A self-regulatory genetic circuit, where a protein acts as a positive regulator of its own production, is known to be a simplest form of biological network with a positive feedback loop. Although at least three components, DNA, RNA, and the protein, are required to form such a circuit, the stability analysis of fixed points of the self-regulatory circuit has been performed only after reducing the system into to a two-component system consisting of RNA and protein only, assuming a fast equilibration of the DNA component. Here, the stability of fixed points of the three-component positive feedback loop is analyzed by obtaining eigenvalues of full three dimensional Hessian matrix. In addition to rigorously identifying the stable fixed points and the saddle points, detailed information can be obtained, such as the number of positive eigenvalues near a saddle point. In particular, complex eigenvalues is shown to exist for sufficiently slow binding and unbinding of the auto-regulatory transcription factor to DNA, leading to oscillatory convergence to the steady states, a novel feature unseen in the two-dimensional analysis.
Genetic regulatory networks enable cells to respond to the changes in internal and external conditions by dynamically coordinating their gene expression profiles. Our ability to make quantitative measurements in these biochemical circuits has deepened our understanding of what kinds of computations genetic regulatory networks can perform and with what reliability. These advances have motivated researchers to look for connections between the architecture and function of genetic regulatory networks. Transmitting information between network's inputs and its outputs has been proposed as one such p…
Genetic regulatory networks with adaptive responses are widely studied in biology. Usually, models consisting only of a few nodes have been considered. They present one input receptor for activation and one output node where the adaptive response is computed. In this work, we design genetic regulatory networks with many receptors and many output nodes able to produce delayed adaptive responses. This design is performed by using an evolutionary algorithm of mutations and selections that minimizes an error function defined by the adaptive response in signal shapes. We present several examples of…
A description for regulatory genetic network based on generalized potential energy is constructed. The potential energy is derived from the steady state solution of linearized Fokker-Plank equation, and the result is shown to be equivalent to the system of coupled oscillators. The correspondence between the quantities from the mechanical picture and the steady-state fluctuations is established. Explicit calculation is given for auto-regulatory networks in which, the force constant associated with the degree of protein is very weak. Negative feedback not only suppresses the fluctuations but als…
Cells receive a wide variety of cellular and environmental signals, which must be processed combinatorially to generate specific and timely genetic responses. We present here a theoretical study on the combinatorial control and integration of transcription signals, with the finding that cis-regulatory systems with specific protein-DNA interaction and glue-like protein-protein interactions, supplemented by distal activation or repression mechanisms, have the capability to execute a wide range of control functions encoded in the regulatory DNA sequences. Using a quantitative model based on the w…
Whereas the relationship between criticality of gene regulatory networks (GRNs) and dynamics of GRNs at a single cell level has been vigorously studied, the relationship between the criticality of GRNs and system properties at a higher level has remained unexplored. Here we aim at revealing a potential role of criticality of GRNs at a multicellular level which are hard to uncover through the single-cell-level studies, especially from an evolutionary viewpoint. Our model simulated the growth of a cell population from a single seed cell. All the cells were assumed to have identical GRNs. We indu…
We study the effects of multiple binding sites in the promoter of a genetic oscillator. We evaluate the regulatory function of a promoter with multiple binding sites in the absence of cooperative binding, and consider different hypotheses for how the number of bound repressors affects transcription rate. Effective Hill exponents of the resulting regulatory functions reveal an increase in the nonlinearity of the feedback with the number of binding sites. We identify optimal configurations that maximize the nonlinearity of the feedback. We use a generic model of a biochemical oscillator to show …
Genes and proteins regulate cellular functions through complex circuits of biochemical reactions. Fluctuations in the components of these regulatory networks result in noise that invariably corrupts the signal, possibly compromising function. Here, we create a practical formalism based on ideas introduced by Wiener and Kolmogorov (WK) for filtering noise in engineered communications systems to quantitatively assess the extent to which noise can be controlled in biological processes involving negative feedback. Application of the theory, which reproduces the previously proven scaling of the low…
An information processing circuit must be flexible to perform multiple tasks: biochemical information processing circuits in living systems can have multiple functions, requiring them to perform distinct computational tasks in different scenarios. Here, we describe a tunable dynamical system that performs different logical operations (such as AND, OR, and XOR) depending on which basin of attraction the dynamics resides in. We analyze the robustness of these dynamically switchable logic gates, and characterize the trade-off between reliability and efficiency in their function.
