Volume 29, Issue 5

The paper describes a newmethod of Information Structure Analysis (ISAN) for protein sequences. The method uses a new approximation for description of protein sequences, which allows us to detect hierarchically organized elements (Information Structure Elements (ISEL)) in them. It is shown that elements of the higher hierarchy level of information structure correspond to stable elements in the spatial structure of globular proteins. Based on the ISAN method, we propose an approach to design of the new sequences of recombinant proteins. The proposed approach was confirmed experimentally in the case of obtaining functionally active recombinant proteins.

We developed a mathematical model that describes heart muscle fiber as a one-dimensional continuous medium of electrically and mechanically coupled cardiomyocytes through which electrical excitation propagates and initiates muscle contraction. The generic model simulates bilateral relations between the electrical and the mechanical activity of cardiomyocytes in the tissue and accounts for both intracellular and intercellular electro-mechanical couplings and mechano-electric feedback mechanisms.

A stochastic model for the spread of tuberculosis is proposed taking into account the reproduction and seasonal immigration of individuals. The system of difference equations majorating the system of equations for mathematical expectations of sizes of considered cohorts of individuals is studied. Conditions for the parameters of the model are obtained so that under those conditions the sizes of cohorts of afflicted individuals do not exceed the given mean level. The results of numerical experiments are presented for the study of dynamics of mean sizes of cohorts of individuals subject to parameters of immigration inflow.

Approaches to use the theory of evolutionary optimality in the study of structured models of biological communities are proposed. Relations of this theory to the stability of equilibrium states are indicated and the formulation of its main result for the case of a quasilinear dynamical systems in normed spaces is presented. For models of communities with age, spatial, and age-spatial structure, functionals optimized over parameters of evolutionary selection are constructed. The functionals are calculated on the basis of the available information concerning steady stationary distributions. The sets of parameters obtained as the result of this optimization can serve for identification of models.

Computer simulation is carried out for unsteady hemodynamics in a cerebral aneurysm of a blood vessel. Using the data of a real patient obtained in medical examination and during surgery, we reconstruct the 3D geometry of the anomaly, calculate hydrodynamic parameters of blood flow (flow velocity, streamline distribution, pressure, shear stress on walls, energy flux) and the deformation and stresses of the vessel walls. The calculations were performed for the following three cases: in the presence of an aneurysm, immediately after stent deployment changing the geometry of the vessel, and one year after the surgery. It is shown what changes of hydrodynamic and mechanical quantities characterize a successful surgery.

In this paper a discrete planar model of the tumour growth is presented. The model is based on hybrid cellular automaton and describes the tumour in a homogeneous tissue. The tissue consists of healthy cells and can have irregular vasculature. The model simulates proliferation processes and necrotic cells appearance which depends on the oxygen supply. There exists a stable solution, which may be used as an approximation of the tissue. Described HCA model can be extended with angiogenesis, nutrients and factors fields.