Lateral diffusion of a protein on a fluctuating membrane

Measurements of lateral diffusion of proteins in a membrane typically assume that the movement of the protein occurs in a flat plane. Real membranes, however, are subject to thermal fluctuations, leading to movement of an inclusion into the third dimension. We calculate the magnitude of this effect by projecting real three-dimensional diffusion onto an effective one on a flat plane. We consider both a protein that is free to diffuse in the membrane and one that also couples to the local curvature. For a freely diffusing inclusion the measured projected diffusion constant is up to 15% smaller than the actual value. Coupling to the curvature enhances diffusion significantly up to a factor of two.Comment: 6 pages, 4 figure

Business modeling and requirements in RUP: a dependency analysis of activities, tasks and work products

Most artifacts developed during the requirements engineering process relate themselves in different ways. In order to understand in detail how they affect each other during the software development process, it is relevant to iden-tify their interdependencies. This paper presents a systematization of the existing interdependencies between the different elements of the Rational Unified Process (RUP) in the Business Modeling and Requirements disciplines. This work, which highlights knowledge about the different interdependencies and traceability of RUP elements, is useful to avoid unconscious decisions during software the de-velopment process and also, to detect potential problems due to the violation of the existing interdependencies.This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT – Fundação para a Ciência e a Tecnologia within the Project Scope: UID/CEC/00319/2013.info:eu-repo/semantics/publishedVersio

Curvature-coupling dependence of membrane protein diffusion coefficients

We consider the lateral diffusion of a protein interacting with the curvature of the membrane. The interaction energy is minimized if the particle is at a membrane position with a certain curvature that agrees with the spontaneous curvature of the particle. We employ stochastic simulations that take into account both the thermal fluctuations of the membrane and the diffusive behavior of the particle. In this study we neglect the influence of the particle on the membrane dynamics, thus the membrane dynamics agrees with that of a freely fluctuating membrane. Overall, we find that this curvature-coupling substantially enhances the diffusion coefficient. We compare the ratio of the projected or measured diffusion coefficient and the free intramembrane diffusion coefficient, which is a parameter of the simulations, with analytical results that rely on several approximations. We find that the simulations always lead to a somewhat smaller diffusion coefficient than our analytical approach. A detailed study of the correlations of the forces acting on the particle indicates that the diffusing inclusion tries to follow favorable positions on the membrane, such that forces along the trajectory are on average smaller than they would be for random particle positions.Comment: 16 pages, 8 figure

Derivatives for smooth representations of GL(n,R) and GL(n,C)

The notion of derivatives for smooth representations of GL(n) in the p-adic case was defined by J. Bernstein and A. Zelevinsky. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations by S. Sahi and called the "adduced" representation. In this paper we define derivatives of all order for smooth admissible Frechet representations (of moderate growth). The archimedean case is more problematic than the p-adic case; for example arbitrary derivatives need not be admissible. However, the highest derivative continues being admissible, and for irreducible unitarizable representations coincides with the space of smooth vectors of the adduced representation. In [AGS] we prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We apply those results to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations, thus completing the results of [Sah89, Sah90, SaSt90, GS12].Comment: First version of this preprint was split into 2. The proofs of two theorems which are technically involved in analytic difficulties were separated into "Twisted homology for the mirabolic nilradical" preprint. All the rest stayed in v2 of this preprint. v3: version to appear in the Israel Journal of Mathematic

Diffusion of molecules on biological membranes of nonplanar form. II. Diffusion anisotropy.

Molecules diffusing on nonplanar membranes, which have different amounts of corrugation in different directions, may experience dissimilar diffusion coefficients in each direction. Smith et al. (1979, Proc. Natl. Acad. Sci. USA, 76:5641-5644) measured diffusion anisotropy on fibroblast cell membranes in which the ratio of the diffusion coefficients, in different directions, was 0.27. In the present work we calculate the effect of anisotropic corrugation on the rate of diffusion of molecules on membranes. We find that part of the anisotropy reported by Smith et al. (1979, Proc. Natl. Acad. Sci. USA, 76:5641-5644) can be explained by the membrane nonplanarity, and we present the way of calculating this geometric factor

Diffusion of molecules on biological membranes of nonplanar form. A theoretical study.

Lateral mobility of molecules on cell membranes has been recently studied by fluorescence photobleaching recovery (FPR) techniques. The interpretation of these results in terms of diffusion along the membranes is based on the assumption that the surface is planar, although biological membranes may have blebs and microvilli. To study the effect of nonplanarity on the diffusion rate, the diffusion equation along curved surfaces was derived and was solved numerically for a "wavy" surface of the form A cos kx cos ky. Calculations show that for k = 10 pi micrometer-1 and a bleached spot of 1 micrometer in diameter, the time dependence of the intensity of fluorescence in the bleached spot depends on A at A less than 0.5 micrometer, while at higher values of A (a and 2 micrometer) the dependence is weak. If one calculates diffusion coefficients from FPR measurements and assumes that the membrane is planar, the resulting diffusion coefficient is not less than about half of the real one. Because of the tortuous shape of the spot boundary, increasing the microvilli length from 0.5 micrometer to 1 or 2 micrometer does not change the diffusion rates. These considerations are valid for times when the diffusion is dominated by molecules that were initially located close to the spot boundary