Langevin dynamics simulations of ds-DNA translocation through synthetic nanopores

We have implemented a coarse-grained model to study voltage-driven as-DNA translocation through nanopores located in synthetic membranes. The simulated trajectory of the DNA through the nanopores was calculated using Langevin dynamics. We present the results based on more than 120,000 individual translocations. We are particularly interested in this work in probing the physical basis of various experimentally observed--yet poorly understood--phenomena. Notably, we observe in our simulations the formation of ds-DNA hairpins, widely suspected to be the basis for quantized blockage. We study the translocation time, a measurable quantity crucially important in polyelectrolyte characterization, as a function of hairpin vertex location along the polymer backbone, finding that this behavior can be tuned to some degree by simulation parameters. We also study the voltage dependence of the tendency of hairpins to serve as the initiators of translocation events. Surprisingly, we find that the resulting probability depends vitally upon whether the events counted are ultimately successful or not. Further details lead us to propose that failed attempts in experimental translocation studies may be more common--and deceptive--than is generally recognized. We find the time taken by successful single file translocations to be directly proportional to the ratio of chain length to the applied voltage. Finally, we address a common yet puzzling phenomenon in translocation experiments: translocation events in which the current through the pore is highly, yet incompletely, blocked. We present the findings that offer a new explanation for such events.

Monte Carlo simulations of single crystals from polymer solutions

A novel "anisotropic aggregation" model is proposed to simulate nucleation and growth of polymer single crystals as functions of temperature and polymer concentration in dilute solutions. Prefolded chains in a dilute solution are assumed to aggregate at a seed nucleus with an anisotropic interaction by a reversible adsorption/desorption mechanism, with temperature, concentration, and seed size being the control variables. The Monte Carlo results of this model resolve the long-standing dilemma regarding the kinetic and thermal roughenings, by producing a rough-flat-rough transition in the crystal morphology with increasing temperature. It is found that the crystal growth rate varies nonlinearly with temperature and concentration without any marked transitions among any regimes of polymer crystallization kinetics. The induction time increases with decreasing the seed nucleus size, increasing temperature, or decreasing concentration. The apparent critical nucleus size is found to increase exponentially with increasing temperature or decreasing concentration, leading to a critical nucleus diagram composed in the temperature-concentration plane with three regions of different nucleation barriers: no growth, nucleation and growth, and spontaneous growth. Melting temperatures as functions of the crystal size, heating rate, and concentration are also reported. The present model, falling in the same category of small molecular crystallization with anisotropic interactions, captures most of the phenomenology of polymer crystallization in dilute solutions.

Continuum theory of polymer crystallization

We present a kinetic model of crystal growth of polymers of finite molecular weight. Experiments help to classify polymer crystallization broadly into two kinetic regimes. One is observed in melts or in high molar mass polymer solutions and is dominated by nucleation control with G approximately exp(1/TDeltaT), where G is the growth rate and DeltaT is the supercooling. The other is observed in low molar mass solutions (as well as for small molecules) and is diffusion controlled with G approximately DeltaT, for small DeltaT. Our model unifies these two regimes in a single formalism. The model accounts for the accumulation of polymer chains near the growth front and invokes an entropic barrier theory to recover both limits of nucleation and diffusion control. The basic theory applies to both melts and solutions, and we numerically calculate the growth details of a single crystal in a dilute solution. The effects of molecular weight and concentration are also determined considering conventional polymer dynamics. Our theory shows that entropic considerations, in addition to the traditional energetic arguments, can capture general trends of a vast range of phenomenology. Unifying ideas on crystallization from small molecules and from flexible polymer chains emerge from our theory.

Microphase separation in polyelectrolytic diblock copolymer melt: Weak segregation limit

The authors present a generalized theory of microphase separation for charged-neutral diblock copolymer melt. The stability limit of the disordered phase for salt-free melt has been calculated using random phase approximation (RPA) and self-consistent-field theory (SCFT). Explicit analytical free energy expressions for different classical ordered microstructures (lamellar, cylinder, and sphere) are presented. The authors demonstrate that the chemical mismatch required for the onset of microphase separation (chi*N) in charged-neutral diblock melt is higher and the period of ordered microstructures is lower than those for the corresponding neutral-neutral diblock system. Theoretical predictions on the period of ordered structures in terms of Coulomb electrostatic interaction strength, chain length, block length, and chemical mismatch between blocks are presented. SCFT has been used to go beyond the stability limit, where electrostatic potential and charge distribution are calculated self-consistently. Stability limits calculated using RPA are in perfect agreement with the corresponding SCFT calculations. Limiting laws for the stability limit and the period of ordered structures are presented and comparisons are made with an earlier theory. Also, transition boundaries between different morphologies have been investigated.

