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Kinetic Analysis of Protein Assembly on the Basis of the Center Manifold around the Critical Point

Protein assembly plays an important role in the regulation of biological systems. The cytoskeleton assembly activity is provided by the binding cofactors GTP (guanidine triphosphate) or ATP(adenosine triphosphate) to monomeric protein, and is initiated by assembling the monomeric proteins. The binding GTP or ATP is hydrolyzed to GDP (guanidine diphosphate) or ADP (adenosine diphosphate) by the monomeric enzymatic activity. This self-limited assembly is characteristic of the cytoskeleton. To quantitatively evaluate the assembly kinetics, we propose a nonlinear and non-equilibrium kinetic model, with the nonlinearity provided by the fluctuation in monomer concentrations during the diffusion. Numerical simulations suggest that the assembly and disassembly oscillates in a chaos-like manner. We use a kinetic analysis of the center manifold around the critical point to show that minimal increases in ATP/GTP concentrations may lead to some attenuation in the amplification of these fluctuations. The present model and our application of center manifold theory illustrate a unique feature of protein assemblies, and our stability analysis provides an analytical methodology for the biological reaction system.