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.Comment: 31 pages,13 figure

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.Comment: 14 pages 10 figure

Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics

Mean-Field Theory Revives in Self-Oscillatory Fields with Non-Local Coupling

A simple mean-field idea is applicable to the pattern dynamics of large assemblies of limit-cycle oscillators with non-local coupling. This is demonstrated by developing a mathematical theory for the following two specific examples of pattern dynamics. Firstly, we discuss propagation of phase waves in noisy oscillatory media, with particular concern with the existence of a critical condition for persistent propagation of the waves throughout the medium, and also with the possibility of noise-induced turbulence. Secondly, we discuss the existence of an exotic class of patterns peculiar to non-local coupling called chimera where the system is composed of two distinct domains, one coherent and the other incoherent, separated from each other with sharp boundaries

Pattern selection in oscillatory media with global coupling

SCOPUS: ar.jinfo:eu-repo/semantics/publishe