Polyelectrolytes between two membranes or colloidal particles

The author investigates the equilibrium behaviour of charged polymers of finite length in a Debye-screened potential between two parallel charged walls. For the polymer he takes the continuum approximation to calculate the spectrum of eigenfunctions for the partition function. For finite but long polymers only the lowest two terms in this expansion contribute to first order to the configurational sum, corresponding to a symmetrical and an antisymmetrical solution. Within this formalism he calculates the monomer density distribution for finite strands of polymer attached to one or both surfaces (tails, loops and bridges) as well as for polymers free in solution. For the free polymer he also finds the free energy as a function of the distance between the plates for several values of the interaction parameters, as well as the effective interaction between the plates due to the polyions. This shows that there can exist an equilibrium separation distance between colloidal particles due to the interactions with charged polymers in solution. This mechanism may also explain the formation of rouleaux for red blood cells

Fractional exponential decay of a membrane protein population due to capture by coated pits

We consider the lateral diffusion of receptors, or other membrane proteins, in the outer membranes of certain cells, and their capture by coated pits. It is shown, for the case in which the coated pits are in fixed random positions, that the long-time decay of the total number of uncaptured proteins is of the fractional exponential form, [...] , and not of the pure exponential form, N(t) = N0 exp(- t/τ), which is usually assume

Lipid aggregate formation at an oscillating bubble surface: A simulation study

We perform a molecular dynamics simulation study of the behavior of a lipid coating layer on an oscillating bubble surface. Micrometer sized bubbles, stabilized with a lipid monolayer coating, are used in acoustic imaging as a contrast agent. The coating layer is expected to be strongly influenced by the oscillation of the bubble in the high frequency sound field, with a period of a microsecond. The typical time scale of molecular motion, however, is of the order of femtoseconds. One of the challenges is to bridge this nine decade gap in time scales. To this end we have developed a model that is highly coarse grained, but still features the essential mechanisms determining lipid dynamics, with time scales of picoseconds. This approach allows us to severely restrict the computing times, although we make use of very modest computing equipment. We show in our simulation that the amphiphilic monolayer folds upon contraction of the bubble, and forms micellar aggregates at the air-water interface. Some micellar structures survive consecutive re-expansion and indeed remain persistent over several cycles. These structures may add to the anisotropic behavior of the bubbles under oscillating conditions. We also investigated temperature and frequency dependenc

Computer simulation of a thin magnetic film with vertical anisotropy

We describe a discrete micromagnetic model for a thin magnetic layer which has been developed to perform computer simulations of the system. The magnetisation in this model is given in terms of a cubic array of interacting microscopic spins. The dynamics of the spins is given by a time discretisation of the Landau-Lifshitz-Gilbert equations of motion. The array is continued periodically in the x- and y-direction in order to reduce boundary effects, and is finite in the z-direction. The mutual interactions that are incorporated are exchange and dipole interaction, and the crystal lattice interaction is modeled by a roughly vertical uniaxial anisotropy term. The strengths of the different interactions are scaled so as to conform to values for CoCr, fitted to experimental results within the context of continuum models. For this setup we have determined full hysteresis curves and compared with experimental results of these films

Period-doubling density waves in a chain

The authors consider a one-dimensional chain of N+2 identical particles with nearest-neighbour Lennard-Jones interaction and uniform friction. The chain is driven by a prescribed periodic motion of one end particle, with frequency v and 'strength' parameter alpha . The other end particle is held fixed. They demonstrate numerically that there is a region in the alpha -v plane where the chain has a stable state in which a density wave runs to and fro between the two ends of the chain, similarly to a ball bouncing between two walls. More importantly, they observe a period-doubling transition to chaos, for fixed v and increasing alpha , while the localised (solitary wave) character of the motion is preserve

Interacting solitary waves in a damped driven Lennard-Jones chain

It is shown analytically that pulse solitary waves in a chain with Lennard-Jones type nearest neighbor interaction are strongly localized and marginally stable in the high energy limit.\ud \ud In a damped and periodically driven chain we obtain numerically families of states whose behavior is similar to that of equally many oscillators. We observe a period doubling sequence in a one-solitary wave family and bifurcation to (quasi-) periodic motion in a family of two solitary waves. We conclude that the damped and driven chain admits asymptotically stable states living on a low-dimensional manifold in phase space. These results depend sensitively on the shape of the driving term

Forward rate constants for receptor clusters variational methods for upper and lower bounds

We are interested in the effect of receptor clustering on k+, the diffusion-limited forward rate constant for the binding of a ligand to a cell surface receptor. Here we estimate the reduction in k+ when receptors are clustered in various configurations. We obtain two alternative expressions for the flux of ligands into receptors distributed on a surface. Next we show through a variational principle that these provide both upper and lower bounds on the flux when evaluated for trial concentration functions which satisfy only the boundary conditions of the Laplace equation. We use an analogy with electrostatics to calculate rigorous bounds within approx. 10% of the exact result for a variety of planar clusters of hemispherical receptor sites. We also obtain an exact result for the flux into a spheroidal receptor and use this result to obtain bounds on the flux into certain receptor clusters

Substrate-induced pairing of Si ad-dimers on the Si(100)surface

The interaction between Si ad-dimers on the Si(100) surface has been studied by total-energy calculations with a three-particle Stillinger-Weber potential. We have found a strong attractive interaction between neighboring Si ad-dimers located in neighboring on-top and deep-channel positions in adjacent substrate dimer rows. This should result in a four-atomic block consisting of two dimers as an important elementary object of the Si(100) kinetics

The behaviour of an ideal polymer chain interacting with two parallel surfaces

The behaviour of a long isolated ideal chain polymer interacting with two parallel surfaces is investigated within the context of a simple cubic lattice model in three dimensions. In order to be able to obtain information about the contacts of the polymer with the plates the full chain is subdivided into trains, loops and bridges. A maximum term method is used to calculate the configuration sum of the polymer. In order to find the distribution of the subchains that maximises the partition function in the limit of infinite molecular weight a Lagrange multiplier method has been applied. This gives a closed set of equations from which one can uniquely calculate all relevant thermodynamic quantities as a function of the interaction energy, the temperature and the distance between the plates. In addition to the free energy and the entropy of the chain also the fraction of monomers on the surface and the number of trains is calculated. Next we give results about the ratio between the number of bridges and loops and the fraction of monomers in these loops and bridges. Finally the effective force between the plates due to the polymer material is calculated. The results for large plate separation are compared with those of the single plate