A mathematical approach to cytoskeletal assembly. 1998

L Edelstein-Keshet
Department of Mathematics, University of British Columbia, Vancouver, Canada. keshet@math.ubc.ca

The cytoskeleton is a fundamental and important part of cell's structure, and is known to play a large role in controlling the shape, function, division, and motility of the cell. In recent years, the traditional biological and biophysical experimental work on the cytoskeleton has been enhanced by a variety of theoretical, physical and mathematical approaches. Many of these approaches have been developed in the traditional frameworks of physicochemical and statistical mechanics or equilibrium thermodynamic principles. An alternative is to use kinetic modelling and couch the analysis in terms of differential equations which describe mean field properties of cytoskeletal networks or assemblies. This paper describes two such recent efforts. In the first part of the paper, a summary of work on the kinetics of polymerization, fragmentation, and dynamics of actin and polymers in the presence of gelsolin (which nulceates, fragments, and caps the filaments) is given. In the second part, some of the kinetic models aimed at elucidating the spatio-angular density distribution of actin filaments interacting via crosslinks is described. This model given insight into effects that govern the formation of clusters and bundles of actin filaments, and their spatial distribution.

UI MeSH Term Description Entries
D007700 Kinetics The rate dynamics in chemical or physical systems.
D008433 Mathematics The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed) Mathematic
D008954 Models, Biological Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment. Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D011485 Protein Binding The process in which substances, either endogenous or exogenous, bind to proteins, peptides, enzymes, protein precursors, or allied compounds. Specific protein-binding measures are often used as assays in diagnostic assessments. Plasma Protein Binding Capacity,Binding, Protein
D003599 Cytoskeleton The network of filaments, tubules, and interconnecting filamentous bridges which give shape, structure, and organization to the cytoplasm. Cytoplasmic Filaments,Cytoskeletal Filaments,Microtrabecular Lattice,Cytoplasmic Filament,Cytoskeletal Filament,Cytoskeletons,Filament, Cytoplasmic,Filament, Cytoskeletal,Filaments, Cytoplasmic,Filaments, Cytoskeletal,Lattice, Microtrabecular,Lattices, Microtrabecular,Microtrabecular Lattices
D000199 Actins Filamentous proteins that are the main constituent of the thin filaments of muscle fibers. The filaments (known also as filamentous or F-actin) can be dissociated into their globular subunits; each subunit is composed of a single polypeptide 375 amino acids long. This is known as globular or G-actin. In conjunction with MYOSINS, actin is responsible for the contraction and relaxation of muscle. F-Actin,G-Actin,Actin,Isoactin,N-Actin,alpha-Actin,alpha-Isoactin,beta-Actin,gamma-Actin,F Actin,G Actin,N Actin,alpha Actin,alpha Isoactin,beta Actin,gamma Actin
D000818 Animals Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA. Animal,Metazoa,Animalia
D001703 Biophysics The study of PHYSICAL PHENOMENA and PHYSICAL PROCESSES as applied to living things. Mechanobiology
D001704 Biopolymers Polymers synthesized by living organisms. They play a role in the formation of macromolecular structures and are synthesized via the covalent linkage of biological molecules, especially AMINO ACIDS; NUCLEOTIDES; and CARBOHYDRATES. Bioplastics,Bioplastic,Biopolymer
D046911 Macromolecular Substances Compounds and molecular complexes that consist of very large numbers of atoms and are generally over 500 kDa in size. In biological systems macromolecular substances usually can be visualized using ELECTRON MICROSCOPY and are distinguished from ORGANELLES by the lack of a membrane structure. Macromolecular Complexes,Macromolecular Compounds,Macromolecular Compounds and Complexes,Complexes, Macromolecular,Compounds, Macromolecular,Substances, Macromolecular

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