[Numerical Analysis of Particle Trajectories in Living Cells under Uncertainty Conditions].

We have developed a numerical method for the analysis of particle trajectories in living cells, where a type of movement is determined by Akaike's information criterion, while model parameters are identified by a weighted least squares method. The method is realized in computer software, written in the Java programming language, that enables us to automatically conduct the analysis of trajectories. The method is tested on synthetic trajectories with known parameters, and applied to the analysis of replication complexes in cells, infected with hepatitis C virus. Results of the analysis are in agreement with available data on the movement of biological objects along microtubules.

Local immobilization of particles in mass transfer described by a Jeffreys-type equation.

We consider the Jeffreys-type equation as the foundation in three different models of mass transfer, namely, the Jeffreys-type and two-phase models and the D(1) approximation to the linear Boltzmann equation. We study two classic (1+1)-dimensional problems in the framework of each model. The first problem is the transfer of a substance initially confined at a point. The second problem is the transfer of a substance from a stationary point source. We calculate the mean-square displacement (MSD) for the solutions of the first problem. The temporal behavior of the MSD in the framework of the first and third models is found to be the same as that in the Brownian motion described by the standard Langevin equation. In addition, we find a remarkable phenomenon when a portion of the substance does not move.

Delayed uncoupled continuous-time random walks do not provide a model for the telegraph equation.

It has been alleged in several papers that the so-called delayed continuous-time random walks (DCTRWs) provide a model for the one-dimensional telegraph equation at microscopic level. This conclusion, being widespread now, is strange, since the telegraph equation describes phenomena with finite propagation speed, while the velocity of the motion of particles in the DCTRWs is infinite. In this paper we investigate the accuracy of the approximations to the DCTRWs provided by the telegraph equation. We show that the diffusion equation, being the correct limit of the DCTRWs, gives better approximations in L(2) norm to the DCTRWs than the telegraph equation. We conclude, therefore, that first, the DCTRWs do not provide any correct microscopic interpretation of the one-dimensional telegraph equation, and second, the kinetic (exact) model of the telegraph equation is different from the model based on the DCTRWs.