Population biology description

For years, the reigning paradigm for the unfolded state has been the random coil, whose properties are given by statistical descriptors appropriate to a freely jointed chain. Is this the most useful description of the unfolded population for polypeptide length scales of biological interest The answer given by this volume is clear there is more to learn. But first a word about the occasion that prompted this volume. 

This type of autocatalytic reaction is a simplification of many biological reactions such as fermentation, where the reaction produces products (species B in the previous example), which accelerates the rate. In fermentation, yeast cells in the solution produce enzymes that catalyze the decomposition of sugar to produce ethanol as a byproduct of yeast reproduction. Since the yeast population increases as the reaction proceeds, the enzyme concentration increases, and the process appears to be autocatalytic. A highly simplified description of fermentation might be... 

Each population that functions as a member of the community m a given habitat has a specialized functional role called a niche. An ecological niche is a functional description of the role that a species plays in a community—how it obtains food, what relationship it has with other species and the services it provides in its biological community. 

A new deterministic population balance model with distributed cell populations has been presented. The model is based on the unstructured approach of Mohler et al. [4]. Concerning outer dynamics the present model is equivalent to the unstructured model which proved to be sufficient to predict virus yields for different initial conditions [4]. The characteristics of the inner dynamics can be simulated except of the decrease of fluorescence intensity at later time points. The biological reasons for this effect are unclear. Presumably there are more states that have to be considered during virus replication like intercellular communication, extent of apoptosis or specific stage in cell cycle. Future computational and experimental research will aim in this directions and concentrate on structured descriptions of the virus replication in mammahan cell culture. 

In the case when P(x) = ax(l — x), a = const, we obtain a model used by Fisher and Kolmogorov for the description of some biological processes (more specifically, the model may represent spread of an epidemic in a certain region or propagation of a favourable gene in a population) ... 

We have seen that chemical and biological interactions lead to mathematical models displaying a variety of linear and nonlinear behavior relaxation to fixed points, multistability, excitability, oscillations, chaos, etc. Despite the different origin of the models, and the diverse nature of the variables they represent (chemical concentrations, population numbers, or even membrane electric potentials) the mathematical structures are quite similar, and it is possible to understand some aspects of the dynamics in one field (e.g. the chemical oscillations in the BZ reaction) with the help of models from other fields (for example the FN model of neurophysiology, or a phytoplankton-zooplankton model). This possibility of common mathematical description will be used in the rest of the book to highlight the similarities and relationships between chemical and biological dynamics when occurring in fluid flows. 

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