Genetic Oscillators Research Articles

Adaptation Mechanisms in Phosphorylation Cycles By Allosteric Binding and Gene Autoregulation

In this article, we study adaptation mechanisms in a class of phosphorylation cycles where allosteric binding and gene autoregulation mechanisms regulate the phosphorylation processes. We show that both mechanisms enable a robust setpoint regulation of the regulator metabolite in the presence of constant, as well as periodic, external stimuli. The allosteric binding mechanism without the presence of gene autoregulation can serve as an integral controller. Furthermore, we show that the incorporation of a gene autoregulation mechanism enables the gene expression system to act as a genetic oscillator, which allows for the adaptation mechanism to periodic external stimuli. These results provide a theoretical explanation to the cell homeostasis under quasi-constant environmental conditions, as well as periodic, biological rhythms.

Synchronization in a multiplex network of gene oscillators

Study of the synchronization in the network of gene oscillator network has vital importance in understanding of rhythmicity of molecular and cellular activities. In this paper, we analyze a network of linearly coupled genetic oscillators in a multiplex structure. The coupling strength values are changed and the coupling range is considered to be fixed, but different in the two layers. The analyses are done in two cases of periodic and chaotic oscillations. By computing the statistical measures, the interlayer and intralayer synchronization states are studied. The results show that the layer with higher coupling range has more enhanced synchrony and is less affected by the turbulent behavior of the other layer. On the other hand, the layer with lower coupling range approaches synchronization by strengthening the interlayer and intralayer couplings. The interlayer synchronization is also achieved in high coupling strength values.

Finite time synchronization of stochastic Markovian jumping genetic oscillator networks with time-varying delay and L\xe9vy noise

This paper is to investigate the finite-time synchronization of stochastic Markovian jumping genetic oscillator networks with time-varying delay and Lévy noise. At first, we generalize the finite-time stability theorem from the systems driven by Brownian motion to the Markovian jumping systems with Lévy noise. And then, we utilize the stochastic Lyapunov functional method and appropriate control to obtain sufficient conditions for finite-time synchronization. Finally, two numerical examples are presented to verify the effectiveness of the proposed criteria.

Chimera state in a two-dimensional network of coupled genetic oscillators

Due to the interaction of the cells, cellular communications are carried out with emergent collective behaviors, such as synchronization. In this paper, a network of coupled genetic oscillators is studied by considering a two-dimensional framework and diffusive coupling. Each genetic oscillator is a simple gene element with delayed self-inhibitions, which can exhibit periodic and chaotic dynamics. The network is investigated under the variation of the diffusion coefficient, in both periodic and chaotic dynamics. The results indicate the emergence of the so-called chimera state, i.e., the coexistence of coherent and incoherent regions, for certain diffusion coefficients. The computing of the strength of incoherence as a statistical measure represents that the local dynamics of the elements have a significant role in the network behavior. Actually, in the chaotic dynamics, the chimera state emerges in higher diffusion coefficients and a wider range. The effect of the time delay on the network behavior is also investigated.

Segmentation clock dynamics is strongly synchronized in the forming somite

During vertebrate somitogenesis an inherent segmentation clock coordinates the spatiotemporal signaling to generate segmented structures that pattern the body axis. Using our experimental and quantitative approach, we study the cell movements and the genetic oscillations of her1 expression level at single-cell resolution simultaneously and scale up to the entire pre-somitic mesoderm (PSM) tissue. From the experimentally determined phases of PSM cellular oscillators, we deduced an in vivo frequency profile gradient along the anterior-posterior PSM axis and inferred precise mathematical relations between spatial cell–level period and tissue-level somitogenesis period. We also confirmed a gradient in the relative velocities of cellular oscillators along the axis. The phase order parameter within an ensemble of oscillators revealed the degree of synchronization in the tailbud and the posterior PSM being only partial, whereas synchronization can be almost complete in the presumptive somite region but with temporal oscillations. Collectively, the degree of synchronization itself, possibly regulated by cell movement and the synchronized temporal phase of the transiently expressed clock protein Her1, can be an additional control mechanism for making precise somite boundaries.

Comparison between Effects of Retroactivity and Resource Competition upon Change in Downstream Reporter Genes of Synthetic Genetic Circuits.

