3,231 research outputs found
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 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
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