Intrinsic noise, gene regulation and steady-state statistics in a two-gene network

The intrinsic noise in a two-gene network model is analysed. The technique of the Fokker-Planck approximation is used to investigate the statistics of noise when the system state is near a stable equilibrium. This is called also the steady-state statistics. The relative size of noise is measured by the Fano factor that is defined as the ratio of the variance to the mean. Our main result shows that in general, the noise control in a two-gene network might be a very complicated process, but for the repressor-repressor system that is a very important case in investigating the genetic switch, the relative size of noise, i.e. the Fano factor, must be bigger than one for both the repressor proteins.     

External noise and feedback regulation: steady-state statistics of auto-regulatory genetic network

The steady-state statistics of a single gene auto-regulatory genetic network with the additive external Gaussian white noises is investigated. The main result shows that the negative feedback will result in that the mRNA noise has a positive contribution to the protein noise, but the positive feedback will result in that the mRNA noise has a negative contribution to the protein noise. If there is no feed back, then the contribution of mRNA noise to protein noise is always positive. On the other hand, the analysis and numerical simulations of linear and nonlinear feedback show that it is possible that the negative feedback increases, but the positive feedback decreases, the protein noise.     

Mutual interaction in network motifs robustly sharpens gene expression in developmental processes

The gene regulatory network of a developmental process contains many mutually repressive interactions between two genes. They are often regulated by or regulate an additional factor, which constitute prominent network motifs, called regulated and regulating mutual loops. Our database analysis on the gene regulatory network for Drosophila melanogaster indicates that those with mutual repression are working specifically for the segmentation process. To clarify their biological roles, we mathematically study the response of the regulated mutual loop with mutual repression to input stimuli. We show that the mutual repression increases the response sensitivity without affecting the threshold input level to activate the target gene expression, as long as the network output is unique for a given input level. This high sensitivity of the motif can contribute to sharpening the spatial domain pattern without changing its position, assuring a robust developmental process. We also study transient dynamics that shows shift of domain boundary, agreeing with experimental observations. Importance of mutual repression is addressed by comparing with other types of regulations.     

Multivariate analysis of noise in genetic regulatory networks

Stochasticity is an intrinsic property of genetic regulatory networks due to the low copy numbers of the major molecular species, such as, DNA, mRNA, and regulatory proteins. Therefore, investigation of the mechanisms that reduce the stochastic noise is essential in understanding the reproducible behaviors of real organisms and is also a key to design synthetic genetic regulatory networks that can reliably work. We use an analytical and systematic method, the linear noise approximation of the chemical master equation along with the decoupling of a stoichiometric matrix. In the analysis of fluctuations of multiple molecular species, the covariance is an important measure of noise. However, usually the representation of a covariance matrix in the natural coordinate system, i.e. the copy numbers of the molecular species, is intractably complicated because reactions change copy numbers of more than one molecular species simultaneously. Decoupling of a stoichiometric matrix, which is a transformation of variables, significantly simplifies the representation of a covariance matrix and elucidates the mechanisms behind the observed fluctuations in the copy numbers. We apply our method to three types of fundamental genetic regulatory networks, that is, a single-gene autoregulatory network, a two-gene autoregulatory network, and a mutually repressive network. We have found that there are multiple noise components differently originating. Each noise component produces fluctuation in the characteristic direction. The resulting fluctuations in the copy numbers of the molecular species are the sum of these fluctuations. In the examples, the limitation of the negative feedback in noise reduction and the trade-off of fluctuations in multiple molecular species are clearly explained. The analytical representations show the full parameter dependence. Additionally, the validity of our method is tested by stochastic simulations.     

