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M F Bishop

Publications and source records attributed to M F Bishop.

7 recordsLinked to original sources
PubMed1998

A lattice model for computing the transmissivity of the cornea and sclera.

The method of photonic band structure is used to calculate the frequencies of light that propagate in lattice models of the cornea and sclera of the mammalian eye, providing an explanation for transparency in the cornea that first properly accounts for multiple scattering of light. Each eye tissue is modeled as an ordered array of collagen rods, and photonic band structure methods are used to solve Maxwell's equations exactly for these models, a procedure that automatically effectively includes all orders of multiple scattering. These calculations show that the dispersion relation for the cornea is linear in the visible range, implying that the cornea is transparent. We show that the transmissivity is approximately 97% by using an effective medium approximation derived from the photonic band structure results and applicable in the visible region. In contrast, the dispersion relation for the model in the sclera is not linear in the visible region, and there are band gaps in this region that could play an important role in the transmission of light in the sclera.

Animals↗
PubMed1989

Calculations of scattered light from rigid polymers by Shifrin and Rayleigh-Debye approximations.

We show that the commonly used Rayleigh-Debye method for calculating light scattering can lead to significant errors when used for describing scattering from dilute solutions of long rigid polymers, errors that can be overcome by use of the easily applied Shifrin approximation. In order to show the extent of the discrepancies between the two methods, we have performed calculations at normal incidence both for polarized and unpolarized incident light with the scattering intensity determined as a function of polarization angle and of scattering angle, assuming that the incident light is in a spectral region where the absorption of hemoglobin is small. When the Shifrin method is used, the calculated intensities using either polarized or unpolarized scattered light give information about the alignment of polymers, a feature that is lost in the Rayleigh-Debye approximation because the effect of the asymmetric shape of the scatterer on the incoming polarized electric field is ignored. Using sickle hemoglobin polymers as an example, we have calculated the intensity of light scattering using both approaches and found that, for totally aligned polymers within parallel planes, the difference can be as large as 25%, when the incident electric field is perpendicular to the polymers, for near forward or near backward scattering (0 degrees or 180 degrees scattering angle), but becomes zero as the scattering angle approaches 90 degrees. For randomly oriented polymers within a plane, or for incident unpolarized light for either totally oriented or randomly oriented polymers, the difference between the two results for near forward or near backward scattering is approximately 15%.

Biopolymers↗
PubMed1987

Nucleation of actin polymerization by villin and elongation at subcritical monomer concentration.

We have obtained a quantitative description of villin-nucleated actin polymerization in physiological salt by determining the concentrations of free villin (V), villin-actin monomer (VA), villin-actin dimer (VA2), and villin-actin oligomer (VAn). Over a range of actin-villin ratios from 0.1 to 20 we determined the concentration of actin-bound villin by measuring the low-intensity pyrenylactin fluorescence of the two terminal actins in each villin-actin polymer. (To this end we first showed that each villin-actin oligomer and polymer contains two low-intensity pyrenylactin molecules.) We determined the concentration of free villin using a calibrated cutting activity assay. The pattern of increase in bound villin together with the pattern of increase in high-intensity pyrenylactin fluorescence with increasing G-actin concentration indicated, first, that villin-actin monomers were not formed at detectable levels even at a 12-fold villin excess over actin. Second, there was no stoichiometric villin-actin dimer formation at actin-villin ratios of 2. Instead there was an equilibrium between free villin, VA2, and VAn. Defining K1 = [VA]/[V][A] and K2 = [VA2]/[VA][A], a good fit of the data was obtained with K1 much less than K2 and a value of K1K2 = Kv = 10(12)-10(13) M-2 = [VA2]/[V][A]2, i.e., 1/Kv1/2 = (0.3-1) X 10(-6) M. We have assumed here that the monomer binding constant of VA2 to form VA3 was equal to the monomer binding constant of pointed filament ends, K infinity = 1/c infinity, obtained as described below.(ABSTRACT TRUNCATED AT 250 WORDS)

Actins↗
PubMed1987

Kinetics of actin elongation and depolymerization at the pointed end.

