Clustering in cell cycle dynamics with general response/signaling feedback

Young, Todd; Fernandez, Bastien; Buckalew, Richard; Moses, Gregory; Boczko, Erik M.

doi:10.1016/j.jtbi.2011.10.002

Cited by 16 publications

(50 citation statements)

References 58 publications

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“…Section 6 covers the effect of a reflection of the feedback function on the cycle maps and in Theorem 6. 4 we prove a relation that gives the cycle maps if the position dependence of the feedback in the receiving region is reflected. This theorem can be used to find interior fixed points in Section 7.…”

Section: Outline Of the Textmentioning

confidence: 87%

“…4 Note that although h and w are defined on the unit interval, we can easily extend them to the real line by periodic continuation.…”

Section: The Modelmentioning

confidence: 99%

“…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%

“…The division of the cycle into different regions comes from [4]. The authors consider two identical oscillators that progress through a cycle with unit speed.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Outline Of the Textmentioning

confidence: 87%

“…4 Note that although h and w are defined on the unit interval, we can easily extend them to the real line by periodic continuation.…”

Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The division of the cycle into different regions comes from [4]. The authors consider two identical oscillators that progress through a cycle with unit speed.…”

Section: Introductionmentioning

confidence: 99%

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Synchronization of Oscillators

Wesselink¹

2013

Encyclopedia of Systems Biology

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“…Among the conclusions of Young et al (2012), the following is most relevant to the current work: there are essentially two ways to produce synchrony in such a model, which we call RS-positive and SR-negative feedback processes. In an RS-positive process, when two nuclei are nearly synchronized, the one that is slightly ahead in the cell cycle (i.e., the one which will enter mitosis sooner) "reaches back" to accelerate the progression of the one that is slightly behind.…”

Section: Developmental Dynamicsmentioning

confidence: 99%

Evidence for internuclear signaling in drosophila embryogenesis

Buckalew

Finley

Tanda

et al. 2015

Developmental Dynamics

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Background: Syncytial nuclei in Drosophila embryos undergo their first 13 divisions nearly synchronously. In the last several cell cycles, these division events travel across the anterior-posterior axis of the syncytial blastoderm in a wave. The phenomenon is well documented but the underlying mechanisms are not yet understood. Results: We study timing and positional data obtained from in vivo imaging of Drosophila embryos. We determine the statistical properties of the distribution of division times within and across generations with the null hypothesis that timing of division events is an independent random variable for each nucleus. We also compare timing data with a model of Drosophila cell cycle regulation that does not include internuclear signaling, and to a universal model of phase-dependent signaling to determine the probable form of internuclear signaling in the syncytial embryo. Conclusions: The statistical variance of division times is lower than one would expect from uncoordinated activity. In fact, the variance decreases between the 10th and 11th divisions, which demonstrates a contribution of internuclear signaling to the observed synchrony and division waves. Our comparison with a coupled oscillator model leads us to conclude that internuclear signaling must be of Response/Signaling type with a positive impulse. Developmental

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Cell cycle dynamics: clustering is universal in negative feedback systems

et al. 2014

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We study a model of cell cycle ensemble dynamics with cell-cell feedback in which cells in one fixed phase of the cycle S (Signaling) produce chemical agents that affect the growth and development rate of cells that are in another phase R (Responsive). For this type of system there are special periodic solutions that we call k-cyclic or clustered. Biologically, a k-cyclic solution represents k cohorts of synchronized cells spaced nearly evenly around the cell cycle. We show, under very general nonlinear feedback, that for a fixed k the stability of the k-cyclic solutions can be characterized completely in parameter space, a 2 dimensional triangle T. We show that T is naturally partitioned into k(2) sub-triangles on each of which the k-cyclic solutions all have the same stability type. For negative feedback we observe that while the synchronous solution (k = 1) is unstable, regions of stability of k ≥ 2 clustered solutions seem to occupy all of T. We also observe bi-stability or multi-stability for many parameter values in negative feedback systems. Thus in systems with negative feedback we should expect to observe cyclic solutions for some k. This is in contrast to the case of positive feedback, where we observe that the only asymptotically stable periodic orbit is the synchronous solution.

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Clustering in cell cycle dynamics with general response/signaling feedback

Cited by 16 publications

References 58 publications

Synchronization of Oscillators

Synchronization of Oscillators

Evidence for internuclear signaling in drosophila embryogenesis

Cell cycle dynamics: clustering is universal in negative feedback systems

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