Aggregation of receptors on cell surface by extracellular multivalent ligand initiates a variety of biochemical reactions at early stages of signal transduction in cells. It is a dynamic process; alterations in kinetics of receptor aggregation can result in different levels of receptor activity. This, in turn, modifies intracellular regulatory pathways that include reactions between cytoplasmic signaling molecules. For example, receptor aggregate formation is vital for proper functioning in many antigen, hormone and cytokine receptor systems that control immunological reactions [1-3]. Recent studies of signal transduction in T cells have shown that receptor aggregation can also be mediated by intracellular molecules, such as adaptor and effector proteins, which act cooperatively [2]. In last two decades, the phenomenon of receptor aggregation has been studied by many groups, both experimentally and mathematically. In experimental systems, however, an exact statistics on receptor aggregates cannot be obtained yet. Therefore, the simulations, in which dynamics of aggregate formation is quantified explicitly, are of great benefit to understanding the kinetics of aggregation. Aggregation phenomenon is associated with the exponential increase in the number of chemical species and distinct cross-linking interactions, therefore, dynamic simulations of such complex biomolecular systems with the help of conventional methods (such as ODEs, etc.) become intractable. To resolve the complexity of this problem, we propose a stochastic algorithm based on Gillespie method [4]. Our kinetic model is originally designed for well-mixed systems, however, in case of diffusion-limited interactions, diffusion effects can be included as corrections to the reaction rates. To validate the simulation results, we use a thermodynamic equilibrium theory that quantifies all possible configurations on the surface [5]. We apply the developed model to simulate recent experimental data obtained for various systems of multivalent biomolecular interactions [2,3]. Using reasonable values of kinetic parameters in the developed model, we are able to reproduce quantitatively the experimental observations. We are currently working on generalization of the algorithm and incorporating it in to a rule-based software [6].

References: [1] Hlavacek et al., Biophys. J., 76, 2421 (1999). [2] Houtman et al., Nat. Struct. Mol. Biol., 13, 798 (2006). [3] Bilgicer et al., J. Am. Chem. Soc., 129, 3722 ( 2007). [4] Gillespie D.T., Ann. Rev. Phys. Chem., 58, 35 (2007). [5] Goldstein et al., Biophys. J., 45, 1109 (1984). [6] Blinov et al., Bioinformatics, 20, 3289 (2004).