Dynamics of a Semiflexible Polymer or Polymer Ring in Shear Flow

Polymers exposed to shear flow exhibit a rich tumbling dynamics. While rigid rods rotate on Jeffery orbits, flexible polymers stretch and coil up during tumbling. Theoretical results show that in both of these asymptotic regimes the tumbling frequency f_c in a linear shear flow of strength \gamma scales as a power law Wi^(2/3) in the Weissenberg number Wi=\gamma \tau, where \tau is a characteristic time of the polymer's relaxational dynamics. For flexible polymers these theoretical results are well confirmed by experimental single molecule studies. However, for the intermediate semiflexible regime the situation is less clear. Here we perform extensive Brownian dynamics simulations to explore the tumbling dynamics of semiflexible polymers over a broad range of shear strength and the polymer's persistence length l_p. We find that the Weissenberg number alone does not suffice to fully characterize the tumbling dynamics, and the classical scaling law breaks down. Instead, both the polymer's stiffness and the shear rate are relevant control parameters. Based on our Brownian dynamics simulations we postulate that in the parameter range most relevant for cytoskeletal filaments there is a distinct scaling behavior with f_c \tau*=Wi^(3/4) f_c (x) with Wi=\gamma \tau* and the scaling variable x=(l_p/L)(Wi)^(-1/3); here \tau* is the time the polymer's center of mass requires to diffuse its own contour length L. Comparing these results with experimental data on F-actin we find that the Wi^(3/4) scaling law agrees quantitatively significantly better with the data than the classical Wi^(2/3) law. Finally, we extend our results to single ring polymers in shear flow, and find similar results as for linear polymers with slightly different power laws.Comment: 17 pages, 14 figure

Coupling of transverse and longitudinal response in stiff polymers

The time-dependent transverse response of stiff polymers, represented as weakly-bending wormlike chains (WLCs), is well-understood on the linear level, where transverse degrees of freedom evolve independently from the longitudinal ones. We show that, beyond a characteristic time scale, the nonlinear coupling of transverse and longitudinal motion in an inextensible WLC significantly weakens the polymer response compared to the widely used linear response predictions. The corresponding feedback mechanism is rationalized by scaling arguments and quantified by a multiple scale approach that exploits an inherent separation of transverse and longitudinal correlation length scales. Crossover scaling laws and exact analytical and numerical solutions for characteristic response quantities are derived for different experimentally relevant setups. Our findings are applicable to cytoskeletal filaments as well as DNA under tension.Comment: 4 pages, 3 figures, 1 table; final versio

Tension dynamics and viscoelasticity of extensible wormlike chains

The dynamic response of prestressed semiflexible biopolymers is characterized by the propagation and relaxation of tension, which arises due to the near inextensibility of a stiff backbone. It is coupled to the dynamics of contour length stored in thermal undulations, but also to the local relaxation of elongational strain. We present a systematic theory of tension dynamics for stiff yet extensible wormlike chains. Our results show that even moderate prestress gives rise to distinct Rouse-like extensibility signatures in the high-frequency viscoelastic response.Comment: 4 pages, 1 figure; corrected typo

Exploring the miRNA Regulatory Network Using Evolutionary Correlations

Post-transcriptional regulation by miRNAs is a widespread and highly conserved phenomenon in metazoans, with several hundreds to thousands of conserved binding sites for each miRNA, and up to two thirds of all genes under miRNA regulation. At the same time, the effect of miRNA regulation on mRNA and protein levels is usually quite modest and associated phenotypes are often weak or subtle. This has given rise to the notion that the highly interconnected miRNA regulatory network exerts its function less through any individual link and more via collective effects that lead to a functional interdependence of network links. We present a Bayesian framework to quantify conservation of miRNA target sites using vertebrate whole-genome alignments. The increased statistical power of our phylogenetic model allows detection of evolutionary correlation in the conservation patterns of site pairs. Such correlations could result from collective functions in the regulatory network. For instance, co-conservation of target site pairs supports a selective benefit of combinatorial regulation by multiple miRNAs. We find that some miRNA families are under pronounced co-targeting constraints, indicating a high connectivity in the regulatory network, while others appear to function in a more isolated way. By analyzing coordinated targeting of different curated gene sets, we observe distinct evolutionary signatures for protein complexes and signaling pathways that could reflect differences in control strategies. Our method is easily scalable to analyze upcoming larger data sets, and readily adaptable to detect high-level selective constraints between other genomic loci. We thus provide a proof-of-principle method to understand regulatory networks from an evolutionary perspective

