Long negative feedback loop enhances period tunability of biological oscillators

Maeda, Kazuhiro; Kurata, Hiroyuki

doi:10.1016/j.jtbi.2017.12.014

Cited by 10 publications

(5 citation statements)

References 56 publications

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“…As in ( 1 ), the functions describe negative feedback mechanisms in the gene network, x 1 = x 1 ( t ), x i = x i ( t ) are concentrations as above. For n =2, the system of equations of the type ( 2 ) is the simplest model of artificial molecular trigger [ 36 , 37 ], for n =3, this is a model of Elowitz-Leibler repressilator [ 38 ], see also [ 39 , 40 ] for more biological interpretations. Detailed mathematical analysis of delayed arguments phenomena in similar models is given in [ 41 ].…”

Section: Resultsmentioning

confidence: 99%

“…Analysis of dynamics of synthetic constructions based on the prokaryotic genes and regulatory circuits with both, positive and negative loops shows that the regulatory signal delay that appears due to the negative autoregulatory loop is the key element of the oscillating construction design [60]. Moreover, numerical experiments show that extension of this loop leads to stable oscillations even in absence of positive regulatory loops [39].…”

Section: Discussionmentioning

confidence: 99%

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Limit cycles in models of circular gene networks regulated by negative feedback loops

2020

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Background The regulatory feedback loops that present in structural and functional organization of molecular-genetic systems and the phenomenon of the regulatory signal delay, a time period between the moment of signal reception and its implementation, provide natural conditions for complicated dynamic regimes in these systems. The delay phenomenon at the intracellular level is a consequence of the matrix principle of data transmission, implemented through the rather complex processes of transcription and translation.However, the rules of the influence of system structure on system dynamics are not clearly understood. Knowledge of these rules is particularly important for construction of synthetic gene networks with predetermined properties. Results We study dynamical properties of models of simplest circular gene networks regulated by negative feedback mechanisms. We have shown existence and stability of oscillating trajectories (cycles) in these models. Two algorithms of construction and localization of these cycles have been proposed. For one of these models, we have solved an inverse problem of parameters identification. Conclusions The modeling results demonstrate that non-stationary dynamics in the models of circular gene networks with negative feedback loops is achieved by a high degree of non-linearity of the mechanism of the autorepressor influence on its own expression, by the presence of regulatory signal delay, the value of which must exceed a certain critical value, and transcription/translation should be initiated from a sufficiently strong promoter/Shine-Dalgarno site. We believe that the identified patterns are key elements of the oscillating construction design.

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Limit cycles in models of circular gene networks regulated by negative feedback loops

2020

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“…The structural and functional organization of FMRP activity regulation includes positive and negative regulatory loops that function in different time ranges [ 19 , 20 ]. At present, it can be considered proven that these aspects of the structural and functional organization of dynamical systems are absolute determinants of the complex dynamics – periodic [ 30 – 32 ], quasi-periodic [ 32 , 33 ], chaos [ 34 – 36 ] and even hyperchaos [ 37 , 38 ]. And, the regulatory circuit of the FMRP-dependent translation at the synapse is not an exception.…”

Section: Discussionmentioning

confidence: 99%

On the dynamical aspects of local translation at the activated synapse

2020

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Background The key role in the dynamic regulation of synaptic protein turnover belongs to the Fragile X Mental Retardation Protein, which regulates the efficiency of dendritic mRNA translation in response to stimulation of metabotropic glutamate receptors at excitatory synapses of the hippocampal pyramidal cells. Its activity is regulated via positive and negative regulatory loops that function in different time ranges, which is an absolute factor for the formation of chaotic regimes that lead to disrupted proteome stability. The indicated condition may cause a number of neuropsychiatric diseases, including autism and epilepsy. The present study is devoted to a theoretical analysis of the local translation system dynamic properties and identification of parameters affecting the chaotic potential of the system. Results A mathematical model that describes the maintenance of a specific pool of active receptors on the postsynaptic membrane via two mechanisms – de novo synthesis of receptor proteins and restoration of protein function during the recycling process – has been developed. Analysis of the model revealed that an increase in the values of the parameters describing the impact of protein recycling on the maintenance of a pool of active receptors in the membrane, duration of the signal transduction via the mammalian target of rapamycin pathway, influence of receptors on the translation activation, as well as reduction of the rate of synthesis and integration of de novo synthesized proteins into the postsynaptic membrane – contribute to the reduced complexity of the local translation system dynamic state. Formation of these patterns significantly depends on the complexity and non-linearity of the mechanisms of exposure of de novo synthesized receptors to the postsynaptic membrane, the correct evaluation of which is currently problematic. Conclusions The model predicts that an increase of “receptor recycling” and reduction of the rate of synthesis and integration of de novo synthesized proteins into the postsynaptic membrane contribute to the reduced complexity of the local translation system dynamic state. Herewith, stable stationary states occur much less frequently than cyclic states. It is possible that cyclical nature of functioning of the local translation system is its “normal” dynamic state.

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“…12,13 Additionally, it has been related with the presence of relaxation oscillations and period tunability rhythms, for example circadian rhythms. 14 Herein we report that, interestingly, the lighttriggered current of crayfish photoreceptors is endowed with a CT-dependent hysteric behavior. We hypothesize that this physical characteristic is the result of the underlying biochemical events that modulate the light-transduction current.…”

Section: Introductionmentioning

confidence: 93%

Electrical response hysteresis of crayfish photoreceptors to light intensity. Dependence on circadian time.

Barriga-Montoya

Gómez-Lagunas

2020

MRAJ

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We studied the light-triggered current of crayfish photoreceptors. We found that when a train of light flashes of either increasing or decreasing intensity is applied, the current waveform presents the non-linear behavior known as hysteresis. Additionally, we observed that the extent of this response depends on the circadian time at which the pulses are applied. We hypothesize that positive feedback loops of biochemical networks underlying light energy transduction are responsible of the observed behavior. It has been demonstrated that a dynamical system hysteresis provides a mechanism that enhances its robustness against random perturbations. Taking into account this characteristic we hypothesize that the electrical-response hysteresis of crayfish photoreceptors: 1) makes the visual system more stable to environmental noise, and hence 2) adds stability to circadian clock oscillations.

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Long negative feedback loop enhances period tunability of biological oscillators

Cited by 10 publications

References 56 publications

Limit cycles in models of circular gene networks regulated by negative feedback loops

Limit cycles in models of circular gene networks regulated by negative feedback loops

On the dynamical aspects of local translation at the activated synapse

Electrical response hysteresis of crayfish photoreceptors to light intensity. Dependence on circadian time.

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