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Register a new userUnwinding dynamics of double-stranded polymers
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We consider the unwinding of two lattice polymer strands of length N that are initially wound around each other in a double-helical conformation and evolve through Rouse dynamics. The problem relates to quickly bringing a double-stranded polymer well above its melting temperature, i.e., the binding interactions between the strands are neglected, and the strands separate from each other as it is entropically favorable for them to do so. The strands unwind by rotating around each other until they separate. We find that the process proceeds from the ends inward; intermediate conformations can be characterized by a tightly wound inner part, from which loose strands are sticking out, with length l~t^0.39. The total time needed for the two strands to unwind scales as a power of N as tu~N^(2.57+-0.03). We present a theoretical argument, which suggests that during this unwinding process, these loose strands are far out of equilibrium.
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Recent magnetic tweezers experiments have reported systematic deviations of the twist response of double-stranded DNA from the predictions of the twistable worm-like chain model. Here we show, by means of analytical results and computer simulations, that these discrepancies can be resolved if a coupling between twist and bend is introduced. We obtain an estimate of 40 $pm$ 10 nm for the twist-bend coupling constant. Our simulations are in good agreement with high-resolution, magnetic-tweezers torque data. Although the existence of twist-bend coupling was predicted long ago (Marko and Siggia, Macromolecules 27, 981 (1994)), its effects on the mechanical properties of DNA have been so far largely unexplored. We expect that this coupling plays an important role in several aspects of DNA statics and dynamics.
We study the statistical mechanics of double-stranded semi-flexible polymers using both analytical techniques and simulation. We find a transition at some finite temperature, from a type of short range order to a fundamentally different sort of short range order. In the high temperature regime, the 2-point correlation functions of the object are identical to worm-like chains, while in the low temperature regime they are different due to a twist structure. In the low temperature phase, the polymers develop a kink-rod structure which could clarify some recent puzzling experiments on actin.
Helicases are molecular motors which unwind double-stranded nucleic acids (dsNA) in cells. Many helicases move with directional bias on single-stranded (ss) nucleic acids, and couple their directional translocation to strand separation. A model of the coupling between translocation and unwinding uses an interaction potential to represent passive and active helicase mechanisms. A passive helicase must wait for thermal fluctuations to open dsNA base pairs before it can advance and inhibit NA closing. An active helicase directly destabilizes dsNA base pairs, accelerating the opening rate. Here we extend this model to include helicase unbinding from the nucleic-acid strand. The helicase processivity depends on the form of the interaction potential. A passive helicase has a mean attachment time which does not change between ss translocation and ds unwinding, while an active helicase in general shows a decrease in attachment time during unwinding relative to ss translocation. In addition, we describe how helicase unwinding velocity and processivity vary if the base-pair binding free energy is changed.
We study the dynamics of a double-stranded DNA (dsDNA) segment, as a semiflexible polymer, in a shear flow, the strength of which is customarily expressed in terms of the dimensionless Weissenberg number Wi. Polymer chains in shear flows are well-known to undergo tumbling motion. When the chain lengths are much smaller than the persistence length, one expects a (semiflexible) chain to tumble as a rigid rod. At low Wi, a polymer segment shorter than the persistence length does indeed tumble as a rigid rod. However, for higher Wi the chain does not tumble as a rigid rod, even if the polymer segment is shorter than the persistence length. In particular, from time to time the polymer segment may assume a buckled form, a phenomenon commonly known as Euler buckling. Using a bead-spring Hamiltonian model for extensible dsDNA fragments, we first analyze Euler buckling in terms of the oriented deterministic state (ODS), which is obtained as the steady-state solution of the dynamical equations by turning off the stochastic (thermal) forces at a fixed orientation of the chain. The ODS exhibits symmetry breaking at a critical Weissenberg number Wi$_{text c}$, analogous to a pitchfork bifurcation in dynamical systems. We then follow up the analysis with simulations and demonstrate symmetry breaking in computer experiments, characterized by a unimodal to bimodal transformation of the probability distribution of the second Rouse mode with increasing Wi. Our simulations reveal that shear can cause strong deformation for a chain that is shorter than its persistence length, similar to recent experimental observations.
We investigate the length distribution of self-assembled, long and stiff polymers at thermal equilibrium. Our analysis is based on calculating the partition functions of stiff polymers of variable lengths in the elastic regime. Our conclusion is that the length distribution of this self-assembled system follows closely the exponential distribution, except at the short length limit. We then discuss the implications of our results on the experimentally observed length distributions in amyloid fibrils.
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