Polymer capture by electro-osmotic flow of oppositely charged nanopores

The authors have addressed theoretically the hydrodynamic effect on the translocation of DNA through nanopores. They consider the cases of nanopore surface charge being opposite to the charge of the translocating polymer. The authors show that, because of the high electric field across the nanopore in DNA translocation experiments, electro-osmotic flow is able to create an absorbing region comparable to the size of the polymer around the nanopore. Within this capturing region, the velocity gradient of the fluid flow is high enough for the polymer to undergo coil-stretch transition. The stretched conformation reduces the entropic barrier of translocation. The diffusion limited translocation rate is found to be proportional to the applied voltage. In the authors' theory, many experimental variables (electric field, surface potential, pore radius, dielectric constant, temperature, and salt concentration) appear through a single universal parameter. They have made quantitative predictions on the size of the adsorption region near the pore for the polymer and on the rate of translocation.

Threading synthetic polyelectrolytes through protein pores

We have measured the ionic current signatures of sodium poly(styrene sulfonate) as its single molecules translocate through an alpha-hemolysin pore embedded into a bilayer in a salty aqueous medium under an externally applied electric field. As in the previous experiments involving DNA and RNA, the pore current, which is a measure of the ionic conductivity of the low molar mass electrolyte ions, is significantly reduced when the polymer molecule translocates through the pore. The magnitude and the duration of the reduction in the pore current are measured for each of the translocation events. By studying thousands of events of reduction in the ionic current, we have constructed distribution functions for the extent of the reduced current and for the translocation time. The details of these distribution functions are significantly different from those for DNA and RNA. By investigating over two orders of magnitude in the molecular weight of the polymer, the average translocation time is found to be proportional to the molecular weight and inversely proportional to the applied voltage. This demonstration of threading a synthetic polyelectrolyte through a protein pore opens up many opportunities to systematically explore the fundamental physical principles behind translocation of single macromolecules, by resorting to the wide variety of synthetically available polymers without the complexities arising from the sequences of biological polymers. In addition, the present experiments suggest yet another experimental protocol for separation of polymer molecules directly in aqueous media.

Effect of deprotection extent on swelling and dissolution regimes of thin polymer films

The response of unentangled polymer thin films to aqueous hydroxide solutions is measured as a function of increasing weakly acidic methacrylic acid comonomer content produced by an in situ reaction-diffusion process. Quartz crystal microbalance with energy dissipation and Fourier transform infrared spectroscopy measurements are used to identify four regimes: (I) nonswelling, (II) quasiequilibrium swelling, (III) swelling coupled with partial film dissolution, and (IV) film dissolution. These regimes result from chemical heterogeneity in local composition of the polymer film. The acid-catalyzed deprotection of a hydrophobic group to the methacrylic acid tends to increase the hydrophilic domain size within the film. This nanoscale structure swells in aqueous base by ionization of the methacrylic acid groups. The swollen film stability, however, is determined by the hydrophobic matrix that can act as physical cross-links to prevent dissolution of the polyelectrolyte chains. These observations challenge current models of photoresist film dissolution that do not include the effects of swelling and partial film dissolution on image quality.

Electrostatic origin of the genome packing in viruses

Many ssRNA/ssDNA viruses bind their genome by highly basic semiflexible peptide arms of capsid proteins. Here, we show that nonspecific electrostatic interactions control both the length of the genome and genome conformations. Analysis of available experimental data shows that the genome length is linear in the net charge on the capsid peptide arms, irrespective of the actual amino acid sequence, with a proportionality coefficient of 1.61 +/- 0.03. This ratio is conserved across all ssRNA/ssDNA viruses with highly basic peptide arms, and is different from the one-to-one charge balance expected of specific binding. Genomic nucleotides are predicted to occupy a radially symmetric spherical shell detached from the viral capsid, in agreement with experimental data.