Reporter genes have contributed to advancements in molecular biology. Binding of an upstream regulatory protein to a downstream reporter promoter allows quantification of the activity of the upstream protein produced from the corresponding gene. In studies of synthetic biology, analyses of reporter gene activities ensure control of the cell with synthetic genetic circuits, as achieved using a combination of in silico and in vivo experiments. However, unexpected effects of downstream reporter genes on upstream regulatory genes may interfere with in vivo observations. This phenomenon is termed as retroactivity. Using in silico and in vivo experiments, we found that a different copy number of regulatory protein-binding sites in a downstream gene altered the upstream dynamics, suggesting retroactivity of reporters in this synthetic genetic oscillator. Furthermore, by separating the two sources of retroactivity (titration of the component and competition for degradation), we showed that, in the dual-feedback oscillator, the level of the fluorescent protein reporter competing for degradation with the circuits’ components is important for the stability of the oscillations. Altogether, our results indicate that the selection of reporter promoters using a combination of in silico and in vivo experiments is essential for the advanced design of genetic circuits.

A Model of Somitogenesis

A quantitative description of the molecular networks that sustain morphogenesis is one of the main challenges of developmental biology. In particular, a molecular understanding of the segmentation of the antero-posterior axis in vertebrates has yet to be achieved. This process known as somitogenesis is believed to result from the interactions between a well-studied genetic oscillator and a less established posterior-moving determination wavefront. Here we describe a molecular model for somitogenesis that couples a moving morphogen wavefront with the somitogenetic oscillator. The wavefront is due to a switch between stable states that results from reciprocal negative feedbacks of Retinoic Acid (RA) on the activation of a kinase ErK and of ErK on RA synthesis. We suggest a molecular mechanism by which that switch can be triggered by the somitogenetic clock. The model quantitatively accounts for the shortening of the pre-somitic mesoderm (PSM) in zebrafish in response to the decrease during somitogenesis in the concentration of a morphogen (Fgf8). The generality and robustness of the model allows for its validation (or invalidation) in other model organisms.

Synchronization Analysis for a Class of Genetic Oscillator Networks

We consider a synchronization problem for genetic oscillator networks. The genetic oscillators are modeled as nonlinear systems of the Lur’e type. Simple and verifiable synchronization conditions are presented for genetic oscillator networks by using the theory of absolute stability and the matrix theory. A network composed of coupled Goodwin models is used as an example of numerical simulation to verify the efficiency of the theoretical method.

Period - control in a coupled system of two genetic oscillators for synthetic biology

Biological complex mechanisms with oscillatory behavior are often modeled by high dimensional nonlinear ODEs systems, which makes the analysis and understanding the dynamics of the system difficult. In this work, we consider two reduced models that mimic the oscillatory dynamics of the cell cycle and the circadian clock, and study their coupling from a synthetic biology perspective. To improve the performance and robustness of the oscillatory dynamics in a living cellular environment, we consider the problem of augmenting the parameter region admitting periodic solutions. Moreover, we study the capacity for mutual period regulation and control of the coupling between the two reduced oscillators.

Waveforms of molecular oscillations reveal circadian timekeeping mechanisms

Circadian clocks play a pivotal role in orchestrating numerous physiological and developmental events. Waveform shapes of the oscillations of protein abundances can be informative about the underlying biochemical processes of circadian clocks. We derive a mathematical framework where waveforms do reveal hidden biochemical mechanisms of circadian timekeeping. We find that the cost of synthesizing proteins with particular waveforms can be substantially reduced by rhythmic protein half-lives over time, as supported by previous plant and mammalian data, as well as our own seedling experiment. We also find that previously enigmatic, cyclic expression of positive arm components within the mammalian and insect clocks allows both a broad range of peak time differences between protein waveforms and the symmetries of the waveforms about the peak times. Such various peak-time differences may facilitate tissue-specific or developmental stage-specific multicellular processes. Our waveform-guided approach can be extended to various biological oscillators, including cell-cycle and synthetic genetic oscillators.

Sigma Factor-Mediated Tuning of Bacterial Cell-Free Synthetic Genetic Oscillators.