We measured the rate of elongation at the pointed filament end with increasing concentrations of G-actin [J(c) function] using villin-capped actin filaments of very small (actin/villin = 3, VA3) and relatively large size (actin/villin = 18, VA18) as nuclei for elongation. The measurements were made under physiological conditions in the presence of both Mg2+ and K+. In both cases the J(c) function was nonlinear. In contrast to the barbed filament end, however, the slope of the J(c) function sharply decreased rather than increased when the monomer concentration was lowered to concentrations near and below the critical concentration c infinity. At zero monomer concentration, depolymerization at the pointed end was very slow with a rate constant of 0.02 s-1 for VA18. When VA3 was used, the nonlinearity of the J(c) function was greatly exaggerated, and the nuclei elongated at actin concentrations below the independently measured critical concentration for the pointed end. This is consistent with and confirms our previous finding [Weber, A., Northrop, J., Bishop, M. F., Ferrone, F. A., & Mooseker, M. S. (1987) Biochemistry (preceding paper in the issue)] that at an actin-villin ratio of 3 a significant fraction of the villin is free and that a series of steady states exist between villin-actin complexes of increasing size and G-actin. The rate constant of elongation seems to increase with increasing G-actin concentrations because of increasing conversion of free villin into villin-actin oligomers during the period of the measurement of the initial elongation rate. The villin-actin oligomers have a much higher rate constant of actin binding than does free villin.(ABSTRACT TRUNCATED AT 250 WORDS)

Actins↗
PubMed1986

Different calcium dependence of the capping and cutting activities of villin.

The concentration of ionized calcium required for the capping of barbed filament ends by villin is about 4 orders of magnitude lower than that required for the cutting activity of villin. Capping was 50% complete at about 10-30 nM Ca2+, a level expected in resting cells, whereas the cutting rate was half-maximal at about 200 microM, making it possible to completely separate filament capping from filament cutting. Analysis of capping in terms of coupled equilibria between calcium binding to villin and calcium-villin binding to the barbed ends of actin filaments gives a value of 10(16)-10(17) M-2 for the product of the two binding constants. By comparison the binding constant reported for the rapidly exchanging calcium sites on villin is 2 X 10(5) M-1 and that for binding of calcium-saturated villin to barbed ends has a minimum value of 10(11) M-1 giving a product of 2 X 10(16) M-1. The close similarity of the two sets of values suggests that capping is regulated by the rapidly exchanging calcium sites on villin. In terms of coupled equilibria the calcium requirement for filament capping decreases with increasing concentrations of free villin. The scant information on the mechanism of cutting allows only an estimate of the maximal value for the calcium-binding constant of the site regulating cutting which is about 2-5 X 10(3) M-1. Cutting is followed by rapid capping of the newly released barbed ends.

Actins↗
PubMed1984

Kinetics of nucleation-controlled polymerization. A perturbation treatment for use with a secondary pathway.

We present a perturbation method for analyzing nucleation-controlled polymerization augmented by a secondary pathway for polymer growth. With this method, the solution to the kinetic equations assumes a simple analytic closed form that can easily be used in fitting data. So long as the formation of polymers by the secondary pathway depends linearly on the concentration of monomers polymerized, the form of the solutions is the same. This permits the analysis of augmented growth models with a minimum number of modeling assumptions, and thus makes it readily possible to distinguish between a variety of secondary processes (heterogeneous nucleation, lateral growth, and fragmentation). In addition, the parameters of the homogeneous process, such as the homogeneous nucleus size, can be determined independent of the nature of the secondary mechanism. We describe applications of this method to the polymerization of actin, collagen, and sickle hemoglobin. We present an extensive analysis of data on actin polymerization (Wegner, A., and P. Savko, 1982, Biochemistry, 21:1909-1913) to illustrate the use of the method. Although our conclusions generally agree with theirs, we find that lateral growth describes the secondary pathway better than the fragmentation model originally proposed. We also show how this method can be used to study the degree of polymerization, the parentage of polymers, and the behavior of polymers in cycling experiments.

Actins↗