Molecular crosstalk: Notch can manipulate Hes1 and miR-9 behavior.

We propose a Hes1-Notch-miR-9 regulatory network and studied the regulating mechanism of miR-9 and Hes1 dynamics driven by Notch. Change in Notch concentration, which serves as a stress signal, can trigger the dynamics of Hes1 and miR-9 at five different states, namely, sTable (2), sustain (1) and mixed (2) states those may correspond to different cellular states. Further, this Notch stress signal introduce time reversal oscillation, which behaves as backward wave, after a certain threshold value of the stress signal and defends the system from moving to apoptosis. We also observe heterogeneous patterns of Hes1, miR-9 and other molecular species in various two dimensional parameter spaces and found that the variability in the patterns is triggered by Hill coefficient and Hes1 stress signal. The phase or bifurcation diagram in time period of oscillation (TN) driven by Notch signal provides all five states, predicts minimum threshold value TNc beyond which tendency to build up backward wave starts and TNc serves as bifurcation point of the system.

Towards the revival of oscillation from complete cessation in stochastic systems for application in molecular biology.

Delay and noise are inevitable in complex systems that are common in biochemical networks. The system is often disturbed at various states irrespective of the size (small or large) of delay and noise. Therefore, it is of interest to describe the significance of delay and noise in stochastic Willamowski-Rossler chemical oscillator model using a delay stochastic (having random probability distribution) simulation algorithm. Oscillating dynamics moves to stable fixed point when delay at a fixed magnitude of noise drives the system from oscillating state to stochastic amplitude death state (complete cessation). However, the amplitude death state is induced to a revived oscillating state in stochastic system (which is far from equilibrium state) for noise with a fixed value of delay. Thus, significantly large and small noise induces the dynamics of the system to amplitude death state. Hence, we describe the interplay of delay and noise in stochastic systems for the proper and efficient functioning of the complex system that are frequent in biological networks.

Stochastic method to control Mycobacterium tuberculosis epidemic.

We study the origin of TB (tuberculosis) epidemic and complex distributions of various populations of TB infection within the stochastic framework. The stochastic nature of this disease infection could be linked to the stochastic behaviour at genome level which is exhibited in SNP (single nucleotide polymorphism) distributions of experimentally identified hotspot driver genes. Our results show the emergence of random clusters, and well-defined discrete domains of the respective species populations in the model driven by demographic stochasticity and intrinsic complex species interaction. The multifractal analysis of the time series of the species populations indicate that TB epidemic could be mainly caused by contact communication and is directional. We propose that any TB epidemic may have high chance of approximately periodic recurrence and can be controlled by optimizing some of the parameters involved in the system modelling.