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. 2009 Apr 8;96(7):2604-23.
doi: 10.1016/j.bpj.2009.01.019.

Aggregation of membrane proteins by cytosolic cross-linkers: theory and simulation of the LAT-Grb2-SOS1 system

Ambarish Nag  1 , Michael I Monine, James R Faeder, Byron Goldstein
Affiliations

Aggregation of membrane proteins by cytosolic cross-linkers: theory and simulation of the LAT-Grb2-SOS1 system

Ambarish Nag et al. Biophys J. .

Abstract

Ligand-induced receptor aggregation is a well-known mechanism for initiating intracellular signals but oligomerization of distal signaling molecules may also be required for signal propagation. Formation of complexes containing oligomers of the transmembrane adaptor protein, linker for the activation of T cells (LAT), has been identified as critical in mast cell and T cell activation mediated by immune response receptors. Cross-linking of LAT arises from the formation of a 2:1 complex between the adaptor Grb2 and the nucleotide exchange factor SOS1, which bridges two LAT molecules through the interaction of the Grb2 SH2 domain with a phosphotyrosine on LAT. We model this oligomerization and find that the valence of LAT for Grb2, which ranges from zero to three, is critical in determining the nature and extent of aggregation. A dramatic rise in oligomerization can occur when the valence switches from two to three. For valence three, an equilibrium theory predicts the possibility of forming a gel-like phase. This prediction is confirmed by stochastic simulations, which make additional predictions about the size of the gel and the kinetics of LAT oligomerization. We discuss the model predictions in light of recent experiments on RBL-2H3 and Jurkat E6.1 cells and suggest that the gel phase has been observed in activated mast cells.

