By Alfonsas Juška
The major problem of the booklet is research of organic methods, the ultimate degree of that's mathematical modeling, i.e. quantitative presentation of the procedures in rigorous mathematical phrases. it really is special for non-mathematicians. Mathematical versions will be in comparison with experimental info hence verifying the validity of the versions and eventually of the preliminary assumptions and verbal descriptions of the methods. The versions (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 relatively refined types a few of them being unique. The ebook is helping the reader to enhance extra basic method of the issues. it can be worthy for knowledgeable readers as well.
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Additional resources for Analysis of biological processes: Verbal description, schemes, and mathematical models
The models are consistent with the available experimental data. The model parameters are quantitatively related to the intrinsic properties of cells (volumes of their compartments) and those of endo-membranes; there is no interdependence between the parameters. The models can be used as the basis for quantitative analysis and the interpretation of experimental data. Ion fluxes via plasma membrane not being possible and via sarco-endoplasmic reticulum calcium ATPases (PMCA and SERCAs) being prevented by drugs, the influx via store-operated calcium channel and sodium/calcium exchanger (SOC and NCX) not being possible because of calcium-free environment, only ion leakage from the stores to the cytosol remaining non-controlled and leading to ion re-distribution in the cell.
Model fitting and verification deal entirely with the values, both with experimental data and model values corresponding to the data points (see Fig. 7), the specific model being of no relevance once it is presented in tabulated form ready for comparing. The phenomenon and its model regain their significance, however, as soon as the analysis is completed and the goodness of the model is verified (see Fig. 3). The mathematical model which cannot be reasonably discarded provides new tools for the description of the phenomenon under analysis (see Fig.
2. The data table, therefore, has to be appended by adding the corresponding column for the number of measurements (or replicates) corresponding to the independent variable, pi, the mean (Yi ) of the measurements, and a weighed square of the difference between the mean and the 2 at each (i-th) point of the corresponding value of the model pi Yi − Yˆi independent variable. 1) i =1 is calculated (see Fig. 2) and presented in a separate cell. The sum is of major importance for the analysis. It is minimized (visually or otherwise).