Image Theory for Neumann Functions in the Prolate Spheroidal Geometry

Xue, Changfeng; Edmiston, Robert; Deng, Shuiquan

doi:10.1155/2018/7683929

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…It will be interesting to extend the analysis to the case of a spheroid or cylinder [38][39][40][41][42]. Since the main effect of confinement is a volume reduction, one can use the results for a three-dimensional cuboid to estimate the overall influence of confinement on protein synthesis rates, even for cells with a spheroid or cylindrical shape.…”

Section: Three-dimensional Cuboidmentioning

confidence: 99%

Modelling the effect of ribosome mobility on the rate of protein synthesis

et al. 2021

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Translation is one of the main steps in the synthesis of proteins. It consists of ribosomes that translate sequences of nucleotides encoded on mRNA into polypeptide sequences of amino acids. Ribosomes bound to mRNA move unidirectionally, while unbound ribosomes diffuse in the cytoplasm. It has been hypothesized that finite diffusion of ribosomes plays an important role in ribosome recycling and that mRNA circularization enhances the efficiency of translation, see e.g. Lodish et al. (Molecular cell biology, 8th edn, W.H. Freeman and Company, San Francisco, 2016). In order to estimate the effect of cytoplasmic diffusion on the rate of translation, we consider a totally asymmetric simple exclusion process coupled to a finite diffusive reservoir, which we call the ribosome transport model with diffusion. In this model, we derive an analytical expression for the rate of protein synthesis as a function of the diffusion constant of ribosomes, which is corroborated with results from continuous-time Monte Carlo simulations. Using a wide range of biological relevant parameters, we conclude that diffusion is not a rate limiting factor in translation initiation because diffusion is fast enough in biological cells. Graphic abstract

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Section: Three-dimensional Cuboidmentioning

confidence: 99%

Modelling the effect of ribosome mobility on the rate of protein synthesis

et al. 2021

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“…coordinate line, to imitate the line image for the sphere problem, but they still needed to correct for this by adding a surface charge on an ellipsoidal surface that encloses the point and line image. This image formulation is specialized for the prolate spheroid in [8]. A recent paper [9] suggested that the best image solution may be to use Sommerfeld images which are placed in a second copy of R 3 , attached at the surface.…”

Section: Introductionmentioning

confidence: 99%

Images of point charges in conducting ellipses and prolate spheroids

Majic

2020

Preprint

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An investigation into the exact forms of images of point charges in conducting spheroids. For a point source close the surface of a spheroid, the standard series solutions for the potential diverge in a region that encompasses the singularities -or equivalently the images -of the reflected potential inside the spheroid. Current image formulations in the literature consist of image point charges and line charges, but are also encompassed by a spheroid of surface charge. But in theory an image can always be found that does not require a closed surface charge; a more compact, reduced image system lies inside. We demonstrate this for a point charge on the axis of a prolate spheroid, uncovering the location and nature of the images by using different series expansions which converge in almost all space, right up to meet the singularity of the potential, exposing the reduced image. The image is found to lie on a line segment that includes the focal segment and extends somewhat further up the axis. A similar analysis is done for the point charge at the center of the spheroid, where the image is found to lie on an infinitely wide, flat sheet with a hole around the spheroid.

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“…For the non-rotational ellipsoid with Neumann boundary condition, the first attempt at finding an image solution is in [46], where they assumed a point image plus a curved line of image charge extending along a spheroidal coordinate line, but they still needed to correct for this by adding a surface charge on an ellipsoidal surface that encloses the point and line image. This image formulation is specialized for the prolate spheroid in [47].…”

Section: Conducting Spheroidmentioning

confidence: 99%

Electrostatic images and T-matrices for simple geometries

Majic¹

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<p>This thesis is concerned with electrostatic boundary problems and how their solutions behave depending on the chosen basis of harmonic functions and the location of the fundamental singularities of the potential. The first part deals with the method of images for simple geometries where the exact nature of the image/fundamental singularity is unknown; essentially a study of analytic continuation for Laplace's equation in 3 dimensions. For the sphere, spheroid and cylinder, new deductions are made on the location of the images of point charges and their linear or surface charge densities, by using different harmonic series solutions that reveal the image. The second part looks for analytic expressions for the T-matrix for electromagnetic scattering of simple objects in the low frequency limit. In this formalism the incident and scattered fields are expanded on an orthogonal basis such as spherical harmonics, and the T-matrix is the transformation between the coefficients of these series, providing the general solution of any electromagnetic scattering problem by a given particle at a given wavelength. For the spheroid, bispherical system and torus, the natural basis of harmonic functions for the geometry of the scatterer are used to determine T-matrix expressed in that basis, which is then transformed onto a basis of canonical spherical harmonics via the linear relationships between different bases of harmonic functions.</p>

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Image Theory for Neumann Functions in the Prolate Spheroidal Geometry

Cited by 4 publications

References 14 publications

Modelling the effect of ribosome mobility on the rate of protein synthesis

Modelling the effect of ribosome mobility on the rate of protein synthesis

Images of point charges in conducting ellipses and prolate spheroids

Electrostatic images and T-matrices for simple geometries

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