Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing

Abstract

BackgroundCollective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise.ResultsInitially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with the help of LMI toolbox in MATLAB easily.ConclusionIf the synchronization robustness criterion, i.e. the synchronization robustness ≥ intrinsic robustness + extrinsic robustness, then the stochastic coupled synthetic oscillators can be robustly synchronized in spite of intrinsic parameter fluctuation and extrinsic noise. If the synchronization robustness criterion is violated, external control scheme by adding inducer can be designed to improve synchronization robustness of coupled synthetic genetic oscillators. The investigated robust synchronization criteria and proposed external control method are useful for a population of coupled synthetic networks with emergent synchronization behavior, especially for multi-cellular, engineered networks.

Finite time synchronization of stochastic Markovian jumping genetic oscillator networks with time-varying delay and Lévy noise

“…Remark 3.1 As far as we know, all the existing stochastic models concerning GONs [7,13,16,41] have considered the situation of Brownian motion. In this paper, the model discussed is universal, which replaces pure-diffusion Brownian motion with jump-diffusion Lévy process.…”

“…[9] it is showed that synchronization can enhance the anticancer activity of 2-deoxyglucose in breast cancer cells due to an increase in cellular glucose metabolism. Therefore, it is not surprising that many theoretical analyses on synchronization with or without control have been established for GONs in these years [6,7,[10][11][12][13][14][15][16]. As we know, in Ref.…”

“…Gene expression is an intrinsically stochastic process [29,30]. It should be pointed out that all of the existing literature about stochastic GONs mainly focuses on a system driven by Brownian motion [7,13,16]. However, researchers observed that the products of mRNAs and proteins occur in a bursty, unpredictable, and intermittent manner from a large number of biology experiments [31].…”

Life Rhythm as a Symphony of Oscillatory Patterns: Electromagnetic Energy and Sound Vibration Modulates gene Expression for Biological Signaling and Healing

“…For example, it has been clearly demonstrated that the generation of circa-dian rhythms at the suprachiasmatic nucleus is the result of the coupling of oscillators across the cellular and multicellular levels, 42 and a general framework for the emergence of synchronization in circadian cooperative systems employs non-linear coupled oscillators, resulting in phase-synchrony across large numbers of cells, 43 In neuronal networks, large scale simulations typically employ electrically phase-coupled systems that give rise to cooperative behaviors across large numbers of neurons 44 . Systems of genetic oscillators governing the synchronization of cells mediated by intercellular communication exhibit synchronous behaviors in spite of intrinsic parameter fluctuations and the presence of extrinsic noise 45 . Several novel behaviors have been noted, including phase synchronization within a system of weakly coupled self-sustained chaotic oscillators, suggesting that even under chaotic conditions, phases between individual oscillators can tend toward synchrony, 45 and there has recently been interest in the existence of “chimera states” in networks of coupled oscillators wherein a wide spectrum of complex states emerge from the underlying dynamics of a system of weakly coupled oscillators containing both synchronous and asynchronous elements 46 .…”

Delay decomposition approach to $$\mathcal {H}_{\infty }$$ H ∞ filtering analysis of genetic oscillator networks with time-varying delays

“…Hence, extrinsic noises resulting from environmental perturbations are unavoidable in modeling genetic oscillator networks (GONs). Based on linear matrix inequality (LMI) approach, the robust synchronization design problem for stochastic genetic oscillators has been discussed in Chen and Hsu (2012) to approximate the nonlinear coupled system. To exhibit more realistic characteristics of GONs, the stochastic synchronous criteria for Markovian jumping GONs with time delays have been derived in Wang et al (2010).…”