Interplay of cellular states: Role of delay as control mechanism

Singh, Shakti; Chanu, Athokpam Langlen; Malik, Md. Zubbair

doi:10.1016/j.physa.2021.125869

Cited by 8 publications

(6 citation statements)

References 45 publications

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“…These two processes are implemented in this algorithm by generating two statistically independent random numbers, namely

and

such that the reaction time is computed using

, where

is the

propensity function given by

, where

is the number of possible molecular combinations of

reaction, and the

reaction will fire when it satisfies

. Intrinsic noise (

) associated with the clock protein dynamics in the system is inversely proportional to the square root of the systems size

(i.e.,

( Gillespie, 2000 ; Singh et al, 2018 ; Sharma et al, 2019 ; Singh et al, 2021 ).…”

Section: Methodsmentioning

confidence: 99%

Disruption in the regulation of casein kinase 2 in circadian rhythm leads to pathological states: cancer, diabetes and neurodegenerative disorders

Malik

Dashti

Fatima

et al. 2023

Front. Mol. Neurosci.

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IntroductionCircadian rhythm maintains the sleep–wake cycle in biological systems. Various biological activities are regulated and modulated by the circadian rhythm, disruption of which can result in onset of diseases. Robust rhythms of phosphorylation profiles and abundances of PERIOD (PER) proteins are thought to be the master keys that drive circadian clock functions. The role of casein kinase 2 (CK2) in circadian rhythm via its direct interactions with the PER protein has been extensively studied; however, the exact mechanism by which it affects circadian rhythms at the molecular level is not known.MethodsHere, we propose an extended circadian rhythm model in Drosophila that incorporates the crosstalk between the PER protein and CK2. We studied the regulatory role of CK2 in the dynamics of PER proteins involved in circadian rhythm using the stochastic simulation algorithm.ResultsWe observed that variations in the concentration of CK2 in the circadian rhythm model modulates the PER protein dynamics at different cellular states, namely, active, weakly active, and rhythmic death. These oscillatory states may correspond to distinct pathological cellular states of the living system. We find molecular noise at the expression level of CK2 to switch normal circadian rhythm to any of the three above-mentioned circadian oscillatory states. Our results suggest that the concentration levels of CK2 in the system has a strong impact on its dynamics, which is reflected in the time evolution of PER protein.DiscussionWe believe that our findings can contribute towards understanding the molecular mechanisms of circadian dysregulation in pathways driven by the PER mutant genes and their pathological states, including cancer, obesity, diabetes, neurodegenerative disorders, and socio-psychological disease.

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“…These two processes are implemented in this algorithm by generating two statistically independent random numbers, namely

and

such that the reaction time is computed using

, where

is the

propensity function given by

, where

is the number of possible molecular combinations of

reaction, and the

reaction will fire when it satisfies

. Intrinsic noise (

) associated with the clock protein dynamics in the system is inversely proportional to the square root of the systems size

(i.e.,

( Gillespie, 2000 ; Singh et al, 2018 ; Sharma et al, 2019 ; Singh et al, 2021 ).…”

Section: Methodsmentioning

confidence: 99%

Disruption in the regulation of casein kinase 2 in circadian rhythm leads to pathological states: cancer, diabetes and neurodegenerative disorders

Malik

Dashti

Fatima

et al. 2023

Front. Mol. Neurosci.

Self Cite

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“…Let µ = 0.9, σ 1 = 0.045, σ 2 = 0.05. According to (7)- (13) in Theorem 1, we know that η − = 1.2, η + = 0.9, ζ = 0.6, σ 1 − (η − +η + )σ 2 η − −ηζ−ln(µ)/σ 2 = 0.0027 > 0. The state trajectories of the whole system and each subsystem with partial state reset in (5) are depicted in Figures 3 and 4 , respectively.…”

Section: Numerical Examplementioning

confidence: 95%

“…Consider the SNNs (5) with only unstable subsystems. Suppose that Assumptions 2 and 3 hold and the conditions ( 7), ( 8), (10), (13) remain unchanged. If (11) and ( 12) are changed into −η + − 1 σ 2 ln µ > 1 µ ζ, then the SNNs (5) with partial state reset are exponentially stable.…”

Section: Remarkmentioning

confidence: 99%

“…Nevertheless, when applying neural networks to practical scenarios, the interactions between collaterals and neurons are generally asynchronous, and time delay effects are inevitable. The presence of time delay will prevent the disturbance of the system from being detected early and the control effect from being effective in time [13][14][15]. For such reasons, the research on the delayed neural networks has always been a problem of great concern in control science.…”

Section: Introductionmentioning

confidence: 99%

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Exponential Stability of Switched Neural Networks with Partial State Reset and Time-Varying Delays

Han

Zhang

2022

Mathematics

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This paper mainly investigates the exponential stability of switched neural networks (SNNs) with partial state reset and time-varying delays, in which partial state reset means that only a fraction of the states can be reset at each switching instant. Moreover, both stable and unstable subsystems are also taken into account and therefore, switched systems under consideration can take several switched systems as special cases. The comparison principle, the Halanay-like inequality, and the time-dependent switched Lyapunov function approach are used to obtain sufficient conditions to ensure that the considered SNNs with delays and partial state reset are exponentially stable. Numerical examples are provided to demonstrate the reliability of the developed results.

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“…Delayed regulation has been implicated in the p53 (Liu et al, 2011) and Hes1 systems (Barrio et al, 2006). Delay has been described as a regulatory motif in its own right, capable of modulating, suppressing, and buffering noise (Bhadana et al, 2021, Gedeon and Bokes, 2012, Singh et al, 2021, Zhang and Zhou, 2019), even beyond Markovian limits (Bhadana et al, 2021, Singh et al, 2021), as well as inducing oscillations (Bratsun et al, 2015, Liu et al, 2011, Miekisz et al, 2011, Singh et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

Transient and delay chemical master equations

Gorin

Yoshida

Pachter

2022

Preprint

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The serial nature of reactions involved in the RNA life-cycle motivates the incorporation of delays in models of transcriptional dynamics. The models couple a bursty or switching promoter to a fairly general set of Markovian or deterministically delayed monomolecular RNA interconversion reactions with no feedback. We provide numerical solutions for the RNA copy number distributions the models induce, and solve several systems with splicing and degradation. An analysis of single-cell and single-nucleus RNA sequencing data using these models reveals that the kinetics of nuclear export do not appear to require invocation of a non-Markovian waiting time.

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Interplay of cellular states: Role of delay as control mechanism

Cited by 8 publications

References 45 publications

Disruption in the regulation of casein kinase 2 in circadian rhythm leads to pathological states: cancer, diabetes and neurodegenerative disorders

Disruption in the regulation of casein kinase 2 in circadian rhythm leads to pathological states: cancer, diabetes and neurodegenerative disorders

Exponential Stability of Switched Neural Networks with Partial State Reset and Time-Varying Delays

Transient and delay chemical master equations

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