting in impaired costimulation via CD28 (eliminating Signal 2). Thus, CTLA4 binding to CD80/CD86 is believed to be crucial for its inhibitory signal. One alternative to the trans-endocytosis hypothesis is the ligand-independent hypothesis, which proposes that suppression of T cell activation by CTLA4 occurs via CTLA4 signaling mechanisms and does not require interaction with and removal of CD80/CD86 from the antigen-presenting cell. The experimental evidence supporting this hypothesis relies on experiments in which T cell expression of CTLA4 mutants that cannot bind CD80/CD86 still was found to reduce T cell activation (24).

We investigated this ligand-independent CTLA4 hypothesis by adjusting our model to eliminate CTLA4 binding to CD80/CD86. (i.e., by using $k_a^{\text{tr}}=0.0\left(1/\text{Ms}\right)$ as the association constant of CTLA4M and CD80 instead of $k_a^{\text{tr}}=3\times {10}^6\left(1/\text{Ms}\right)$). The predicted dynamics of CD80 and CTLA4 from this alternative model are shown in Fig. S19, indicated by blue dashed lines, while the red lines represent the results of the original trans-endocytosis model. As would be expected, the lack of interaction with CD80 leads to a relative preservation of free CD80 levels in the APC. A slight reduction occurs due to Signal 2 formation, but no degradation occurs in the alternative model. Signal 2 is increased relative to the trans-endocytosis model Fig. S19, C and D while Signal 1 is unchanged (Fig. 2, E and F). These results are consonant with the prediction of the ligand-independent hypothesis, as despite the formation of Signal 1 and Signal 2, T cell activation is observed to be reduced experimentally.

However, the dynamics of membrane CTLA4 (Fig. S19) raise a question about the biological relevance of the experimental support for the ligand-independent hypothesis. Because CTLA4M does not form complexes, it is predicted to generate levels of membrane expression that are vastly in excess of what would be expected were CTLA4M complexation to occur. Note that the high level of CTLA4M arises, despite the fact that the uncomplexed CTLA4M still internalizes (see Table 1). This high level of membrane CTLA4 may lead to effects on signaling or protein trafficking (that could interfere with T cell activation) that are only seen at excessive CTLA4M concentrations. Walker and Sansom (25) have previously questioned the experimental support for the ligand-independent hypothesis on the grounds that exogenous expression of CTLA4 may lead to higher levels of expression and cellular effects not related to its natural biological role. Our simulation raises the additional concern that high membrane CTLA4 levels and altered temporal dynamics may occur purely from the loss of complex formation even if initial levels of expression are comparable. Our simulations suggest it would be crucial to measure the CTLA4M dynamics to demonstrate that suppression of T cell activation can occur at physiological nonbinding CTLA4M concentrations. Because of the concern about nonspecific effects of high CTLA4 levels in the membrane raised by our simulations, in the absence of additional experimental data our studies favor the trans-endocytosis hypothesis.

Modeling the ligand competition hypothesis

The ligand competition hypothesis is another major alternative to the trans-endocytosis hypothesis. As noted earlier, the association rate of CD80 to CTLA4M is approximately five times higher than that to CD28 (26). This higher affinity provides the basis for the ligand competition hypothesis to explain the inhibitory role of CTLA4M, i.e., CTLA4 restricts ligand availability for CD28, because of its higher affinity to CD80/86.

To model this competition hypothesis, we create the following two modified versions of our original model: 1) The CTLA4M:CD80 complex forms but the complex is not internalized. However, CTLA4M may still internalize after dissociation through the original CTLA4 internalization process shown in Table 1. 2) After the CTLA4M:CD80 complex is formed, instead of internalizing as a complex, only the CTLA4M component internalizes and the CD80 remains on the APC surface without requiring internalization. The first competition hypothesis version is modeled by blocking the initial process of CD80:CTLA4M internalization (see Table 1): $\left[CD80:CTLA4M\right]+\left[\overline{\overline{CTLA4}}\right]\to \left[CD80:CTLA4M:\overline{\overline{CTLA4}}\right]$ by taking the respective association constant $k_a^{\text{tr}}=0.0\left(1/\text{Ms}\right)$. The second version is modeled by eliminating the virtual form of CD80 used to model internalization $\left(\overline{\overline{CD80}}\right)$ in the processes used to represent CD80:CTLA4 internalization in the original model (see Table 1). i.e., the new model replaces the CD80:CTLA4 internalization steps in Table 1 with:

$$\begin{array}{l}\left[CD80:CTLA4M\right]+\left[\overline{\overline{CTLA4}}\right]\to \left[CD80:CTLA4M:\overline{\overline{CTLA4}}\right]\to \\ \left[CD80:\overline{\overline{CTLA4M}}:CTLA4\right]\to \left[CD80:\overline{\overline{CTLA4M}}\right]+\left[CTLA4\right],\end{array}$$

$$\left[CD80:\overline{\overline{CTLA4M}}\right]\to \left[CD80\right]+\left[\overline{\overline{CTLA4M}}\right].$$

The results of simulations of these two competition model versions are included in Fig. S19 by the green and pink dotted lines, respectively. In model version 1, uncomplexed CD80 and CTLA4M do not decrease as a consequence of CD80 trans-endocytosis. However, uncomplexed CD80 does decrease as a consequence of CD80:CTLA4M formation. Thus, the steady-state levels of CD80 and CTLA4M in model version 1 are in between the levels seen in the trans-endocytosis and ligand unbinding model simulations (see Fig. S19, B and F, respectively). Note that, as in the case of the ligand-independent model, the steady-state level of CTLA4M is vastly higher than in the case of the trans-endocytosis model. In model version 1, CD80 is involved in the formation of two types of complexes, CD28:CD80 and CD80:CTLA4M; the steady-state level of Signal 2 is lower than in the case of the ligand-independent model where CD80 is involved only in the formation of one type of complex, CD28:CD80.

