Nonlinear dynamics of the distributed biochemical systems functioning in the dissipative structure formation mode

Nonlinear dynamical biomolecular systems can evidently be considered as prototypes of information processing devices at molecular level capable to solve problems of high computational complexity. Keeping in mind this goal the dynamics of biochemical system based on enzymatic oxidation of uric acid was considered. The system was studied in the version of distributed biomolecular structure having predetermined geometry of enzyme distribution on a porous planar medium. Being in the regime of stepwise dissipative structure formation this system demonstrated complicated modes of behaviour.     

Autowaves in a model of invasive tumor growth

A mathematical model for invasive tumor growth is proposed, which takes into account cell division, death, and motility. The model includes local cell density and the distribution of nutrient (oxygen) concentration. Cancer cells die in the absence of nutrients; therefore, the distribution of oxygen in tissue substantially affects both the tumor proliferation rate and its structure. The model adequately describes the experimentally measured rate of tumor proliferation. The existence of autowave solutions is demonstrated, and their properties are investigated. The results are compared with the properties of the Kolmogorov-Petrovskii-Piskunov and Fisher equations. It is shown that the nutrient distribution influences the selection of speed and the convergence of the initial conditions to the automodel solution.     

Transition from an excitable to an oscillatory state in dictyostelium discoideum

Under conditions of starvation, populations of the amoebae Dictyostelium discoideum aggregate are mediated by chemical excitation waves of cAMP. Two types of waves can be observed, either spiral or circular-shaped ones. We investigate transitions from rotating spirals to circular shaped waves (target patterns). Two different experiments demonstrating this phenomenon are presented. In the first case a continuous transition from the spiral type pattern to target waves was observed at the later stages of aggregation. In the second case the transition was induced by annihilation of waves by a spatially homogeneous cAMP pulse. Instead of the originally present spiral waves, oscillating spots bearing target patterns emerged. On the basis of a model for Dictyostelium aggregation, we provide a theoretical explanation for such transitions. It is shown that cell density can be an effective bifurcation parameter. Under certain conditions, the system is shifted from the excitable to the oscillatory state while the frequency of oscillations is proportional to the square root of the cell density. Thus, the regions with the highest cell density during the early stages of the spatial rearrangement of the cells become pacemakers and produce target patterns. The analytic results were confirmed in numerical simulations of the model.     

On kinetics of phase transitions in cell membranes

Phase transitions in a bicomponent lipid membrane are considered. It is shown that in this case metastable states practically do not arise and phase transitions are smooth and hysteresisless. An elastic frame on the surface of the membrane changes the character of phase transitions: they become sharp and hysteretic. The role of membrane phase transitions for regulation of cell processes is considered.     

Influence of temperature on cell membranes and cell cycles of mammals

Within the membrane model of cell division regulation the following effects are considered: (1) cell accumulation in the S-phase of the cycle at a temporary increase of the temperature; (2) cells coming out of the rest state into proliferation as temperature increases.Some mechanisms are suggested explaining selective death of transformed cells under hyperthermia and the change of lipid composition in membranes under a long-period cell cultivation at a non-optimal temperature.     

New muscle formation following transplantation of muscle treated with trypan blue]

The sources and mechanism of muscle formation de novo were investigated under the transplantation of skeletal muscle fibers treated in the 1% water solution of Trypan Blue for 48 hrs after Levander under skin and in omentum in rabbits and rats. In some cases the pieces of Trypan Blue stained muscles were placed in the diffusion chambers. Besides, 3H-thymidine autoradiography was used. It was established that after the above described treatment the muscles appeared morphologically as necrotized. They do not develop in the diffusion chambers in which cells do not penetrate. Under the transplantation of such muscles under skin and in omentum, they are phagocytized and disintegrate and in the close neighbourhood myoblasts arise which transform into muscle tubules and differentiated cross-striated muscle fibers. If prior to the transplantation the rats--recipients were labeled by 3H-thymidine, the muscle fibers formed de novo with the labeled nuclei, i. e. from the recipient cells in omentum where there are no muscles, apparently from polyblasts. Under the definite experimental conditions, myoblasts appear to arise from cells of non-myogenic origin by means of induction.