On robustness of phase resetting to cell division under entrainment

Ahmed, Hafiz; Ushirobira, Rosane; Efimov, Denis

doi:10.1016/j.jtbi.2015.09.033

Cited by 11 publications

(4 citation statements)

References 36 publications

(69 reference statements)

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“…In the present case, phase resetting (switching from the high to the low state) is also probably dependent on cell division, as shown in Figure 4b. It has been previously analytically demonstrated that, phase resetting can be achieved through cell division for a population of biological oscillators under entrainment (Ahmed et al, 2015). In the present study case, it can be suspected that cell division is one of the main components driving the relaxation process profile from the high to the low state, with at least two subpopulations of cells exhibiting different growth rates.…”

Section: Discussionmentioning

confidence: 99%

Reducing phenotypic instabilities of a microbial population during continuous cultivation based on cell switching dynamics

Nguyen

Telek

Zicler

et al. 2021

Biotech & Bioengineering

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Predicting the fate of individual cells among a microbial population (i.e., growth and gene expression) remains a challenge, especially when this population is exposed to very dynamic environmental conditions, such as those encountered during continuous cultivation. Indeed, the dynamic nature of a continuous cultivation process implies the potential diversification of the microbial population resulting in genotypic and phenotypic heterogeneity. The present work focused on the induction of the arabinose operon in Escherichia coli as a model system to study this diversification process in continuous cultivations. As a preliminary step, the green fluorescent protein (GFP) level triggered by an arabinose‐inducible ParaBAD promoter was tracked by flow cytometry in chemostat cultivations with glucose‐arabinose co‐feeding. For a wide range of glucose‐arabinose co‐feeding concentrations in the chemostats, the simultaneous occurrence of GFP positive and negative subpopulation was observed. In the second set of experiments, continuous cultivation was performed by adding glucose continuously and arabinose based on the capability of individual cells to switch from low GFP to high GFP expression states, performed with a technology setup called segregostat. In the segregostat cultivation mode, on‐line flow cytometry analysis was used for adjusting the arabinose/glucose transitions based on the phenotypic switching profiles of the microbial population. This strategy allowed finding an appropriate arabinose pulsing frequency, leading to prolonged maintenance of the induction level with a limited increase in the phenotypic diversity for more than 60 generations. The results suggest that the steady forcing of individual cells into a given phenotypic trajectory may not be the best strategy for controlling cell populations. Instead, allowing individual cells to switch periodically around a predefined threshold seems to be a more robust strategy leading to oscillations, but within a predictable cell population behavior range.

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Section: Discussionmentioning

confidence: 99%

Reducing phenotypic instabilities of a microbial population during continuous cultivation based on cell switching dynamics

Nguyen

Telek

Zicler

et al. 2021

Biotech & Bioengineering

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show abstract

“…In our case, phase resetting (switching from the high the low state) has indeed been shown to be dependent on cell division (Figure 4B). It has been previously demonstrated analytically that for a population of biological oscillator under entrainment, phase resetting can be achieved through cell division [41]. In our case, it is indeed suspected that cell division is implied into the relaxation from the high to the low state, with at least two subpopulation of cells exhibiting different growth rate.…”

Section: Discussionmentioning

confidence: 58%

Reducing phenotypic instabilities of microbial population during continuous cultivation based on cell switching dynamics

Nguyen

Telek

Zicler

et al. 2021

Preprint

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Predicting the fate of a microbial population (i.e., growth, gene expression…) remains a challenge, especially when this population is exposed to very dynamic environmental conditions, such as those encountered during continuous cultivation processes. Indeed, the dynamic nature of continuous cultivation process implies the potential deviation of the microbial population involving genotypic and phenotypic diversification. This work has been focused on the induction of the arabinose operon in Escherichia coli as a model system. As a preliminary step, the GFP level triggered by an arabinose-inducible PBAD promoter has been tracked by flow cytometry in chemostat with glucose-arabinose co-feeding. Ampicillin was used as an “unstable” selective marker, allowing the simultaneous investigation of the effect of phenotypic diversification and genetic instability in continuous cultures. Under classical chemostat operation, the system was very unstable, with only a small fraction of cells (less than 10%) being able to accumulate GFP to a large extent, this fraction rapidly collapsing with time and going below 10% of the total population. On the long run, this phenotypic diversification was followed by an extensive loss of plasmid. In a second set of experiments, continuous cultivation was performed by adding either glucose or arabinose, based on the ability of individual cells for switching from low GFP to high GFP states, according to a technology called segregostat. In segregostat mode of cultivation, on-line flow cytometry analysis was used for adjusting the arabinose/glucose transitions based on the stochastic switching capabilities of the microbial population. This strategy allowed finding an appropriate arabinose pulsing frequency, leading to a prolonged maintenance of the induction level with limited impact of phenotypic diversification and genetic instability for more than 68 generations

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“…The magnitude of this jump is phase dependent, that is, the same stimulus affects oscillator differently at different parts of its cycle. The correspondence between the phase and its jump is described by the phase response (resetting) curve (PRC), which can be considered as a counterpart of the impulse response function in linear systems and used as a control tool [90][91][92][93]. The reader is referred to [91,93] for the relevant mathematical theory.…”

Section: Network Of Oscillatorsmentioning

confidence: 99%

Mathematical modeling of endocrine regulation subject to circadian rhythm

Medvedev

Proskurnikov

Zhusubaliyev

2018

Annual Reviews in Control

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The 2017 Nobel Prize in Physiology or Medicine awarded for discoveries of molecular mechanisms controlling the circadian rhythm has called attention to the challenging area of nonlinear dynamics that deals with synchronization and entrainment of oscillations. Biological circadian clocks keep time in living organisms, orchestrating hormonal cycles and other periodic rhythms. The periodic oscillations of circadian pacemakers are self-sustained; at the same time, they are entrainable by external periodic signals that adjust characteristics of autonomous oscillations. Whereas modeling of biological oscillators is a well-established research topic, mathematical analysis of entrainment, i.e. the nonlinear phenomena imposed by periodic exogenous signals, remains an open problem. Along with sustained periodic rhythms, periodically forced oscillators can exhibit various "irregular" behaviors, such as quasiperiodic or chaotic trajectories.In this paper, we present an overview of the mathematical models of circadian rhythm with respect to endocrine regulation, as well as biological background. Dynamics of the human endocrine system, comprising numerous glands and hormones operating under neural control, are highly complex. Therefore, only endocrine subsystems (or axes) supporting certain biological functions are usually studied. Low-order dynamical models that capture the essential characteristics and interactions between a few hormones can than be derived. Goodwin's oscillator often serves as such a model and widely regarded as a prototypical biological oscillator. A comparative analysis of forced dynamics arising in two versions of Goodwin's oscillator is provided in the present paper: the classical continuous oscillator and a more recent impulsive one, capturing e.g. pulsatile secretion of hormones due to neural regulation. The main finding of this study is that, while the continuous oscillator is always forced to a periodic solution by a sufficiently large exogenous signal amplitude, the impulsive one commonly exhibits a quasiperiodic or chaotic behavior due to non-smooth dynamics in entrainment.

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On robustness of phase resetting to cell division under entrainment

Cited by 11 publications

References 36 publications

Reducing phenotypic instabilities of a microbial population during continuous cultivation based on cell switching dynamics

Reducing phenotypic instabilities of a microbial population during continuous cultivation based on cell switching dynamics

Reducing phenotypic instabilities of microbial population during continuous cultivation based on cell switching dynamics

Mathematical modeling of endocrine regulation subject to circadian rhythm

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