Cell-free transcription–translation provides a simplified prototyping environment to rapidly design and study synthetic networks. Despite the presence of a well characterized toolbox of genetic elements, examples of genetic networks that exhibit complex temporal behavior are scarce. Here, we present a genetic oscillator implemented in an E. coli-based cell-free system under steady-state conditions using microfluidic flow reactors. The oscillator has an activator–repressor motif that utilizes the native transcriptional machinery of E. coli: the RNAP and its associated sigma factors. We optimized a kinetic model with experimental data using an evolutionary algorithm to quantify the key regulatory model parameters. The functional modulation of the RNAP was investigated by coupling two oscillators driven by competing sigma factors, allowing the modification of network properties by means of passive transcriptional regulation.

Identification of Nonlinear State-Space Systems From Heterogeneous Datasets

This paper proposes a new method to identify nonlinear state-space systems from heterogeneous datasets. The method is described in the context of identifying biochemical/gene networks (i.e., identifying both reaction dynamics and kinetic parameters) from experimental data. Simultaneous integration of various datasets has the potential to yield better performance for system identification. Data collected experimentally typically vary depending on the specific experimental setup and conditions. Typically, heterogeneous data are obtained experimentally through 1) replicate measurements from the same biological system or 2) application of different experimental conditions such as changes/perturbations in biological inductions, temperature, gene knock-out, gene over-expression, etc. We formulate here the identification problem using a Bayesian learning framework that makes use of “sparse group” priors to allow inference of the sparsest model that can explain the whole set of observed heterogeneous data. To enable scale up to large number of features, the resulting nonconvex optimization problem is relaxed to a reweighted Group Lasso problem using a convex–concave procedure. As an illustrative example of the effectiveness of our method, we use it to identify a genetic oscillator (generalized eight species repressilator). Through this example we show that our algorithm outperforms Group Lasso when the number of experiments is increased, even when each single time-series dataset is short. We additionally assess the robustness of our algorithm against noise by varying the intensity of process noise and measurement noise.

Homogeneous Time Constants Promote Oscillations in Negative Feedback Loops.

Biological oscillators are present in nearly all self-regulating systems, from individual cells to entire organisms. In any oscillator structure, a negative feedback loop is necessary, but not sufficient to guarantee the emergence of periodic behaviors. The likelihood of oscillations can be improved by careful tuning of the system time constants and by increasing the loop gain, yet it is unclear whether there is any general relationship between optimal time constants and loop gain. This issue is particularly relevant in genetic oscillators resulting from a chain of different subsequent biochemical events, each with distinct (and uncertain) kinetics. Using two families of genetic oscillators as model examples, we show that the loop gain required for oscillations is minimum when all elements in the loop have the same time constant. On the contrary, we show that homeostasis is ensured if a single element is considerably slower than the others.

Computational Re-design of Synthetic Genetic Oscillators for Independent Amplitude and Frequency Modulation.

To perform well in biotechnology applications, synthetic genetic oscillators must be engineered to allow independent modulation of amplitude and period. This need is currently unmet. Here, we demonstrate computationally how two classic genetic oscillators, the dual-feedback oscillator and the repressilator, can be re-designed to provide independent control of amplitude and period and improve tunability-that is, a broad dynamic range of periods and amplitudes accessible through the input "dials." Our approach decouples frequency and amplitude modulation by incorporating an orthogonal "sink module" where the key molecular species are channeled for enzymatic degradation. This sink module maintains fast oscillation cycles while alleviating the translational coupling between the oscillator's transcription factors and output. We characterize the behavior of our re-designed oscillators over a broad range of physiologically reasonable parameters, explain why this facilitates broader function and control, and provide general design principles for building synthetic genetic oscillators that are more precisely controllable.

Local and global analysis of endocrine regulation as a non-cyclic feedback system

To understand the sophisticated control mechanisms of the human’s endocrine system is a challenging task that is a crucial step towards precise medical treatment of many dysfunctions and diseases. Although mathematical models describing the endocrine system as a whole are still elusive, recently some substantial progress has been made in analyzing theoretically its subsystems (or axes) that regulate the production of specific hormones. Secretion of many vital hormones, responsible for growth, reproduction and metabolism, is orchestrated by feedback mechanisms that are similar in structure to the model of simple genetic oscillators, proposed first by B.C. Goodwin. Unlike the celebrated Goodwin’s model, the endocrine regulation mechanisms are in fact known to have non-cyclic structures and involve multiple feedbacks; a Goodwin-type model thus represents only a part of such a complicated mechanism. In this paper, we examine a non-cyclic feedback system of hormonal regulation, obtained from the classical Goodwin’s oscillator by introducing an additional negative feedback. We establish global properties of this model and show, in particular, that the local instability of its unique equilibrium implies that almost all system’s solutions oscillate; furthermore, under additional restrictions these solutions converge to periodic or homoclinic orbits.

