[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.

[A method for solution of the multi-objective inverse problems under uncertainty].

We describe a method to solve multi-objective inverse problems under uncertainty. The method was tested on non-linear models of dynamic series and population dynamics, as well as on the spatiotemporal model of gene expression in terms of non-linear differential equations. We consider how to identify model parameters when experimental data contain additive noise and measurements are performed in discrete time points. We formulate the multi-objective problem of optimization under uncertainty. In addition to a criterion of least squares difference we applied a criterion which is based on the integral of trajectories of the system spatiotemporal dynamics, as well as a heuristic criterion CHAOS based on the decision tree method. The optimization problem is formulated using a fuzzy statement and is constrained by penalty functions based on the normalized membership functions of a fuzzy set of model solutions. This allows us to reconstruct the expression pattern of hairy gene in Drosophila even-skipped mutants that is in good agreement with experimental data. The reproducibility of obtained results is confirmed by solution of inverse problems using different global optimization methods with heuristic strategies.