S. A. Pirogov

CORRELATION FUNCTIONS AND INVARIANT MEASURES IN CONTINUOUS CONTACT MODEL

We study the continuous version of the contact model. Using an analytic approach, we construct the non-equilibrium contact process as a Markov process on configuration space. The construction is based on the analysis of correlation functions evolution. The problem concerning invariant measures as well as asymptotics of correlation functions are also studied.

Reversibility and irreversibility in stochastic chemical kinetics

Mathematical models with mean field and local type interaction are considered in connection with stochastic chemical kinetics. Special emphasis is placed on various notions of reversibility, their consequences (Boltzmann type equations, fluctuations, Onsager relations, and so on), and the emergence of irreversibility.

Model of gene expression regulation in bacteria via formation of RNA secondary structures

A model was proposed for the classical attenuating mRNA regulation of gene expression via transcription termination. The model is based on the concept of secondary structure macrostates in the RNA regulatory region between the ribosome and RNA polymerase, utilizes resonant equations for estimating the deceleration of RNA polymerase by a set of hairpins located in this RNA region, and takes into account views on the initiation and elongation of transcription and translation. Special attention was paid to selecting the model parameters. To test the model, computations were performed to estimate, in particular, the probability of translation termination as dependent on the charged tRNA concentration and the amino acid concentration for several regulatory regions of the bacterial genome (as exemplified by trpE of Streptomyces spp., Bradyrhizobium japonicum, and Escherichia coli). Analysis was performed with different values of three parameters isolated as major ones. The resulting dependences agreed with the available experimental data, including those characterizing an enzymatic activity as dependent on the amino acid concentration in a culture (e.g., the anthranylate synthase activity as dependent on the tryptophan concentration in S. venezuelae). The following possible application was proposed for the model. Attenuating regulation is usually predicted on the basis of multiple sequence alignment, which requires several sequences. With the model, an individual sequence can be analyzed with proper parameters to generate a concentration-enzymatic activity curve. The curve characteristic of attenuation or its absence provides an additional argument for the presence or absence of attenuation.

On ground state of some non local Schrödinger operators

We study a ground state of some non-local Schrödinger operator associated with an evolution equation for the density of population in the stochastic contact model in continuum with inhomogeneous mortality rates. We found a new effect in this model, when even in the high-dimensional case the existence of a small positive perturbation of a special form (so-called, small paradise) implies the appearance of the ground state. We consider the problem in the Banach space of bounded continuous functions and in the Hilbert space .

Adaptive estimation of seismic parameter fields from earthquake catalogs

A new approach to estimation of the parameters of inhomogeneous spatio-temporal marked point fields is considered. The approach is based on the adaptive weights smoothing (AWS) method. A generalized version of the ASW method for constructing spatial and spatiotemporal fields of density, mean values, and correlation (fractal) dimension of marked point fields is proposed. It is shown that the method can be used in constructing fields of seismic-process parameters from earthquake catalogs.

Modeling RNA polymerase interaction in mitochondria of chordates.

