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.

&nbsp;

IIT Palakkad

The functional application of RNA-guided CRISPR-associated Cas9 protein, a bacterial immune system-based protein complex, via which in vivo, highly specific, and well-regulated, gene-editing processes are being monitored at an unprecedented level, has led to remarkable progress in genetic engineering and technology. The complicated in vivo process of genome interrogation followed by gene editing by the Cas9 complex was recently reported by Knight et al. (Science, 2015, 350, 823-826) using an elegant single-particle tracking method, aided by the two-photon fluorescence correlation spectroscopic technique. In contrast to the usually observed fast target-searching and protein-binding events in biophysical systems, an interesting slow genome-interrogation process by the RNA-guided CRISPR-Cas9 system through a crowded chromatin environment of a mammalian cell has been revealed in Knight et al.'s study. Motivated by this experiment, in this paper, we provide a generalized theoretical framework to capture this particular target-searching mechanism of the CRISPR-Cas9 protein complex. We show that an analysis on the basis of 3D subdiffusion under a cylindrical volume, created by several nonspecific off-target interactions from the DNA strands, can capture the essential details of the process. Moreover, on the basis of this model, we quantify the dynamics of this process and estimate the survival probability, first passage time, and the intensity correlation function of the tagged proteins of the experiment. The results from our theoretical predictions are found to be consistent with the experimental observations, and hence, seem to provide a plausible microscopic picture of the process. © 2020 American Chemical Society.

World University root node

Department of Chemistry

Journal of Physical Chemistry B

CRISPR-Cas9 Genome Interrogation: A Facilitated Subdiffusive Target Search Strategy

The structural determination and manipulation of bottle-brush polymers, a class of polymers with serially grafted side-chains, is challenging due to the interplay of side-chain and backbone interactions over various length scales. The present work performs a detailed analysis, using molecular dynamics simulation techniques, to unravel these interactions by probing the distinct rod to a flexible real-chain with self-avoiding walk (SAW) type crossover in the backbone static structure factor. This analysis elucidates the deviation from flexible chain behavior, while also providing a quantitative measure of persistence length, lp. Significantly, the results identify a trend in lp which is consistent with the debated theoretical prediction of lp Ns 15/8, where Ns is the number of monomers in each side-chain of the bottle-brush polymer. (Figure presented.). © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Macromolecular Theory and Simulations

Scaling Laws of Bottle-Brush Polymers in Dilute Solutions

The folding-unfolding mechanism of a protein in a living cell is the result of its molecular response to various perturbations due to changes in the chemical environment such as pH, ion concentration, ligand binding and many other complex chemical reactions. In this letter, a theoretical scheme based on single molecule force spectroscopy experiments and related theories, has been followed to capture the effect of the change of pH for a slow protonation-coupled folding-unfolding process, and the free energy landscape has been quantified in terms of protonation numbers, barrier height and pH, following Kramer's barrier crossing formalism. © 2014 Elsevier B.V. All rights reserved.

Chemical Physics Letters

PH dependent protein stability: A quantitative approach based on Kramer's barrier escape

Theoretical Studies Of The Thermodynamics And Kinetics Of Selected Single-Molecule Systems

Cargo transport through the nuclear pore complex continues to be a subject of considerable interest to experimentalists and theorists alike. Several recent studies have revealed details of the process that have still to be fully understood, among them the apparent nonlinearity between cargo size and the pore crossing time, the skewed, asymmetric nature of the distribution of such crossing times, and the non-exponentiality in the decay profile of the dynamic autocorrelation function of cargo positions. In this paper, we show that a model of pore transport based on subdiffusive particle motion is in qualitative agreement with many of these observations. The model corresponds to a process of stochastic binding and release of the particle as it moves through the channel. It suggests that the phenylalanine-glycine repeat units that form an entangled polymer mesh across the channel may be involved in translocation, since these units have the potential to intermittently bind to hydrophobic receptor sites on the transporter protein. © 2011 American Institute of Physics.

