Local and global synchronization transitions induced by time delays in small-world neuronal networks with chemical synapses

Effects of time delay on the local and global synchronization in small-world neuronal networks with chemical synapses are investigated in this paper. Numerical results show that, for both excitatory and inhibitory coupling types, the information transmission delay can always induce synchronization transitions of spiking neurons in small-world networks. In particular, regions of in-phase and out-of-phase synchronization of connected neurons emerge intermittently as the synaptic delay increases. For excitatory coupling, all transitions to spiking synchronization occur approximately at integer multiples of the firing period of individual neurons; while for inhibitory coupling, these transitions appear at the odd multiples of the half of the firing period of neurons. More importantly, the local synchronization transition is more profound than the global synchronization transition, depending on the type of coupling synapse. For excitatory synapses, the local in-phase synchronization observed for some values of the delay also occur at a global scale; while for inhibitory ones, this synchronization, observed at the local scale, disappears at a global scale. Furthermore, the small-world structure can also affect the phase synchronization of neuronal networks. It is demonstrated that increasing the rewiring probability can always improve the global synchronization of neuronal activity, but has little effect on the local synchronization of neighboring neurons.     

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.     

Induction and propagation of transient synchronous activity in neural networks endowed with short-term plasticity

Transient, task related synchronous activity within neural populations has been recognized as the substrate of temporal coding in the brain. The mechanisms underlying inducing and propagation of transient synchronous activity are still unknown, and we propose that short-term plasticity (STP) of neural circuits may serve as a supplemental mechanism therein. By computational modeling, we showed that short-term facilitation greatly increases the reactivation rate of population spikes and decreases the latency of response to reactivation stimuli in local recurrent neural networks. Meanwhile, the timing of population spike reactivation is controlled by the memory effect of STP, and it is mediated primarily by the facilitation time constant. Furthermore, we demonstrated that synaptic facilitation dramatically enhances synchrony propagation in feedforward neural networks and that response timing mediated by synaptic facilitation offers a scheme for information routing. In addition, we verified that synaptic strengthening of intralayer or interlayer coupling enhances synchrony propagation, and we verified that other factors such as the delay of synaptic transmission and the mode of synaptic connectivity are also involved in regulating synchronous activity propagation. Overall, our results highlight the functional role of STP in regulating the inducing and propagation of transient synchronous activity, and they may inspire testable hypotheses for future experimental studies.     

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.     

生物钟体系中色噪音诱导的日夜节律振荡和内信号随机共振

利用脉孢菌生物钟体系,研究了色噪音对其进行诱导所产生的日夜节律振荡信号及其内信号随机共振的行为．结果表明,色噪音的相关时间对该体系内信号随机共振的强弱起较大的影响作用．当无外信号存在时,色噪音的相关时间对体系内信号随机共振强度起抑制的作用,且随相关时间的增大,抑制作用增强．当外信号加到体系中时,由于相关时间和外信号的协同作用,相关时间不仅对其内信号随机共振强度起抑制的作用,而且还影响内信号随机共振峰的数目,即随相关时间的增大,可使单峰随机共振变为随机双共振．存在最佳的外信号频率使体系的内信号随机共振强度得到最大的增强,而其他频率的外信号却起抑制作用．色内噪音和色外噪音相比,前者对该体系进行诱导所得的内信号随机共振强度比后者的更强,而且体系对前者更敏感．另外,存在极限的噪音强度使白噪音和色噪音对该体系内信号随机共振的影响差异得以消失．所得结果可为治疗生物钟紊乱综合症提供理论依据,同时可更好地理解其他节奏机理,如心脏搏动节奏、呼吸节奏以及荷尔蒙水平的波动节奏等．     

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.