Binny J. Cherayil

Complex chemical kinetics in single enzyme molecules: Kramers's model with fractional Gaussian noise.

A model of barrier crossing dynamics governed by fractional Gaussian noise and the generalized Langevin equation is used to study the reaction kinetics of single enzymes subject to conformational fluctuations. The direct application of Kramerss flux-over-population method to this model yields analytic expressions for the time-dependent transmission coefficient and the distribution of waiting times for barrier crossing. These expressions are found to reproduce the observed trends in recent simulations and experiments.

Polypeptide dynamics: Experimental tests of an optimized Rouse–Zimm type model

A theory for long time random coil peptide dynamics is developed based on a generalization of the optimized Rouse–Zimm model of Perico et al. [J. Chem. Phys. 87, 3677 (1987)] and Perico [J. Chem. Phys. 88, 3996 (1988) and Biopolymers 28, 1527 (1989)]. The generalized model employs the rotational potential energy for specific amino acid residues and amino acid friction coefficients to compute all input parameters in the model. Calculations of the fluorescence depolarization correlation function P2(t ) and of the local persistence length are found to be sensitive to the amino acid sequence, the length of the polypeptide chain, and the location of the probe. Model computations of P2(t ) are compared with new experimentally determined rotational correlation times (of the order of nanoseconds) from fluorescence depolarization measurements of three different synthetic 17‐residue peptides, each containing a single tryptophan (TRP) residue as a probe. In addition, the previous anisotropy measurements on ACTH, glu...

The dynamics of chain closure in semiflexible polymers

The mean first passage time of cyclization \tau of a semiflexible polymer with reactive ends is calculated using the diffusion-reaction formalism of Wilemski and Fixman [J. Chem. Phys. 60, 866 (1974)]. The approach is based on a Smoluchowski-type equation for the time evolution, in the presence of a sink, of a many-body probability distribution function. In the present calculations, which are an extension of work carried out by Pastor et al. [J. Chem. Phys. 105, 3878 (1996)] on completely flexible Gaussian chains, the polymer is modeled as a continuous curve with a nonzero energy of bending. Inextensibility is enforced on average through chain-end contributions that suppress the excess fluctuations that lead to departures from the Kratky–Porod result for the mean-square end-to-end distance. The sink term in the generalized diffusion equation that describes the dynamics of the chain is modeled as a modified step function along the lines suggested by Pastor et al. Detailed calculations of \tau as a function of the chain length N, the reaction distance a, and the stiffness parameter z are presented. Among other results, \tau is found to be a power law in N, with a z-dependent scaling exponent that ranges between about 2.2–2.4.

Radial dimensions of starburst polymers

Radial properties of starburst polymers are calculated by renormalization group techniques starting from the Edwards model of the chain. The calculations are carried out for a polymer in good solvents grown out to an arbitrary number of generations g and having an arbitrary branch functionality f. Excludd volume effects are modeled by delta function pseudopotentials. Only pair interactions are included in the calculations, which specifically determine the amplitude of the average center-to-end distance R of the starburst for definite values of f and g. Our first order in E estimates of the exponents for R and the number of configurations C coincide with results obtained earlier by direct methods for networks of arbitrary topology in specific limits.

Dynamics of chain closure: approximate treatment of nonlocal interactions.

The Wilemski-Fixman model of diffusion controlled-reactions [J. Chem. Phys. 58, 4009 (1973)] is combined with a generalized random walk description of chain conformations to predict the dependence of the closure time tau on the chain length N of polymers with reactive end groups and nonlocal interactions. The nonlocal interactions are modeled by a modification to the connectivity term in the Edwards continuum representation of the polymer. The modification involves a parameter h lying between 0 and 1 that is a measure of the extent of correlation between adjacent monomers on the chain backbone. Different choices of h correspond to chain conformations of different average radial dimensions. In particular, the values 1/3, 1/2 and 3/5 provide approximations to the statistics of polymers in poor, theta and good solvents, respectively. The closure time tau of such chains is calculated analytically for different N. In all cases, tau is found to vary as a power law in N, Nb, with b a function of h. For the special case h = 1/3, which models collapsed polymers and globular proteins, b is about 1.6-1.7.

Chain dynamics in steady shear flow

Recent experimental measurements of the static and dynamic properties of single fluorescently labeled molecules of DNA in steady shear flow are compared with the predictions of a theoretical model of chain dynamics. The model is based on a set of coupled kinetic equations for the evolution of chain conformations and solvent fluctuations. The polymer is represented as a continuous curve with no excluded volume or hydrodynamic interactions, while the solvent is described by a time and space-varying velocity field. In the absence of constraints that enforce the finite extensibility of the chain at large shear rates, the calculated curves of the normalized dynamic autocorrelation function of the mean extension reproduce the qualitative features of the measured curves, but otherwise deviate significantly from them. We develop an analytically tractable finitely extensible model of the Gaussian chain that is more successful in reproducing the experimental data.

Confinement and viscoelastic effects on chain closure dynamics

Chemical reactions inside cells are typically subject to the effects both of the cells confining surfaces and of the viscoelastic behavior of its contents. In this paper, we show how the outcome of one particular reaction of relevance to cellular biochemistry--the diffusion-limited cyclization of long chain polymers--is influenced by such confinement and crowding effects. More specifically, starting from the Rouse model of polymer dynamics, and invoking the Wilemski-Fixman approximation, we determine the scaling relationship between the mean closure time t(c) of a flexible chain (no excluded volume or hydrodynamic interactions) and the length N of its contour under the following separate conditions: (a) confinement of the chain to a sphere of radius d and (b) modulation of its dynamics by colored Gaussian noise. Among other results, we find that in case (a) when d is much smaller than the size of the chain, t(c) ~ Nd(2), and that in case (b), t(c) ~ N(2/(2-2H)), H being a number between 1/2 and 1 that characterizes the decay of the noise correlations. H is not known a priori, but values of about 0.7 have been used in the successful characterization of protein conformational dynamics. At this value of H (selected for purposes of illustration), t(c) ~ N(3.4), the high scaling exponent reflecting the slow relaxation of the chain in a viscoelastic medium.

Polymer collapse in supercritical solvents

We show analytically that in dilute solutions of high molecular weight polymers, a collapse transition of the chain can be induced by proximity to the critical point of the solvent. The transition is driven by the fluctuations in the medium, which lead to an effective attractive interaction of long range between different parts of the polymer. At the critical point itself, however, the chain adopts the same average conformations that characterize its size in the off-critical limit. In other words, on approach to the critical point, the polymer is found first to contract and collapse, and then subsequently to return to its original dimensions. This behavior has recently been observed in simulations of polymer-solvent mixtures near the lower critical solution temperature of the system, and it is also known to be characteristic of solutions of polymers in bicomponent solvent mixtures near the critical consolute point of the two solvents.

Phase separation in polymer solutions near the critical point

The Edwards path-integral description of chain statistics is used to derive an effective

Density dependent vibrational relaxation in supercritical fluids

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