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Figures

Figure 1
Figure 1
Model for the interactions of Grb2 with SOS1 and the formation of a Grb2-SOS1-Grb2 dimer. For Grb2 to form a stable complex with SOS1, both SH3 domains of Grb2 must simultaneously bind to SOS1. The value σ is the factor by which the presence of a Grb2 bound to SOS1 reduces the equilibrium constant for the binding of the second Grb2 to SOS1. The value l is the length of a Grb2 and d is the length between the SH2 domains of Grb2 in a Grb2-SOS1-Grb2 dimer.
Figure 2
Figure 2
Reactions in the oligomerization of LAT. The dotted ellipse indicates the molecule in the complex involved in the reaction. Only the C-terminal domain of SOS1, which contains the binding sites for the SH3 domains of Grb2, is shown. (a) Solution to surface binding: The binding of a bivalent ligand in solution to a LAT with two sites free that is at the end of a chain. (b) Surface to surface cross-linking that extends a chain: The binding of a free LAT to a Grb2 dimer that is part of a surface complex. (c) Surface to surface cross-linking that extends a chain: A bivalent ligand bound to LAT binds through its free SH2 domain to a free site on a LAT at the end of a chain. (d) Surface-to-surface cross-linking that adds a branch to a complex: A bivalent ligand bound to LAT binds through its free SH2 domain to a free site on a LAT in the complex. The value rx is a steric hindrance factor. (e) Surface to surface cross-linking that extends a chain: A Grb2-LAT complex binds through the free Grb2 SH3 domain to a SOS1 at the end of a chain.
Figure 3
Figure 3
For bivalent LAT, the partition function Ql0 for linear chains that begin and end with a LAT with one site free. Solid circles indicate phosphorylated Grb2 binding sites on LAT.
Figure 4
Figure 4
(a) Predicted average aggregate size for bi- and trivalent LAT when the number of Grb2 and SOS1 molecules per cell are those estimated for Jurkat E6.1 cells, GT = 1.3 × 106 molecules/cell and ST = 1.3 × 105 molecules/cell. (a and c) Open circles (trivalent LAT) and open triangles (bivalent LAT) are simulation results. The solid curves in panels a and c were obtained by solving Eqs. 13–15 simultaneously and then calculating the average aggregate size from Eq. 31. The dashed lines are for a trivalent LAT concentration that is two-thirds that of the upper curve and therefore has the same number of Grb2 binding sites as the dimer curve. (b) The quantity x = (1 − 2δw)/(2δw) for the same set of concentrations of Grb2 and SOS1 used in panel a. The quantity x is a measure of how close the system is to the sol-gel coexistence region. At the gel point, x = 1. (c) Predicted average aggregate size for bi- and trivalent LAT when number of Grb2 and SOS1 molecules per cell were 7.5 × 105 and 3.75 × 105, respectively. (d) For the concentrations used in panel c, the quantity x asymptotically approaches one with increasing LAT concentration.
Figure 5
Figure 5
Aggregate size distribution for trivalent LAT from theory (solid lines) and simulation (solid circles), (a) below the gel point, (b) in the sol-gel phase, and (c) above the gel point. (a–c) GT = 7.5 × 105 and ST = 3.75 × 105. (a) LT = 3.0 × 104. (b) LT = 2.0 × 105. (c) LT = 4.25 × 105. The appearance of a peak in the distribution at large aggregate sizes in panel b corresponds to gel formation in the simulation system of finite size. Each of the plots was generated by averaging over 30 simulations taking Fx = 100.
Figure 6
Figure 6
(a) Sol and gel coexistence regions for four values of the total Grb2 concentration: GT = 1.3 × 106, 7.5 × 105, 3.75 × 105, and 2.625 × 105 molecules/cell. The total area of the sol-gel coexistence region is a decreasing function of GT. (b) Boundary of the sol-gel coexistence region for GT = 7.5 × 105. The horizontal line corresponds to ST = 3.75 × 105. The open circles correspond to the concentrations used in Fig. 5, a–c, respectively. (c) The lower-left corner of panel a is replotted. The horizontal line corresponds to the SOS1 concentration, ST = 1.3 × 105 molecules per cell, the estimated average value for Jurkat E6.1 cells.
Figure 7
Figure 7
(a–d) GT = 7.5 × 105. (a) Contour plots of fg, the fraction of LAT molecules in the gel phase, from theory and simulations. The boundary enclosing the sol-gel region (solid line) is the same as in Fig. 6b. In the gel phase, four regions are shown that are characterized by different theoretical ranges of fg. These are separated by dotted, dashed and dotted-dashed lines. Symbols show the simulation results: 0.05 < fg < 0.1 (crosses), 0.1 < fg < 0.3 (dots), 0.3 < fg < 0.65 (open dots), and fg > 0.65 (stars). The simulation results were obtained using one simulation run per pair of (LT, ST) values, with Fx = 10. (b) Comparison of theory and simulations for LT = 2.0 × 105 (vertical line in a). SlT and SuT in panel a are the SOS1 concentrations at the gel points. The simulations are for Fx = 100 (dotted line), and Fx = 10 (dashed line). (c) Comparison of theory and simulations for ST = 3.75 × 105 (horizontal line in a). LlT and LuT are the LAT concentrations at the gel points. As in panel b, simulations are for Fx = 100 (dotted line), and Fx = 10 (dashed line). The solid circle corresponds to the concentrations used in panel b and in Fig. 5b. (d) LAT aggregate size distribution from simulation (dashed line) and theory (solid lines) for LT = 3.5 × 105 and ST = 3.75 × 105 corresponding to the open circle in panel c. Simulations are for Fx = 10.
Figure 8
Figure 8
LAT aggregation in the absence (solid line) and presence (dashed line) of a SOS1 fragment that binds only one Grb2 (CSOS1). The concentration of CSOS1 is 1.5 × 106, GT = 7.5 × 105, and ST = 3.75 × 105 molecules/cell. In all panels, the solid and dashed lines are predictions from the theory and the solid circles are simulation results. (a–c) LT = 2 × 104 molecules/cell and (d–f) LT = 2 × 105 molecules/cell. The simulations are the averages of 40 runs with Fx = 100. (b, c, e, and f) Trivalent LAT is introduced at t = 100 s. The solid and dashed lines are the predicted equilibrium values from the theory.
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