Role of noises in neural networks

Reconstruction of gene regulatory networks for Caenorhabditis elegans using tree-shaped gene expression data

Constructing gene regulatory networks is a widely adopted approach for investigating gene regulation, offering diverse applications in biology and medicine. A great deal of research focuses on using time series data or single-cell RNA-sequencing data to infer gene regulatory networks. However, such gene expression data lack either cellular or temporal information. Fortunately, the advent of time-lapse confocal laser microscopy enables biologists to obtain tree-shaped gene expression data of Caenorhabditis elegans, achieving both cellular and temporal resolution. Although such tree-shaped data provide abundant knowledge, they pose challenges like non-pairwise time series, laying the inaccuracy of downstream analysis. To address this issue, a comprehensive framework for data integration and a novel Bayesian approach based on Boolean network with time delay are proposed. The pre-screening process and Markov Chain Monte Carlo algorithm are applied to obtain the parameter estimates. Simulation studies show that our method outperforms existing Boolean network inference algorithms. Leveraging the proposed approach, gene regulatory networks for five subtrees are reconstructed based on the real tree-shaped datatsets of Caenorhabditis elegans, where some gene regulatory relationships confirmed in previous genetic studies are recovered. Also, heterogeneity of regulatory relationships in different cell lineage subtrees is detected. Furthermore, the exploration of potential gene regulatory relationships that bear importance in human diseases is undertaken. All source code is available at the GitHub repository https://github.com/edawu11/BBTD.git.

Effects of correlated and synchronized stochastic inputs to leaky integrator neuronal model

We present an analysis of neuronal model behaviour with correlated synaptic inputs including the cases that correlated inputs are equivalent to exactly synchronized inputs and correlated inputs are not equivalent to exactly synchronized inputs. For the former case, it is found that the fully (synaptically) correlated inputs assumption (see Section 1 for definition), which is used in most, if not all, theoretical and experimental work in the past few years, results in a waste of resources and might be an unrealistic assumption; with an exactly balanced excitatory and inhibitory, and synaptically correlated input, the integrate-and-fire model simply behaves as a synchrony detector in certain parameter regions; the well-known diffusion model, upon which most theoretical work is based, fails to approximate the model with synaptically correlated Poisson inputs. A novel way to approximate synaptically correlated Poisson inputs is then presented;an optimization principle on neuronal models with partially (synaptically) correlated inputs is proposed, which enables us to predict microscopic structures in neuronal systems. For the latter case,with tightly synchronized inputs (see Section 1 for definition), the model behaviour depends on its integration time of input signals and could exhibit bursting discharge.for loosely synchronized inputs, we found that correlated inputs are equivalent to the post-spike voltage reset mechanism proposed in the literature.

Impact of geometrical structures on the output of neuronal models: a theoretical and numerical analysis

What is the difference between the efferent spike train of a neuron with a large soma versus that of a neuron with a small soma? We propose an analytical method called the decoupling approach to tackle the problem. Two limiting cases-the soma is much smaller than the dendrite or vica versa-are theoretically investigated. For both the two-compartment integrate-and-fire model and Pinsky-Rinzel model, we show, both theoretically and numerically, that the smaller the soma is, the faster and the more irregularly the neuron fires. We further conclude, in terms of numerical simulations, that cells falling in between the two limiting cases form a continuum with respect to their firing properties (mean firing time and coefficient of variation of inter-spike intervals).

Is the integrate-and-fire model good enough?--a review

We review some recent results on the behaviour of the integrate-and-fire (IF) model, the FitzHugh-Nagumo (FHN) model, a simplified version of the FHN (IF-FHN) model and the Hodgkin-Huxley (HH) model with correlated inputs. The effect of inhibitory inputs on the model behaviour is also taken into account. Here, inputs exclusively take the form of diffusion approximation and correlated inputs mean correlated synaptic inputs (Sections 2 and 3). It is found that the IF and HH models respond to correlated inputs in totally opposite ways, but the IF-FHN model shows similar behaviour to the HH model. Increasing inhibitory input to single neuronal models, such as the FHN model and the HH model can sometimes increase their firing rates, which we termed inhibition-boosted firing (IBF). Using the IF model and the IF-FHN model, we theoretically explore how and when IBF can happen. The computational complexity of the IF-FHN model is very similar to the conventional IF model, but the former captures some interesting and essential features of biophysical models and could serve as a better model for spiking neuron computation.

Behavior of integrate-and-fire and Hodgkin-Huxley models with correlated inputs

We assess, both numerically and theoretically, how positively correlated Poisson inputs affect the output of the integrate-and-fire and Hodgkin-Huxley models. For the integrate-and-fire model the variability of efferent spike trains is an increasing function of input correlation, and of the ratio between inhibitory and excitatory inputs. Interestingly for the Hodgkin-Huxley model the variability of efferent spike trains is a decreasing function of input correlation, and for fixed input correlation it is almost independent of the ratio between inhibitory and excitatory inputs. In terms of the signal to noise ratio of efferent spike trains the integrate-and-fire model works better in an environment of asynchronous inputs, but the Hodgkin-Huxley model has an advantage for more synchronous (correlated) inputs. In conclusion the integrate-and-fire and Hodgkin-Huxley models respond to correlated inputs in totally opposite ways.

Stochastic resonance tuned by correlations in neural models

The idea that neurons might use stochastic resonance (SR) to take advantage of random signals has been extensively discussed in the literature. However, there are a few key issues that have not been clarified and thus it is difficult to assess that whether SR in neuronal models occurs inside plausible physiology parameter regions or not. We propose and show that neurons can adjust correlations between synaptic inputs, which can be measured in experiments and are dynamical variables, to exhibit SR. The benefit of such a mechanism over the conventional SR is also discussed.

Synchronization due to common pulsed input in Stein's model

It is known that stimulus-evoked oscillatory synchronization among neurones occurs in widely separated cortical regions. In this paper we provide a possible mechanism to explain the phenomenon. When a common, random input is presented, we find that a group of neurones-of Stein's (integrate-and-fire) model type with or without reversal potentials-are capable of quickly synchronizing their firing. Interestingly the optimal average synchronization time occurs when the common input has a high coefficient of variation of interspike intervals (greater than 0.5) for this model with or without reversal potentials. The model with reversal potentials more quickly synchronizes than that without reversal potentials.

Lyapunov functions for neural nets with nondifferentiable input-output characteristics

I construct Lyapunov functions for asynchronous dynamics and synch ronous dynamics of neural networks with nondifferentiable input-output characteristics.