Polymer translocation through a nanopore. II. Excluded volume effect

Following our previous study of a Gaussian chain translocation, we have investigated the transport of a self-avoiding chain from one sphere to another sphere through a narrow pore, using the self-consistent field theory formalism. The free energy landscape for polymer translocation is significantly modified by excluded volume interactions among monomers. The free energy barrier for the placement of one of the chain ends at the pore depends on the chain length N nonmonotonically, in contrast to the N-independence for Gaussian chains. This results in a nonmonotonic dependence of the average arrival time [tau0] on N for self-avoiding chains. When the polymer chain is partitioned between the donor and recipient spheres, a local free energy minimum develops, depending on the strength w of the excluded volume interaction and the relative sizes of the donor and recipient spheres. If the sizes of spheres are comparable, the average translocation time tau (the average time taken by the polymer, after the arrival at the pore, to convert from the donor to the recipient) increases with an increase in w for a fixed N value. On the other hand, for the highly asymmetric sizes of the donor and recipient spheres, tau decreases with an increase in w. As in the case of Gaussian chains, tau depends nonmonotonically on the pore length.

Entropy and enthalpy of polyelectrolyte complexation: Langevin dynamics simulations

We report a systematic study by Langevin dynamics simulation on the energetics of complexation between two oppositely charged polyelectrolytes of same charge density in dilute solutions of a good solvent with counterions and salt ions explicitly included. The enthalpy of polyelectrolyte complexation is quantified by comparisons of the Coulomb energy before and after complexation. The entropy of polyelectrolyte complexation is determined directly from simulations and compared with that from a mean-field lattice model explicitly accounting for counterion adsorption. At weak Coulomb interaction strengths, e.g., in solvents of high dielectric constant or with weakly charged polyelectrolytes, complexation is driven by a negative enthalpy due to electrostatic attraction between two oppositely charged chains, with counterion release entropy playing only a subsidiary role. In the strong interaction regime, complexation is driven by a large counterion release entropy and opposed by a positive enthalpy change. The addition of salt reduces the enthalpy of polyelectrolyte complexation by screening electrostatic interaction at all Coulomb interaction strengths. The counterion release entropy also decreases in the presence of salt, but the reduction only becomes significant at higher Coulomb interaction strengths. More significantly, in the range of Coulomb interaction strengths appropriate for highly charged polymers in aqueous solutions, complexation enthalpy depends weakly on salt concentration and counterion release entropy exhibits a large variation as a function of salt concentration. Our study quantitatively establishes that polyelectrolyte complexation in highly charged Coulomb systems is of entropic origin.

Langevin dynamics simulations of genome packing in bacteriophage

We use Langevin dynamics simulations to study the process by which a coarse-grained DNA chain is packaged within an icosahedral container. We focus our inquiry on three areas of interest in viral packing: the evolving structure of the packaged DNA condensate; the packing velocity; and the internal buildup of energy and resultant forces. Each of these areas has been studied experimentally, and we find that we can qualitatively reproduce experimental results. However, our findings also suggest that the phage genome packing process is fundamentally different than that suggested by the inverse spool model. We suggest that packing in general does not proceed in the deterministic fashion of the inverse-spool model, but rather is stochastic in character. As the chain configuration becomes compressed within the capsid, the structure, energy, and packing velocity all become dependent upon polymer dynamics. That many observed features of the packing process are rooted in condensed-phase polymer dynamics suggests that statistical mechanics, rather than mechanics, should serve as the proper theoretical basis for genome packing. Finally we suggest that, as a result of an internal protein unique to bacteriophage T7, the T7 genome may be significantly more ordered than is true for bacteriophage in general.

Simulation of polymer translocation through protein channels

A modeling algorithm is presented to compute simultaneously polymer conformations and ionic current, as single polymer molecules undergo translocation through protein channels. The method is based on a combination of Langevin dynamics for coarse-grained models of polymers and the Poisson-Nernst-Planck formalism for ionic current. For the illustrative example of ssDNA passing through the alpha-hemolysin pore, vivid details of conformational fluctuations of the polymer inside the vestibule and beta-barrel compartments of the protein pore, and their consequent effects on the translocation time and extent of blocked ionic current are presented. In addition to yielding insights into several experimentally reported puzzles, our simulations offer experimental strategies to sequence polymers more efficiently.

