Minimal Bending Energies of Bilayer Polyhedra

Motivated by recent experiments on bilayer polyhedra composed of amphiphilic molecules, we study the elastic bending energies of bilayer vesicles forming polyhedral shapes. Allowing for segregation of excess amphiphiles along the ridges of polyhedra, we find that bilayer polyhedra can indeed have lower bending energies than spherical bilayer vesicles. However, our analysis also implies that, contrary to what has been suggested on the basis of experiments, the snub dodecahedron, rather than the icosahedron, generally represents the energetically favorable shape of bilayer polyhedra

Non-local fluctuation correlations in active gels

Many active materials and biological systems are driven far from equilibrium by embedded agents that spontaneously generate forces and distort the surrounding material. Probing and characterizing these athermal fluctuations is essential for understanding the properties and behaviors of such systems. Here we present a mathematical procedure to estimate the local action of force-generating agents from the observed fluctuating displacement fields. The active agents are modeled as oriented force dipoles or isotropic compression foci, and the matrix on which they act is assumed to be either a compressible elastic continuum or a coupled network-solvent system. Correlations at a single point and between points separated by an arbitrary distance are obtained, giving a total of three independent fluctuation modes that can be tested with microrheology experiments. Since oriented dipoles and isotropic compression foci give different contributions to these fluctuation modes, ratiometric analysis allows us characterize the force generators. We also predict and experimentally find a high-frequency ballistic regime, arising from individual force generating events in the form of the slow build-up of stress followed by rapid but finite decay. Finally, we provide a quantitative statistical model to estimate the mean filament tension from these athermal fluctuations, which leads to stiffening of active networks.Comment: 12 pages, 7 figures; some clarifications and ammended figure notation

INCORPORATION OF QUANTUM STATISTICAL FEATURES IN MOLECULAR DYNAMICS

We formulate a method for incorporating quantum fluctuations into molecular- dynamics simulations of many-body systems, such as those employed for energetic nuclear collision processes. Based on Fermi's Golden Rule, we allow spontaneous transitions to occur between the wave packets which are not energy eigenstates. The ensuing diffusive evolution in the space of the wave packet parameters exhibits appealing physical properties, including relaxation towards quantum- statistical equilibrium.Comment: 8 latex pages + 1 uuencoded ps figur

Effect of symmetry energy on two-nucleon correlation functions in heavy-ion collisions induced by neutron-rich nuclei

Using an isospin-dependent transport model, we study the effects of nuclear symmetry energy on two-nucleon correlation functions in heavy ion collisions induced by neutron-rich nuclei. We find that the density dependence of the nuclear symmetry energy affects significantly the nucleon emission times in these collisions, leading to larger values of two-nucleon correlation functions for a symmetry energy that has a stronger density dependence. Two-nucleon correlation functions are thus useful tools for extracting information about the nuclear symmetry energy from heavy ion collisions.Comment: Revised version, to appear in Phys. Rev. Let

Intermittency and Exotic Channels

It is pointed out that accurate measurements of short-range two-particle correlations in like-charge $K\pi$ and in $\pi^ 0\pi^ 0$ channels should be very helpful in determining the origin of the \lq\lq intermittency\rq\rq\ phenomenon observed recently for the like-charge pion pairs.Comment: 5 p., plain tex, preprint T94/078(Saclay), LPTHE 94/58(Orsay

Soft swimming: Exploiting deformable interfaces for low-Reynolds number locomotion

Reciprocal movement cannot be used for locomotion at low-Reynolds number in an infinite fluid or near a rigid surface. Here we show that this limitation is relaxed for a body performing reciprocal motions near a deformable interface. Using physical arguments and scaling relationships, we show that the nonlinearities arising from reciprocal flow-induced interfacial deformation rectify the periodic motion of the swimmer, leading to locomotion. Such a strategy can be used to move toward, away from, and parallel to any deformable interface as long as the length scales involved are smaller than intrinsic scales, which we identify. A macro-scale experiment of flapping motion near a free surface illustrates this new result

Lipid membranes with an edge

Consider a lipid membrane with a free exposed edge. The energy describing this membrane is quadratic in the extrinsic curvature of its geometry; that describing the edge is proportional to its length. In this note we determine the boundary conditions satisfied by the equilibria of the membrane on this edge, exploiting variational principles. The derivation is free of any assumptions on the symmetry of the membrane geometry. With respect to earlier work for axially symmetric configurations, we discover the existence of an additional boundary condition which is identically satisfied in that limit. By considering the balance of the forces operating at the edge, we provide a physical interpretation for the boundary conditions. We end with a discussion of the effect of the addition of a Gaussian rigidity term for the membrane.Comment: 8 page

Direct Electrochemistry of Endonuclease III in the Presence and Absence of DNA

The electrochemistry of the base excision repair enzyme Endonuclease III (Endo III) in the presence and absence of DNA has been examined on highly oriented pyrolytic graphite (HOPG). At the surface modified with pyrenated DNA, a reversible signal is observed at 20 mV versus NHE for the [4Fe−4S]^(3+/2+) couple of Endo III, similar to Au. Without DNA modification, oxidative and reductive signals for the [4Fe−4S] cluster of Endo III are found on bare HOPG, allowing a direct comparison between DNA-bound and free redox potentials. These data indicate a shift of approximately −200 mV in the 3+/2+ couple upon binding of Endo III to DNA. This potential shift reflects a difference in affinity for DNA of more than 3 orders of magnitude between the oxidized 3+ and reduced 2+ protein and provides quantitative support for our model utilizing DNA-mediated charge transport to redistribute base excision repair enzymes in the vicinity of damaged DNA

Elastic energy of polyhedral bilayer vesicles

In recent experiments [M. Dubois, B. Dem\'e, T. Gulik-Krzywicki, J.-C. Dedieu, C. Vautrin, S. D\'esert, E. Perez, and T. Zemb, Nature (London) Vol. 411, 672 (2001)] the spontaneous formation of hollow bilayer vesicles with polyhedral symmetry has been observed. On the basis of the experimental phenomenology it was suggested [M. Dubois, V. Lizunov, A. Meister, T. Gulik-Krzywicki, J. M. Verbavatz, E. Perez, J. Zimmerberg, and T. Zemb, Proc. Natl. Acad. Sci. U.S.A. Vol. 101, 15082 (2004)] that the mechanism for the formation of bilayer polyhedra is minimization of elastic bending energy. Motivated by these experiments, we study the elastic bending energy of polyhedral bilayer vesicles. In agreement with experiments, and provided that excess amphiphiles exhibiting spontaneous curvature are present in sufficient quantity, we find that polyhedral bilayer vesicles can indeed be energetically favorable compared to spherical bilayer vesicles. Consistent with experimental observations we also find that the bending energy associated with the vertices of bilayer polyhedra can be locally reduced through the formation of pores. However, the stabilization of polyhedral bilayer vesicles over spherical bilayer vesicles relies crucially on molecular segregation of excess amphiphiles along the ridges rather than the vertices of bilayer polyhedra. Furthermore, our analysis implies that, contrary to what has been suggested on the basis of experiments, the icosahedron does not minimize elastic bending energy among arbitrary polyhedral shapes and sizes. Instead, we find that, for large polyhedron sizes, the snub dodecahedron and the snub cube both have lower total bending energies than the icosahedron

Imaging of Sources in Heavy-Ion Reactions

Imaging of sources from data within the intensity interferometry is discussed. In the two-pion case, the relative pion source function may be determined through the Fourier transformation of the correlation function. In the proton-proton case, the discretized source function may be fitted to the correlation data.Comment: 12 pages, 3 postscript figures, accepted Physics Letters