Transient resetting: a novel mechanism for synchrony and its biological examples

Frequency-difference-dependent stochastic resonance in neural systems

Biological neurons receive multiple noisy oscillatory signals, and their dynamical response to the superposition of these signals is of fundamental importance for information processing in the brain. Here we study the response of neural systems to the weak envelope modulation signal, which is superimposed by two periodic signals with different frequencies. We show that stochastic resonance occurs at the beat frequency in neural systems at the single-neuron as well as the population level. The performance of this frequency-difference-dependent stochastic resonance is influenced by both the beat frequency and the two forcing frequencies. Compared to a single neuron, a population of neurons is more efficient in detecting the information carried by the weak envelope modulation signal at the beat frequency. Furthermore, an appropriate fine-tuning of the excitation-inhibition balance can further optimize the response of a neural ensemble to the superimposed signal. Our results thus introduce and provide insights into the generation and modulation mechanism of the frequency-difference-dependent stochastic resonance in neural systems.

Dynamical structure underlying inverse stochastic resonance and its implications

We investigate inverse stochastic resonance (ISR), a recently reported phenomenon in which the spiking activity of a Hodgkin-Huxley model neuron subject to external noise exhibits a pronounced minimum as the noise intensity increases. We clarify the mechanism that underlies ISR and show that its most surprising features are a consequence of the dynamical structure of the model. Furthermore, we show that the ISR effect depends strongly on the procedures used to measure it. Our results are important for the experimentalist who seeks to observe the ISR phenomenon.

Firing rate propagation through neuronal-astrocytic network

Understanding the underlying mechanism of the propagation of neuronal activities within the brain is a fundamental issue in neuroscience. Traditionally, communication and information processing have been exclusively considered as the province of synaptic coupling between neurons. Astrocytes, however, have recently been acknowledged as active partners in neuronal information processing. So, it is more reasonable and accurate to study the nature of neuronal signal propagation with the participation of astrocytes. In this paper, we first propose a feedforward neuronal-astrocytic network (FNAsN), which includes the mutual neuron-astrocyte interaction. Besides, we also consider the unreliability of both the synaptic transmission between neurons and the coupling between neurons and astrocytes. Then, the performance of firing rate propagation through the proposed FNAsN is studied through a series of simulations. Results show that the astrocytes can mediate neuronal activities, and consequently improve the performance of firing rate propagation, especially in a weak and noisy environment. From this point of view, astrocytes can be regarded as a realistic internal source of noise, which collaborates with an externally applied weak noise to prevent synchronous neuron firing within the same layer and thus to ensure reliable transmission.

Stochastic resonance in Hodgkin-Huxley neuron induced by unreliable synaptic transmission

We systematically investigate the stochastic dynamics of a single Hodgkin-Huxley neuron driven by stochastic excitatory and inhibitory input spikes via unreliable synapses in this paper. Based on the mean-filed theory, a novel intrinsic neuronal noise regulation mechanism stemming from unreliable synapses is presented. Our simulation results show that, under certain conditions, the stochastic resonance phenomenon is able to be induced by the unreliable synaptic transmission, which can be well explained by the theoretical prediction. To a certain degree, the results presented here provide insights into the functional roles of unreliable synapses in neural information processing.

Inhibition of rhythmic spiking by colored noise in neural systems

We study the effect of colored noise on the rhythmic spiking activity of neural systems in this paper. The phenomenon of the so-called inverse stochastic resonance , that is, noise with appropriate intensity suppresses the spiking activity in neural systems, is clearly observed in a special parameter regime. We find that the inhibition effect of colored noise is stronger than that of Gaussian white noise. Furthermore, our simulation results show that the inhibition effect of colored noise provides a useful mechanism for the generation of synchronized burst in type-2 mixed-feed-forward-feedback loop neuronal network motif, which indicates that such inhibition effect might have some biological implications.

