Robert M. Mazo

A model for shape generation by strain and cell-cell adhesion in the epithelium of an arthropod leg segment☆

We present a model for the energetic factors determining the most stable shape of a tubular epithelium such as the hypodermis of an arthropod leg segment. The model uses the analysis by Steinberg (1963) of rearrangement of cells in aggregates under the influence of differential adhesion, combining this analysis with the assumption that the epithelium behaves as an elastic sheet. The epithelium is assumed to consist of blocks of cells with different adhesive affinities, which remain unmixed in a quilt pattern. Rearrangement of cells within each block can adjust the shape of the tube by changing the shapes of the blocks. By means of such rearrangements the tube develops that shape which minimizes a free energy. The free energy is the difference between the energy of mechanical strain due to bending of the epithelium and the work of adhesion among cells. Minimization of the free energy for a cylindrical segment yields a scaling relation involving the length and radius of the segment. Leg segments of Drosophila conformed approximately to this relation, with deviations which suggest that a whole-limb pattern of adhesive affinities modulates the shaping effects of an adhesive pattern repeated in each leg segment. The model also predicts a transient deformation in an epithelium following a grafting operation. For example, deleting a slab of tissue from a tubular segment and reuniting the cut ends should produce a constriction of the tube at the host-graft junction. We propose that patterns of strain and adhesion can provide positional information which regulates subsequent development. Local increases in strain or adhesive disparity may stimulate mitoses; the resulting changes in distribution of cells will affect morphogenesis.

Hydrodynamic Properties of a Plane‐Polygonal Polymer, According to Kirkwood–Riseman Theory

An exact solution of Kirkwoods formalism of transport processes for dilute polymer solutions has been found for the model of a planar rigid ring. Translational and rotatory diffusion tensors and the perturbation in the stress tensor were calculated. Non‐Newtonian behavior was found in the intrinsic viscosity, the intrinsic rigidity, and in the existence of normal stresses. In addition to the elastic response at the principal frequency ω for oscillatory fluid flow, non‐Newtonian elastic stresses appear at higher harmonics of ω.

On the Theory of the Concentration Dependence of the Self‐Diffusion Coefficient of Micelles

A theory is given for the ratio of initial slope to intercept in a plot of 1/D versus concentration of colloid particles; D is the self‐diffusion coefficient of the charged colloid particles (micelles). The theory starts from the Einstein relation, and the autocorrelation function expression for the friction constant. The main approximation is the use of Brownian motion theory to describe the effect of the solvent on micelle motion. There is good agreement with experiment in salt solutions, but the agreement is poor when there is no added salt. It is concluded that the theory is probably appropriate for solutions of high ionic strength, but the possibility that the data in salt‐free solution have not been interpreted properly, i.e., that the theory has a wider validity, is also discussed.

Dielectric friction and ionic hydration near boundaries: Image charge effects

The effects of image charges on ions and polar particles near boundaries are calculated for several simple models. These are: dielectric friction of a translating charge and of a rotating dipole, and the electrostatic contribution to the hydration energy of an ion, all near a boundary. Image charge induced changes in dielectric friction and electrostatic free energy are found to be minor for molecular size particles, but appreciable for larger particles, e.g., macromolecules near membranes.

Theory of Brownian Motion. IV. A Hydrodynamic Model for the Friction Factor

The hydrodynamical theory of the velocity correlation function of a Brownian particle, due to Widom, is combined with the non‐Markovian generalized Fokker–Planck equation given by the molecular theory of Brownian motion. An expression for the friction kernel (force autocorrelation) is derived. On the basis of the model here considered, the friction kernel decays as t−3/2 for long times.

On the theory of brownian motion. III. Two-body distribution function

The equation of evolution governing the probability density of a pair of heavy particles in a fluid of lighter particles is derived. The derivation starts from the Liouville equation and proceeds by expansion in the ratio of light to heavy masses, using the technique previously applied successfully to the singlet distribution.

On the Theory of Brownian Motion. I. Interaction Between Brownian Particles

The molecular theory of the Brownian motion of heavy particles in a homogeneous solvent of light particles is extended to cover the case of interactions between the Brownian particles. This will have physical effects in the concentration dependence of the Brownian particle self-diffusion coefficient. A density expansion for the Brownian particle friction coefficient is derived, and an approximation permitting the first density correction to be calculated is suggested.

Free Energy of a System with Random Elements

It is shown that the free energy of a system containing random elements, whose distribution is subject to some fixed probability law, is given by the expectation value of the logarithm of the partition function, considered as a random variable.

On the Theory of Solute Solubility in Mixed Solvents

A series of equations are developed for the study of the effects of cosolvents on the solubility of a solute in mixed solutions where the solute displays a finite solubility. The equations differ depending on the scale used for the solute (and cosolvent) concentrations. The expressions use Kirkwood-Buff integrals to relate the changes in solubility to changes in the local solution composition around the solute and can be applied to study any type of ternary system including electrolyte cosolvents. The expressions provided here differ from previous approaches because of the use of a semi-open ensemble and the extension to finite solute solubilities.

On the theory of Brownian motion. II. Nonuniform systems

An equation of evolution for a heavy particle immersed in a solvent of lighter particles is derived for the case when the system suffers gradients of temperature composition, or velocity. The derivation unifies the theory by applying the same methods which have proved useful in the uniform case. The final equation contains some new terms due to concentration gradients in the solvent, and is applicable to the case when the heavy particles are present at finite concentration and interact with each other.