Arti Dua

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.

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.

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.

Single-molecule enzyme kinetics in the presence of inhibitors

Recent studies in single-molecule enzyme kinetics reveal that the turnover statistics of a single enzyme is governed by the waiting time distribution that decays as mono-exponential at low substrate concentration and multi-exponential at high substrate concentration. The multi-exponentiality arises due to protein conformational fluctuations, which act on the time scale longer than or comparable to the catalytic reaction step, thereby inducing temporal fluctuations in the catalytic rate resulting in dynamic disorder. In this work, we study the turnover statistics of a single enzyme in the presence of inhibitors to show that the multi-exponentiality in the waiting time distribution can arise even when protein conformational fluctuations do not influence the catalytic rate. From the Michaelis-Menten mechanism of inhibited enzymes, we derive exact expressions for the waiting time distribution for competitive, uncompetitive, and mixed inhibitions to quantitatively show that the presence of inhibitors can induce dynamic disorder in all three modes of inhibitions resulting in temporal fluctuations in the reaction rate. In the presence of inhibitors, dynamic disorder arises due to transitions between active and inhibited states of enzymes, which occur on time scale longer than or comparable to the catalytic step. In this limit, the randomness parameter (dimensionless variance) is greater than unity indicating the presence of dynamic disorder in all three modes of inhibitions. In the opposite limit, when the time scale of the catalytic step is longer than the time scale of transitions between active and inhibited enzymatic states, the randomness parameter is unity, implying no dynamic disorder in the reaction pathway.

The thermodynamics of reversible cyclization in semiflexible polymers

A recent model of the irreversible kinetics of ring formation in semiflexible polymers [J. Chem. Phys. 116, 399 (2002)] is generalized to the case of equilibrium cyclization, for which the rate constants for the forward and backward reaction are finite. The model is based on the diffusion-reaction formalism of Wilemski and Fixman [J. Chem. Phys. 60, 866 (1974)], and employs a path integral representation of the semiflexible chain (within a certain Gaussian approximation) to derive an expression for the steady state probability of occurrence of open configurations for given values of the chain length N, the reaction radius a, the degree of stiffness z, and the ratio of forward to backward reaction rates k/kr. The steady state probability is used to calculate the free energy changes for the open-to-close transition. Chain rigidity is found to strongly influence the standard Gibbs free energy and enthalpy for the transition. While flexible chains tend to cyclize by virtue of their entropic elasticity alone, cyclization in semiflexible chains is also governed by the change in enthalpy between the open and closed states. The results are in qualitative agreement with the experimental measurements of Libchaber and co-workers.

Effects of stiffness on the flow behavior of polymers

A recent model of the behavior of Gaussian chains in steady shear flow [J. Chem. Phys. 112, 8707 (2000)] is extended to include the effects of stiffness and finite extensibility. Calculations of the shear rate dependence of fractional elongation and of the time dependence of size fluctuations are found to be in good agreement with results from an experimental study of the behavior of single chains of DNA in steady shear flow. As in the earlier approach to the polymer-flow problem, we have ignored excluded volume and hydrodynamic interactions, but have instead added a bending energy contribution to the Hamiltonian of the chain, and have treated the usual connectivity term as a contribution to chain stretching that can be adjusted to ensure that the average size of the chain is fixed. The inclusion of stiffness and finite extensibility in the present treatment is found to produce significant improvements over the approach based purely on flexible chains.

Weak polyelectrolytes in the presence of counterion condensation with ions of variable size and polarizability

Light scattering and viscometric measurements on weak polyelectrolytes show two important aspects of counterion condensation, namely, non-monotonic variation in the polyelectrolyte size with the increase in the electrostatic strength, and, monovalent counterion selectivity in determining the nature of collapse transition at high electrostatic strengths. Here, we present a self-consistent variational theory for weak polyelectrolytes which includes the effects of the polarizability of monovalent counterions. Our theory reproduces several experimental findings including non-monotonic conformational size with the variation in the electrostatic strength and a shift from a continuous to a discontinuous collapse transition with the increase in the dipole strength of condensed ions. At low dipole strength and high electrostatic strength, our theory predicts a series of solvent quality driven size transitions spanning the re-entrant poor, theta and good solvent regimes. At high dipole strength, the size remains that of a compact globule independent of solvent quality. The dipole strength of the ion-pair formed due to counterion condensation, which depends on the size and polarizability of the monovalent counterions, is found to be an important molecular parameter in determining the nature of collapse transition, and the size of the collapsed state at high electrostatic strength.

