By Alfonsas Juška
The major challenge of the booklet is research of organic strategies, the ultimate level of that's mathematical modeling, i.e. quantitative presentation of the strategies in rigorous mathematical phrases. it really is particular for non-mathematicians. Mathematical types may be in comparison with experimental info hence verifying the validity of the types and at last of the preliminary assumptions and verbal descriptions of the tactics. The types (usually within the kind of mathematical equations) are completed painlessly through the schemes summarising verbal description of what's recognized in regards to the tactics. to unravel the equations software program is used. The step by step research results in rather subtle versions a few of them being unique. The ebook is helping the reader to improve extra basic method of the issues. it can be precious for skilled readers as well.
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Extra info for Analysis of biological processes: Verbal description, schemes, and mathematical models
Now the transition depicted in Fig. 5 has to be considered. The dependence of the probability of the state of the (macro)molecule induced by the ligand on its concetration will be stationary rather than temporal. The corresponding equations are based on the above scheme (Fig. 5). It is clear that at equilibrium at any ligand concentration the algebraic sum of the rates of forming a complex of these molecules with the (macro)molecules and the decay of the complex is nil (that makes an equation), and the sum of the states remains constant (it is convenient to suppose it to be equal to unity) making another equation.
7. Fig. 5 Scheme of filling up (the required filling up is framed) the Solver dialog box Notations Used in Verification Data points Mean Y ij Deviations Model curve − Yi × Yˆ i Dispersion Model value Y i ( j + 1) Deviations Data points Yij Datum value Column number _ Notations: Row number Yi Yˆi Mean value Model value Fig. 6 Scheme of experimental data and model curve. The definitions and notations of the values used in the analysis are summarized in the scheme 28 3 Model Fitting & Verification Fig.
Also of interest are the conclusions that a complicated process comprised of the processes proceeding on different temporal scales can be split up, the constituents considered to be independent; that ligand binding does not depend on its futurities; that the second ligand is not necessarily inhibitor. Those conclusions facilitate the analysis. Only the basic mathematical knowledge is required to model the processes. Mathematics should be considered as a tool. The computer programs should be considered similarly.