Department of Physics

Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

We study the stochastic kinetics of a signaling module consisting of a two-state stochastic point process with negative feedback. In the active state, a product is synthesized which increases the active-to-inactive transition rate of the process. We analyze this simple autoregulatory module using a path-integral technique based on the temporal statistics of state flips of the process. We develop a systematic framework to calculate averages, autocorrelations, and response functions by treating the feedback as a weak perturbation. Explicit analytical results are obtained to first order in the feedback strength. Monte Carlo simulations are performed to test the analytical results in the weak feedback limit and to investigate the strong feedback regime. We conclude by relating some of our results to experimental observations in the olfactory and visual sensory systems. © 2007 The American Physical Society.

World University root node

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Response and fluctuations of a two-state signaling module with feedback

We study a random fiber bundle model with tips of the fibers placed on a graph having co-ordination number 3. These fibers follow local load sharing with uniformly distributed threshold strengths of the fibers. We have studied the critical behavior of the model numerically using a finite size scaling method and the mean field critical behavior is established. The avalanche size distribution is also found to exhibit a mean field nature in the asymptotic limit. © World Scientific Publishing Company.

Fulltext

International Journal of Modern Physics C

Fibers on a graph with local load sharing

Ligand binding to receptors is the initial event in many signaling processes, and a quantitative understanding of this interaction is important for modeling cell behavior. In this paper, we study the kinetics of reversible ligand binding to receptors on a spherical cell surface using a self-consistent stochastic theory. Binding, dissociation, diffusion and rebinding of ligands are incorporated into the theory in a systematic manner. We derive explicitly the time evolution of the ligand-bound receptor fraction p(t) in various regimes. Contrary to the commonly accepted view, we find that the well-known Berg-Purcell scaling for the association rate is modified as a function of time. Specifically, the effective on-rate changes non-monotonically as a function of time and equals the intrinsic rate at very early as well as late times, while being approximately equal to the Berg-Purcell value at intermediate times. The effective dissociation rate, as it appears in the binding curve or measured in a dissociation experiment, is strongly modified by rebinding events and assumes the Berg-Purcell value except at very late times, where the decay is algebraic and not exponential. In equilibrium, the ligand concentration everywhere in the solution is the same and equals its spatial mean, thus ensuring that there is no depletion in the vicinity of the cell. Implications of our results for binding experiments and numerical simulations of ligand-receptor systems are also discussed. © 2007 IOP Publishing Ltd.

Physical Biology

Self-consistent theory of reversible ligand binding to a spherical cell

The critical behavior of a random fiber bundle model with mixed uniform distribution of threshold strengths and global load sharing rule is studied with a special emphasis on the nature of distribution of avalanches for different parameters of the distribution. The discontinuity in the threshold strength distribution of fibers nontrivially modifies the critical stress as well as puts a restriction on the allowed values of parameters for which the recursive dynamics approach holds good. The discontinuity leads to a nonuniversal behavior in the avalanche size distribution for smaller values of avalanche size. We observe that apart from the mean field behavior for larger avalanches, a new behavior for smaller avalanche size is observed as a critical threshold distribution is approached. The phenomenological understanding of the above result is provided using the exact analytical result for the avalanche size distribution. Most interestingly, the prominence of nonuniversal behavior in avalanche size distribution depends on the system parameters. © 2007 The American Physical Society.

Effect of discontinuity in the threshold distribution on the critical behavior of a random fiber bundle