Simulations of stochastic sensing of proteins

We have performed Langevin dynamics and Poisson-Nernst-Planck calculations to simulate detection of proteins by genetically engineered alpha-hemolysin channels. In the recent stochastic sensing experiments, one end of a flexible polymer chain is permanently anchored inside the protein channel at a specified location, and the other end undergoes complexation with an analyte. Our simulations, using coarse-grained modeling, reproduce all essential qualitative results of the electrophysiology measurements of stochastic sensing. In addition, the underlying macromolecular mechanisms behind stochastic sensing are revealed in vivid details. The entropic fluctuations of the conformations of the tethered polymer chain dictate crucially the unique signatures of the ionic current trace of the channel and provide design rules for successful stochastic sensing. The origin of strong fluctuations in the ionic current of the channel is found to arise from the obstruction of the entrance at the beta-barrel of the channel by the fluctuating segments of the tether. Silencing of the pore is due to the suppression of conformational fluctuations of the chain, and the permanent blockade of ionic current is due to the threading of the tether through the channel. The onset of silencing and permanent blockade of the channel current cannot necessarily be attributed to the capture of analytes. In order for detection events to be timed accurately, the length and anchoring location of the tether must be tuned appropriately.

Theory of counter-ion condensation on flexible polyelectrolytes: Adsorption mechanism

A new model is presented for counterion distribution around flexible polyelectrolytes by considering (i) free energy of the polyelectrolyte chain, (ii) translational entropy of adsorbed counterions, (iii) adsorption energy, (iv) translational entropy of unadsorbed counterions, (v) fluctuations of dissociated ions, and (vi) correlation among ion-pairs formed by adsorbed counterions on the polymer. The effective charge and size of the polymer are calculated self-consistently. The degree of ionization f of the polymer decreases continuously with 1/epsilonT (epsilon and T are the dielectric constant of the solvent and temperature, respectively), depending sensitively on local dielectric heterogeneity. Further, f decreases with an increase in salt concentration, monomer concentration, or chain flexibility. The polymer size, accompanying the changes in f, depends nonmonotonically on 1/epsilonT. The predictions of the model are consistent with all trends observed previously in simulations and are distinctly different from the Manning argument for rodlike chains.

Triple points in solutions of polydisperse semiflexible polymers

When a mother solution of semiflexible polymers with differing molecular weights is forced to undergo phase transition, cloud and shadow curves emerge instead of a coexistence curve. For the first time, we calculate the cloud and shadow curves for an isotropic-nematic transition coupled to polydispersity and predict novel triple points. Because of the emergence of new triple points, polydispersity allows the occurrence of anisotropic phases at much lower polymer concentrations than for the monodisperse solutions.

Leprosy situation in endemic states of India and prospects of elimination of the disease

In India there is a dramatic fall in the prevalence rate (PR) of leprosy, but the new case-detection rate (NCDR) has not been reduced concomitantly. It is the operational efficiency of the National Leprosy Eradication Programme (NLEP) that has led to a significant reduction in the NCDR in Andhra Pradesh and Tamil Nadu. The ratio of PR to NCDR has been declining in these two states and it reveals that elimination could be reached even with the high NCDR level of 3 to 4 per 10000 population, particularly if single skin lesion (SSL) cases are discharged through single dose treatment of rifampicin, ofloxacin and minocycline (ROM). On the other hand, the significant number of cases detected in Bihar and Orissa during modified leprosy elimination campaigns (MLECs) reveals that there are lacunae in operational activities in new case-detection resulting in a large number of undetected cases in the community. Only one-third of the cases are reporting voluntarily. Awareness of leprosy is not adequate to motivate the patients to report voluntarily and complete their treatment, thus underscoring the need for relying on active case-detection so that transmission can be broken and elimination of leprosy achieved. In addition, the influence of socio-economic factors on continued occurrence of leprosy cannot be ruled out. The establishment of a sentinel surveillance system along with a computerized simplified information system to gain in-depth knowledge on the functioning of the NLEP will ensure operational efficiency. In view of this situation, the NLEP should adopt a more realistic approach towards reaching the elimination goal.