History-dependent excitability as a single-cell substrate of transient memory for information discrimination

Neurons react differently to incoming stimuli depending upon their previous history of stimulation. This property can be considered as a single-cell substrate for transient memory, or context-dependent information processing: depending upon the current context that the neuron "sees" through the subset of the network impinging on it in the immediate past, the same synaptic event can evoke a postsynaptic spike or just a subthreshold depolarization. We propose a formal definition of History-Dependent Excitability (HDE) as a measure of the propensity to firing in any moment in time, linking the subthreshold history-dependent dynamics with spike generation. This definition allows the quantitative assessment of the intrinsic memory for different single-neuron dynamics and input statistics. We illustrate the concept of HDE by considering two general dynamical mechanisms: the passive behavior of an Integrate and Fire (IF) neuron, and the inductive behavior of a Generalized Integrate and Fire (GIF) neuron with subthreshold damped oscillations. This framework allows us to characterize the sensitivity of different model neurons to the detailed temporal structure of incoming stimuli. While a neuron with intrinsic oscillations discriminates equally well between input trains with the same or different frequency, a passive neuron discriminates better between inputs with different frequencies. This suggests that passive neurons are better suited to rate-based computation, while neurons with subthreshold oscillations are advantageous in a temporal coding scheme. We also address the influence of intrinsic properties in single-cell processing as a function of input statistics, and show that intrinsic oscillations enhance discrimination sensitivity at high input rates. Finally, we discuss how the recognition of these cell-specific discrimination properties might further our understanding of neuronal network computations and their relationships to the distribution and functional connectivity of different neuronal types.

Synchronization of the small-world neuronal network with unreliable synapses

As is well known, synchronization phenomena are ubiquitous in neuronal systems. Recently a lot of work concerning the synchronization of the neuronal network has been accomplished. In these works, the synapses are usually considered reliable, but experimental results show that, in biological neuronal networks, synapses are usually unreliable. In our previous work, we have studied the synchronization of the neuronal network with unreliable synapses; however, we have not paid attention to the effect of topology on the synchronization of the neuronal network. Several recent studies have found that biological neuronal networks have typical properties of small-world networks, characterized by a short path length and high clustering coefficient. In this work, mainly based on the small-world neuronal network (SWNN) with inhibitory neurons, we study the effect of network topology on the synchronization of the neuronal network with unreliable synapses. Together with the network topology, the effects of the GABAergic reversal potential, time delay and noise are also considered. Interestingly, we found a counter-intuitive phenomenon for the SWNN with specific shortcut adding probability, that is, the less reliable the synapses, the better the synchronization performance of the SWNN. We also consider the effects of both local noise and global noise in this work. It is shown that these two different types of noise have distinct effects on the synchronization: one is negative and the other is positive.

Global robust power-rate stability of delayed genetic regulatory networks with noise perturbations

In this paper, by using the Lyapunov method, Itô's differential formula and linear matrix inequality (LMI) approach, the global robust power-rate stability in mean square is discussed for genetic regulatory networks with unbounded time-varying delay, noise perturbations and parameter uncertainties. Sufficient conditions are given to ensure the robust power-rate stability (in mean square) of the genetic regulatory networks. Meanwhile, the criteria ensuring global power-rate stability in mean square are a byproduct of the criteria guaranteeing global robust power-rate stability in mean square. The obtained conditions are derived in terms of linear matrix inequalities (LMIs) which are easy to be verified via the LMI toolbox. An illustrative example is given to show the effectiveness of the obtained result.

Stochastic and coherence resonance in feed-forward-loop neuronal network motifs

The relationships between noise and complex dynamic behaviors of neuronal ensembles are key questions in computational neuroscience, particularly in understanding some basic signal transmission mechanisms of the brain. Here we systemically investigate both the stochastic resonance (SR) and coherence resonance (CR) in the triple-neuron feed-forward-loop (FFL) network motifs by computational modeling. We use the Izhikevich neuron model as well as the chemical coupling to build the FFL motifs, and consider all possible motif types. The simulation results demonstrate that these motifs can exploit noise to enrich its dynamic performance. With a proper choice of noise intensities, both the SR and CR can be exhibited in many types of the FFLs. On the other hand, our results also indicate that the coupling strength serves as a control parameter, which has great impacts on the stochastic dynamics of the FFL motifs. Additionally, biological implications of presented results in the field of neuroscience are outlined.