Inverse Ising inference with correlated samples

Correlations between two variables of a high-dimensional system can be indicative of an underlying interaction, but can also result from indirect effects. Inverse Ising inference is a method to distinguish one from the other. Essentially, the parameters of the least constrained statistical model are learned from the observed correlations such that direct interactions can be separated from indirect correlations. Among many other applications, this approach has been helpful for protein structure prediction, because residues which interact in the 3D structure often show correlated substitutions in a multiple sequence alignment. In this context, samples used for inference are not independent but share an evolutionary history on a phylogenetic tree. Here, we discuss the effects of correlations between samples on global inference. Such correlations could arise due to phylogeny but also via other slow dynamical processes. We present a simple analytical model to address the resulting inference biases, and develop an exact method accounting for background correlations in alignment data by combining phylogenetic modeling with an adaptive cluster expansion algorithm. We find that popular reweighting schemes are only marginally effective at removing phylogenetic bias, suggest a rescaling strategy that yields better results, and provide evidence that our conclusions carry over to the frequently used mean-field approach to the inverse Ising problem.Comment: 18 pages, 6 figures; accepted at New J Phy

Longitudinal Response of Confined Semiflexible Polymers

The longitudinal response of single semiflexible polymers to sudden changes in externally applied forces is known to be controlled by the propagation and relaxation of backbone tension. Under many experimental circumstances, realized, e.g., in nano-fluidic devices or in polymeric networks or solutions, these polymers are effectively confined in a channel- or tube-like geometry. By means of heuristic scaling laws and rigorous analytical theory, we analyze the tension dynamics of confined semiflexible polymers for various generic experimental setups. It turns out that in contrast to the well-known linear response, the influence of confinement on the non-linear dynamics can largely be described as that of an effective prestress. We also study the free relaxation of an initially confined chain, finding a surprising superlinear t^(9/8) growth law for the change in end-to-end distance at short times.Comment: 18 pages, 1 figur

The prebiotic evolutionary advantage of transferring genetic information from RNA to DNA.

In the early 'RNA world' stage of life, RNA stored genetic information and catalyzed chemical reactions. However, the RNA world eventually gave rise to the DNA-RNA-protein world, and this transition included the 'genetic takeover' of information storage by DNA. We investigated evolutionary advantages for using DNA as the genetic material. The error rate of replication imposes a fundamental limit on the amount of information that can be stored in the genome, as mutations degrade information. We compared misincorporation rates of RNA and DNA in experimental non-enzymatic polymerization and calculated the lowest possible error rates from a thermodynamic model. Both analyses found that RNA replication was intrinsically error-prone compared to DNA, suggesting that total genomic information could increase after the transition to DNA. Analysis of the transitional RNA/DNA hybrid duplexes showed that copying RNA into DNA had similar fidelity to RNA replication, so information could be maintained during the genetic takeover. However, copying DNA into RNA was very error-prone, suggesting that attempts to return to the RNA world would result in a considerable loss of information. Therefore, the genetic takeover may have been driven by a combination of increased chemical stability, increased genome size and irreversibility

Periodic vs. intermittent adaptive cycles in quasispecies co-evolution

We study an abstract model for the co-evolution between mutating viruses and the adaptive immune system. In sequence space, these two populations are localized around transiently dominant strains. Delocalization or error thresholds exhibit a novel interdependence because immune response is conditional on the viral attack. An evolutionary chase is induced by stochastic fluctuations and can occur via periodic or intermittent cycles. Using simulations and stochastic analysis, we show how the transition between these two dynamic regimes depends on mutation rate, immune response, and population size.Comment: 5 pages, 3 figures, 11 pages supplementary material; updated formatting; accepted at Phys. Rev. Let

Stress-Energy Tensor for the Massless Spin 1/2 Field in Static Black Hole Spacetimes

The stress-energy tensor for the massless spin 1/2 field is numerically computed outside and on the event horizons of both charged and uncharged static non-rotating black holes, corresponding to the Schwarzschild, Reissner-Nordstrom and extreme Reissner-Nordstr\"om solutions of Einstein's equations. The field is assumed to be in a thermal state at the black hole temperature. Comparison is made between the numerical results and previous analytic approximations for the stress-energy tensor in these spacetimes. For the Schwarzschild (charge zero) solution, it is shown that the stress-energy differs even in sign from the analytic approximation. For the Reissner-Nordstrom and extreme Reissner-Nordstrom solutions, divergences predicted by the analytic approximations are shown not to exist.Comment: 5 pages, 4 figures, additional discussio