Biomedical subjects
Publications and source records attributed to R M Mazo.
The Green's function of a random walk on a lattice is defined as the inverse of the operator K - z1, where K is the matrix of transition rates and z is an arbitrary complex parameter. The Green's function for a symmetrical random walk in one dimension is here explicitly given in closed form for reflecting, periodic, and absorbing boundaries, and also for an infinite lattice.
The computer simulation technique of molecular dynamics was applied to a model two-dimensional fluid mixture system to examine the short-range ordering of lipid and protein molecules in biological membranes. The model system consists of small disks (lipids) and large disks (proteins) with a radius ratio of 6, constrained to move in a plane. The particles interact with pairwise additive repulsive short range potentials, so as to simulate hard disks. Periodic boundary conditions are assumed in order to minimize boundary effects. For values of the number density of the small disks and of the temperature appropriate for a lipid membrane, the fraction, f, of small disks 'next to' at least one large disk was computed by molecular dynamics. This was done as a function of concentration and for several definitions of 'next to'. The molecular dynamics results show that, at moderately low mole fractions of the large disks, the calculated values of f deviate noticeably from the linear relation which would be expected in the absence of protein-protein proximity effects. The results are discussed in terms of current models of lipid-protein ordering in biological membranes.
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.
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