Diffusion and the physics of chemoreception

This review provides a manual which enables the reader to perform calculations on the rate with which a biological cell can capture certain chemical compounds (ligands) which are essential to its survival and which diffuse in its environment. After a discussion of spatial diffusion and the capture of ligands by a single receptor in the cell membrane, the theory of one-stage chemoreception is developed for the general case in which the cell is spherical and arbitrary forces act between the ligand and the cell. Our method can also be applied to cells with other shapes. Next we discuss membrane diffusion and develop a theory of two-stage chemoreception. Some hydrodynamic effects are also discussed

Pore-size distribution in a biomembrane model

It is shown that spontaneous formation of pores occurs in a recently proposed exactly solvable model for a two-dimensional lipid bilayer. The statistical distributions of number and size of these pores are calculated from first principles

Translational friction coefficient of a permeable cylinder in a sheet of viscous fluid

The author calculates the translational friction coefficient and the translational diffusion coefficient of a permeable cylinder moving in a sheet of fluid which is embedded on both sides in a fluid of much lower viscosity. The result, which is an asymptotic expression valid in the limit of small ratios of the viscosities, is derived by the method of matched asymptotic expansions

Path integrals with topological constraints: Aharonov-Bohm effect and polymer entanglements

For Wiener- and Feynman integrals over paths with certain topological properties we compare various methods for explicit calculation. This leads to a one-to-one correspondence between the Aharonov-Bohm effect and a certain polymer entanglement problem. We briefly comment on two generalizations of the Aharonov-Bohm effect. First, we consider this effect due to a closed magnetic flux loop of arbitrary shape; next, we consider the combined effect due to a gas of microscopic magnetic flux loops

The effective coordination number of self-avoiding two-dimensional random walks

It is demonstrated that the effective coordination number of self-avoiding random walks in a plane is given by exp(−π2/24) = 0.66283

Asymptotic expansions for a remarkable class of random walks

This paper extends the research of Wiegel (J. Math. Phys. 21 (1980) 2111) on random walks which differ from free random walks through the occurrence of an extra weightfactor (−1) at every crossing of a half-line. Starting from a new closed-form expression for the weight distribution of these walks, we derive various integral representations and asymptotic expansions for the total weight of all walks

Transport coefficients for rigid spherically symmetric polymers or aggregates

In this paper we investigate the transport properties for rigid spherically symmetric macromolecules, having a segment density distribution falling off as r- lambda . We calculate the rotational and translational diffusion coefficient for a spherically symmetric polymer and the shear viscosity for a dilute suspension of these molecules, starting from a continuum description based on the Debye-Brinkman equation. Instead of numerical methods for solving equations we use perturbative methods, especially methods from boundary-layer analysis. The calculations provide simple analytical formulae for the shear viscosity eta , and the translational and rotational diffusion coefficients DT and DR. The results can also be applied to suspensions of other porous objects, such as aggregates of colloidal particles in which D=3- lambda is called the fractal dimension of the aggregate

Stochastic area distributions: optimal trajectories, Maslov indices and asymptotic results

In this paper we study the semi-classical approximation for the distribution of area associated with (i) planar polymer rings constrained to enclose a fixed algebraic area and (ii) planar rings subject to an external electric field and constrained to enclose a fixed algebraic area. We demonstrate that the results are accurate in the asymptotic regime. Moreover, we also show that in case (i) it is possible to reconstruct the exact expression for the distribution, provided the contributions from all optimal trajectories are taken into account, as well as the proper Maslov indices

Comments on the Debije-Brinkman equation

We present a macroscopic derivation of the Debije-Brinkman equation for the flow of a fluid through a polymer coil. By using an exact relation between the sedimentation coefficient and the permeability it is found that the permeability of the coil is strongly dependent on the nature of the fluid, due to local clustering of the polymer segments

Intrinsic viscosity and friction coefficient of polymer molecules in solution: Porous sphere model

The intrinsic viscosity [] and the translational friction coefficient f of polymer molecules in solution are calculated on the basis of the porous sphere model. The only information needed to predict [] and f is the polymer molecular weight, the radius of gyration in the solvent, and the permeability as a function of position in the porous sphere. For systems for which this information is available there is satisfactory agreement between predicated and directly measured values of [] and f. No adjustment of parameters is required. The influence of solvent quality is more complex than is suggested by the experimentally verified Flory-Fox relation for []; the simple form of this relation stems from the fact that two quite large effects of solvent quality approximately compensate each other. The complete flow pattern of the solvent around and through the polymer coil can be calculated. Contrary to what is usually believed the solvent flow in the polymer coil is not effectively blocked, even at the center. The connection between the present treatment and the microscopic theory of Kirkwood and Riseman is investigated