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Journal ArticleDOI

Polymer in a double well: dynamics of translocation of short chains over a barrier

12 Apr 2006-Journal of Physics: Condensed Matter (IOP Publishing)-Vol. 18, Iss: 14
TL;DR: In this article, the authors consider the dynamics of a short chain polymer crossing over a free energy barrier in space and find exact expressions for the activation energy and the rate of crossing.
Abstract: We consider the dynamics of a short chain polymer crossing over a free energy barrier in space. Adopting the continuum version of the Rouse model, we find exact expressions for the activation energy and the rate of crossing. For this model, the analysis of barrier crossing is analogous to semiclassical treatment of quantum tunnelling. Finding the saddle point for the process requires solving a Newton-like equation of motion for a fictitious particle. The analysis shows that short chains would cross the barrier as a globule. The activation free energy for this would increase linearly with the number of units N in the polymer. The saddle point for longer chains is an extended conformation, in which the chain is stretched out. The stretching out lowers the energy and hence the activation free energy is no longer linear in N. The rates in both the cases are calculated using a multidimensional approach and analytical expressions are derived, using a new formula for evaluating the infinite products. However, due to the harmonic approximation made in the derivation, the rates are found to diverge at the point where the saddle point changes over from the globule to the stretched out conformation. The reason for this is identified to be the bifurcation of the saddle to give two new saddles, and a correction formula is derived for the rate in the vicinity of this point. Numerical results using the formulae are presented. As a function of N, it is possible for the rate to have a minimum. This is due to confinement effects in the initial state.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the dynamics of polymers in a viscous medium containing self-propelled particles in two dimensions by using Brownian dynamics simulations were studied and it was shown that the polymer center of mass exhibits a superdiffusive motion at short to intermediate times and the motion turns normal at long times, but with a greatly enhanced diffusivity.
Abstract: While the dynamics of polymer chains in equilibrium media is well understood by now, the polymer dynamics in active non-equilibrium environments can be very different. Here we study the dynamics of polymers in a viscous medium containing self-propelled particles in two dimensions by using Brownian dynamics simulations. We find that the polymer center of mass exhibits a superdiffusive motion at short to intermediate times and the motion turns normal at long times, but with a greatly enhanced diffusivity. Interestingly, the long time diffusivity shows a non-monotonic behavior as a function of chain length and stiffness. We analyze how the polymer conformation and the accumulation of self-propelled particles, and therefore the directed motion of the polymer, are correlated. At the point of maximal polymer diffusivity, the polymer has preferentially bent conformations maintained by the balance between the chain elasticity and the propelling force generated by the active particles. We also consider the barrier crossing dynamics of actively-driven polymers in a double-well potential. The barrier crossing times are demonstrated to have a peculiar non-monotonic dependence, related to that of the diffusivity. This effect can be potentially utilized for sorting polymers from solutions in in vitro experiments.

33 citations

Journal ArticleDOI
TL;DR: Methodology for finding optimal tunneling paths and evaluating tunneling rates for atomic rearrangements is described and an example is presented where tunneling is the dominant mechanism well above room temperature as an H3BNH3 molecule dissociates to form H2.
Abstract: Methodology for finding optimal tunneling paths and evaluating tunneling rates for atomic rearrangements is described. First, an optimal JWKB tunneling path for a system with fixed energy is obtained using a line integral extension of the nudged elastic band method. Then, a calculation of the dynamics along the path is used to determine the temperature at which it corresponds to an optimal Feynman path for thermally activated tunneling (instanton) and a harmonic approximation is used to estimate the transition rate. The method is illustrated with calculations for a modified two-dimensional Muller-Brown surface but is efficient enough to be used in combination with electronic structure calculations of the energy and atomic forces in systems containing many atoms. An example is presented where tunneling is the dominant mechanism well above room temperature as an H3BNH3 molecule dissociates to form H2. Also, a solid-state example is presented where density functional theory calculations of H atom tunneling in a Ta crystal give close agreement with experimental measurements on hydrogen diffusion over a wide range in temperature.

31 citations

Journal ArticleDOI
TL;DR: In this paper, the role of colored noise in two biological systems: adults of Nezara viridula (L) (Heteroptera: Pentatomidae), and polymer translocation is investigated.
Abstract: We investigate the role of the colored noise in two biological systems: (i) adults of Nezara viridula (L) (Heteroptera: Pentatomidae), and (ii) polymer translocation In the first system we analyze, by directionality tests, the response of N viridula individuals to subthreshold signals plus noise in their mating behaviour The percentage of insects that react to the subthreshold signal shows a nonmonotonic behaviour, characterized by the presence of a maximum, as a function of the noise intensity This is the signature of the non-dynamical stochastic resonance phenomenon By using a “soft” threshold model we find that the maximum of the input-output cross correlation occurs in the same range of noise intensity values for which the behavioural activation of the insects has a maximum Moreover this maximum value is lowered and shifted towards higher noise intensities, compared to the case of white noise In the second biological system the noise driven translocation of short polymers in crowded solutions is analyzed An improved version of the Rouse model for a flexible polymer is adopted to mimic the molecular dynamics by taking into account both the interactions between adjacent monomers and the effects of a Lennard-Jones potential between all beads The polymer dynamics is simulated in a two-dimensional domain by numerically solving the Langevin equations of motion in the presence of thermal fluctuations and a colored noise source At low temperatures or for strong colored noise intensities the translocation process of the polymer chain is delayed At low noise intensity, as the polymer length increases, we find a nonmonotonic behaviour for the mean first translocation time of the polymer centre of inertia We show how colored noise influences the motion of short polymers, by inducing two different regimes of translocation in the dynamics of molecule transport

