论文信息 - A diffusion model for patch formation on cellular surfaces

A diffusion model for patch formation on cellular surfaces

A number of phenomena of interest in the biology of the cellular membrane can be modeled by a diffusion process which is undergone by certain objects on the cellular surface.We consider one such model and are led to the task of estimating the principal eigenvalue of an elliptic operator with homogeneous Dirichlet boundary conditions.The requested estimate is carried out by two different methods: one makes use of a Lyapunov-type technique and the other applies the Cameron—Martin—Girsanov formula. These methods apply to much more general situations than the specific one considered here.

[1] M. Pinsky. The first eigenvalue of a spherical cap , 1981 .

[2] M. Poo,et al. Electrophoresis and diffusion in the plane of the cell membrane. , 1979, Biophysical journal.

[3] J. Callis,et al. Pyrene. A probe of lateral diffusion in the hydrophobic region of membranes. , 1974, Biochemistry.

[4] S. Varadhan,et al. On a variational formula for the principal eigenvalue for operators with maximum principle. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

[5] G. Nicolson,et al. The cancer cell: dynamic aspects and modifications in cell-surface organization (first of two parts). , 1976, The New England journal of medicine.

[6] I. V. Girsanov. On Transforming a Certain Class of Stochastic Processes by Absolutely Continuous Substitution of Measures , 1960 .

[7] H. Berg,et al. Physics of chemoreception. , 1977, Biophysical journal.

[8] K. Naqvi,et al. Diffusion-controlled reactions in two-dimensional fluids: discussion of measurements of lateral diffusion of lipids in biological membranes , 1974 .

[9] M. Dembo,et al. A method for measuring membrane microviscosity using pyrene excimer formation. Application to human erythrocyte ghosts. , 1979, Biochimica et biophysica acta.