arXiv subjects

Dorjsuren Battogtokh

Publications and source records attributed to Dorjsuren Battogtokh.

6 recordsLinked to original sources

arXiv2017

Comparison of Domain Nucleation Mechanisms in a Minimal Model of Shoot Apical Meristem

Existing mathematical models of the shoot apical meristem (SAM) explain nucleation and confinement of a stem cell domain by Turing's mechanism, assuming that the diffusion coefficients of the activator (WUSCHEL) and inhibitor (CLAVATA) are significantly different. As there is no evidence for this assumption of differential diffusivity, we recently proposed a new mechanism based on a bistable switch model of the SAM. Here we study the bistable-switch mechanism in detail, demonstrating that it can be understood as localized switches of WUSHEL activity in individual cells driven by a non-uniform field of a peptide hormone. By comparing domain formation by Turing and bistable-switch mechanisms on a cell network, we show that the latter does not require the assumptions needed by the former, which are not supported by biological evidences.

q-bio.MN↗

arXiv2015

Domain Nucleation and Confinement In Agent Controlled Bistable Systems

We report a new mechanism of pattern formation in growing bistable systems coupled indirectly. A modified Fujita et. al. model is studied as an example of a reaction-diffusion system of nondiffusive activator and inhibitor molecules immersed in the medium of a fast diffusive agent. Here we show that, as the system grows, a new domain nucleates spontaneously in the area where the local level of the agent becomes critical. Newly nucleated domains are stable and the pattern formation is different from Turing's mechanism in monostable systems. Domains are spatially confined by the agent even if the activator and inhibitor molecules diffuse. With the spatial extension of the system, a larger domain may undergo a wavenumber instability and the concentrations of active molecules within the neighboring elements of a domain can become sharply different. The new mechanism reported in this work can be generic for pattern formation systems involving multistability, growth, and indirect coupling.

nlin.PS↗

arXiv2004

Bifurcation analysis of a model of the budding yeast cell cycle

We study the bifurcations of a set of nine nonlinear ordinary differential equations that describe the regulation of the cyclin-dependent kinase that triggers DNA synthesis and mitosis in the budding yeast, Saccharomyces cerevisiae. We show that Clb2-dependent kinase exhibits bistability (stable steady states of high or low kinase activity). The transition from low to high Clb2-dependent kinase activity is driven by transient activation of Cln2-dependent kinase, and the reverse transition is driven by transient activation of the Clb2 degradation machinery. We show that a four-variable model retains the main features of the nine-variable model. In a three-variable model exhibiting birhythmicity (two stable oscillatory states), we explore possible effects of extrinsic fluctuations on cell cycle progression.

q-bio.MN↗

arXiv2004

Turbulence near cyclic fold bifurcations in birhythmic media

We show that at the onset of a cyclic fold bifurcation, a birhythmic medium composed of glycolytic oscillators displays turbulent dynamics. By computing the largest Lyapunov exponent, the spatial correlation function, and the average transient lifetime, we classify it as a weak turbulence with transient nature. Virtual heterogeneities generating unstable fast oscillations are the mechanism of the transient turbulence. In the presence of wavenumber instability, unstable oscillations can be reinjected leading to stationary turbulence. We also find similar turbulence in a cell cycle model. These findings suggest that weak turbulence may be universal in biochemical birhythmic media exhibiting cyclic fold bifurcations.

q-bio.SC↗

arXiv2003

Nonlinear Effects in Site Blocking Induced Oscillations

Higher order nonlinear effects of site blocking, which induces oscillations in the Monte Carlo simulation of CO oxidation, are outlined here. It is shown that the rate equations which include these effects exhibit a supercritical Hopf bifurcation in parameter domains where Monte Carlo simulations lead to oscillations.

cond-mat.soft↗

arXiv2002

Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators

The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into two domains, one composed of mutually synchronized oscillators with unique frequency and the other composed of desynchronized oscillators with distributed frequencies. We apply a theory similar to the one which successfully explained the onset of collective synchronization in globally coupled phase oscillators with frequency distribution. A space-dependent order parameter is thus introduced, and an exact functional self-consistency equation is derived for this quantity. Its numerical solution is confirmed to reproduce the simulation results accurately.

cond-mat.stat-mech↗