22 citations

Journal ArticleDOI
TL;DR: The dynamics of polymers in a viscous medium containing self-propelled particles in two dimensions are studied by using Brownian dynamics simulations and it is found that the polymer center of mass exhibits a superdiffusive motion at short to intermediate times and the motion turns normal at long times, but with a greatly enhanced diffusivity.
Abstract: While the dynamics of polymer chains in equilibrium media is well understood by now, the polymer dynamics in active non-equilibrium environments can be very different. Here we study the dynamics of polymers in a viscous medium containing self-propelled particles in two dimensions by using Brownian dynamics simulations. We find that the polymer center of mass exhibits a superdiffusive motion at short to intermediate times and the motion turns normal at long times, but with a greatly enhanced diffusivity. Interestingly, the long time diffusivity shows a non-monotonic behavior as a function of the chain length and stiffness. We analyze how the polymer conformation and the accumulation of the self-propelled particles, and therefore the directed motion of the polymer, are correlated. At the point of maximal polymer diffusivity, the polymer has preferentially bent conformations maintained by the balance between the chain elasticity and the propelling force generated by the active particles. We also consider the barrier crossing dynamics of actively-driven polymers in a double-well potential. The barrier crossing times are demonstrated to have a peculiar non-monotonic dependence, related to that of the diffusivity. This effect can be potentially utilized for sorting of polymers from solutions in \textit{in vitro} experiments.

21 citations

Journal ArticleDOI
TL;DR: This work applies transition state theory to out-of-equilibrium transport through confined environments: the thermally activated translocation of single DNA molecules over an entropic barrier helped by an external force field.
Abstract: Transition state theory (TST) provides a simple interpretation of many thermally activated processes. It applies successfully on timescales and length scales that differ several orders of magnitude: to chemical reactions, breaking of chemical bonds, unfolding of proteins and RNA structures and polymers crossing entropic barriers. Here we apply TST to out-of-equilibrium transport through confined environments: the thermally activated translocation of single DNA molecules over an entropic barrier helped by an external force field. Reaction pathways are effectively one dimensional and so long that they are observable in a microscope. Reaction rates are so slow that transitions are recorded on video. We find sharp transition states that are independent of the applied force, similar to chemical bond rupture, as well as transition states that change location on the reaction pathway with the strength of the applied force. The states of equilibrium and transition are separated by micrometres as compared with angstroms/nanometres for chemical bonds.

13 citations

References
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Book
01 Jan 1986
TL;DR: In this article, the viscoelasticity of polymeric liquids was studied in the context of rigid rod-like polymers and concentrated solutions of rigid rods like polymers.
Abstract: Introduction Static properties of polymers Brownian motion Dynamics of flexible polymers in dilute solution Many chain systems Dynamics of a polymer in a fixed network Molecular theory for the viscoelasticity of polymeric liquids Dilute solutions of rigid rodlike polymers Semidilute solutions of rigid rodlike polymers Concentrated solutions of rigid rodlike polymers Index.

10,225 citations

Journal ArticleDOI
TL;DR: In this paper, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry.
Abstract: The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

5,180 citations

Journal ArticleDOI
TL;DR: It is shown that an electric field can drive single-stranded RNA and DNA molecules through a 2.6-nm diameter ion channel in a lipid bilayer membrane, which could in principle provide direct, high-speed detection of the sequence of bases in single molecules of DNA or RNA.
Abstract: We show that an electric field can drive single-stranded RNA and DNA molecules through a 2.6-nm diameter ion channel in a lipid bilayer membrane. Because the channel diameter can accommodate only a single strand of RNA or DNA, each polymer traverses the membrane as an extended chain that partially blocks the channel. The passage of each molecule is detected as a transient decrease of ionic current whose duration is proportional to polymer length. Channel blockades can therefore be used to measure polynucleotide length. With further improvements, the method could in principle provide direct, high-speed detection of the sequence of bases in single molecules of DNA or RNA.

3,251 citations

Book
01 Jan 1971

1,960 citations

Journal ArticleDOI
TL;DR: Because nanopores can rapidly discriminate and characterize unlabeled DNA molecules at low copy number, refinements of the experimental approach demonstrated here could eventually provide a low-cost high-throughput method of analyzing DNA polynucleotides.
Abstract: A variety of different DNA polymers were electrophoretically driven through the nanopore of an alpha-hemolysin channel in a lipid bilayer. Single-channel recording of the translocation duration and current flow during traversal of individual polynucleotides yielded a unique pattern of events for each of the several polymers tested. Statistical data derived from this pattern of events demonstrate that in several cases a nanopore can distinguish between polynucleotides of similar length and composition that differ only in sequence. Studies of temperature effects on the translocation process show that translocation duration scales as approximately T(-2). A strong correlation exists between the temperature dependence of the event characteristics and the tendency of some polymers to form secondary structure. Because nanopores can rapidly discriminate and characterize unlabeled DNA molecules at low copy number, refinements of the experimental approach demonstrated here could eventually provide a low-cost high-throughput method of analyzing DNA polynucleotides.

1,055 citations