Nonlinear assembly kinetics and mechanical properties of biopolymers

This paper discusses the role of nonlinearities in the physical description of key biomolecules that participate in crucial subcellular processes, namely actin, microtubules and ions crowding around these filaments. The assembly kinetics of actin is that of a nonlinear process that is governed by coupled nonlinear equations involving monomer concentration and filament number as the dynamical variables. The dendritic growth of actin networks in cell motility phenomena is described by the coupling of actin filaments to the protein Arp2/3. We then discuss how coupled differential equations describing the interactions between ions in solution and the filament they surround can lead to solitonic signal transmission. We also investigate the role of nonlinear dynamics in the formation of microtubules. Space-flight laboratory experiments have shown that the self-organization of microtubules is sensitive to gravitational conditions. We propose a model of self-organization of microtubules in a gravitational field based on the dominant chemical kinetics. The pattern formation of microtubule concentration is obtained in terms of a moving kink. Finally, we present a model of elastic properties of microtubules describing a microtubule as an elastic rod. We found that when the microtubule is subjected to bending forces, the tangent angle satisfies a Sine-Gordon equation whose solutions describe kink and anti-kink bending modes that may propagate at a range of velocities along the length of the microtubule.