arXiv subjects

Roland R. Netz

Publications and source records attributed to Roland R. Netz.

At least 91 records · Page 5Linked to original sources

arXiv2011

Conformational dynamics and internal friction in homo-polymer globules: equilibrium vs. non-equilibrium simulations

We study the conformational dynamics within homo-polymer globules by solvent-implicit Brownian dynamics simulations. A strong dependence of the internal chain dynamics on the Lennard-Jones cohesion strength ε and the globule size NG is observed. We find two distinct dynamical regimes: a liquid- like regime (for ε < εs) with fast internal dynamics and a solid-like regime (for ε > εs) with slow internal dynamics. The cohesion strength εs of this freezing transition depends on NG. Equilibrium simulations, where we investigate the diffusional chain dynamics within the globule, are compared with non-equilibrium simulations, where we unfold the globule by pulling the chain ends with prescribed velocity (encompassing low enough velocities so that the linear-response, viscous regime is reached). From both simulation protocols we derive the internal viscosity within the globule. In the liquid-like regime the internal friction increases continuously with ε and scales extensive in NG. This suggests an internal friction scenario where the entire chain (or an extensive fraction thereof) takes part in conformational reorganization of the globular structure.

cond-mat.soft↗

arXiv2011

Anisotropic Hydrodynamic Mean-Field Theory for Semiflexible Polymers under Tension

We introduce an anisotropic mean-field approach for the dynamics of semiflexible polymers under intermediate tension, the force range where a chain is partially extended but not in the asymptotic regime of a nearly straight contour. The theory is designed to exactly reproduce the lowest order equilibrium averages of a stretched polymer, and treats the full complexity of the problem: the resulting dynamics include the coupled effects of long-range hydrodynamic interactions, backbone stiffness, and large-scale polymer contour fluctuations. Validated by Brownian hydrodynamics simulations and comparison to optical tweezer measurements on stretched DNA, the theory is highly accurate in the intermediate tension regime over a broad dynamical range, without the need for additional dynamic fitting parameters.

cond-mat.soft↗

arXiv2011

Deconvolution of dynamic mechanical networks

Time-resolved single-molecule biophysical experiments yield data that contain a wealth of dynamic information, in addition to the equilibrium distributions derived from histograms of the time series. In typical force spectroscopic setups the molecule is connected via linkers to a read-out device, forming a mechanically coupled dynamic network. Deconvolution of equilibrium distributions, filtering out the influence of the linkers, is a straightforward and common practice. We have developed an analogous dynamic deconvolution theory for the more challenging task of extracting kinetic properties of individual components in networks of arbitrary complexity and topology. Our method determines the intrinsic linear response functions of a given molecule in the network, describing the power spectrum of conformational fluctuations. The practicality of our approach is demonstrated for the particular case of a protein linked via DNA handles to two optically trapped beads at constant stretching force, which we mimic through Brownian dynamics simulations. Each well in the protein free energy landscape (corresponding to folded, unfolded, or possibly intermediate states) will have its own characteristic equilibrium fluctuations. The associated linear response function is rich in physical content, since it depends both on the shape of the well and its diffusivity---a measure of the internal friction arising from such processes like the transient breaking and reformation of bonds in the protein structure. Starting from the autocorrelation functions of the equilibrium bead fluctuations measured in this force clamp setup, we show how an experimentalist can accurately extract the state-dependent protein diffusivity using a straightforward two-step procedure.

q-bio.BM↗

arXiv2011

Secondary structure formation of homopolymeric single-stranded nucleic acids including force and loop entropy: implications for DNA hybridization

Loops are essential secondary structure elements in folded DNA and RNA molecules and proliferate close to the melting transition. Using a theory for nucleic acid secondary structures that accounts for the logarithmic entropy c ln m for a loop of length m, we study homopolymeric single-stranded nucleic acid chains under external force and varying temperature. In the thermodynamic limit of a long strand, the chain displays a phase transition between a low temperature / low force compact (folded) structure and a high temperature / high force molten (unfolded) structure. The influence of c on phase diagrams, critical exponents, melting, and force extension curves is derived analytically. For vanishing pulling force, only for the limited range of loop exponents 2 < c < 2.479 a melting transition is possible; for c <= 2 the chain is always in the folded phase and for 2.479 < c always in the unfolded phase. A force induced melting transition with singular behavior is possible for all loop exponents c < 2.479 and can be observed experimentally by single molecule force spectroscopy. These findings have implications for the hybridization or denaturation of double stranded nucleic acids. The Poland-Scheraga model for nucleic acid duplex melting does not allow base pairing between nucleotides on the same strand in denatured regions of the double strand. If the sequence allows these intra-strand base pairs, we show that for a realistic loop exponent c ~ 2.1 pronounced secondary structures appear inside the single strands. This leads to a lower melting temperature of the duplex than predicted by the Poland-Scheraga model. Further, these secondary structures renormalize the effective loop exponent c^, which characterizes the weight of a denatured region of the double strand, and thus affect universal aspects of the duplex melting transition.