The anomalous diffusion of polymers in random media

We re-examine the problem of the diffusion of a Gaussian chain in a fixed array of obstacles using the projection operator formalism introduced by Loring [J. Chem. Phys. 88, 6631 (1988)]. We show that in the limit of long wavelengths, the frequency-dependent monomer friction coefficient that is used in the calculation of the mean square displacement of the center of mass can be rewritten exactly in terms of the time correlation function of the total force on the chain. When the decay profile of the force correlation function is assumed to be exponential, and its dependence on the density of obstacles written in an approximate resummed form, the dynamics of the center of mass is found to be diffusive at long and short times, and subdiffusive (anomalous) at intermediate times. Moreover, the diffusion coefficient D that describes the long-time behavior of the chain at high concentrations of small obstacles is found to vary with chain length N as N-2, which is in qualitative agreement with the predictions of the reptation model. These results are obtained in the absence of any mechanism that might incorporate the notion of reptation directly into the calculations, in contrast to Loring’s approach, which treats the monomer friction coefficient approximately using a decoupling of segmental motion into parallel and perpendicular components.

Protein dynamics modulated electron transfer kinetics in early stage photosynthesis

A recent experiment has probed the electron transfer kinetics in the early stage of photosynthesis in Rhodobacter sphaeroides for the reaction center of wild type and different mutants [Science 316, 747 (2007)]. By monitoring the changes in the transient absorption of the donor-acceptor pair at 280 and 930 nm, both of which show non-exponential temporal decay, the experiment has provided a strong evidence that the initial electron transfer kinetics is modulated by the dynamics of protein backbone. In this work, we present a model where the electron transfer kinetics of the donor-acceptor pair is described along the reaction coordinate associated with the distance fluctuations in a protein backbone. The stochastic evolution of the reaction coordinate is described in terms of a non-Markovian generalized Langevin equation with a memory kernel and Gaussian colored noise, both of which are completely described in terms of the microscopics of the protein normal modes. This model provides excellent fits to the transient absorption signals at 280 and 930 nm associated with protein distance fluctuations and protein dynamics modulated electron transfer reaction, respectively. In contrast to previous models, the present work explains the microscopic origins of the non-exponential decay of the transient absorption curve at 280 nm in terms of multiple time scales of relaxation of the protein normal modes. Dynamic disorder in the reaction pathway due to protein conformational fluctuations which occur on time scales slower than or comparable to the electron transfer kinetics explains the microscopic origin of the non-exponential nature of the transient absorption decay at 930 nm. The theoretical estimates for the relative driving force for five different mutants are in close agreement with the experimental estimates obtained using electrochemical measurements.

Bond fluctuation model of polymers in random media

Conventional descriptions of polymers in random media often characterize the disorder by way of a spatially random potential. When averaged, the potential produces an effective attractive interaction between chain segments that can lead to chain collapse. As an alternative to this approach, we consider here a model in which the effects of disorder are manifested as a random alternation of the Kuhn length of the polymer between two average values. A path integral formulation of this model generates an effective Hamiltonian whose interaction term (representing the disorder in the medium) is quadratic and nonlocal in the spatial coordinates of the monomers. The average end-to-end distance of the chain is computed exactly as a function of the ratio of the two Kuhn lengths for different values of the frequency of alternation. For certain parameter values, chain contraction is found to occur to a state that is chain length dependent. In both the expanded and compact configurations, the scaling exponent that characterizes this dependence is found to be the same.