A delay model for noise-induced bi-directional switching

Many biological systems can switch between two distinct states. Once switched, the system remains stable for a period of time and may switch back to its original state. A gene network with bistability is usually required for the switching and stochastic effect in the gene expression may induce such switching. A typical bistable system allows one-directional switching, in which the switch from the low state to the high state or from the high state to the low state occurs under different conditions. It is usually difficult to enable bi-directional switching such that the two switches can occur under the same condition. Here, we present a model consisting of standard positive feedback loops and an extra negative feedback loop with a time delay to study its capability to produce bi-directional switching induced by noise. We find that the time delay in the negative feedback is critical for robust bi-directional switching and the length of delay affects its switching frequency.

Small but influential: the role of microRNAs on gene regulatory network and 3 ' UTR evolution

MicroRNAs (miRNAs) are endogenous similar to 22 nucleotide noncoding RNAs that regulate the expression of complementary messenger RNAs (mRNAs). Thousands of miRNA genes have been found in diverse species, and many of them are highly conserved. With the mi

Potential energy landscape and robustness of a gene regulatory network: Toggle switch

Finding a multidimensional potential landscape is the key for addressing important global issues, such as the robustness of cellular networks. We have uncovered the underlying potential energy landscape of a simple gene regulatory network: a toggle switch. This was realized by explicitly constructing the steady state probability of the gene switch in the protein concentration space in the presence of the intrinsic statistical fluctuations due to the small number of proteins in the cell. We explored the global phase space for the system. We found that the protein synthesis rate and the unbinding rate of proteins to the gene were small relative to the protein degradation rate; the gene switch is monostable with only one stable basin of attraction. When both the protein synthesis rate and the unbinding rate of proteins to the gene are large compared with the protein degradation rate, two global basins of attraction emerge for a toggle switch. These basins correspond to the biologically stable functional states. The potential energy barrier between the two basins determines the time scale of conversion from one to the other. We found as the protein synthesis rate and protein unbinding rate to the gene relative to the protein degradation rate became larger, the potential energy barrier became larger. This also corresponded to systems with less noise or the fluctuations on the protein numbers.

Population genetic structure of the parasitic nematode Camallanus cotti inferred from DNA sequences of ITS1 rDNA and the mitochondrial COI gene

The population genetic structure of fish parasitic nematode, Camallanus cotti, collected from the Yangtze River, Pearl River and Minjiang River in China was investigated. From these parasites, the similar to 730 bp of the first internal transcribed spacer of ribosomal DNA (ITS1 rDNA) and the 428 bp of mitochondrial cytochrome c oxidase subunit I (COI) gene were sequenced. For the ITS1 rDNA data set, highly significant Fst values and low rates of migration were detected between the Pearl River group and both the Yangtze River (Fst = 0.70, P < 0.00001; Nm = 0.21) and Minjiang River (Fst = 0.73, P < 0.00001; Nm = 0.18) groups, while low Fst value (Fst = 0.018, P > 0.05) and high rate of migration (Nm = 28.42) were found between the Minjiang and the Yangtze rivers. When different host/locality populations (subpopulations) within each river were considered, subpopulations between the Yangtze River and Minjiang River had low Fst values (<= 0.12) and high Nm values (>3.72), while Pearl River subpopulations were significantly different from the Yangtze River and Minjiang River subpopulations (Fst >= 0.59; Nm < 1). The COI gene data set revealed a similar genetic structure. Both phylogenetic analyses and a statistical parsimony network grouped the Pearl River haplotypes into one phylogroup, while the Yangtze River and Minjiang River haplotypes formed a second group. These results suggested that the Yangtze River and Minjiang River subpopulations constituted a single reproductive pool that was distinct from the Pearl River subpopulations. In addition, the present study did not find host-related genetic differentiation occurring in the same drainage. (C) 2009 Published by Elsevier B.V.

Robustness and dissipation of mitogen-activated protein kinases signal transduction network: Underlying funneled landscape against stochastic fluctuations

We uncovered the underlying energy landscape of the mitogen-activated protein kinases signal transduction cellular network by exploring the statistical natures of the Brownian dynamical trajectories. We introduce a dimensionless quantity: The robustness ratio of energy gap versus local roughness to measure the global topography of the underlying landscape. A high robustness ratio implies funneled landscape. The landscape is quite robust against environmental fluctuations and variants of the intrinsic chemical reaction rates.

Single molecule dynamics and statistical fluctuations of gene regulatory networks: A repressilator

The authors developed a time dependent method to study the single molecule dynamics of a simple gene regulatory network: a repressilator with three genes mutually repressing each other. They quantitatively characterize the time evolution dynamics of the repressilator. Furthermore, they study purely dynamical issues such as statistical fluctuations and noise evolution. They illustrated some important features of the biological network such as monostability, spirals, and limit cycle oscillation. Explicit time dependent Fano factors which describe noise evolution and show statistical fluctuations out of equilibrium can be significant and far from the Poisson distribution. They explore the phase space and the interrelationships among fluctuations, order, amplitude, and period of oscillations of the repressilators. The authors found that repressilators follow ordered limit cycle orbits and are more likely to appear in the lower fluctuating regions. The amplitude of the repressilators increases as the suppressing of the genes decreases and production of proteins increases. The oscillation period of the repressilators decreases as the suppressing of the genes decreases and production of proteins increases.

Dynamics and intrinsic statistical fluctuations of a gene switch

We studied a simple gene regulatory network, the toggle switch. Specifically, we examined the means and statistical fluctuations in numbers of proteins. We found that when omega, the ratio of rates of protein-gene unbinding to protein degradation, was between similar to 10(-3) and similar to 10, the fluctuations were much larger than those we would have expected from Poisson statistics. In addition, we examined characteristic time values for system relaxation and found both that they increased with omega and that they have significant phase transition effects, with a secondary time scale appearing near the boundary between bistable and other phases. Last, we discuss the bistability of the toggle switch.

Quantifying robustness and dissipation cost of yeast cell cycle network: The funneled energy landscape perspectives

We study the origin of robustness of yeast cell cycle cellular network through uncovering its underlying energy landscape. This is realized from the information of the steady-state probabilities by solving a discrete set of kinetic master equations for the network. We discovered that the potential landscape of yeast cell cycle network is funneled toward the global minimum, G1 state. The ratio of the energy gap between G1 and average versus roughness of the landscape termed as robustness ratio ( RR) becomes a quantitative measure of the robustness and stability for the network. The funneled landscape is quite robust against random perturbations from the inherent wiring or connections of the network. There exists a global phase transition between the more sensitive response or less self-degradation phase leading to underlying funneled global landscape with large RR, and insensitive response or more self-degradation phase leading to shallower underlying landscape of the network with small RR. Furthermore, we show that the more robust landscape also leads to less dissipation cost of the network. Least dissipation and robust landscape might be a realization of Darwinian principle of natural selection at cellular network level. It may provide an optimal criterion for network wiring connections and design.