cond-mat.stat-mech↗

arXiv2011

Theory for RNA folding, stretching, and melting including loops and salt

Secondary structure formation of nucleic acids strongly depends on salt concentration and temperature. We develop a theory for RNA folding that correctly accounts for sequence effects, the entropic contributions associated with loop formation, and salt effects. Using an iterative expression for the partition function that neglects pseudoknots, we calculate folding free energies and minimum free energy configurations based on the experimentally derived base pairing free energies. The configurational entropy of loop formation is modeled by the asymptotic expression -c ln m, where m is the length of the loop and c the loop exponent, which is an adjustable constant. Salt effects enter in two ways: first, we derive salt induced modifications of the free energy parameters for describing base pairing and, second, we include the electrostatic free energy for loop formation. Both effects are modeled on the Debye-Hueckel level including counterion condensation. We validate our theory for two different RNA sequences: For tRNA-phe, the resultant heat capacity curves for thermal denaturation at various salt concentrations accurately reproduce experimental results. For the P5ab RNA hairpin, we derive the global phase diagram in the three-dimensional space spanned by temperature, stretching force, and salt concentration and obtain good agreement with the experimentally determined critical unfolding force. We show that for a proper description of RNA melting and stretching, both salt and loop entropy effects are needed.

physics.bio-ph↗

arXiv2011

Salt Modulated Structure of Polyelectrolyte-Macroion Complex Fibers

The structure and stability of strongly charged complex fibers formed by complexation of a single long semi-flexible polyelectrolyte (PE) chain and many oppositely charged spherical macroions are investigated numerically at the ground-state level using a chain-sphere cell model. The model takes into account chain elasticity as well as electrostatic interactions between charged spheres and chain segments. Using a numerical optimization method based on a periodically repeated unit cell, we obtain fiber configurations that minimize the total energy. The optimal configurations exhibit a variety of helical structures for the arrangement of macroions including zig-zag, solenoidal and beads-on-a-string patterns. These structures are determined by a competition between attraction between spheres and the PE chain (which favors chain wrapping around the spheres), chain bending and electrostatic repulsion between chain segments (which favor unwrapping of the chain), and the interactions between neighboring sphere-chain complexes which can be attractive or repulsive depending on the system parameters such as medium salt concentration, macroion charge and chain length per macroion (linker size). At about physiological salt concentration, dense zig-zag patterns are found to be energetically most stable when parameters appropriate for the DNA-histone system in a chromatin fiber are adopted. In fact, the predicted fiber diameter in this regime is found to be around 30nm, which appears to agree with the thickness observed in in vitro experiments on chromatin. We also find a macroion density of 5-6 per 11nm which agrees with the zig-zag or cross-linker models of chromatin. Since our study deals primarily with a generic model, these findings suggest that chromatin-like structures should also be observable for PE-macroion complexes formed in solutions of DNA and synthetic nano-colloids of opposite charge.

cond-mat.soft↗

arXiv2010

DNA-Protein Binding Rates: Bending Fluctuation and Hydrodynamic Coupling Effects

We investigate diffusion-limited reactions between a diffusing particle and a target site on a semiflexible polymer, a key factor determining the kinetics of DNA-protein binding and polymerization of cytoskeletal filaments. Our theory focuses on two competing effects: polymer shape fluctuations, which speed up association, and the hydrodynamic coupling between the diffusing particle and the chain, which slows down association. Polymer bending fluctuations are described using a mean field dynamical theory, while the hydrodynamic coupling between polymer and particle is incorporated through a simple heuristic approximation. Both of these we validate through comparison with Brownian dynamics simulations. Neither of the effects has been fully considered before in the biophysical context, and we show they are necessary to form accurate estimates of reaction processes. The association rate depends on the stiffness of the polymer and the particle size, exhibiting a maximum for intermediate persistence length and a minimum for intermediate particle radius. In the parameter range relevant to DNA-protein binding, the rate increase is up to 100% compared to the Smoluchowski result for simple center-of-mass motion. The quantitative predictions made by the theory can be tested experimentally.

cond-mat.soft↗

arXiv2010

Single polymer adsorption in shear: flattening versus hydrodynamic lift and corrugation effects