Synchronization of genetic oscillators

Synchronization of genetic or cellular oscillators is a central topic in understanding the rhythmicity of living organisms at both molecular and cellular levels. Here, we show how a collective rhythm across a population of genetic oscillators through synchronization-induced intercellular communication is achieved, and how an ensemble of independent genetic oscillators is synchronized by a common noisy signaling molecule. Our main purpose is to elucidate various synchronization mechanisms from the viewpoint of dynamics, by investigating the effects of various biologically plausible couplings, several kinds of noise, and external stimuli. To have a comprehensive understanding on the synchronization of genetic oscillators, we consider three classes of genetic oscillators: smooth oscillators (exhibiting sine-like oscillations), relaxation oscillators (displaying jump dynamics), and stochastic oscillators (noise-induced oscillation). For every class, we further study two cases: with intercellular communication (including phase-attractive and repulsive coupling) and without communication between cells. We find that an ensemble of smooth oscillators has different synchronization phenomena from those in the case of relaxation oscillators, where noise plays a different but key role in synchronization. To show differences in synchronization between them, we make comparisons in many aspects. We also show that a population of genetic stochastic oscillators have their own synchronization mechanisms. In addition, we present interesting phenomena, e.g., for relaxation-type stochastic oscillators coupled to a quorum-sensing mechanism, different noise intensities can induce different periodic motions (i.e., inhomogeneous limit cycles).

A model of stimulus-specific neural assemblies in the insect antennal lobe

It has been proposed that synchronized neural assemblies in the antennal lobe of insects encode the identity of olfactory stimuli. In response to an odor, some projection neurons exhibit synchronous firing, phase-locked to the oscillations of the field potential, whereas others do not. Experimental data indicate that neural synchronization and field oscillations are induced by fast GABA(A)-type inhibition, but it remains unclear how desynchronization occurs. We hypothesize that slow inhibition plays a key role in desynchronizing projection neurons. Because synaptic noise is believed to be the dominant factor that limits neuronal reliability, we consider a computational model of the antennal lobe in which a population of oscillatory neurons interact through unreliable GABA(A) and GABA(B) inhibitory synapses. From theoretical analysis and extensive computer simulations, we show that transmission failures at slow GABA(B) synapses make the neural response unpredictable. Depending on the balance between GABA(A) and GABA(B) inputs, particular neurons may either synchronize or desynchronize. These findings suggest a wiring scheme that triggers stimulus-specific synchronized assemblies. Inhibitory connections are set by Hebbian learning and selectively activated by stimulus patterns to form a spiking associative memory whose storage capacity is comparable to that of classical binary-coded models. We conclude that fast inhibition acts in concert with slow inhibition to reformat the glomerular input into odor-specific synchronized neural assemblies.

Noise-induced dynamics in the mixed-feedback-loop network motif

In this paper, we present a stochastic model for the mixed-feedback loop (MFL), a motif found in integrated cellular networks of transcription regulation and protein-protein interaction. Previous bifurcation analysis indicates that this motif can serve as a bistable switch or a clock. We investigate how extrinsic and intrinsic noise affects its dynamic behaviors systematically. We find that this motif can exploit noise to enrich its dynamical performance. When the MFL is in the bistable region, under fluctuation of extrinsic noise, the MFL system can switch from one steady state to the other and meanwhile one protein's production is amplified for more than three orders of magnitude. Further, from an engineering perspective, this noise-based switch and amplifier for gene expression is very easy to control. Without extrinsic noise, spontaneous transition between states occurs as the consequence of intrinsic noise. Such a switch is controlled by the parameters and system size. On the other hand, intrinsic noise can induce sustained stochastic oscillation when the corresponding deterministic system does not oscillate. Such stochastic oscillation shows the best performance at an optimal noise level, indicating the occurrence of intrinsic noise stochastic resonance which can contribute to the robustness of this oscillator. When considering the effects of extrinsic noise near bifurcation points, a similar phenomenon of extrinsic noise stochastic resonance is unveiled.

