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.     

Intrinsic and external noise in an auto-regulatory genetic network

A single gene auto-regulatory network is analysed. The main goal is to investigate the effects of the negative and positive feedbacks on the intrinsic and external noises. The central finding of this paper is that: for the intrinsic noise, both the negative and positive feedback regulations increase the fluctuation strength of mRNA levels (where the fluctuation strength is measured by the Fano factor for both the fluctuations of mRNAs and proteins), and the negative feedback decreases, but the positive feedback increases, the fluctuation strength of proteins; for the external noise, the negative feedback not only increase the fluctuation strength of mRNA levels but also the fluctuation strength of proteins, and though the effect of the positive feedback on the fluctuation strength of mRNA levels depends on the size of positive feedback parameter k, the positive feedback must decrease the fluctuation strength of proteins.     

Robust synchronization analysis in nonlinear stochastic cellular networks with time-varying delays, intracellular perturbations and intercellular noise

Naturally, a cellular network consisted of a large amount of interacting cells is complex. These cells have to be synchronized in order to emerge their phenomena for some biological purposes. However, the inherently stochastic intra and intercellular interactions are noisy and delayed from biochemical processes. In this study, a robust synchronization scheme is proposed for a nonlinear stochastic time-delay coupled cellular network (TdCCN) in spite of the time-varying process delay and intracellular parameter perturbations. Furthermore, a nonlinear stochastic noise filtering ability is also investigated for this synchronized TdCCN against stochastic intercellular and environmental disturbances. Since it is very difficult to solve a robust synchronization problem with the Hamilton-Jacobi inequality (HJI) matrix, a linear matrix inequality (LMI) is employed to solve this problem via the help of a global linearization method. Through this robust synchronization analysis, we can gain a more systemic insight into not only the robust synchronizability but also the noise filtering ability of TdCCN under time-varying process delays, intracellular perturbations and intercellular disturbances. The measures of robustness and noise filtering ability of a synchronized TdCCN have potential application to the designs of neuron transmitters, on-time mass production of biochemical molecules, and synthetic biology. Finally, a benchmark of robust synchronization design in Escherichia coli repressilators is given to confirm the effectiveness of the proposed methods.     

Prediction of translation initiation sites in human mRNA sequences with AUG start codon in weak Kozak context: A neural network approach

Translation of eukaryotic mRNAs is often regulated by nucleotides around the start codon. A purine at position −3 and a guanine at position +4 contribute significantly to enhance the translation efficiency. Algorithms to predict the translation initiation site often fail to predict the start site if the sequence context is not present. We have developed a neural network method to predict the initiation site of mRNA sequences that lack the preferred nucleotides at the positions −3 and +4 surrounding the translation initiation site. Neural networks of various architectures comprising different number of hidden layers were designed and tested for various sizes of windows of nucleotides surrounding translation initiation sites. We found that the neural network with two hidden layers showed a sensitivity of 83% and specificity of 73% indicating a vastly improved performance in successfully predicting the translation initiation site of mRNA sequences with weak Kozak context. WeakAUG server is freely available at http://bioinfo.iitk.ac.in/AUGPred/.     

Time-varying Markov regression random-effect model with Bayesian estimation procedures: Application to dynamics of functional recovery in patients with stroke

The rates of functional recovery after stroke tend to decrease with time. Time-varying Markov processes (TVMP) may be more biologically plausible than time-invariant Markov process for modeling such data. However, analysis of such stochastic processes, particularly tackling reversible transitions and the incorporation of random effects into models, can be analytically intractable. We make use of ordinary differential equations to solve continuous-time TVMP with reversible transitions. The proportional hazard form was used to assess the effects of an individual’s covariates on multi-state transitions with the incorporation of random effects that capture the residual variation after being explained by measured covariates under the concept of generalized linear model. We further built up Bayesian directed acyclic graphic model to obtain full joint posterior distribution. Markov chain Monte Carlo (MCMC) with Gibbs sampling was applied to estimate parameters based on posterior marginal distributions with multiple integrands. The proposed method was illustrated with empirical data from a study on the functional recovery after stroke.