Rajarshi Chakrabarti

Dynamics of end-to-end loop formation for an isolated chain in viscoelastic fluid

We theoretically investigate the looping dynamics of a linear chain immersed in a viscoelastic fluid. The dynamics of the chain is governed by a Rouse model with a fractional memory kernel recently proposed by Weber et al. [S.C. Weber, J.A. Theriot, A.J. Spakowitz, Phys. Rev. E 82 (2010) 011913]. Using the Wilemski–Fixman [G. Wilemski, M. Fixman, J. Chem. Phys. 60 (1974) 866] formalism we calculate the looping time for a chain in a viscoelastic fluid where the mean square displacement of the center of mass of the chain scales as t1/2. We observe that the looping time is faster for the chain in a viscoelastic fluid than for a Rouse chain in a Newtonian fluid up to a chain length and above this chain length the trend is reversed. Also no stable scaling of the looping time with the length of the chain seems to exist for the chain in a viscoelastic fluid.

Chain reconfiguration in active noise

In a typical single molecule experiment, the dynamics of an unfolded protein is studied by determining the reconfiguration time using long-range Forster resonance energy transfer, where the reconfiguration time is the characteristic decay time of the position correlation between two residues of the protein. In this paper we theoretically calculate the reconfiguration time for a single flexible polymer in the presence of active noise. The study suggests that though the mean square displacement grows faster, the chain reconfiguration is always slower in the presence of long-lived active noise with exponential temporal correlation. Similar behavior is observed for a worm-like semi-flexible chain and a Zimm chain. However it is primarily the characteristic correlation time of the active noise and not the strength that controls the increase in the reconfiguration time. In brief, such active noise makes the polymer move faster but the correlation loss between the monomers becomes slow.

Rate processes with dynamical disorder: A direct variational approach

Using path integral approach, we develop variational approximations to the calculation of survival probability for rate processes with dynamical disorder. We derive both upper and lower bounds to the survival probability using Jensens inequality. The inequalities involve the use of a trial action for which the path integrals can be evaluated exactly. Any parameter in the trial action can be varied to optimize the bounds. We have also derived a lower bound to the rate of the process. As a simple illustration, we apply the method to the problem of a particle undergoing Brownian motion in a harmonic potential well, in the presence of a delta function sink, for which one can calculate the exact survival probability numerically. The calculation confirms the two inequalities. The method should be very useful in similar but more complex problems where even numerical solution is not possible.

Ion assisted structural collapse of a single stranded DNA: A molecular dynamics approach

Abstract The structure and dynamics of negatively charged nucleic acids strongly correlate with the concentration and charge of the oppositely charged counterions. It is well known that the structural collapse of DNA is favoured in the presence of additional salt, a source of excess oppositely charged ions. Under such conditions single stranded DNA adopts a collapsed coil like conformation, typically characterized by stacking base pairs. Using atomistic molecular dynamics simulation, we demonstrate that in the presence of additional divalent salt (MgCl 2 ) single stranded DNA with base sequence 5′-CGCGAATTCGCG-3′ (Dickerson Drew dodecamer) initially collapses and then expands with increasing salt concentration. This is due to the overcharging induced DNA chain swelling, a dominant factor at a higher divalent salt concentration. In a nutshell, our simulations show how in the presence of divalent salt, non-sequential base stacking and overcharging competes and affect single stranded DNA dynamics unlike a monovalent salt.

Dynamics of end-to-end loop formation: A flexible chain in the presence of hydrodynamic interaction

Based on the Wilemski-Fixman approach (J. Chem. Phys. 60, 866 (1974)) we showed that for a flexible chain in θ solvent hydrodynamic interaction treated with an pre-averaging approximation makes ring closing faster if the chain is not very short. Only for a very short chain the ring closing is slower with hydrodynamic interaction on. We have also shown that the ring closing time for a chain with hydrodynamic interaction in θ solvent scales with the chain length (N) as N1.527, in good agreement with previous renormalization group calculation based prediction by Freidman et al. (Phys. Rev. A. 40, 5950 (1989)).

