On the relationship between the load and the variance of relative fitness.

BACKGROUND: Operation of natural selection can be characterized by a variety of quantities. Among them, variance of relative fitness V and load L are the most fundamental. RESULTS: Among all modes of selection that produce a particular value V of the variance of relative fitness, the minimal value L min of load L is produced by a mode under which fitness takes only two values, 0 and some positive value, and is equal to V/(1+V). CONCLUSIONS: Although it is impossible to deduce the load from knowledge of the variance of relative fitness alone, it is possible to determine the minimal load consistent with a particular variance of relative fitness. The concept of minimal load consistent with a particular biological phenomenon may be applicable to studying several aspects of natural selection.

On propagation of excitation waves in moving media: the FitzHugh-Nagumo model.

BACKGROUND: Existence of flows and convection is an essential and integral feature of many excitable media with wave propagation modes, such as blood coagulation or bioreactors. METHODS/RESULTS: Here, propagation of two-dimensional waves is studied in parabolic channel flow of excitable medium of the FitzHugh-Nagumo type. Even if the stream velocity is hundreds of times higher that the wave velocity in motionless medium (), steady propagation of an excitation wave is eventually established. At high stream velocities, the wave does not span the channel from wall to wall, forming isolated excited regions, which we called "restrictons". They are especially easy to observe when the model parameters are close to critical ones, at which waves disappear in still medium. In the subcritical region of parameters, a sufficiently fast stream can result in the survival of excitation moving, as a rule, in the form of "restrictons". For downstream excitation waves, the axial portion of the channel is the most important one in determining their behavior. For upstream waves, the most important region of the channel is the near-wall boundary layers. The roles of transversal diffusion, and of approximate similarity with respect to stream velocity are discussed. CONCLUSIONS: These findings clarify mechanisms of wave propagation and survival in flow.

A molecular-mechanical model of the microtubule.

Dynamic instability of MTs is thought to be regulated by biochemical transformations within tubulin dimers that are coupled to the hydrolysis of bound GTP. Structural studies of nucleotide-bound tubulin dimers have recently provided a concrete basis for understanding how these transformations may contribute to MT dynamic instability. To analyze these ideas, we have developed a molecular-mechanical model in which structural and biochemical properties of tubulin are used to predict the shape and stability of MTs. From simple and explicit features of tubulin, we define bond energy relationships and explore the impact of their variations on integral MT properties. This modeling provides quantitative predictions about the GTP cap. It specifies important mechanical features underlying MT instability and shows that this property does not require GTP-hydrolysis to alter the strength of tubulin-tubulin bonds. The MT plus end is stabilized by at least two layers of GTP-tubulin subunits, whereas the minus end requires at least one; this and other differences between the ends are explained by asymmetric force balances. Overall, this model provides a new link between the biophysical characteristics of tubulin and the physiological behavior of MTs. It will also be useful in building a more complete description of MT dynamics and mechanics.

Blood coagulation and propagation of autowaves in flow.

This study analyses the effect of flow and boundary reactions on spatial propagation of waves of blood coagulation. A simple model of coagulation in plasma consisting of three differential reaction-diffusion equations was used for numerical simulations. The vessel was simulated as a two-dimensional channel of constant width, and the anticoagulant influence of thrombomodulin present on the undamaged vessel wall was taken into account. The results of the simulations showed that this inhibition could stop the coagulation process in the absence of flow in narrow channels. For the used mathematical model of coagulation this was the case if the width was below 0.2 mm. In wider vessels, the process could be stopped by the rapid blood flow. The required flow rate increased with the increase of the damage region size. For example, in a 0.5-mm wide channel with 1-mm long damage region, the propagation of coagulation may be terminated at the flow rate of more than 20 mm/min.