Generalized stability conditions for coupled neural networks with delay feedbacks.

We present a generalization of the existing models of delayed neural networks (DNNs) with positive delay feedback. A generalized criterion for stability of the system of delay differential equations (DDEs), which governs the dynamics of DNNs, around the trivial local equilibrium is also provided.

Stochastic synchronization of neurons: the topologicalimpacts.

Cross-talk among coupled stochastic Hindmarsh-Rose (HR) neurons is significantly affected by the topology of the neurons organization. If the coupled stochastic HR neurons are arranged in the form of ring topology with odd number of neurons, the neurons are in anti-phase synchronization with homogeneous distribution of phase ordering of the oscillators. On the other hand, if the coupled HR oscillators are arranged in the ring topology with even number of oscillators, the oscillators are formed into two groups which are anti-phase synchronized, but all the oscillators in each group are in in-phase synchronization.Synchronization of the HR oscillators due to coupling in all topological arrangements is affected by the noise.However, noise can induce optimal coherence of the cross-talked oscillators at a particular value at which signal processing is the most favorable with amplified signal, the phenomenon known as stochastic resonance.

Complex multifractal nature in Mycobacterium tuberculosis genome.

The mutifractal and long range correlation (C(r)) properties of strings, such as nucleotide sequence can be a useful parameter for identification of underlying patterns and variations. In this study C(r) and multifractal singularity function f(α) have been used to study variations in the genomes of a pathogenic bacteria Mycobacterium tuberculosis. Genomic sequences of M. tuberculosis isolates displayed significant variations in C(r) and f(α) reflecting inherent differences in sequences among isolates. M. tuberculosis isolates can be categorised into different subgroups based on sensitivity to drugs, these are DS (drug sensitive isolates), MDR (multi-drug resistant isolates) and XDR (extremely drug resistant isolates). C(r) follows significantly different scaling rules in different subgroups of isolates, but all the isolates follow one parameter scaling law. The richness in complexity of each subgroup can be quantified by the measures of multifractal parameters displaying a pattern in which XDR isolates have highest value and lowest for drug sensitive isolates. Therefore C(r) and multifractal functions can be useful parameters for analysis of genomic sequences.

Dynamics of p53 and Wnt cross talk.

We present the mechanism of interaction of Wnt network module, which is responsible for periodic somitogenesis, with p53 regulatory network, which is one of the main regulators of various cellular functions, and switching of various oscillating states by investigating p53-Wnt model. The variation in Nutlin concentration in p53 regulating network drives the Wnt network module to different states, stabilized, damped and sustain oscillation states, and even to cycle arrest. Similarly, the change in Axin2 concentration in Wnt could able to modulate the p53 dynamics at these states. We then solve the set of coupled ordinary differential equations of the model using quasi steady state approximation. We, further, demonstrate the change of p53 and GSK3 interaction rate, due to hypothetical catalytic reaction or external stimuli, can able to regulate the dynamics of the two network modules, and even can control their dynamics to protect the system from cycle arrest (apoptosis).

Apoptosis regulatory protein-protein interaction demonstrates hierarchical scale-free fractal network.

Dysregulation or inhibition of apoptosis favors cancer and many other diseases. Understanding of the network interaction of the genes involved in apoptotic pathway, therefore, is essential, to look for targets of therapeutic intervention. Here we used the network theory methods, using experimentally validated 25 apoptosis regulatory proteins and identified important genes for apoptosis regulation, which demonstrated a hierarchical scale-free fractal protein-protein interaction network. TP53, BRCA1, UBIQ and CASP3 were recognized as a four key regulators. BRCA1 and UBIQ were also individually found to control highly clustered modules and play an important role in the stability of the overall network. The connection among the BRCA1, UBIQ and TP53 proteins was found to be important for regulation, which controlled their own respective communities and the overall network topology. The feedback loop regulation motif was identified among NPM1, BRCA1 and TP53, and these crucial motif topologies were also reflected in high frequency. The propagation of the perturbed signal from hubs was found to be active upto some distance, after which propagation started decreasing and TP53 was the most efficient signal propagator. From the functional enrichment analysis, most of the apoptosis regulatory genes associated with cardiovascular diseases and highly expressed in brain tissues were identified. Apart from TP53, BRCA1 was observed to regulate apoptosis by influencing motif, propagation of signals and module regulation, reflecting their biological significance. In future, biochemical investigation of the observed hub-interacting partners could provide further understanding about their role in the pathophysiology of cancer.

Microtubule dynamics regulated by stathmin.

Microtubules perform a variety of functions which lead to the complex regulation of intracellular transport and cell division. However, the regulation of microtubule growth is not clearly known. Based on a recent experimental finding, we explore the possibility of spatial regulation of microtubule growth by stathmin-tubulin interaction gradients. Computer simulation of the model with stathmin-tubulin interaction gradients gave regulated growth as seen in experiments. In future, the stathmin-tubulin interaction gradients can be made dynamic and its impact on the microtubule growth can be explored.