Fulltext

Journal of Chemical Physics

Subdiffusion as a model of transport through the nuclear pore complex

Static disorder has recently been implicated in the non-exponential kinetics of the unfolding of single molecules of poly-ubiquitin under a constant force Kuo, Garcia-Manyes, Li, Barel, Lu, Berne, Urbakh, Klafter, and Fernndez, Proc. Natl. Acad. Sci. U.S.A. 107, 11336 (2010)10.1073/pnas.1006517107. In the present paper, it is suggested that dynamic disorder may provide a plausible, alternative description of the experimental observations. This suggestion is made on the basis of a model in which the barrier to chain unfolding is assumed to be modulated by a control parameter r that evolves in a parabolic potential under the action of fractional Gaussian noise according to a generalized Langevin equation. The treatment of dynamic disorder within this model is pursued using Zwanzigs indirect approach to noise averaging Acc. Chem. Res. 23, 148 (1990). In conjunction with a self-consistent closure scheme developed by Wilemski and Fixman J. Chem. Phys. 58, 4009 (1973)10.1063/1.1679757; ibid. 60, 866 (1974)10.1063/1.1681162, this approach eventually leads to an expression for the chain unfolding probability that can be made to fit the corresponding experimental data very closely. © 2011 American Institute of Physics.

The stretching of single poly-ubiquitin molecules: Static versus dynamic disorder in the non-exponential kinetics of chain unfolding

Interest in the applicability of fluctuation theorems to the thermodynamics of single molecules in external potentials has recently led to calculations of the work and total entropy distributions of Brownian oscillators in static and time-dependent electromagnetic fields. These calculations, which are based on solutions to a Smoluchowski equation, are not easily extended to a consideration of the other thermodynamic quantity of interest in such systems - the heat exchanges of the particle alone - because of the nonlinear dependence of the heat on a particle's stochastic trajectory. In this paper, we show that a path integral approach provides an exact expression for the distribution of the heat fluctuations of a charged Brownian oscillator in a static magnetic field. This approach is an extension of a similar path integral approach applied earlier by our group to the calculation of the heat distribution function of a trapped Brownian particle, which was found, in the limit of long times, to be consistent with experimental data on the thermal interactions of single micron-sized colloids in a viscous solvent. © 2011 IOP Publishing Ltd and SISSA.

Journal of Statistical Mechanics: Theory and Experiment

Single-molecule thermodynamics: The heat distribution function of a charged particle in a static magnetic field

Using path integrals, we derive an exact expression-valid at all times t -for the distribution P (Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P (Q,t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t→∞ exactly recovers the heat distribution function obtained recently by Imparato [Phys. Rev. E 76, 050101(R) (2007)]10.1103/PhysRevE.76.050101 from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen [Phys. Rev. E 69, 056121 (2004)]10.1103/PhysRevE.69.056121; however, this calculation does not provide an expression for P (Q,t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P (Q,t) for the case v=0. © 2010 The American Physical Society.

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

Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator

We show that a model of target location involving n noninteracting particles moving subdiffusively along a line segment (a generalization of a model introduced by Sokolov et al. [Biophys. J. 2005, 89, 895.]) provides a basis for understanding recent experiments by Pelta et al. [Phys. Rev. Lett. 2007, 98, 228302.] on the kinetics of diffusion-limited gel degradation. These experiments find that the time tc taken by the enzyme thermolysin to completely hydrolyze a gel varies inversely as roughly the 3/2 power of the initial enzyme concentration [E]. In general, however, this time would be expected to vary either as [E]-1or as[E]-2, depending on whether the Brownian diffusion of the enzyme to the site of cleavage took place along the network chains (1-d diffusion) or through the pore spaces (3-d diffusion). In our model, the unusual dependence of tc on [E] is explained in terms of a reaction-diffusion equation that is formulated in terms of fractional rather than ordinary time derivatives. © 2010 American Chemical Society.

A model of anomalous enzyme-catalyzed gel degradation kinetics

We show that data from recent experiments carried out on the kinetics of DNA escape from α -hemolysin nanopores [M. Wiggin, C. Tropini, C. T. Cossa, N. N. Jetha, and A. Marziali, Biophys. J. 95, 5317 (2008)] may be rationalized by a model of chain dynamics based on the anomalous diffusion of a particle moving in a harmonic well in the presence of a delta function sink. The experiments of Wiggin found, among other things, that the occasional occurrence of unusually long escape times in the distribution of chain trapping events led to nonexponential decays in the survival probability, S(t), of the DNA molecules within the nanopore. Wiggin ascribed this nonexponentiality to the existence of a distribution of trapping potentials, which they suggested was the result of stochastic interactions between the bases of the DNA and the amino acids located on the surface of the nanopore. Based on this idea, they showed that the experimentally determined S(t) could be well fit in both the short and long time regimes by a function of the form (1+t/τ)-α (the so called Becquerel function). In our model, S(t) is found to be given by a Mittag-Leffler function at short times and by a generalized Mittag-Leffler function at long times. By suitable choice of certain parameter values, these functions are found to fit the experimental S(t) even better than the Becquerel function. Anomalous diffusion of DNA within the trap prior to escape over a barrier of fixed height may therefore provide a second, plausible explanation of the data, and may offer fresh perspectives on similar trapping and escape problems. © 2010 American Institute of Physics.