Stochastic Fluctuations Through Intrinsic Noise in Evolutionary Game Dynamics

A one-step (birth–death) process is used to investigate stochastic noise in an elementary two-phenotype evolutionary game model based on a payoff matrix. In this model, we assume that the population size is finite but not fixed and that all individuals have, in addition to the frequency-dependent fitness given by the evolutionary game, the same background fitness that decreases linearly in the total population size. Although this assumption guarantees population extinction is a globally attracting absorbing barrier of the Markov process, sample trajectories do not illustrate this result even for relatively small carrying capacities. Instead, the observed persistent transient behavior can be analyzed using the steady-state statistics (i.e., mean and variance) of a stochastic model for intrinsic noise that assumes the population does not go extinct. It is shown that there is good agreement between the theory of these statistics and the simulation results. Furthermore, the ESS of the evolutionary game can be used to predict the mean steady state.     

Intrinsic noise and the design of the genetic machinery

Darwinian theory envisages 'selection pressure' as a stress imposed on the genotype by the environment. However, noise in the replicative and translational mechanisms in itself imposes a significant 'pressure' on the adaptive fitness of the organism. We propose that the biosphere has been shaped by both extrinsic (environmental) and intrinsic (noise-generated) factors. Because noise has been a remorseless and ever-present background to the evolutionary process, adaptations to this intrinsic pressure include not only a variety of familiar genetic mechanisms but also many anatomical and life-style characteristics that focus on the transmission of information between generations.     

Formulas for intrinsic noise evaluation in oscillatory genetic networks

The linear noise approximation is a useful method for stochastic noise evaluations in genetic regulatory networks, where the covariance equation described as a Lyapunov equation plays a central role. We discuss the linear noise approximation method for evaluations of an intrinsic noise in autonomously oscillatory genetic networks; in such oscillatory networks, the covariance equation becomes a periodic differential equation that provides generally an unbounded covariance matrix, so that the standard method of noise evaluation based on the covariance matrix cannot be adopted directly. In this paper, we develop a new method of noise evaluation in oscillatory genetic networks; first, we investigate structural properties, e.g., orbital stability and periodicity, of the solutions to the covariance equation given as a periodic Lyapunov differential equation by using the Floquet-Lyapunov theory, and propose a global measure for evaluating stochastic amplitude fluctuations on the periodic trajectory; we also derive an evaluation formula for the period fluctuation. Finally, we apply our method to a model of circadian oscillations based on negative auto-regulation of gene expression, and show validity of our method by comparing the evaluation results with stochastic simulations.     

Extracellular noise-induced stochastic synchronization in heterogeneous quorum sensing network

Quorum sensing is a bacterial mechanism used to synchronize the coordinated response of a microbial population. Because quorum sensing in Gram-negative bacteria depends on release and detection of a diffusible signaling molecule (autoinducer) among a multicellular group, it is considered a simple form of cell-cell communication for the purposes of mathematical analysis. Stochastic equation systems have provided a common approach to model biochemical or biophysical processes. Recently, the effect of noise to synchronize a specific homogeneous quorum sensing network was successfully modeled using a stochastic equation system with fixed parameters. The question remains of how to model quorum sensing networks in a general setting. To address this question, we first set a stochastic equation system as a general model for a heterogeneous quorum sensing network. Then, using two relevant biophysical characteristics of Gram-negative bacteria (the permeability of the cell membrane to the autoinducer and the symmetry of autoinducer diffusion) we construct the solution of the stochastic equation system at an abstract level. The solution indicates that stable synchronization of a quorum sensing network is robustly induced by an environment with a heterogenous distribution of extracellular and intracellular noise. The synchronization is independent of the initial state of the system and is solely the result of the connectivity of the cell network established through the effects of extracellular noise.     

Stochastic variation in the concentration of a repressor activates GAL genetic switch: implications in evolution of regulatory network

In Saccharomyces cerevisiae, a recessive mutation in the signal transducer encoded by GAL3 leads to a significant lag in the induction of GAL genes, referred to as long term adaptation phenotype (LTA). Further, gal3 mutation in combination with other genetic defects leads to the non-inducibility of GAL genes. It was shown that the expression of GAL1 encoded galactokinase, a redundant GAL3 like signal transducer, eventually substitutes for the lack of GAL3 signal transduction function. However, how GAL1 gets induced in the absence of GAL3 is not clear. We hypothesize that GAL1 induction in gal3 cells exposed to galactose is due to a stochastic decrease in the repressor, Gal80p concentration, leading to heterogeneity in the population. This observation explains not only LTA observed in gal3 cells but also explains the non-inducibility of gal3 mutants in combination with other genetic defects. By recruiting a dedicated signal transducer, GAL3, S. cerevisiae GAL switch has evolved to overcome the fortuitous induction, which occurs due to low signal to noise ratio in certain mutants of Escherichia coli and Kluveromyces lactis.     

