Tethered DNA dynamics in shear flow

Self-Attractive Semiflexible Polymers under an External Force Field

The dynamical response of a tethered semiflexible polymer with self-attractive interactions and subjected to an external force field is numerically investigated by varying stiffness and self-interaction strength. The chain is confined in two spatial dimensions and placed in contact with a heat bath described by the Brownian multi-particle collision method. For strong self-attraction the equilibrium conformations range from compact structures to double-stranded chains, and to rods when increasing the stiffness. Under the external field at small rigidities, the initial close-packed chain is continuously unwound by the force before being completely elongated. For double-stranded conformations the transition from the folded state to the open one is sharp being steeper for larger stiffnesses. The discontinuity in the transition appears in the force-extension relation, as well as in the probability distribution function of the gyration radius. The relative deformation with respect to the equilibrium case along the direction normal to the force is found to decay as the inverse of the applied force.

Wall-anchored semiflexible polymer under large amplitude oscillatory shear flow

The properties of semiflexible polymers tethered by one end to an impenetrable wall and exposed to oscillatory shear flow are investigated by mesoscale simulations. A polymer, confined in two dimensions, is described by a linear bead-spring chain, and fluid interactions are incorporated by the Brownian multiparticle collision dynamics approach. At small strain, the polymers follow the applied flow field. However, at high strain, we find a strongly nonlinear response with major conformational changes. Polymers are stretched along the flow direction and exhibit U-shaped conformations while following the flow. As a consequence of confinement in the half-space, frequency doubling in the time-dependent polymer properties appears along the direction normal to the wall.

Tethered Semiflexible Polymer under Large Amplitude Oscillatory Shear

The properties of a semiflexible polymer with fixed ends exposed to oscillatory shear flow are investigated by simulations. The two-dimensionally confined polymer is modeled as a linear bead-spring chain, and the interaction with the fluid is described by the Brownian multiparticle collision dynamics approach. For small shear rates, the tethering of the ends leads to a more-or-less linear oscillatory response. However, at high shear rates, we found a strongly nonlinear reaction, with a polymer (partially) wrapped around the fixation points. This leads to an overall shrinkage of the polymer. Dynamically, the location probability of the polymer center-of-mass position is largest on a spatial curve resembling a limaçon, although with an inhomogeneous distribution. We found shear-induced modifications of the normal-mode correlation functions, with a frequency doubling at high shear rates. Interestingly, an even-odd asymmetry for the Cartesian components of the correlation functions appears, with rather similar spectra for odd x- and even y-modes and vice versa. Overall, our simulations yielded an intriguing nonlinear behavior of tethered semiflexible polymers under oscillatory shear flow.

Nonequilibrium Markov state modeling of the globule-stretch transition

We describe a systematic approach to construct coarse-grained Markov state models from molecular dynamics data of systems driven into a nonequilibrium steady state. We apply this method to study the globule-stretch transition of a single tethered model polymer in shear flow. The folding and unfolding rates of the coarse-grained model agree with the original detailed model. We demonstrate that the folding and unfolding proceeds through the same narrow region of configuration space but along different cycles.

Optimal estimation of diffusion coefficients from single-particle trajectories

How does one optimally determine the diffusion coefficient of a diffusing particle from a single-time-lapse recorded trajectory of the particle? We answer this question with an explicit, unbiased, and practically optimal covariance-based estimator (CVE). This estimator is regression-free and is far superior to commonly used methods based on measured mean squared displacements. In experimentally relevant parameter ranges, it also outperforms the analytically intractable and computationally more demanding maximum likelihood estimator (MLE). For the case of diffusion on a flexible and fluctuating substrate, the CVE is biased by substrate motion. However, given some long time series and a substrate under some tension, an extended MLE can separate particle diffusion on the substrate from substrate motion in the laboratory frame. This provides benchmarks that allow removal of bias caused by substrate fluctuations in CVE. The resulting unbiased CVE is optimal also for short time series on a fluctuating substrate. We have applied our estimators to human 8-oxoguanine DNA glycolase proteins diffusing on flow-stretched DNA, a fluctuating substrate, and found that diffusion coefficients are severely overestimated if substrate fluctuations are not accounted for.

Brownian dynamics simulations of confined tethered polymers in shear flow: the effect of attractive surfaces

Coarse grain Brownian dynamics simulations of the bead-spring model are used to investigate the effect of attractive surfaces on the stretching of confined tethered polymers under shear flow. The weak and strong adsorbed regimes have been addressed by means of a coarse grain van der Waals potential to simulate polymer substrate interactions. Different stationary cyclic dynamics are observed upon varying shear flow intensity and surface potential strength. Polymer stretching decreases as increasing the attractive potential strength, breaking down the scaling predictions for non-adsorbed polymers. We found that adsorption is enhanced by the shear flow strength in agreement to simulations of adsorbed non-tethered polymers.

