ODE, RDE and SDE models of cell cycle dynamics and clustering in yeast

Boczko, Erik M.; Gedeon, Tomáš; Stowers, Chris C.; Young, Todd

doi:10.1080/17513750903288003

Cited by 20 publications

(31 citation statements)

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“…Guided by these mathematical results, we verified the existence of clusters in two types of oscillating yeast cultures using both bud index and cell density data [2,26]. Experimental evidence in [24] also supports the existence of clusters in some YMO experiments.…”

Section: Introductionsupporting

confidence: 58%

Cell cycle dynamics in a response/signalling feedback system with a gap

Gong

Buckalew

Young

et al. 2014

Journal of Biological Dynamics

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We consider a dynamical model of cell cycles of n cells in a culture in which cells in one specific phase (S for signalling) of the cell cycle produce chemical agents that influence the growth/cell cycle progression of cells in another phase (R for responsive). In the case that the feedback is negative, it is known that subpopulations of cells tend to become clustered in the cell cycle; while for a positive feedback, all the cells tend to become synchronized. In this paper, we suppose that there is a gap between the two phases. The gap can be thought of as modelling the physical reality of a time delay in the production and action of the signalling agents. We completely analyse the dynamics of this system when the cells are arranged into two cell cycle clusters. We also consider the stability of certain important periodic solutions in which clusters of cells have a cyclic arrangement and there are just enough clusters to allow interactions between them. We find that the inclusion of a small gap does not greatly alter the global dynamics of the system; there are still large open sets of parameters for which clustered solutions are stable. Thus, we add to the evidence that clustering can be a robust phenomenon in biological systems. However, the gap does effect the system by enhancing the stability of the stable clustered solutions. We explain this phenomenon in terms of contraction rates (Floquet exponents) in various invariant subspaces of the system. We conclude that in systems for which these models are reasonable, a delay in signalling is advantageous to the emergence of clustering.

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Section: Introductionsupporting

confidence: 58%

Cell cycle dynamics in a response/signalling feedback system with a gap

Gong

Buckalew

Young

et al. 2014

Journal of Biological Dynamics

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“…7 As introduced in Equation (8) in Section 5. 8 Note that the statement trivially holds for q = 0 and q = 1.…”

Section: Interior Fixed Pointsmentioning

confidence: 95%

“…Also groups of bacteria may show synchronized oscillatory behaviour when coupled via signalling molecules [7], and in yeast populations periodic-like oxygen consumption oscillations can be seen [8], [4]. In human beta pancreas cells, oscillations are seen due to increasing population density [9], and size-structured population models can exhibit cohort-synchronization [10].…”

Section: Introductionmentioning

confidence: 99%

Synchronization of Oscillators

Wesselink¹

2013

Encyclopedia of Systems Biology

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In this thesis we consider a system of coupled oscillators: 'cells' that progress through a cycle and neither reproduce nor die. The cycle the oscillators progress through is divided into a region in which oscillators can send signals and a region in which they can receive and react to those signals by speeding up or slowing down their progression, as a generalisation of the integrate-and-fire model of Mirollo & Strogatz.We say oscillators are synchronized if they have identical phase and we are interested in the stability of the synchronized population. Does a population that is split in two return to the synchronized state or not. Instead of solving a system of coupled ODE's exactly, we analyse the dynamics of the oscillators by a Poincaré-like map on the unit interval, called full cycle map, that gives the position of a group when the other has completed one cycle.Since the synchronized state corresponds to the two boundary fixed points of the full cycle map, we can analyse the (local) stability of the synchronized state by considering the derivative of the full cycle map. Also conjectures can be made about the full cycle map itself. In this way we investigate the influence of the sign and amount of feedback on the stability of synchronization and the existence and stability of cycle phase-locked configurations: two oscillators that neither converge nor diverge after one cycle completion.Another approach focuses on the result of feedback on oscillators going from signalling to receiving or vice versa. This method gives intuitive results on synchronization that can easily be generalized to any number of oscillators, but lacks the precision to calculate the existence and stability of cycle phase-locked configurations.

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“…The difference can be explained with the smallness of α functions near the firing moments. Clustering phenomenon has been also investigated for an interesting model of cell cycle dynamics in paper [56]. We plan to adapt our method of analysis to the model in [56] and discuss the clustering and periodicity phenomena of integrate-and-fire models in [57].…”

Section: Introductionmentioning

confidence: 99%

Self-synchronization of the integrate-and-fire pacemaker model with continuous couplings

Akhmet

2012

Nonlinear Analysis: Hybrid Systems

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ODE, RDE and SDE models of cell cycle dynamics and clustering in yeast

Cited by 20 publications

References 50 publications

Cell cycle dynamics in a response/signalling feedback system with a gap

Cell cycle dynamics in a response/signalling feedback system with a gap

Synchronization of Oscillators

Self-synchronization of the integrate-and-fire pacemaker model with continuous couplings

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