ActinActin is a family of globular multi-functional proteins that form microfilaments in the cytoskeleton, and the thin filaments in muscle fibrils. It is found in essentially all eukaryotic cells, where it may be present at a concentration of over 100 μM; its mass is roughly 42 kDa, with a diameter of 4 to 7 nm. An actin protein is the monomeric subunit of two types of filaments in cells: microfilaments, one of the three major components of the cytoskeleton, and thin filaments, part of the contractile apparatus in muscle cells.
MicrofilamentMicrofilaments, also called actin filaments, are protein filaments in the cytoplasm of eukaryotic cells that form part of the cytoskeleton. They are primarily composed of polymers of actin, but are modified by and interact with numerous other proteins in the cell. Microfilaments are usually about 7 nm in diameter and made up of two strands of actin. Microfilament functions include cytokinesis, amoeboid movement, cell motility, changes in cell shape, endocytosis and exocytosis, cell contractility, and mechanical stability.
Mathematical modelA mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
Cell cortexThe cell cortex, also known as the actin cortex, cortical cytoskeleton or actomyosin cortex, is a specialized layer of cytoplasmic proteins on the inner face of the cell membrane. It functions as a modulator of membrane behavior and cell surface properties. In most eukaryotic cells lacking a cell wall, the cortex is an actin-rich network consisting of F-actin filaments, myosin motors, and actin-binding proteins. The actomyosin cortex is attached to the cell membrane via membrane-anchoring proteins called ERM proteins that plays a central role in cell shape control.
CytoskeletonThe cytoskeleton is a complex, dynamic network of interlinking protein filaments present in the cytoplasm of all cells, including those of bacteria and archaea. In eukaryotes, it extends from the cell nucleus to the cell membrane and is composed of similar proteins in the various organisms. It is composed of three main components, microfilaments, intermediate filaments and microtubules, and these are all capable of rapid growth or disassembly dependent on the cell's requirements.
Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
Intermediate filamentIntermediate filaments (IFs) are cytoskeletal structural components found in the cells of vertebrates, and many invertebrates. Homologues of the IF protein have been noted in an invertebrate, the cephalochordate Branchiostoma. Intermediate filaments are composed of a family of related proteins sharing common structural and sequence features. Initially designated 'intermediate' because their average diameter (10 nm) is between those of narrower microfilaments (actin) and wider myosin filaments found in muscle cells, the diameter of intermediate filaments is now commonly compared to actin microfilaments (7 nm) and microtubules (25 nm).
Mathematical economicsMathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
Applied mathematicsApplied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.
Mathematical psychologyMathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance). The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations.