Chaotic gene regulatory networks can be robust against mutations and noise

Robustness to mutations and noise has been shown to evolve through stabilizing selection for optimal phenotypes in model gene regulatory networks. The ability to evolve robust mutants is known to depend on the network architecture. How do the dynamical properties and state-space structures of networks with high and low robustness differ? Does selection operate on the global dynamical behavior of the networks? What kind of state-space structures are favored by selection? We provide damage propagation analysis and an extensive statistical analysis of state spaces of these model networks to show that the change in their dynamical properties due to stabilizing selection for optimal phenotypes is minor. Most notably, the networks that are most robust to both mutations and noise are highly chaotic. Certain properties of chaotic networks, such as being able to produce large attractor basins, can be useful for maintaining a stable gene-expression pattern. Our findings indicate that conventional measures of stability, such as damage propagation, do not provide much information about robustness to mutations or noise in model gene regulatory networks.     

基于组学数据构建基因调控网络

在生命体内,基因以及其它分子间相互作用形成复杂调控网络,生命过程都是以调控网络的形式存在,如从代谢通路网络到转录调控网络,从信号转导网络到蛋白质相互作用网络等等。因此,网络现象是生命现象的复杂本质和主要特征。本文系统地介绍了基于表达谱数据构建基因调控网络的布尔网络模型,线性模型,微分方程模型和贝叶斯网络模型,并对各种网络构建模型进行了深入的分析和总结。同时,文章从基因组序列信息、蛋白质相互作用信息和生物医学文献信息等方面讨论了基因调控网络方面构建的研究,这对从系统生物学水平揭示生命复杂机制具有重要的参考价值。     

Synchronization and stochastic resonance of the small-world neural network based on the CPG

According to biological knowledge, the central nervous system controls the central pattern generator (CPG) to drive the locomotion. The brain is a complex system consisting of different functions and different interconnections. The topological properties of the brain display features of small-world network. The synchronization and stochastic resonance have important roles in neural information transmission and processing. In order to study the synchronization and stochastic resonance of the brain based on the CPG, we establish the model which shows the relationship between the small-world neural network (SWNN) and the CPG. We analyze the synchronization of the SWNN when the amplitude and frequency of the CPG are changed and the effects on the CPG when the SWNN’s parameters are changed. And we also study the stochastic resonance on the SWNN. The main findings include: (1) When the CPG is added into the SWNN, there exists parameters space of the CPG and the SWNN, which can make the synchronization of the SWNN optimum. (2) There exists an optimal noise level at which the resonance factor Q gets its peak value. And the correlation between the pacemaker frequency and the dynamical response of the network is resonantly dependent on the noise intensity. The results could have important implications for biological processes which are about interaction between the neural network and the CPG.     

Database and interaction network of genes involved in oral cancer: Version II

The oral cancer gene database has been compiled to enable fast retrieval of updated information and role of the genes implicated in oral cancer. The first version of the database with 242 genes was published in Online Journal of Bioinformatics 8(1), 41-44, 2007. In the second version, the database has been enlarged to include 374 genes by adding 132 gene entries. The architecture and format of the database is similar to the earlier version, and includes updated information and external hyperlinks for all the genes. The functional gene interaction network for important biological processes and molecular functions has been rebuilt based on 374 genes using 'String 8.3'. The database is freely available at http://www.actrec.gov.in/OCDB/index.htm and provides the scientist information and external links for the genes involved in oral cancer, interactions between them, and their role in the biology of oral cancer along with clinical relevance.