The adsorption of a single polymer to a flat surface in shear is investigated using Brownian hydrodynamics simulations and scaling arguments. Competing effects are disentangled: in the absence of hydrodynamic interactions, shear drag flattens the chain and thus enhances adsorption. Hydrodynamic lift on the other hand gives rise to long-ranged repulsion from the surface which preempts the surface-adsorbed state via a discontinuous desorption transition, in agreement with theoretical arguments. Chain flattening is dominated by hydrodynamic lift, so overall, shear flow weakens the adsorption of flexible polymers. Surface friction due to small-wavelength surface potential corrugations is argued to weaken the surface attraction as well.

cond-mat.soft↗

arXiv2010

Exotic Electrostatics: Unusual Features of Electrostatic Interactions between Macroions

We present an overview of our understanding of electrostatic interactions between charged macromolecular surfaces mediated by mobile counter- and coions. The dichotomy between the weak and the strong coupling regimes is described in detail and the way they engender repulsive and attractive interactions between nominally equally charged macroions. We also introduce the concept of dressed counterions in the case of many-component Coulomb fluids that are partially weakly and partially strongly coupled to local electrostatic fields leading to non-monotonic interactions between equally charged macroions. The effect of quenched surface charge disorder on the counterion-mediated electrostatic interactions is analyzed within the same conceptual framework and shown to lead to unexpected and extraordinary electrostatic interactions between randomly charged surfaces with equal mean surface charge densities or even between effectively neutral macroion surfaces. As a result, these recent developments challenge some cherished notions of pop culture.

cond-mat.soft↗

arXiv2010

How the diffusivity profile reduces the arbitrariness of protein folding free energies

The concept of a protein diffusing in its free energy folding landscape has been fruitful for both theory and experiment. Yet the choice of the reaction coordinate (RC) introduces an undesirable degree of arbitrariness into the problem. We analyze extensive simulation data of an alpha-helix in explicit water solvent as it stochastically folds and unfolds. The free energy profiles for different RCs exhibit significant variation, some having an activation barrier, others not. We show that this variation has little effect on the predicted folding kinetics if the diffusivity profiles are properly taken into account. This kinetic quasi-universality is rationalized by an RC rescaling, which, due to the reparameterization invariance of the Fokker-Planck equation, allows the combination of free energy and diffusivity effects into a single function, the rescaled free energy profile. This rescaled free energy indeed shows less variation among different RCs than the bare free energy and diffusivity profiles separately do, if we properly distinguish between RCs that contain knowledge of the native state and those that are purely geometric in nature. Our method for extracting diffusivity profiles is easily applied to experimental single molecule time series data and might help to reconcile conflicts that arise when comparing results from different experimental probes for the same protein.

physics.bio-ph↗

arXiv2010

A three-state model with loop entropy for the over-stretching transition of DNA

We introduce a three-state model for a single DNA chain under tension that distinguishes between B-DNA, S-DNA and M (molten or denatured) segments and at the same time correctly accounts for the entropy of molten loops, characterized by the exponent c in the asymptotic expression S ~ - c ln n for the entropy of a loop of length n. Force extension curves are derived exactly employing a generalized Poland-Scheraga approach and compared to experimental data. Simultaneous fitting to force-extension data at room temperature and to the denaturation phase transition at zero force is possible and allows to establish a global phase diagram in the force-temperature plane. Under a stretching force, the effects of the stacking energy, entering as a domain-wall energy between paired and unpaired bases, and the loop entropy are separated. Therefore we can estimate the loop exponent c independently from the precise value of the stacking energy. The fitted value for c is small, suggesting that nicks dominate the experimental force extension traces of natural DNA.

physics.bio-ph↗

arXiv2009

Ionic force field optimization based on single-ion and ion-pair solvation properties

Molecular dynamics simulations of ionic solutions depend sensitively on the force fields employed for the ions. To resolve the fine differences between ions of the same valence and roughly similar size and in particular to correctly describe ion-specific effects, it is clear that accurate force fields are necessary. In the past, optimization strategies for ionic force fields either considered single-ion properties (such as the solvation free energy at infinite dilution or the ion-water structure) or ion-pair properties (in the form of ion-ion distribution functions). In this paper we investigate strategies to optimize ionic force fields based on single-ion and ion-pair properties simultaneously. To that end, we simulate five different salt solutions, namely CsCl, KCl, NaI, KF, and CsI, at finite ion concentration. The force fields of these ions are systematically varied under the constraint that the single-ion solvation free energy matches the experimental value, which reduces the two-dimensional $\{σ,ε\}$ parameter space of the Lennard Jones interaction to a one dimensional line for each ion. From the finite-concentration simulations, the pair-potential is extracted and the osmotic coefficient is calculated, which is compared to experimental data. We find a strong dependence of the osmotic coefficient on the force field, which is remarkable as the single-ion solvation free energy and the ion-water structure remain invariant under the parameter variation. Optimization of the force field is achieved for the cations Cs$^+$ and K$^+$, while for the anions I$^-$ and F$^-$ the experimental osmotic coefficient cannot be reached. This suggests that in the long run, additional parameters might have to be introduced into the modeling, for example by modified mixing rules.

