Regular articleBifurcation Analysis of a Model of Mitotic Control in Frog Eggs
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A design principle of spindle oscillations in mammalian sleep
2022, iScienceCitation Excerpt :Overall, we proposed a theoretical design principle of spindle oscillation by leveraging a minimal model of groups of neurons, and discovered that the balance of background inward and outward currents could flexibly control spindle density along with intracellular calcium concentration. A bifurcation in the dynamical system occurs when a continuous change in a parameter value causes a qualitative or topological change in the system, as has been implied in many biological systems (e.g., cell cycles, developmental processes, and predator-prey systems) (Borisuk and Tyson 1998; Fussmann et al., 2000; Marco et al., 2014). These previously proposed design principles of biological systems have helped to understand the complex behavior of the system (Jolley et al., 2012; Sugai et al., 2017; Yamaguchi et al., 2021).
A Dynamical Paradigm for Molecular Cell Biology
2020, Trends in Cell BiologyDeciphering the Dynamics of Interlocked Feedback Loops in a Model of the Mammalian Circadian Clock
2018, Biophysical JournalBifurcation analysis for intracellular regulation networks based on their circuit structure
2015, IFAC-PapersOnLineTransitions between symmetric and nonsymmetric regimes in binary-mixture convection
2015, Physica D: Nonlinear PhenomenaCitation Excerpt :This Takens–Bogdanov point was found to be associated with a saddle–node-separatrix loop (SNSL) bifurcation and with a cusp. This conjunction of codimension-two bifurcations has been found in many problems of very different nature, from systems biology [22] to lasers [23]. In [3] it was found that this conjunction and all the low-Rayleigh number dynamics could be described as a part of the unfolding of a degenerate (codimension-three) Takens–Bogdanov point, the saddle case found by Dumortier et al. [24].
Computational study of a budding yeast model of Tyson and Novák
2014, Mathematics and Computers in SimulationCitation Excerpt :The coordination of growth and cell size at division was experimentally investigated in [11] in the case of budding yeast; it was found that a specific early event in G1 cannot be completed until a critical size is attained. The earliest and one of the most detailed papers that link bifurcation theory and cell cycle models is [2]; this paper deals with mitotic control in frog eggs. In a series of papers and book chapters Tyson and Novák and their collaborators have studied the cell cycles of various organisms as an alternation between two stable steady states of a system of kinetic equations (see e.g. [1,7,15–19]).
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