Correction to "Probing the Salt Concentration Dependent Nucleobase Distribution in a Single-Stranded DNA-Single-Walled Carbon Nanotube Hybrid with Molecular Dynamics".

The hybrids of single-walled carbon nanotube (SWCNT) and single stranded DNA (ssDNA) are novel nanoscale materials having remarkable applications in nanotechnology. The absorption of nucleobases on the surface of a SWCNT depends strongly on the ionic strength of the medium. In this paper, using atomistic molecular dynamics we have shown that at low salt concentration ssDNA wraps on the surface of SWCNT through hydrophobic π–π stacking between the DNA bases and the sp2-hybridized carbon atoms of the carbon nanotube. At high salt concentration, however, the DNA molecule adopts a partially folded structure and the ssDNA–SWCNT wrapping gets weakened significantly due to the self-stacking of the DNA bases. Our study can find relevance in CNT mediated gene delivery processes where subsequent unwrapping of the gene from its carrier is anticipated across the cell membrane regulated by an existing salt concentration gradient.

Tracer diffusion in a crowded cylindrical channel.

Based on a coarse-grained model, we carry out molecular dynamics simulations to analyze the diffusion of a small tracer particle inside a cylindrical channel whose inner wall is covered with randomly grafted short polymeric chains. We observe an interesting transient subdiffusive behavior along the cylindrical axis at high attraction between the tracer and the chains, however, the long-time diffusion is always normal. This process is found to be enhanced for the case that we immobilize the grafted chains, i.e., the subdiffusive behavior sets in at an earlier time and spans over a longer time period before becoming diffusive. Even if the grafted chains are replaced with a frozen sea of repulsive, nonconnected particles in the background, a transient subdiffusion is observed. The intermediate subdiffusive behavior only disappears when the grafted chains are replaced with a mobile background sea of mutually repulsive particles. Overall, the long-time diffusion coefficient of the tracer along the cylinder axis decreases with an increase in system volume fraction, the strength of the attraction between the tracer and the background, and also on freezing the background.

Tracer diffusion in a sea of polymers with binding zones: mobile vs. frozen traps

We use molecular dynamics simulations to investigate the tracer diffusion in a sea of polymers with specific binding zones for the tracer. These binding zones act as traps. Our simulations show that the tracer can undergo normal yet non-Gaussian diffusion under certain circumstances, e.g., when the polymers with traps are frozen in space and the volume fraction and the binding strength of the traps are moderate. In this case, as the tracer moves, it experiences a heterogeneous environment and exhibits confined continuous time random walk (CTRW) like motion resulting in a non-Gaussian behavior. Also the long time dynamics becomes subdiffusive as the number or the binding strength of the traps increases. However, if the polymers are mobile then the tracer dynamics is Gaussian but could be normal or subdiffusive depending on the number and the binding strength of the traps. In addition, with increasing binding strength and number of polymer traps, the probability of the tracer being trapped increases. On the other hand, removing the binding zones does not result in trapping, even at comparatively high crowding. Our simulations also show that the trapping probability increases with the increasing size of the tracer and for a bigger tracer with the frozen polymer background the dynamics is only weakly non-Gaussian but highly subdiffusive. Our observations are in the same spirit as found in many recent experiments on tracer diffusion in polymeric materials and question the validity of using Gaussian theory to describe diffusion in a crowded environment in general.

Looping and reconfiguration dynamics of a flexible chain with internal friction

In recent past, experiments and simulations have suggested that apart from the solvent friction, friction arising from the protein itself plays an important role in protein folding by affecting the intra-chain loop formation dynamics. This friction is termed as internal friction in the literature. Using a flexible Gaussian chain with internal friction we analyze the intra-chain reconfiguration and loop formation times for all three topology classes namely end-to-end, end-to-interior and interior-to-interior. In a nutshell, bypassing expensive simulations we show how simple models like that of Rouse and Zimm can support the single molecule experiment and computer simulation results on intra-chain diffusion coefficients, looping time and even can predict the effects of tail length on the looping time.

A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensens inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.