Non-equilibrium relaxation and tumbling times of polymers in semidilute solution

The end-over-end tumbling dynamics of individual polymers in dilute and semidilute solutions is studied under shear flow by large-scale mesoscale hydrodynamic simulations. End-to-end vector relaxation times are determined along the flow, gradient, and vorticity directions. Along the flow and gradient directions, the correlation functions decay exponentially with sinusoidal modulations at short times. In dilute solution, the decay times of the various directions are very similar. However, in semidilute solutions, the relaxation behaviors are rather different along the various directions, with the longest relaxation time in the vorticity direction and the shortest time in the flow direction. The various relaxation times exhibit a power-law shear-rate dependence with the exponent  - 2/3 at high shear rates. Quantitatively, the relaxation times are equal to the tumbling times extracted from cross-correlation functions of fluctuations of radius-of-gyration components along the flow and gradient direction.

Simulation of tethered oligomers in nanochannels using multi-particle collision dynamics

The effect of a high Reynold's number, pressure-driven flow of a compressible gas on the conformation of an oligomer tethered to the wall of a square channel is studied under both ideal solvent and poor solvent conditions using a hybrid multiparticle collision dynamics and molecular dynamics algorithm. Unlike previous studies, the flow field contains an elongational component in addition to a shear component as well as fluid slip near the walls and results in a Schmidt number for the polymer beads that is less than unity. In both solvent regimes the oligomer is found to extend in the direction of flow. Under the ideal solvent conditions, torsional twisting of the chain and aperiodic cyclical dynamics are observed for the end of the oligomer. Under poor solvent conditions, a metastable helix forms in the end of the chain despite the lack of any attractive potential between beads in the oligomeric chain. The formation of the helix is postulated to be the result of a solvent induced chain collapse that has been confined to a single dimension by a strong flow field.

Identifying hydrodynamic interaction effects in tethered polymers in uniform flow

Using Brownian dynamics simulations, we investigate how hydrodynamic interaction (HI) affects the behavior of tethered polymers in uniform flow. While it is expected that the HI within the polymer will lead to a dependency of the polymer's drag coefficient on the flow velocity, the interchain HI causes additional screening effects. For the case of two polymers in uniform flow with their tether points a finite distance apart, it is shown that the interchain HI not only causes a further reduction of the drag per polymer with decreasing distance between the tether points but simultaneously induces a polymer-polymer attraction as well. This attraction exhibits a characteristic maximum at intermediate flow velocities when the drag forces are of the order of the entropic forces. The effects uniquely attributed to the presence of HI can be verified experimentally.

Numerical simulation of tethered DNA in shear flow

The behavior of tethered DNA in shear flow is investigated numerically by the smoothed dissipative particle dynamics (SDPD) method. Unlike numerical methods used in previous studies, SDPD models the solvent explicitly, takes into account the fully coupled hydrodynamic interactions and is free of the numerical artifact of wall sticking. Based on numerical simulations the static and dynamic properties of a tethered DNA is studied both qualitatively and quantitatively. The observed properties are in general agreement with previous experimental, numerical and theoretical work. Furthermore, the cyclic-motion phenomenon is studied by power spectrum density and cross-correlation function analysis, which suggest that there is only a very weak coherent motion of tethered DNA for a characteristic timescale larger than the relaxation time. Cyclic motion is more likely relevant as an isolated event than a typical mode of DNA motion.

Hydrodynamic effects in proteins

Experimental and numerical results pertaining to flow-induced effects in proteins are reviewed. Special emphasis is placed on shear-induced unfolding and on the role of solvent mediated hydrodynamic interactions in the conformational transitions in proteins.

Dynamics of two trapped Brownian particles: Shear-induced cross-correlations

The dynamics of two Brownian particles trapped by two neighboring harmonic potentials in a linear shear flow is investigated. The positional correlation functions in this system are calculated analytically and analyzed as a function of the shear rate and the trap distance. Shear-induced cross-correlations between particle fluctuations along orthogonal directions in the shear plane are found. They are linear in the shear rate, asymmetric in time, and occur for one particle as well as between both particles. Moreover, the shear rate enters as a quadratic correction to the well-known correlations of random displacements along parallel spatial directions. The correlation functions depend on the orientation of the connection vector between the potential minima with respect to the flow direction. As a consequence, the inter-particle cross-correlations between orthogonal fluctuations can have zero, one or two local extrema as a function of time. Possible experiments for detecting these predicted correlations are described.