The Influence Of Inner Interaction Of Cytoskeleton To The Dynamics Of Cytoskeletal Filaments

Cytoskeleton proteins such as microtubules and actin filaments play a central role in many biological processes including cytoplasmic organization, cell division, cellular transport, and motility. Biological functions of cytoskeleton proteins are determined by their dynamic processes, and generous theoretical and experimental researches have been done to study the dynamics of microtubules and actin filaments. In spite of cytoskeleton’s great importance and fruitful researches in past years, the mechanism about dynamic behaviors of cytoskeleton is very limited.The eukaryotic cytoskeleton is composed of three basic types of filaments and their associated proteins. Cytoskeleton can be viewed as complex multifilament structures. Microtubules have 13 parallel protofilaments and actin filaments have two polymer chains. Cytoskeleton can be viewed as dynamic polymers that function in nonequilibrium conditions stimulated by hydrolysis of guanosine triphosphate(GTP) or adenosine triphosphate(ATP) molecules bound to their monomer. Cytoskeleton have some interesting states such as treadmilling and dynamic instability. Treadmilling means that a filament grows at plus end and shrinks at minus end with the same velocity. Dynamic instability means that individual microtubule can alternate between a period of slow growth and a period of rapid disassembly.In this paper we investigate the influence of inner interaction of cytoskeleton to the dynamics of cytoskeletal filaments. We propose a continuum model which possess exactly analytical solution. Our results show that the cooperativity leading to non negative-exponential distribution of ATP-subunits/GTP-tubulin. We investigate the treadmilling phenomenon using continuum cooperativity model. We show that the cooperativity remarkably influence the length of filament.We also investigate the dynamic instability of microtubules by a cooperative hydrolysis model. Using a new theoretical method, we calculate the steady state of this model. The influences of its neighbors to the dynamics instability of microtubules are discussed. The results show that the cooperativity influences the distribution of ATP-subunits/GTP-tubulin and cap size obviously.We discuss the dynamic of cytoskeletal filaments by a two-filament random hydrolysis model. Using the mean field approximation, we calculate the steady state of this model. The results show that the influences of cytoskeletal same-filament neighbors and adjacent-filament neighbor can influence the dynamic of cytoskeletal filaments clearly.Our models show that the influence of inner interaction of cytoskeleton can influence the dynamics of cytoskeleton clearly. The combination of the theoretical models and experimental research can give us better understanding of the dynamics of cytoskeleton.