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

Receptor-ligand binding is a critical first step in signal transduction and the duration of the interaction can impact signal generation. In mammalian cells, clustering of receptors may be facilitated by heterogeneous zones of lipids, known as lipid rafts. In vitro experiments show that disruption of rafts significantly alters the dissociation of fibroblast growth factor-2 (FGF-2) from heparan sulfate proteoglycans (HSPGs), co-receptors for FGF-2. In this article, we develop a continuum stochastic formalism to address how receptor clustering might influence ligand rebinding. We find that clusters reduce the effective dissociation rate dramatically when the clusters are dense and the overall surface density of receptors is low. The effect is much less pronounced in the case of high receptor density and shows nonmonotonic behavior with time. These predictions are verified via lattice Monte Carlo simulations. Comparison with FGF-2-HSPG experimental results is made and suggests that the theory could be used to analyze similar biological systems. We further present an analysis of an additional cooperative internal-diffusion model that might be used by other systems to increase ligand retention when simple rebinding is insufficient. © 2005 by the Biophysical Society.

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Biophysical Journal

Effects of receptor clustering on ligand dissociation kinetics: Theory and simulations

Rebinding of dissociated ligands from cell surface proteins can confound quantitative measurements of dissociation rates important for characterizing the affinity of binding interactions. This can be true also for in vitro techniques such as surface plasmon resonance (SPR). We present experimental results using SPR for the interaction of insulin-like growth factor-I (IGF-I) with one of its binding proteins, IGF binding protein-3 (IGFBP-3), and show that the dissociation, even with the addition of soluble heparin in the dissociation phase, does not exhibit the expected exponential decay characteristic of a 1:1 binding reaction. We thus consider the effect of (multiple) rebinding events and, within a self-consistent mean-field approximation, we derive the complete mathematical form for the fraction of bound ligands as a function of time. We show that, except for very low association rate and surface coverage, this function is nonexponential at all times, indicating that multiple rebinding events strongly influence dissociation even at early times. We compare the mean-field results with numerical simulations and find good agreement, although deviations are measurable in certain cases. Our analysis of the IGF-I-IGFBP-3 data indicates that rebinding is prominent for this system and that the theoretical predictions fit the experimental data well. Our results provide a means for analyzing SPR biosensor data where rebinding is problematic and a methodology to do so is presented. © EBSA 2005.

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European Biophysics Journal

Ligand rebinding: Self-consistent mean-field theory and numerical simulations applied to surface plasmon resonance studies

We study the motion of a particle sliding under the action of an external field on a stochastically fluctuating one-dimensional Edwards-Wilkinson surface. Numerical simulations using the single-step model shows that the mean-square displacement of the sliding particle shows distinct dynamic scaling behavior, depending on whether the surface fluctuates faster or slower than the motion of the particle. When the surface fluctuations occur on a time scale much smaller than the particle motion, we find that the characteristic length scale shows anomalous diffusion with [Formula presented] where [Formula presented] from numerical data. On the other hand, when the particle moves faster than the surface, its dynamics is controlled by the surface fluctuations and [Formula presented] A self-consistent approximation predicts that the anomalous diffusion exponent is [Formula presented] in good agreement with simulation results. We also discuss the possibility of a slow crossover toward asymptotic diffusive behavior. The probability distribution of the displacement has a Gaussian form in both the cases. © 2004 The American Physical Society.

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Dynamics of a passive sliding particle on a randomly fluctuating surface

The motion of a particle sliding under the action of an external field on a stochastically fluctuating one-dimensional Edwards-Wilkinson surface was studied. The results show that the motion of a passive sliding particle on a fluctuating surface may show nontrivial behavior even when the surface is Gaussian. The results also show that the the characteristic length scale shows anomalous diffusion when the surface fluctuations occur on a time scale smaller than the particle motion. The possibility of a slow crossover toward asymptotic diffusive behavior was also discussed.

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

The binding of basic fibroblast growth factor (FGF-2) to its cell surface receptor (CSR) and subsequent signal transduction is known to be enhanced by heparan sulfate proteoglycans (HSPGs). HSPGs bind FGF-2 with low affinity and likely impact CSR-mediated signaling via stabilization of FGF-2-CSR complexes via association with both the ligand and the receptor. What is unknown is whether HSPG associates with CSR in the absence of FGF-2. In this paper, we determine conditions by which pre-association would impact CSR-FGF-2-HSPG triad formation assuming diffusion-limited surface reactions. Using mean-field rate equations, we show that (i) when [HSPG] is much higher than [CSR], the presence of pre-formed complexes does not affect the steady state of FGF-2 binding, and (ii) when the concentrations are comparable, the presence of pre-formed complexes substantially increases the steady-state concentration of FGF-2 bound to CSR. These findings are supported by explicit cellular automaton simulations, which justify the mean-field treatment. We discuss the advantages of such a two-receptor system compared to a single-receptor model, when the parameters are comparable. Further, we speculate that the observed high concentration of HSPG in intact cells ([HSPG]∼100[CSR]) provides a way to ensure that the binding levels of FGF-2 to its signaling receptor remains high, irrespective of the presence of pre-formed CSR-HSPG complexes on the cell surface, while allowing the cell to finely tune the response to FGF-2 via down-regulation of the signaling receptor. © 2003 Elsevier Ltd. All rights reserved.