Anomalous reaction-diffusion as a model of nonexponential DNA escape kinetics

A recent theoretical model developed by Imparato of the experimentally measured heat and work effects produced by the thermal fluctuations of single micron-sized polystyrene beads in stationary and moving optical traps has proved to be quite successful in rationalizing the observed experimental data. The model, based on the overdamped Brownian dynamics of a particle in a harmonic potential that moves at a constant speed under a time-dependent force, is used to obtain an approximate expression for the distribution of the heat dissipated by the particle at long times. In this paper, we generalize the above model to consider particle dynamics in the presence of colored noise, without passing to the overdamped limit, as a way of modeling experimental situations in which the fluctuations of the medium exhibit long-lived temporal correlations, of the kind characteristic of polymeric solutions, for instance, or of similar viscoelastic fluids. Although we have not been able to find an expression for the heat distribution itself, we do obtain exact expressions for its mean and variance, both for the static and for the moving trap cases. These moments are valid for arbitrary times and they also hold in the inertial regime, but they reduce exactly to the results of Imparato in appropriate limits. © 2009 The American Physical Society.

Brownian particles in stationary and moving traps: The mean and variance of the heat distribution function

A harmonic oscillator that evolves under the action of both a systematic time-dependent force and a random time-correlated force can do work w. This work is a random quantity, and Mai and Dhar have recently shown, using the generalized Langevin equation (GLE) for the oscillator's position x, that it satisfies a fluctuation theorem. In principle, the same result could have been derived from the Fokker-Planck equation (FPE) for the probability density function, P(x,w,t), for the oscillator being at x at time t, having done work w. Although the FPE equivalent to the above GLE is easily constructed and solved, one finds, unexpectedly, that its predictions for the mean and variance of w do not agree with the fluctuation theorem. We show that to resolve this contradiction, it is necessary to construct an FPE that includes the velocity of the oscillator, v, as an additional variable. The FPE for P(x,v,w,t) does indeed yield expressions for the mean and variance of w that agree with the fluctuation theorem. © 2008 IOP Publishing Ltd.

Resolving a puzzle concerning fluctuation theorems for forced harmonic oscillators in non-Markovian heat baths

The utility of an approximate heuristic version of Kramers' theory of reaction rates that was earlier used [Chaudhury and Cherayil, J. Chem. Phys. 125, 024904 (2006)] to successfully describe the nonexponential waiting time distributions of the enzyme Β -galactosidase is reassessed. The original model, based on the Smoluchowski equation, is reformulated in terms of the phase space variables of the reaction coordinate, without neglecting inertial contributions. A new derivation of the Fokker-Planck equation (FPE) that describes the dynamics of this coordinate is presented. This derivation, based on functional methods, provides a more direct alternative to the existing distribution function approach used by Hanggi and Mojtabai [Phys. Rev. A 26, 1168 (1982)]. The time-dependent coefficients in the FPE, when incorporated into the exact expression for the transmission coefficient obtained from a reactive-flux formalism [Kohen and Tannor, J. Chem. Phys. 103, 6013 (1995)], are found to yield virtually the same results as the earlier heuristic model. © 2008 American Institute of Physics.

The dynamics of single enzyme reactions: A reconsideration of Kramers' model for colored noise processes

The transient rupture and reformation of hydrogen bonds between base pairs on distinct chains of double-stranded DNA ("bubble" dynamics) is modeled in terms of the fluctuating distance between the bases. The fluctuations in the distance are assumed to be governed by a simple Langevin equation with a quadratic potential under conditions of high friction. A critical distance of separation L must be achieved before a bubble defect is considered to have been formed. The decay of the dynamic correlations between states of the DNA that have such defects and those that do not has been calculated from the above model and has been found to reproduce the trends in experimental measurements of the same quantity. © 2007 American Institute of Physics.