We study the zero-temperature quenching dynamics of various extensions of the transverse Ising model (TIM) for when the transverse field is linearly quenched from to (or zero) at a finite and uniform rate. The rate of quenching is dictated by a characteristic scale given by τ. The density of kinks produced in these extended models while crossing the quantum critical points during the quenching process is calculated using a many-body generalization of the Landau-Zener transition theory. The density of kinks in the final state is found to decay as τ-1/2. In the first model considered here, the transverse Ising Hamiltonian includes an additional ferromagnetic three-spin interaction term of strength J3. For J3&lt;0.5, the kink density is found to increase monotonically with J3 whereas it decreases with J3 for J3&gt;0.5. The point with J 3 = 0.5 and the transverse field h = -0.5 is multicritical, where the density shows a slower decay given by τ-1/6. We also study the effect of ferromagnetic or antiferromagnetic next nearest neighbor (NNN) interactions on the dynamics of the TIM under the same quenching scheme. In a mean field approximation, the transverse Ising Hamiltonians with NNN interactions are identical to the three-spin Hamiltonian. The NNN interactions non-trivially modify the dynamical behavior; for example an antiferromagnetic NNN interaction results in a larger number of kinks in the final state in comparison to the case when the NNN interaction is ferromagnetic. © IOP Publishing Ltd.

Journal of Statistical Mechanics: Theory and Experiment

The effect of the three-spin interaction and the next nearest neighbor interaction on the quenching dynamics of a transverse Ising model

A random fiber bundle model with a mixed Weibull distribution is studied under the global load sharing scheme. The mixed model consists of two sets of fibers. The threshold strength of one set of fibers is randomly chosen from a Weibull distribution with a particular Weibull index, and another set of fibers with a different index. The mixing tunes the critical stress of the bundle and the variation of critical stress with the amount of mixing is determined using a probabilistic method where the external load is increased quasistatically. In a special case which we illustrate, the critical stress is found to vary linearly with the mixing parameter. The critical exponents and power-law behavior of burst avalanche size distribution is found to remain unaltered due to mixing. © 2007 The American Physical Society.

Critical behavior of random fibers with mixed Weibull distribution

The proposed existence of cholesterol-rich lipid rafts in eucaryotic plasma membranes has led to a large number of studies on the influence of cholesterol on the structure and phase behaviour of model membranes. In this article we first give a brief overview of the phase behaviour of membranes made up of binary and ternary lipid-cholesterol mixtures determined from these experiments, and then present the results of our recent x-ray diffraction and fluorescence microscopy studies on these systems. Our observations suggest a possible resolution of the reported discrepancy in the phase behaviour of these systems obtained using different experimental techniques. © 2006 Elsevier Ltd. All rights reserved.

Solid State Communications

Phase behaviour of lipid-cholesterol membranes

The breakdown phenomena of materials is a very complex process which involves a study of formation of microscopic cracks, their evolution to the other regions of the materials via some interaction and the ultimate collapse of the structure [1]. Random Fibre Bundle Model (RFBM) [2, 3] is a paradigmatic model, simple yet subtle, which captures the essential physics of breakdown processes. It consists of N parallel, vertical fibres whose ends are connected to two horizontal rods. The upper rod is fixed and a load F is applied to the lower one so that a stress σ (= F/N) is generated on each fibre. The fibres are assigned a threshold strength chosen randomly from a cumulative distribution function P (σ) with a corresponding density function ρ (σ). © 2006 Springer.

Lecture Notes in Physics

Critical behaviour of mixed fibres with uniform distribution

Phase behaviour of phosphatidylcholine (PC)-cholesterol membranes

We study the diffusion of gas molecules through a two-dimensional network of polymers with the help of Monte Carlo simulations. The polymers are modelled as non-interacting random walks on the bonds of a two-dimensional square lattice, while the gas particles occupy the lattice cells. When a particle attempts to jump to a nearest-neighbour empty cell, it has to overcome an energy barrier which is determined by the number of polymer segments on the bond separating the two cells. We investigate the gas current J as a function of the mean segment density ρ, the polymer length and the probability q m for hopping across m segments. Whereas J decreases monotonically with ρ for fixed , its behaviour for fixed ρ and increasing depends strongly on q. For small, non-zero q, J appears to increase slowly with . In contrast, for q = 0, it is dominated by the underlying percolation problem and can be non-monotonic. We provide heuristic arguments to put these interesting phenomena into context. © 2005 IOP Publishing Ltd.