Journal of Theoretical Biology

Ligand-induced coupling versus receptor pre-association: Cellular automaton simulations of FGF-2 binding

We study bond percolation of N non-interacting Gaussian polymers of l segments on a 2D square lattice of size L with reflecting boundaries. Through simulations, we find the fraction of configurations displaying no connected cluster which span from one edge to the opposite edge. From this fraction, we define a critical segment density ΡpcL(l) and the associated critical fraction of occupied bonds pcL (l), so that they can be identified as the percolation threshold in the L ∞ limit. Whereas pcL (l) is found to decrease monotonically with l for a wide range of polymer lengths, pcL (l) is non-monotonic. We give physical arguments for this intriguing behaviour in terms of the competing effects of multiple bond occupancies and polymerization.

Journal of Physics A: Mathematical and General

Bond percolation of polymers

The persistence properties of the T=0 coarsening dynamics of one-dimensional q-state Potts model was studied. A modified mean-field approximation (MMFA) was used for the study purpose. In the approximation, the correct time dependence of the mean density of persistent spins was imposed while the spatial correlations between the interfaces separating spins with different Potts states was ignored.

Persistence in q-state Potts model: A mean-field approach

We study the persistence properties of the [Formula presented] coarsening dynamics of one-dimensional q-state Potts model using a modified mean-field approximation (MMFA). In this approximation, the spatial correlations between the interfaces separating spins with different Potts states is ignored, but the correct time dependence of the mean density [Formula presented] of persistent spins is imposed. For this model, it is known that [Formula presented] follows a power-law decay with time, [Formula presented] where [Formula presented] is the q-dependent persistence exponent. We study the spatial structure of the persistent region within the MMFA. We show that the persistent site pair correlation function [Formula presented] has the scaling form [Formula presented] for all values of the persistence exponent [Formula presented] The scaling function has the limiting behavior [Formula presented] [Formula presented] and [Formula presented] [Formula presented] We then show within the independent interval approximation (IIA) that the distribution [Formula presented] of separation k between two consecutive persistent spins at time t has the asymptotic scaling form [Formula presented] where the dynamical exponent has the form [Formula presented] The behavior of the scaling function for large and small values of the arguments is found analytically. We find that for small separations [Formula presented] where [Formula presented] while for large separations [Formula presented] [Formula presented] decays exponentially with x. The unusual dynamical scaling form and the behavior of the scaling function is supported by numerical simulations. © 2003 The American Physical Society.

Persistence in [Formula presented]-state Potts model: A mean-field approach

We study phase separation in a system of hard-core particles driven by a fluctuating two-dimensional self-affine potential landscape which evolves through Kardar-Parisi-Zhang (KPZ) dynamics. We find that particles tend to cluster together on a length scale which grows in time. The final phase-separated steady state is characterized by an unusual cusp singularity in the scaled correlation function and a broad distribution for the order parameter. Unlike the one-dimensional case studied earlier, the cluster-size distribution is asymmetric between particles and holes, reflecting the broken reflection symmetry of the KPZ dynamics, and has a contribution from an infinite cluster in addition to a power law part. A study of the surface in terms of coarse-grained depth variables helps understand many of these features.

Journal of Statistical Physics

Phase Separation Driven by a Fluctuating Two-Dimensional Self-Affine Potential Field

We study the distribution of persistent sites (sites unvisited by particles A) in the one-dimensional A+A → ∅ reaction-diffusion model. We define the empty intervals as the separations between adjacent persistent sites, and study their size distribution n(k, t) as a function of interval length k and time t. The decay of persistence is the process of irreversible coalescence of these empty intervals, which we study analytically under the independent interval approximation (IIA). Physical considerations suggest that the asymptotic solution is given by the dynamic scaling form n(k, t) = s-2 f (k/s) with the average interval size s ∼ t1/2. We show under the IIA that the scaling function f(x) ∼ x-τ as x → 0 and decays exponentially at large x. The exponent τ is related to the persistence exponent θ through the scaling relation τ = 2(1-θ). We compare these predictions with the results of numerical simulations. We determine the two-point correlation function C(r, t) under the IIA. We find that for r ≪ s, C(r, t) ∼ r-α where α = 2 - τ, in agreement with our earlier numerical results.