BackgroundIn previous work, we introduced a concept, a mathematical model and its computer realization that describe the interaction between bacterial and phage type RNA polymerases, protein factors, DNA and RNA secondary structures during transcription, including transcription initiation and termination. The model accurately reproduces changes of gene transcription level observed in polymerase sigma-subunit knockout and heat shock experiments in plant plastids. The corresponding computer program and a user guide are available at http://lab6.iitp.ru/en/rivals. Here we apply the model to the analysis of transcription and (partially) translation processes in the mitochondria of frog, rat and human. Notably, mitochondria possess only phage-type polymerases. We consider the entire mitochondrial genome so that our model allows RNA polymerases to complete more than one circle on the DNA strand.ResultsOur model of RNA polymerase interaction during transcription initiation and elongation accurately reproduces experimental data obtained for plastids. Moreover, it also reproduces evidence on bulk RNA concentrations and RNA half-lives in the mitochondria of frog, human with or without the MELAS mutation, and rat with normal (euthyroid) or hyposecretion of thyroid hormone (hypothyroid). The transcription characteristics predicted by the model include: (i) the fraction of polymerases terminating at a protein-dependent terminator in both directions (the terminator polarization), (ii) the binding intensities of the regulatory protein factor (mTERF) with the termination site and, (iii) the transcription initiation intensities (initiation frequencies) of all promoters in all five conditions (frog, healthy human, human with MELAS syndrome, healthy rat, and hypothyroid rat with aberrant mtDNA methylation). Using the model, absolute levels of all gene transcription can be inferred from an arbitrary array of the three transcription characteristics, whereas, for selected genes only relative RNA concentrations have been experimentally determined. Conversely, these characteristics and absolute transcription levels can be obtained using relative RNA concentrations and RNA half-lives known from various experimental studies. In this case, the “inverse problem” is solved with multi-objective optimization.ConclusionsIn this study, we demonstrate that our model accurately reproduces all relevant experimental data available for plant plastids, as well as the mitochondria of chordates. Using experimental data, the model is applied to estimate binding intensities of phage-type RNA polymerases to their promoters as well as predicting terminator characteristics, including polarization. In addition, one can predict characteristics of phage-type RNA polymerases and the transcription process that are difficult to measure directly, e.g., the association between the promoter’s nucleotide composition and the intensity of polymerase binding. To illustrate the application of our model in functional predictions, we propose a possible mechanism for MELAS syndrome development in human involving a decrease of Phe-tRNA, Val-tRNA and rRNA concentrations in the cell. In addition, we describe how changes in methylation patterns of the mTERF binding site and three promoters in hypothyroid rat correlate with changes in intensities of the mTERF binding and transcription initiations. Finally, we introduce an auxiliary model to describe the interaction between polysomal mRNA and ribonucleases.

Mathematical modeling of the pollutants overland flow and transport

Modeling of the natural and technogenic processes in diverse geomorphological environments is one of the basic tools for forecasting and preventing unfavorable development of the urban ecology. One of the causes of its deterioration lies in pollution. The paper considers mathematical modeling of the spread of pollutants transported with water. The complicated process of pollutant spread was modeled as an aggregate of four simpler models such as overland water flow, influent seepage, pollutants transport with surface runoff, and pollutant deposition (accumulation) on the land surface. The model relies on the diffusion equation with supplementary addends in the right-hand side of which one reflects the effect of the terrain relief and the other, which depends on the lithologic structure of the territory, defines the intensity of pollutant uptake rate by the land surface. This equation is satisfied in the two-dimensional domain corresponding physically to an area covered with water. Both the form of the boundary and topology of this area are time-dependent because of appearance of dry “islands” surrounded by water.

Comparative Analysis of Apicoplast-Targeted Protein Extension Lengths in Apicomplexan Parasites.

In general, the mechanism of protein translocation through the apicoplast membrane requires a specific extension of a functionally important region of the apicoplast-targeted proteins. The corresponding signal peptides were detected in many apicomplexans but not in the majority of apicoplast-targeted proteins in Toxoplasma gondii. In T. gondii signal peptides are either much diverged or their extension region is processed, which in either case makes the situation different from other studied apicomplexans. We propose a statistic method to compare extensions of the functionally important regions of apicoplast-targeted proteins. More specifically, we provide a comparison of extension lengths of orthologous apicoplast-targeted proteins in apicomplexan parasites. We focus on results obtained for the model species T. gondii, Neospora caninum, and Plasmodium falciparum. With our method, cross species comparisons demonstrate that, in average, apicoplast-targeted protein extensions in T. gondii are 1.5-fold longer than in N. caninum and 2-fold longer than in P. falciparum. Extensions in P. falciparum less than 87 residues in size are longer than the corresponding extensions in N. caninum and, reversely, are shorter if they exceed 88 residues.

Information technology for forecasting geological processes and phenomena

The information technology and instrumental environment GEO are described. The technology implemented in GEO integrates the geographic information technology with case-based and knowledge-based system technologies. The applications to seismic hazard assessment for the region of the Lesser Caucasus and the Eastern part of the Great Caucasus are discussed.

Large fluctuations of radiation in stochastically activated two-level systems

We study the large fluctuations of emitted radiations in the system of