Chemical event chain model of coupled genetic oscillators.

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

Long-lived protein expression in hydrogel particles: towards artificial cells.

Herein we report a new type of cell-mimic particle capable of long-lived protein expression. We constructed the cell-mimic particles by immobilizing the proteinaceous factors of the cell-free transcription and translation system on the polymer backbone of hydrogel particles and encapsulating the plasmid template and ribosome inside the hydrogel. With the continuous supply of nutrients and energy, the protein expression in the cell-mimic particles remained stable for at least 11 days. We achieved the regulation of protein expression in the cell-mimic particles by the usage of lac operon. The cell-mimic particles quickly responded to the concentration change of isopropyl β-d-1-thiogalactopyranoside (IPTG) in the feeding buffer to regulate the mCherry expression level. We also constructed an in vitro genetic oscillator in the cell-mimic particles. Protein LacI provided a negative feedback to the expression of both LacI itself and eGFP, and the expression level change of eGFP presented an oscillation. We expect the cell-mimic particles to be a useful platform for gene circuit engineering, metabolic engineering, and biosensors.

Synchrony and pattern formation of coupled genetic oscillators on a chip of artificial cells

Understanding how biochemical networks lead to large-scale nonequilibrium self-organization and pattern formation in life is a major challenge, with important implications for the design of programmable synthetic systems. Here, we assembled cell-free genetic oscillators in a spatially distributed system of on-chip DNA compartments as artificial cells, and measured reaction-diffusion dynamics at the single-cell level up to the multicell scale. Using a cell-free gene network we programmed molecular interactions that control the frequency of oscillations, population variability, and dynamical stability. We observed frequency entrainment, synchronized oscillatory reactions and pattern formation in space, as manifestation of collective behavior. The transition to synchrony occurs as the local coupling between compartments strengthens. Spatiotemporal oscillations are induced either by a concentration gradient of a diffusible signal, or by spontaneous symmetry breaking close to a transition from oscillatory to nonoscillatory dynamics. This work offers design principles for programmable biochemical reactions with potential applications to autonomous sensing, distributed computing, and biomedical diagnostics.

Excitable Dynamics and Yap-Dependent Mechanical Cues Drive the Segmentation Clock

The periodic segmentation of the vertebrate body axis into somites, and later vertebrae, relies on a genetic oscillator (the segmentation clock) driving the rhythmic activity of signaling pathways in the presomitic mesoderm (PSM). To understand whether oscillations are an intrinsic property of individual cells or represent a population-level phenomenon, we established culture conditions for stable oscillations at the cellular level. This system was used to demonstrate that oscillations are a collective property of PSM cells that can be actively triggered invitro by a dynamical quorum sensing signal involving Yap and Notch signaling. Manipulation of Yap-dependent mechanical cues is sufficient to predictably switch isolated PSM cells from a quiescent to an oscillatory state invitro, a behavior reminiscent of excitability in other systems. Together, our work argues that the segmentation clock behaves as an excitable system, introducing a broader paradigm to study such dynamics in vertebrate morphogenesis.

Dynamic Analysis of Quorum-sensing Genetic Oscillators with the Influence of External Medium

Living organisms have the capacity to exhibit elaborate rhythmic behaviors. These complex behaviors are controlled by biochemical networks themselves as well as environmental clues. Quorum sensing refers to the typical intercellular communication mechanism executed by certain small molecule. This paper undertakes a dynamic analysis of single amoeba Dictyostelium cell, which is a representative genetic unicellular oscillator, communicating with others through quorum sensing. Apply the theory of vibration rather than center manifold method, our focal attention is dedicated to the kinetic influence of external signaling medium cAMP. The equilibrium existence condition is discussed, and near Hopf bifurcation point, the approximate solution is derived by Lindstedt’s method. Several numerical simulations are conducted to demonstrate our results.