physics.chem-ph↗

arXiv2009

Critical Percolation Phase and Thermal BKT Transition in a Scale-Free Network with Short-Range and Long-Range Random Bonds

Percolation in a scale-free hierarchical network is solved exactly by renormalization-group theory, in terms of the different probabilities of short-range and long-range bonds. A phase of critical percolation, with algebraic (Berezinskii-Kosterlitz-Thouless) geometric order, occurs in the phase diagram, in addition to the ordinary (compact) percolating phase and the non-percolating phase. It is found that no connection exists between, on the one hand, the onset of this geometric BKT behavior and, on the other hand, the onsets of the highly clustered small-world character of the network and of the thermal BKT transition of the Ising model on this network. Nevertheless, both geometric and thermal BKT behaviors have inverted characters, occurring where disorder is expected, namely at low bond probability and high temperature, respectively. This may be a general property of long-range networks.

cond-mat.dis-nn↗

arXiv2009

Global cross-over dynamics of single semiflexible polymers

We present a mean-field dynamical theory for single semiflexible polymers which can precisely capture, without fitting parameters, recent fluorescence correlation spectroscopy results on single monomer kinetics of DNA strands in solution. Our approach works globally, covering three decades of strand length and five decades of time: it includes the complex cross-overs occurring between stiffness-dominated and flexible bending modes, along with larger-scale rotational and center-of-mass motion. The accuracy of the theory stems in part from long-range hydrodynamic coupling between the monomers, which makes a mean-field description more realistic. Its validity extends even to short, stiff fragments, where we also test the theory through Brownian hydrodynamics simulations.

cond-mat.soft↗

arXiv2009

Plectoneme creation reduces the rotational friction of a polymer

The torsional dynamics of a semiflexible polymer with a contour length $L$ larger than its persistence length L_p that is rotated at fixed frequency omega_0 at one end is studied by scaling arguments and hydrodynamic simulations. We find a non-equilibrium transition at a critical frequency omega_*: In the linear regime, omega_0 < omega_*, axial spinning is the dominant dissipation mode. In the non-linear regime, omega_0 > omega_*, the twist-dissipation mode involves the continuous creation of plectonemes close to the driven end and the rotational friction is substantially reduced.

cond-mat.soft↗

arXiv2009

End-monomer dynamics in semiflexible polymers

Spurred by an experimental controversy in the literature, we investigate the end-monomer dynamics of semiflexible polymers through Brownian hydrodynamic simulations and dynamic mean-field theory. Precise experimental observations over the last few years of end-monomer dynamics in the diffusion of double-stranded DNA have given conflicting results: one study indicated an unexpected Rouse-like scaling of the mean squared displacement (MSD) r^2(t) ~ t^(1/2) at intermediate times, corresponding to fluctuations at length scales larger than the persistence length but smaller than the coil size; another study claimed the more conventional Zimm scaling r^2(t) ~ t^(2/3) in the same time range. We find a novel intermediate dynamical regime where the effective local exponent of the end-monomer MSD, alpha(t) = d log r^2(t)/ d log t, drops below the Zimm value of 2/3 for sufficiently long chains. The deviation from the Zimm prediction increases with chain length, though it does not reach the Rouse limit of 1/2. The qualitative features of this intermediate regime, in particular the variation of alpha(t) with chain and persistence lengths, can be reproduced through a heuristic scaling argument. Anomalously low values of the effective exponent alpha are explained by hydrodynamic effects related to the slow crossover from dynamics on length scales smaller than the persistence length to dynamics on larger length scales.

cond-mat.soft↗

arXiv2009

Salt-Induced Counterion-Mobility Anomaly in Polyelectrolyte Electrophoresis

We study the electrokinetics of a single polyelectrolyte chain in salt solution using hydrodynamic simulations. The salt-dependent chain mobility compares well with experimental DNA data. The mobility of condensed counterions exhibits a salt-dependent change of sign, an anomaly that is also reflected in the counterion excess conductivity. Using Green's function techniques this anomaly is explained by electrostatic screening of the hydrodynamic interactions between chain and counterions.

cond-mat.soft↗

arXiv2008

Impact of loop statistics on the thermodynamics of RNA folding

Loops are abundant in native RNA structures and proliferate close to the unfolding transition. By including a statistical weight ~ l^{-c} for loops of length l in the recursion relation for the partition function, we show that the calculated heat capacity depends sensitively on the presence and value of the exponent c, even of short t-RNA. For homo-RNA we analytically calculate the critical temperature and critical exponents which exhibit a non-universal dependence on c.

cond-mat.soft↗