A model for the force stretching double-stranded chain molecules

We modify and extend the recently developed statistical mechanical model for predicting the thermodynamic properties of chain molecules having noncovalent double-stranded conformations, as in RNA or ssDNA, and $\beta-$sheets in protein, by including the constant force stretching at one end of molecules as in a typical single-molecule experiment. The conformations of double-stranded regions of the chain are calculated based on polymer graph-theoretic approach [S-J. Chen and K. A. Dill, J. Chem. Phys. {\bf109}, 4602(1998)], while the unpaired single-stranded regions are treated as self-avoiding walks. Sequence dependence and excluded volume interaction are taken into account explicitly. Two classes of conformations, hairpin and RNA secondary structure are explored. For the hairpin conformations, all possible end-to-end distances corresponding to the different types of double-stranded regions are enumerated exactly. For the RNA secondary structure conformations, a new recursive formula incorporating the secondary structure and end-to-end distribution has been derived. Using the model, we investigate the extension-force curves, contact and population distributions and re-entering phenomena, respectively. we find that the force stretching homogeneous chains of hairpin and secondary structure conformations are very different: the unfolding of hairpins is two-state, while unfolding the latter is one-state. In addition, re-entering transitions only present in hairpin conformations, but are not observed in secondary structure conformations.Comment: 19 pages, 28 figure

New Approach on the General Shape Equation of Axisymmetric Vesicles

The general Helfrich shape equation determined by minimizing the curvature free energy describes the equilibrium shapes of the axisymmetric lipid bilayer vesicles in different conditions. It is a non-linear differential equation with variable coefficients. In this letter, by analyzing the unique property of the solution, we change this shape equation into a system of the two differential equations. One of them is a linear differential equation. This equation system contains all of the known rigorous solutions of the general shape equation. And the more general constraint conditions are found for the solution of the general shape equation.Comment: 8 pages, LaTex, submit to Mod. Phys. Lett.

Spheres and Prolate and Oblate Ellipsoids from an Analytical Solution of Spontaneous Curvature Fluid Membrane Model

An analytic solution for Helfrich spontaneous curvature membrane model (H. Naito, M.Okuda and Ou-Yang Zhong-Can, Phys. Rev. E {\bf 48}, 2304 (1993); {\bf 54}, 2816 (1996)), which has a conspicuous feature of representing the circular biconcave shape, is studied. Results show that the solution in fact describes a family of shapes, which can be classified as: i) the flat plane (trivial case), ii) the sphere, iii) the prolate ellipsoid, iv) the capped cylinder, v) the oblate ellipsoid, vi) the circular biconcave shape, vii) the self-intersecting inverted circular biconcave shape, and viii) the self-intersecting nodoidlike cylinder. Among the closed shapes (ii)-(vii), a circular biconcave shape is the one with the minimum of local curvature energy.Comment: 11 pages, 11 figures. Phys. Rev. E (to appear in Sept. 1999

Numerical observation of non-axisymmetric vesicles in fluid membranes

By means of Surface Evolver (Exp. Math,1,141 1992), a software package of brute-force energy minimization over a triangulated surface developed by the geometry center of University of Minnesota, we have numerically searched the non-axisymmetric shapes under the Helfrich spontaneous curvature (SC) energy model. We show for the first time there are abundant mechanically stable non-axisymmetric vesicles in SC model, including regular ones with intrinsic geometric symmetry and complex irregular ones. We report in this paper several interesting shapes including a corniculate shape with six corns, a quadri-concave shape, a shape resembling sickle cells, and a shape resembling acanthocytes. As far as we know, these shapes have not been theoretically obtained by any curvature model before. In addition, the role of the spontaneous curvature in the formation of irregular crenated vesicles has been studied. The results shows a positive spontaneous curvature may be a necessary condition to keep an irregular crenated shape being mechanically stable.Comment: RevTex, 14 pages. A hard copy of 8 figures is available on reques

Force Modulating Dynamic Disorder: Physical Theory of Catch-slip bond Transitions in Receptor-Ligand Forced Dissociation Experiments

Recently experiments showed that some adhesive receptor-ligand complexes increase their lifetimes when they are stretched by mechanical force, while the force increase beyond some thresholds their lifetimes decrease. Several specific chemical kinetic models have been developed to explain the intriguing transitions from the "catch-bonds" to the "slip-bonds". In this work we suggest that the counterintuitive forced dissociation of the complexes is a typical rate process with dynamic disorder. An uniform one-dimension force modulating Agmon-Hopfield model is used to quantitatively describe the transitions observed in the single bond P-selctin glycoprotein ligand 1(PSGL-1)$-$P-selectin forced dissociation experiments, which were respectively carried out on the constant force [Marshall, {\it et al.}, (2003) Nature {\bf 423}, 190-193] and the force steady- or jump-ramp [Evans {\it et al.}, (2004) Proc. Natl. Acad. Sci. USA {\bf 98}, 11281-11286] modes. Our calculation shows that the novel catch-slip bond transition arises from a competition of the two components of external applied force along the dissociation reaction coordinate and the complex conformational coordinate: the former accelerates the dissociation by lowering the height of the energy barrier between the bound and free states (slip), while the later stabilizes the complex by dragging the system to the higher barrier height (catch).Comment: 8 pages, 3 figures, submitte

Dynamic disorder in receptor-ligand forced dissociation experiments

Recently experiments showed that some biological noncovalent bonds increase their lifetimes when they are stretched by an external force, and their lifetimes will decrease when the force increases further. Several specific quantitative models have been proposed to explain the intriguing transitions from the "catch-bond" to the "slip-bond". Different from the previous efforts, in this work we propose that the dynamic disorder of the force-dependent dissociation rate can account for the counterintuitive behaviors of the bonds. A Gaussian stochastic rate model is used to quantitatively describe the transitions observed recently in the single bond P-selctin glycoprotein ligand 1(PSGL-1)$-$P-selectin force rupture experiment [Marshall, {\it et al.}, (2003) Nature {\bf 423}, 190-193]. Our model agrees well to the experimental data. We conclude that the catch bonds could arise from the stronger positive correlation between the height of the intrinsic energy barrier and the distance from the bound state to the barrier; classical pathway scenario or {\it a priori} catch bond assumption is not essential.Comment: 4 pages, 2 figure

Electric Current Focusing Efficiency in Graphene Electric Lens

In present work, we theoretically study the electron wave's focusing phenomenon in a single layered graphene pn junction(PNJ) and obtain the electric current density distribution of graphene PNJ, which is in good agreement with the qualitative result in previous numerical calculations [Science, 315, 1252 (2007)]. In addition, we find that for symmetric PNJ, 1/4 of total electric current radiated from source electrode can be collected by drain electrode. Furthermore, this ratio reduces to 3/16 in a symmetric graphene npn junction. Our results obtained by present analytical method provide a general design rule for electric lens based on negative refractory index systems.Comment: 13 pages, 7 figure