Zhong-can Ou-Yang

Lipid membranes with free edges

Lipid membrane with freely exposed edge is regarded as smooth surface with curved boundary. Exterior differential forms are introduced to describe the surface and the boundary curve. The total free energy is defined as the sum of Helfrichs free energy and the surface and line tension energy. The equilibrium equation and boundary conditions of the membrane are derived by taking the variation of the total free energy. These equations can also be applied to the membrane with several freely exposed edges. Analytical and numerical solutions to these equations are obtained under the axisymmetric condition. The numerical results can be used to explain recent experimental results obtained by Saitoh et al. [Proc. Natl. Acad. Sci. 95, 1026 (1998)].

Flexoelectric origin of nanomechanic deflection in DNA-microcantilever system

The membrane theory is used to study the recently observed nanomechanical bending of cantilevers, which have processed biomolecular adsorption or biochemical reactions. To be different from entropy-controlling bending mechanism discussed before, we propose that the flexoelectric effect induces cantilever bending. With the introduction of flexoelectric spontaneous curvature, the relation between the bending and biopolymer character is constructed by a simple analytical formula. The cantilever motion induced by adsorption of single-strand DNA and DNA hybridization reaction is quantified analytically and our results show good agreement with experiments.

Single molecule Michaelis-Menten equation beyond quasistatic disorder.

The classic Michaelis-Menten equation describes the catalytic activities for ensembles of enzyme molecules very well. But recent single-molecule experiments showed that the waiting time distribution and other properties of single enzyme molecules were not consistent with the prediction based on the ensemble viewpoint. They have contributed to the slow conformational changes of a single enzyme in the catalytic processes. In this work, we study the general dynamics of single enzymes in the presence of dynamic disorder. We find that, within the time separation regimes, i.e., the slow reaction and nondiffusion limits, the Michaelis-Menten equation holds exactly. In particular, by employing the decoupling approximation we demonstrate analytically that the classic Michaelis-Menten equation is still an excellent approximation in the presence of general dynamic disorder.

Study of axial strain-induced torsion of single-wall carbon nanotubes using the 2D continuum anharmonic anisotropic elastic model

Recent molecular dynamic simulations have found that chiral single-walled carbon nanotubes (SWCNTs) twist during stretching, resembling the motion of a screw. Obviously this phenomenon, as a type of curvature?chirality effect, cannot be explained by the usual isotropic elastic theory of SWCNTs. More interestingly, with larger axial strains (before buckling), the axial strain-induced torsion (a-SIT) shows asymmetric behaviors for axial tensile and compressing strains, which suggests the anharmonic elasticity of SWCNTs plays an important role in real a-SIT responses. In order to study the a-SIT of chiral SWCNTs with actual sizes, and to avoid possible deviation of computer simulation results due to the finite-size effect, we propose a two-dimensional (2D) analytical continuum model which can be used to describe SWCNTs of arbitrary chirality, curvature, and length, and which is concerned with their anisotropic and anharmonic elasticity. The elastic energy of the present model comes from the continuum limit of lattice energy based on second generation reactive empirical bond order potential (REBO-II), a well-established empirical potential for solid carbons. Our model has no adjustable parameters, except for those presented in REBO-II, and all the coefficients in the model can be calculated analytically. Using our method, we obtain the a-SIT responses of chiral SWCNTs with arbitrary radii, chiralities and lengths. Our results are in reasonable agreement with recent molecular dynamic simulations (Liang et al 2006 Phys. Rev. Lett.?96 165501). Our approach can also be used to calculate other curvature?chirality-dependent anharmonic mechanical responses of SWCNTs.

A Kinetic Model of Transcription Initiation by RNA Polymerase

We establish a sequence-dependent kinetic model for the later stage of transcription initiation by RNA polymerase. We suggest that there are three reaction pathways, the abortive pathway, the scrunching pathway and the escape pathway, competitive with each other at each site during the transcription initiation. Using this three-pathway model, we mainly calculate the maximum sizes of the abortive transcripts, the abortive probabilities and the abortive/productive ratios for different promoters by Monte Carlo simulation and analytical methods. These results are quantitatively comparable with the experimental observations. In particular, our model can account for the unproductive initial transcribing complex and the nucleoside triphosphate concentration dependence of the transcription initiation, which have been found in the experiments and were hardly understood by the previous two-pathway kinetic competition model.

Force modulating dynamic disorder: A physical model of catch-slip bond transitions in receptor-ligand forced dissociation experiments

Recent experiments found that some adhesive receptor-ligand complexes have counterintuitive catch-slip transition behaviors: the mean lifetimes of these complexes first increase (catch) with initial application of a small external force, and then decrease (slip) when the force is beyond some threshold. In this work we suggest that the forced dissociation of these complexes might be a typical rate process with dynamic disorder. The one-dimensional force modulating Agmon-Hopfield model is used to describe the transitions in the single-bond P-selectin glycoprotein ligand 1-P-selectin forced dissociation experiments, which were respectively performed in the constant force [Marshall, Nature (Landon) 423, 190 (2003)] and the ramping force [Evans, Proc. Natl. Acad. Sci. U.S.A 98, 11281 (2004)] modes. We find that, an external force can not only accelerate the bond dissociation, but also modulate the complex from the lower-energy barrier to the higher one; the catch-slip bond transition can arise from a particular energy barrier shape. The agreement between our calculation and the experimental data is satisfactory.

Polar orientational phase transition and differential dielectric constant of smectic monolayers on a water surface

We build up a self-consistent equation and derive a general equation of orientational phase transition between a normal-director phase and a tilted-director phase for smectic monolayers on a water surface under monolayer compression with a consideration of molecular configuration. A differential dielectric constant for monolayer films is discovered and discussed. The change of the first orientational order parameter and the dielectric constant at the polar orientational phase transition point is also examined. It is found that the influence of the polar orientational phase transition on the first orientational order parameter in monolayer films is clear compared with that on the dielectric constant. This reveals that Maxwell-displacement-current measuring technique would be a useful way to measure such a phase transition.

Linear response theory and transient fluctuation relations for diffusion processes: a backward point of view

On the basis of perturbed Kolmogorov backward equations and path integral representation, we unify the derivations of the linear response theory and transient fluctuation theorems for continuous diffusion processes from a backward point of view. We find that a variety of transient fluctuation theorems could be interpreted as a consequence of a generalized Chapman-Kolmogorov equation, which intrinsically arises from the Markovian characteristic of diffusion processes.

Domain shapes in lipid monolayers studied as polar cholesteric liquid crystals

Both bulk and boundary orientations, and boundary shape equations for tilted lipid domain are derived in analogy with a polar cholesteric liquid crystal. It shows that in a two-dimensional (2D) system the 3D spontaneous splay and chiral elastic energies, the s0 and q0 terms of Frank energy, can be regarded as an orientation-dependent line tension, and the domain formation is the equilibrium between the line tension, the surface pressure, the orientational stress, and the dipole-dipole interaction. An obvious and analytic shape solution for pinned boundary orientation for maximum boundary tension has been found and the diverse domain shapes observed in lipid monolayers in the past two decades, such as star, boojum, cardioid, ellipse, bola, and clover-leaf shapes, are dramatically well described by the solution.

Generalized integral fluctuation theorem for diffusion processes

Using Feynman-Kac and Cameron-Martin-Girsanov formulas, we find a generalized integral fluctuation theorem (GIFT) for general diffusion processes by constructing a time-invariable integral. The existing integral fluctuation theorems can be derived as its specific cases. We interpret the origin of the GIFT in terms of time reversal of stochastic systems.