Fluctuation formulas for the elastic constants of an arbitrary system

[[abstract]]We derive the general fluctuation expressions for both the isothermal and adiabatic elastic constants of systems with arbitrary interparticle interactions and under arbitrary loading. We find that the expressions for these two kinds of elastic constants have exactly the same form though in general their values would be different. These formulas have the advantage that all elastic constants can be calculated in a single computer simulation run without performing any deformation on the system.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙

Elasticity of randomly diluted central force networks under tension

[[abstract]]We study the rigidity of two-dimensional site-diluted central force triangular networks under tension. We calculate the shear modulus μ directly and fit it with a power law of the form μ∼(p-p*)f, where p is the concentration of sites, p* its critical value, and f the critical exponent. We find that the critical behavior of μ is quite sensitive to tension. As the tension is increased there is at first a sharp drop in the values of both p* and f, followed by a slower decrease towards the values of the diluted Gaussian spring network (or random resistor network). We find that the size of the critical region is also sensitive to tension. The tension-free system has a narrower critical regime with the power law failing for p>0.8. In contrast, a small tension is sufficient to extend the power law to near p=1. The physical basis for these behaviors is discussed.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙

Elasticity of two-dimensional filaments with constant spontaneous curvature

[[abstract]]We study the mechanical property of a two-dimensional filament with constant spontaneous curvature and under uniaxial applied force. We derive the equation that governs the stable shape of the filament and obtain analytical solutions for the equation. We find that for a long filament with positive initial azimuth angle (the azimuth angle is the angle between x axis and the tangent of the filament) and under large stretching force, the azimuth angle is a two-valued function of the arclength, decreases first, and then increases with increasing arclength. Otherwise, the azimuth angle is a monotonic function of arclength. At finite temperature, we derive the differential equation that governs the partition function and find exact solution of the partition function for a filament free of force. We obtain closed-form expressions on the force-extension relation for a filament under low force and for a long filament under strong stretching force. Our results show that for a biopolymer with moderate length and not too small spontaneous curvature, the effect of the spontaneous curvature cannot be replaced by a simple renormalization of the persistence length in the wormlike chain model.[[incitationindex]]SCI[[booktype]]紙

Elasticity and stability of a helical filament

[[abstract]]We derive the general shape equations in terms of Euler angles for a uniform elastic rod with spontaneous torsion and curvatures and subjected to external force and torque. Our results based on an analytic formalism show that the extension of a helical rod may undergo a one-step discontinuous transition with increasing stretching force. This agrees quantitatively with experimental observations for a helix in a chemically defined lipid concentrate. The larger the twisting rigidity, the larger the jump in the extension. The effect of torque on the jump is, however, dependent on the value of the spontaneous torsion. In contrast, increasing the spontaneous torsion encourages the continuous variation of the extension. An “over-collapse” behavior is observed for the rod with asymmetric bending rigidity, and an intrinsic asymmetric elasticity under twisting force is found.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙

Sequence-Dependent Effects on the Properties of Semiflexible Biopolymers

Using path integral technique, we show exactly that for a semiflexible biopolymer in constant extension ensemble, no matter how long the polymer and how large the external force, the effects of short range correlations in the sequence-dependent spontaneous curvatures and torsions can be incorporated into a model with well-defined mean spontaneous curvature and torsion as well as a renormalized persistence length. Moreover, for a long biopolymer with large mean persistence length, the sequence-dependent persistence lengths can be replaced by their mean. However, for a short biopolymer or for a biopolymer with small persistence lengths, inhomogeneity in persistence lengths tends to make physical observables very sensitive to details and therefore less predictable

Disordered, stretched, and semiflexible biopolymers in two dimensions

We study the effects of intrinsic sequence-dependent curvature for a two dimensional semiflexible biopolymer with short-range correlation in intrinsic curvatures. We show exactly that when not subjected to any external force, such a system is equivalent to a system with a well-defined intrinsic curvature and a proper renormalized persistence length. We find the exact expression for the distribution function of the equivalent system. However, we show that such an equivalent system does not always exist for the polymer subjected to an external force. We find that under an external force, the effect of sequence-disorder depends upon the averaging order, the degree of disorder, and the experimental conditions, such as the boundary conditions. Furthermore, a short to moderate length biopolymer may be much softer or has a smaller apparent persistent length than what would be expected from the "equivalent system". Moreover, under a strong stretching force and for a long biopolymer, the sequence-disorder is immaterial for elasticity. Finally, the effect of sequence-disorder may depend upon the quantity considered