For the time dependence of CD80 and CD28:CD80, model version 2 gives the same result as the ligand-independent model; however, the CTLA4M amount levels off only slightly higher than for the trans-endocytosis model. The steady-state level of Signal 2 becomes as high as in the case of the ligand-independent model because CD80 is rapidly released from the $CD80:\overline{\overline{CTLA4M}}$ complex and becomes available for the formation of CD28:CD80 complex. (Indeed, because the curves for Signal 2 in the ligand-independent model and version 2 competition model completely overlap, the two curves cannot be distinguished in Fig. S19, C and D). The steady-state level of CTLA4M is lower than in model version 1 because here there are two, rather than one, mechanisms for the endocytosis of CTLA4M. So, in this case we do not have the concern, regarding the very high steady-state level of CTLA4M seen with both model version 1 and the ligand-independent model.

Notably, the preservation of high CD28:CD80 Signal 2 complex formation in both versions of the competition models appears to be inconsistent with the underlying hypothesis of this model that the high affinity of the CTLA4:CD80 complex competes for and significantly reduces Signal 2 formation. Only the trans-endocytosis hypothesis model provides a mechanism by which CTLA4 can eliminate Signal 2 formation.

Conclusions

The good correspondence of experimental data and model simulations provide support for the trans-endocytosis hypothesis that underlies the model. In modeling the T cell-AP cell interactions, we did not do any parameter fitting. Despite this fact, there is good agreement between the experimentally reported CD86 depletion data and the simulated kinetics of CD80 (see Fig. 3 F). Qureshi et al. (11) measured substantial depletion of GFP-labeled CD86 from the plasma membrane of the CD86 donor cell (see Fig. S4B in Qureshi et al. (11)). The measured fluorescence of GFP-labeled CD86 intensity decreases by 50% within 33–48 min, while the calculated amount of CD80 decreases by 50% within 33 min (see Fig. 3 F). Note that experimentally the depletion of CD80 and CD86 has been found to be similar (see Fig. S5 in Qureshi et al. (11)).

The model also allows exploration of processes involved that differ widely in their timescales. The depletion of CD80 starts with fast transmembrane complexations at the opposing surfaces of the interacting cells. The time range of these fast reactions is 0.1–1 s. Within 1–30 s, this localized complexation develops concentration gradient between the flat and spherical part of the membrane of each cell and triggers lateral diffusion of membrane associated compounds mainly toward the flat part of the membrane. Only CTLA4, expressed in the flat part of the membrane, diffuses toward the spherical part of T cell membrane. In agreement with experiment (18), a ring of maximal concentration of MHC:TCR and other higher-order complexes appears for a short time next to the edge of the flat contact region, then diffuses toward the center of the flat contact region. These diffusion-limited processes are very slow: 90% depletion of CD80 takes ∼14,000 s. This example shows that cellular processes may take place within a very broad timescale, covering five orders of magnitude. This is the case because, besides the fast chemical reactions, diffusion-limited processes (especially lateral diffusion of compounds in cell membranes) and geometrical constraints considerably slow down cellular processes.

Our simulations of models of alternative hypotheses for the inhibitory mechanism of CTLA4, namely the ligand-independent hypothesis and the ligand competition hypothesis, suggest that the trans-endocytosis hypothesis provides the most plausible mechanism. The ligand-independent hypothesis model simulation leads to extremely high levels of CLTA4 and preserves Signal 2 formation. As we do not model CTLA4 signaling, our ligand-independent model simulations, while raising concerns about the physiological relevance of the experiments supporting this mechanism, does not represent a full evaluation of this hypothesis. The competition models show preservation of strong Signal 2 formation, which appears contradictory to that hypothesis. Although the trans-endocytosis model simulation shows good conformity to the available experimental data, the caveat remains that the dynamic data available for testing model predictions are limited. As additional data become available, the assumptions underlying these models can be tested further and the models should provide useful tools to help discriminate among alternative mechanistic interpretations.

Our model is related to the suggested mechanisms for T cell receptor triggering (i.e., to the process by which the TCR transduces signals across the plasma membrane after binding to its ligand—an agonist peptide complexed with an MHC molecule). One of these mechanisms emphasizes that aggregates of agonist and self-peptide-MHC molecules could induce clustering of TCRs simply by binding to the TCR (1). According to our model, formation of MHC:TCR complexes results in diffusion of both MHC and TCR molecules from the spherical to the flat part of the membrane of the AP cell and T cell, respectively. The increase in the amount of MHC and TCR (complexed and uncomplexed) molecules by 56 and 86%, respectively, may result in their aggregation (or clustering) within the flat part of the membrane. Similarly, in the case of two-component phospholipid membranes, aggregation (or clustering) of the minor component was detected above a critical concentration (27). It was shown theoretically that clustering above a critical concentration takes place in two-component membranes when the lateral interaction energies between the similar components are on average more attractive than the interaction energy between the dissimilar ones (28). In addition, our model emphasizes the role of lateral diffusion over larger timescales in contributing to the formation of high levels of both Signal 1 and Signal 2 complex during immune synapse formation.

Author Contributions

I.P.S. designed and performed research, analyzed data, and wrote the article; J.D. and C.J. contributed to interpretation of the modeling and revision of the article; and S.C.S. helped design the study, analyzed data, and wrote the article.

Editor: Richard Bertram.

Supporting Citations

References (29, 30, 31, 32, 33) appear in the Supporting Material.