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Register a new userThermal breakage of a semiflexible polymer: Breakage profile and rate
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Chiu Fan Lee
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Understanding fluctuation-induced breakages in polymers has important implications for basic and applied sciences. Here I present for the first time an analytical treatment of the thermal breakage problem of a semi-flexible polymer model that is asymptotically exact in the low temperature and high friction limits. Specifically, I provide analytical expressions for the breakage propensity and rate, and discuss the generalities of the results and their relevance to biopolymers.
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We study the dynamical properties of semiflexible polymers with a recently introduced bead-spring model. We focus on double-stranded DNA. The two parameters of the model, $T^*$ and $ u$, are chosen to match its experimental force-extension curve. The bead-spring Hamiltonian is approximated in the first order by the Hessian that is quadratic in the bead positions. The eigenmodels of the Hessian provide the longitudinal (stretching) and transverse (bending) eigenmodes of the polymer, and the corresponding eigenvalues match well with the established phenomenology of semiflexible polymers. Using the longitudinal and transverse eigenmodes, we obtain analytical expressions of (i) the autocorrelation function of the end-to-end vector, (ii) the autocorrelation function of a bond (i.e., a spring, or a tangent) vector at the middle of the chain, and (iii) the mean-square displacement of a tagged bead in the middle of the chain, as sum over the contributions from the modes. We also perform simulations with the full dynamics of the model. The simulations yield numerical values of the correlation functions (i-iii) that agree very well with the analytical expressions for the linearized dynamics. We also study the mean-square displacement of the longitudinal component of the end-to-end vector that showcases strong nonlinear effects in the polymer dynamics, and we identify at least an effective $t^{7/8}$ power-law regime in its time-dependence. Nevertheless, in comparison to the full mean-square displacement of the end-to-end vector the nonlinear effects remain small at all times --- it is in this sense we state that our results demonstrate that the linearized dynamics suffices for dsDNA fragments that are shorter than or comparable to the persistence length. Our results are consistent with those of the wormlike chain (WLC) model, the commonly used descriptive tool of semiflexible polymers.
Using a recently developed bead-spring model for semiflexible polymers that takes into account their natural extensibility, we report an efficient algorithm to simulate the dynamics for polymers like double-stranded DNA (dsDNA) in the absence of hydrodynamic interactions. The dsDNA is modelled with one bead-spring element per basepair, and the polymer dynamics is described by the Langevin equation. The key to efficiency is that we describe the equations of motion for the polymer in terms of the amplitudes of the polymers fluctuation modes, as opposed to the use of the physical positions of the beads. We show that, within an accuracy tolerance level of $5%$ of several key observables, the model allows for single Langevin time steps of $approx1.6$, 8, 16 and 16 ps for a dsDNA model-chain consisting of 64, 128, 256 and 512 basepairs (i.e., chains of 0.55, 1.11, 2.24 and 4.48 persistence lengths) respectively. Correspondingly, in one hour, a standard desktop computer can simulate 0.23, 0.56, 0.56 and 0.26 ms of these dsDNA chains respectively. We compare our results to those obtained from other methods, in particular, the (inextensible discretised) WLC model. Importantly, we demonstrate that at the same level of discretisation, i.e., when each discretisation element is one basepair long, our algorithm gains about 5-6 orders of magnitude in the size of time steps over the inextensible WLC model. Further, we show that our model can be mapped one-on-one to a discretised version of the extensible WLC model; implying that the speed-up we achieve in our model must hold equally well for the latter. We also demonstrate the use of the method by simulating efficiently the tumbling behaviour of a dsDNA segment in a shear flow.
In manufacture, steel and other metals are mainly cut and shaped during the fabrication process by computer numerical control (CNC) machines. To keep high productivity and efficiency of the fabrication process, engineers need to monitor the real-time process of CNC machines, and the lifetime management of machine tools. In a real manufacturing process, breakage of machine tools usually happens without any indication, this problem seriously affects the fabrication process for many years. Previous studies suggested many different approaches for monitoring and detecting the breakage of machine tools. However, there still exists a big gap between academic experiments and the complex real fabrication processes such as the high demands of real-time detections, the difficulty in data acquisition and transmission. In this work, we use the spindle current approach to detect the breakage of machine tools, which has the high performance of real-time monitoring, low cost, and easy to install. We analyze the features of the current of a milling machine spindle through tools wearing processes, and then we predict the status of tool breakage by a convolutional neural network(CNN). In addition, we use a BP neural network to understand the reliability of the CNN. The results show that our CNN approach can detect tool breakage with an accuracy of 93%, while the best performance of BP is 80%.
Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, we study the orientationally ordered phases in two-dimensional networks of randomly cross-linked semiflexible polymers. We consider permanent cross-links which prescribe a finite angle and treat them as quenched disorder in a semi-microscopic replica field theory. Starting from a fluid of un-cross-linked polymers and small polymer clusters (sol) and increasing the cross-link density, a continuous gelation transition occurs. In the resulting gel, the semiflexible chains either display long range orientational order or are frozen in random directions depending on the value of the crossing angle, the crosslink concentration and the stiffness of the polymers. A crossing angle $thetasim 2pi/M$ leads to long range $M$-fold orientational order, e.g., hexatic or tetratic for $theta=60^{circ}$ or $90^{circ}$, respectively. The transition is discontinuous and the critical cross-link density depends on the bending stiffness of the polymers and the cross-link geometry: the higher the stiffness and the lower $M$, the lower the critical number of cross-links. In between the sol and the long range ordered state, we always observe a gel which is a statistically isotropic amorphous solid (SIAS) with random positional and random orientational localization of the participating polymers.
It has become clear in recent years that the simple uniform wormlike chain model needs to be modified in order to account for more complex behavior which has been observed experimentally in some important biopolymers. For example, the large flexibility of short ds-DNA has been attributed to kink or hinge defects. In this paper, we calculate analytically, within the weak bending approximation, the force-extension relation of a wormlike chain with a permanent hinge defect along its contour. The defect is characterized by its bending energy (which can be zero, in the completely flexible case) and its position along the polymer contour. Besides the bending rigidity of the chain, these are the only parameters which describe our model. We show that a hinge defect causes a significant increase in the differential tensile compliance of a pre-stressed chain. In the small force limit, a hinge defect significantly increases the entropic elasticity. Our results apply to any pair of semiflexible segments connected by a hinge. As such, they may also be relevant to cytoskeletal filaments (F-actin, microtubules), where one may treat the cross-link connecting two filaments as a hinge defect.
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