Abstract
BackgroundNon-linear kinetic analysis is a useful method for illustration of the dynamic behavior of cellular biological systems. To date, center manifold theory (CMT) has not been sufficiently applied for stability analysis of biological systems. The aim of this study is to demonstrate the application of CMT to kinetic analysis of protein assembly and disassembly, and to propose a novel framework for nonlinear multi-parametric analysis. We propose a protein assembly model with nonlinear kinetics provided by the fluctuation in monomer concentrations during their diffusion.ResultsWhen the diffusion process of a monomer is self-limited to give kinetics non-linearity, numerical simulations suggest the probability that the assembly and disassembly oscillate near the critical point. We applied CMT to kinetic analysis of the center manifold around the critical point in detail, and successfully demonstrated bifurcation around the critical point, which explained the observed oscillation.ConclusionsThe stability kinetics of the present model based on CMT illustrates a unique feature of protein assembly, namely non-linear behavior. Our findings are expected to provide methodology for analysis of biological systems.
Highlights
Non-linear kinetic analysis is a useful method for illustration of the dynamic behavior of cellular biological systems
General formulation of an assembly The model consists of several steps: (i) the monomer achieves an interactive state by binding a cofactor (ATP/guanidine triphosphate (GTP)) that provides the monomer with the ability to interact; (ii) the monomer itself possesses the ability to hydrolyze the cofactor and lose assembly activity; (iii) the monomer has the ability to exchange the inactive hydrolyzed cofactor (ADP/GDP) with an active non-hydrolyzed one; and (iv) adenosine triphosphate (ATP)/GTP are supplied continuously from the external environment
In this work, we presented a model for protein assembly kinetics and analyzed the stability around the critical point using center manifold theory (CMT)
Summary
Non-linear kinetic analysis is a useful method for illustration of the dynamic behavior of cellular biological systems. Center manifold theory (CMT) has not been sufficiently applied for stability analysis of biological systems. The aim of this study is to demonstrate the application of CMT to kinetic analysis of protein assembly and disassembly, and to propose a novel framework for nonlinear multi-parametric analysis. Numerical simulation based upon multi-parametric kinetic equations is the principal methodology for the analysis of the behavior of biological systems. We introduce the center manifold theory (CMT) for simplification of the study of dynamic biological systems. The aim of this study was to provide a simple algorithm for the application of CMT to multi-parametric kinetic
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