Zicong Zhou

Fluctuations and thermodynamics properties of the constant shear strain ensemble

We develop the statistical mechanics of a pair of new ensembles called the constant shear strain ensembles that include the uniform dilation ensemble used frequently in computer simulations. We present a direct calculation of fluctuation formulas for the elastic constants, the specific heat, and the thermal expansion tensor in these new ensembles.

On the consistency of two elastic models for double-stranded DNA

We present an analytical based proof for the consistency between a new model, proposed by Zhou et al. [Phys. Rev. Lett. 82 (1999) 4560], of the double-stranded DNA (dsDNA) and the well accepted wormlike rod chain (WLRC) model in the regime around the undistorted B-form. The relationship between the Zhou, Zhang, and Ou-Yang (ZZO) model and a recent proposed asymmetric elastic ribbon model is also discussed. It gives one more evidence that the ZZO model could provide a unified description for the novel elasticity of dsDNA and supports the conclusion that the base-stacking interaction plays an important role for the elasticity of dsDNA.

Stretching a double-stranded DNA: Nature of the B-form to the S-form transition

The abrupt extension of the contour length and the self-unwinding of the double helix in the transition from the B-form to S-form of a double-stranded DNA under a stretching force is investigated in the framework of the model with basepair interactions and bending [Phys. Rev. Lett. 22, 4560 (1999)]. In the region where thermal fluctuations can be neglected the classical mechanical approach is employed and equations governing the detail structure of the DNA are derived with some analytical results obtained. The transition from the B-form to S-form can be understood in terms of an effective potential with a barrier separating these two states and resulting in a first-order transition. The double helix of the DNA is almost fully unwound across the transition. Detail structural configurations, such as the loci of the two strands, relative extension, linear extension coefficient, and the threshold stretching force are calculated. The mean torque release as the dsDNA untwist across the transition is also estimated. These results are in agreement with various experimental data.

ELASTICITY AND STABILITY OF A HELICAL FILAMENT WITH SPONTANEOUS CURVATURES AND ISOTROPIC BENDING RIGIDITY

We derive the shape equations in terms of Euler angles for a uniform elastic rod with isotropic bending rigidity and spontaneous curvature, and study within this model the elasticity and stability of a helical filament under uniaxial force and torque. We find that due to the special requirements on the boundary conditions, a static slightly distorted helix cannot exist in this system except in some special cases. We show analytically that the extension of a helix may undergo a one-step sharp transition. This agrees quantitatively with experimental observations for a stretched helix in a chemically-defined lipid concentrate (CDLC). We predict further that under twisting, the extension of a helix in CDLC may also exhibit similar behavior. We find that a negative twist tends to destabilize a helix.

Sequence-dependent effects on the properties of semiflexible biopolymers.

Using a 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.

B- to S-form transition in double-stranded DNA with basepair interactions

When a DNA in its nature double-helical state is stretched by an external force, its length undergoes a sharp extension from the B-form to the 1.7 times elongated S-form. This phenomenon is investigated in the framework of a model of a double-stranded with basepair interactions and bending. Shape equations governing the structure of the DNA under external forces and torques are derived using a classical mechanical approach. The first-order nature of the B- to S-form transition is revealed clearly in terms of an effective potential with a barrier separating these two states. All the structural properties of the DNA in both forms can be calculated in detail. The configurations of the double strands, relative extension, amount of self-untwisting and the threshold stretching force of the DNA under stretched are obtained and compare well with experimental observations.

Stability of the helical configuration of an intrinsically straight semiflexible biopolymer inside a cylindrical cell

We examine the effects of the external force, torque, temperature, confinement, and excluded volume interactions (EVIs) on the stability of the helical configuration of an intrinsically straight semiflexible biopolymer inside a cylindrical cell. We find that to stabilize a helix, the confinement from both ends of the cell is more effective than a uniaxial force. We show that under a uniaxial force and in absence of confinement from bottom of the cell, a stable helix is very short. Our results reveal that to maintain a low pitch helix, a torque acting at both ends of the filament is a necessity, and the confinement can reduce the required torque to less than half making it much easier to form a stable helix. Moreover, we find that thermal fluctuations and EVIs have little impact on the stability of a helix. Our results can help understand the existence of the helix and ring configurations of some semiflexible biopolymers, such as MreB homologs, inside a rod-shaped bacteria.

Effect of a force-free end on the mechanical property of a biopolymer — A path integral approach*

We study the effect of a force-free end on the mechanical property of a stretched biopolymer. The system can be divided into two parts. The first part consists of the segment counted from the fixed point (i.e., the origin) to the forced point in the biopolymer, with arclength L f . The second part consists of the segment counted from the forced point to the force-free end with arclength ΔL. We apply the path integral technique to find the relationship between these two parts. At finite temperature and without any constraint at the end, we show exactly that if we focus on the quantities related to the first part, then we can ignore the second part completely. Monte Carlo simulation confirms this conclusion. In contrast, the effect for the quantities related to the second part is dependent on what we want to observe. A force-free end has little effect on the relative extension, but it affects seriously the value of the end-to-end distance if ΔL is comparable to L f .

The role of dislocations in structural transformations

The status of dislocation theories of melting (DTM) is assessed. The role of dislocations in two other structural transformations is also discussed, namely vacancy annealing kinetics and fracture, ductile versus brittle. In these three problems the observed and predicted behaviors are correlated with the properties of the dislocations.