Cellular behavior is governed by gene regulatory processes that are intrinsically dynamic and nonlinear, and are subject to non-negligible amounts of random fluctuations. Such conditions are ubiquitous in physical systems, where they have been studied for decades using the tools of statistical and nonlinear physics. The goal of this review is to show how approaches traditionally used in physics can help in reaching a systems-level understanding of living cells. To that end, we present an overview of the dynamical phenomena exhibited by genetic circuits and their functional significance. We als…
We study a system of dynamical units, each of which shows excitable or oscillatory behavior, depending on the choice of parameters. When we couple these units with repressive bonds, we can control the duration of collective oscillations for an intermediate period between collective fixed-point behavior. The control mechanism works by monotonically increasing a single bifurcation parameter. Both the onset and arrest of oscillations are due to bifurcations. Depending on the coupling strength, the network topology and the tuning speed, our numerical simulations reveal a rich dynamics out-of-equil…
This work is devoted to investigating the evolution of concentration in a genetic regulation system, when the synthesis reaction rate is under additive and multiplicative asymmetric stable Lévy fluctuations. By focusing on the impact of skewness (i.e., non-symmetry) in the probability distributions of noise, we find that via examining the mean first exit time (MFET) and the first escape probability (FEP), the asymmetric fluctuations, interacting with nonlinearity in the system, lead to peculiar likelihood for transcription. This includes, in the additive noise case, realizing higher likelihood…
Many viruses have the cunning ability to enter a hibernative or off state, termed latency or lysogeny. When in a latent state, the virus is unable to replicate, and its gene expression program is largely shut down. This facility for lying dormant typically ensures lifelong persistence of the virus in the host; it is also a particularly problematic obstacle in the treatment of HIV. For most viruses, the molecular regulation of entry into latency is not completely understood, but it is believed that viral gene expression must be deactivated in some way. In this study, we introduce a new regulato…
The intrinsic stochasticity of gene expression is usually mitigated in higher eukaryotes by post-transcriptional regulation channels that stabilise the output layer, most notably protein levels. The discovery of small non-coding RNAs (miRNAs) in specific motifs of the genetic regulatory network has led to identifying noise buffering as the possible key function they exert in regulation. Recent in vitro} and in silico studies have corroborated this hypothesis. It is however also known that miRNA-mediated noise reduction is hampered by transcriptional bursting in simple topologies. Here, using s…
From a coarse-grained perspective the motif of a self-activating species, activating a second species which acts as its own repressor, is widely found in biological systems, in particular in genetic systems with inherent oscillatory behavior. Here we consider a specific realization of this motif as a genetic circuit, in which genes are described as directly producing proteins, leaving out the intermediate step of mRNA production. We focus on the effect that inherent time scales on the underlying fine-grained scale can have on the bifurcation patterns on a coarser scale in time. Time scales are…
Electronic circuits are useful tools for studying potential dynamical behaviors of synthetic genetic networks. The circuit models are complementary to numerical simulations of the networks, especially providing a framework for verification of dynamical behaviors in the presence of intrinsic and extrinsic noise of the electrical systems. Here we present an improved version of our previous design of an electronic analog of genetic networks that includes the 3-gene Repressilator and we show conversions between model parameters and real circuit component values to mimic the numerical results in ex…
Gene networks exhibiting oscillatory dynamics are widespread in biology. The minimal regulatory designs giving rise to oscillations have been implemented synthetically and studied by mathematical modeling. However, most of the available analyses generally neglect the coupling of regulatory circuits with the cellular "chassis" in which the circuits are embedded. For example, the intracellular macromolecular composition of fast-growing bacteria changes with growth rate. As a consequence, important parameters of gene expression, such as ribosome concentration or cell volume, are growth-rate depen…
A wide range of organisms features molecular machines, circadian clocks, which generate endogenous oscillations with ~24 h periodicity and thereby synchronize biological processes to diurnal environmental fluctuations. Recently, it has become clear that plants harbor more complex gene regulatory circuits within the core circadian clocks than other organisms, inspiring a fundamental question: are all these regulatory interactions between clock genes equally crucial for the establishment and maintenance of circadian rhythms? Our mechanistic simulation for Arabidopsis thaliana demonstrates that a…
Understanding computational capabilities of simple biological circuits, such as the regulatory circuits of single-cell organisms, remains an active area of research. Recent theoretical work has shown that a simple regulatory architecture based on end-product inhibition can exhibit predictive behavior by learning fluctuation statistics of one or two environmental parameters. Here we extend this analysis to higher dimensions. We show that as the number of inputs increases, a generalized version of the circuit can learn not only the dominant direction of fluctuations, as shown previously, but als…
Finding out statistically significant words in DNA and protein sequences forms the basis for many genetic studies. By applying the maximal entropy principle, we give one systematic way to study the nonrandom occurrence of words in DNA or protein sequences. Through comparison with experimental results, it was shown that patterns of regulatory binding sites in Saccharomyces cerevisiae(yeast) genomes tend to occur significantly in the promoter regions. We studied two correlated gene family of yeast. The method successfully extracts the binding sites varified by experiments in each family. Many pu…
We assess the impact of cell cycle noise on gene circuit dynamics. For bistable genetic switches and excitable circuits, we find that transitions between metastable states most likely occur just after cell division and that this concentration effect intensifies in the presence of transcriptional delay. We explain this concentration effect with a 3-states stochastic model. For genetic oscillators, we quantify the temporal correlations between daughter cells induced by cell division. Temporal correlations must be captured properly in order to accurately quantify noise sources within gene network…
