Study of DNA binding sites using the Rényi parametric entropy measure

Shannon's definition of uncertainty or surprisal has been applied extensively to measure the information content of aligned DNA sequences and characterizing DNA binding sites. In contrast to Shannon's uncertainty, this study investigates the applicability and suitability of a parametric uncertainty measure due to Rényi. It is observed that this measure also provides results in agreement with Shannon's measure, pointing to its utility in analysing DNA binding site region. For facilitating the comparison between these uncertainty measures, a dimensionless quantity called "redundancy" has been employed. It is found that Rényi's measure at low parameter values possess a better delineating feature of binding sites (of binding regions) than Shannon's measure. The critical value of the parameter is chosen with an outlier criterion.     

Neuronal model with distributed delay: analysis and simulation study for gamma distribution memory kernel

A single neuronal model incorporating distributed delay (memory)is proposed. The stochastic model has been formulated as a Stochastic Integro-Differential Equation (SIDE) which results in the underlying process being non-Markovian. A detailed analysis of the model when the distributed delay kernel has exponential form (weak delay) has been carried out. The selection of exponential kernel has enabled the transformation of the non-Markovian model to a Markovian model in an extended state space. For the study of First Passage Time (FPT) with exponential delay kernel, the model has been transformed to a system of coupled Stochastic Differential Equations (SDEs) in two-dimensional state space. Simulation studies of the SDEs provide insight into the effect of weak delay kernel on the Inter-Spike Interval(ISI) distribution. A measure based on Jensen-Shannon divergence is proposed which can be used to make a choice between two competing models viz. distributed delay model vis-á-vis LIF model. An interesting feature of the model is that the behavior of (CV(t))((ISI)) (Coefficient of Variation) of the ISI distribution with respect to memory kernel time constant parameter η reveals that neuron can switch from a bursting state to non-bursting state as the noise intensity parameter changes. The membrane potential exhibits decaying auto-correlation structure with or without damped oscillatory behavior depending on the choice of parameters. This behavior is in agreement with empirically observed pattern of spike count in a fixed time window. The power spectral density derived from the auto-correlation function is found to exhibit single and double peaks. The model is also examined for the case of strong delay with memory kernel having the form of Gamma distribution. In contrast to fast decay of damped oscillations of the ISI distribution for the model with weak delay kernel, the decay of damped oscillations is found to be slower for the model with strong delay kernel.     

Stochastic Mesocortical Dynamics and Robustness of Working Memory during Delay-Period

The role of prefronto-mesoprefrontal system in the dopaminergic modulation of working memory during delayed response tasks is well-known. Recently, a dynamical model of the closed-loop mesocortical circuit has been proposed which employs a deterministic framework to elucidate the system’s behavior in a qualitative manner. Under natural conditions, noise emanating from various sources affects the circuit’s functioning to a great extent. Accordingly in the present study, we reformulate the model into a stochastic framework and investigate its steady state properties in the presence of constant background noise during delay-period. From the steady state distribution, global potential landscape and signal-to-noise ratio are obtained which help in defining robustness of the circuit dynamics. This provides insight into the robustness of working memory during delay-period against its disruption due to background noise. The findings reveal that the global profile of circuit’s robustness is predominantly governed by the level of D1 receptor activity and high D1 receptor stimulation favors the working memory-associated sustained-firing state over the spontaneous-activity state of the system. Moreover, the circuit’s robustness is further fine-tuned by the levels of excitatory and inhibitory activities in a way such that the robustness of sustained-firing state exhibits an inverted-U shaped profile with respect to D1 receptor stimulation. It is predicted that the most robust working memory is formed possibly at a subtle ratio of the excitatory and inhibitory activities achieved at a critical level of D1 receptor stimulation. The study also paves a way to understand various cognitive deficits observed in old-age, acute stress and schizophrenia and suggests possible mechanistic routes to the working memory impairments based on the circuit’s robustness profile.     

A Semi-Markovian Model for Cell Survival after Irradiation

To study the behaviour of a living cell exposed to radiations we investigate a stochastic model, employing for its analysis the theory of semi-Markov and Markov renewal processes. Four states of the cell namely, normal state, damaged state 1, damaged state 2 and altered state are defined and various characteristics of interest pertaining to the cell behaviour are studied.     

A one-compartment model with stochastic parameter

We consider a one-compartment system with stochastic transfer rate characterized either by Gaussian or by two-level jump process and study the time evolution of the (statistical) moments of the (random) amount of the substance present in the system. The effect of the coloured as well as of the white noise is investigated and it is found that the presence of stochasticity in the transfer rate parameter increases the relaxation time of the system. Finally, we obtain the conditions for the stability of the system in the moment sense.