Discovering functions and revealing mechanisms at molecular level from biological networks

With the increasingly accumulated data from high-throughput technologies, study on biomolecular networks has become one of key focuses in systems biology and bioinformatics. In particular, various types of molecular networks (e.g., protein-protein interaction (PPI) network; gene regulatory network (GRN); metabolic network (MN); gene coexpression network (GCEN)) have been extensively investigated, and those studies demonstrate great potentials to discover basic functions and to reveal essential mechanisms for various biological phenomena, by understanding biological systems not at individual component level but at a system-wide level. Recent studies on networks have created very prolific researches on many aspects of living organisms. In this paper, we aim to review the recent developments on topics related to molecular networks in a comprehensive manner, with the special emphasis on the computational aspect. The contents of the survey cover global topological properties and local structural characteristics, network motifs, network comparison and query, detection of functional modules and network motifs, function prediction from network analysis, inferring molecular networks from biological data as well as representative databases and software tools.

Synchronization-induced rhythmicity of circadian oscillators in the suprachiasmatic nucleus

The suprachiasmatic nuclei (SCN) host a robust, self-sustained circadian pacemaker that coordinates physiological rhythms with the daily changes in the environment. Neuronal clocks within the SCN form a heterogeneous network that must synchronize to maintain timekeeping activity. Coherent circadian output of the SCN tissue is established by intercellular signaling factors, such as vasointestinal polypeptide. It was recently shown that besides coordinating cells, the synchronization factors play a crucial role in the sustenance of intrinsic cellular rhythmicity. Disruption of intercellular signaling abolishes sustained rhythmicity in a majority of neurons and desynchronizes the remaining rhythmic neurons. Based on these observations, the authors propose a model for the synchronization of circadian oscillators that combines intracellular and intercellular dynamics at the single-cell level. The model is a heterogeneous network of circadian neuronal oscillators where individual oscillators are damped rather than self-sustained. The authors simulated different experimental conditions and found that: (1) in normal, constant conditions, coupled circadian oscillators quickly synchronize and produce a coherent output; (2) in large populations, such oscillators either synchronize or gradually lose rhythmicity, but do not run out of phase, demonstrating that rhythmicity and synchrony are codependent; (3) the number of oscillators and connectivity are important for these synchronization properties; (4) slow oscillators have a higher impact on the period in mixed populations; and (5) coupled circadian oscillators can be efficiently entrained by light-dark cycles. Based on these results, it is predicted that: (1) a majority of SCN neurons needs periodic synchronization signal to be rhythmic; (2) a small number of neurons or a low connectivity results in desynchrony; and (3) amplitudes and phases of neurons are negatively correlated. The authors conclude that to understand the orchestration of timekeeping in the SCN, intracellular circadian clocks cannot be isolated from their intercellular communication components.

Stochastic synchronization of genetic oscillator networks

Background

The study of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic networks are intrinsically noisy due to natural random intra- and inter-cellular fluctuations. Therefore, it is important to study the effects of noise perturbation on the synchronous dynamics of genetic oscillators. From the synthetic biology viewpoint, it is also important to implement biological systems that minimizing the negative influence of the perturbations.

Results

In this paper, based on systems biology approach, we provide a general theoretical result on the synchronization of genetic oscillators with stochastic perturbations. By exploiting the specific properties of many genetic oscillator models, we provide an easy-verified sufficient condition for the stochastic synchronization of coupled genetic oscillators, based on the Lur'e system approach in control theory. A design principle for minimizing the influence of noise is also presented. To demonstrate the effectiveness of our theoretical results, a population of coupled repressillators is adopted as a numerical example.

Conclusion

In summary, we present an efficient theoretical method for analyzing the synchronization of genetic oscillator networks, which is helpful for understanding and testing the synchronization phenomena in biological organisms. Besides, the results are actually applicable to general oscillator networks.