Analysis of biological processes: Verbal description, by Alfonsas Juška

By Alfonsas Juška

The major predicament of the publication is research of organic strategies, the ultimate level of that's mathematical modeling, i.e. quantitative presentation of the techniques in rigorous mathematical phrases. it's distinct for non-mathematicians. Mathematical types might be in comparison with experimental information therefore verifying the validity of the versions and eventually of the preliminary assumptions and verbal descriptions of the approaches. The types (usually within the type of mathematical equations) are completed painlessly through the schemes summarising verbal description of what's identified in regards to the approaches. to unravel the equations software program is used. The step by step research results in rather subtle types a few of them being unique. The publication is helping the reader to enhance extra common method of the issues. it can be worthy for skilled readers as well.

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Extra resources for Analysis of biological processes: Verbal description, schemes, and mathematical models

Sample text

1 (see Fig. 1). To express calcium concentration in the cytosol directly (in the algebraic form), the initial conditions have to be specified. While the initial ion concentration in the cytosol can be estimated experimentally and assumed to be y0, that in the stores (x0) is not observable in these experiments. It can be determined, however, on the basis of Mass Conservation. As a result of re-distribution, the asymptotic concentrations of the ions in both the stores and cytosol become equal. The latter can be estimated (let it be y∞ ).

In platelets, no contribution of Na/Ca exchange to calcium extrusion has been found (Rosado and Sage 2000), PMCA playing the major role in the extrusion at low calcium concentrations (Rink and Sage 1990). In other non-excitable cells, the possible involvement of the exchange in calcium extrusion would manifest itself in the shape of the dynamics of calcium re-distribution in the absence of its reuptake and extrusion of its excess. The models discussed in this chapter may be the best means for the moment to relate quantitatively the dynamics of calcium redistribution in platelets suspended in calcium-free medium to the volumes of the stores and the cytoplasm and permeability of endo-membrane.

The ratio of volumes of the compartments (vstores/vcytosol = a) takes into account the non-equivalence of ion concentration to their mass. The transition X → Y together with cellular morphology determine the re-distribution. Fig. 1 Top: cartoon depicting intact platelet suspended in a calcium-free medium. Only what is essential for calcium fluxes is presented here. The stores are considered to be homogeneous. SERCA and PMCA, endo-membrane and plasma membrane calcium ATPases; NCX, sodium/calcium exchanger; SOC, store-operated calcium channel.

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