Biomathematics: Mathematics of Biostructures and Biodynamics - download pdf or read online

By S. Andersson, K. Larsson, M. Larsson, M. Jacob

ISBN-10: 0444502734

ISBN-13: 9780444502735

This publication offers new arithmetic for the outline of constitution and dynamics in molecular and mobile biology. On an exponential scale it's attainable to mix capabilities describing internal business enterprise, together with finite periodicity, with services for out of doors morphology right into a whole definition of constitution. This arithmetic is very fruitful to use at molecular and atomic distances. The constitution descriptions can then be relating to atomic and molecular forces and supply info on structural mechanisms. The calculations were focussed on lipid membranes forming the skin layers of cellphone organelles. Calculated surfaces symbolize the mid-surface of the lipid bilayer. Membrane dynamics reminiscent of vesicle delivery are defined during this new language. Periodic membrane assemblies convey conformations in response to the status wave oscillations of the bilayer, thought of to mirror the genuine dynamic nature of periodic membrane buildings. for instance the constitution of an endoplasmatic reticulum has been calculated. The transformation of such mobile membrane assemblies into cubosomes turns out to mirror a transition into vegetative states. The employer of the lipid bilayer of nerve cells is analyzed, taking into consideration an previous saw lipid bilayer section transition linked to the depolarisation of the membrane. proof is given for a brand new constitution of the alveolar floor, referring to the mathematical floor defining the bilayer business enterprise to new experimental info. the skin layer is proposed to include a coherent section, along with a lipid-protein bilayer curved in keeping with a classical floor - the CLP floor. with no utilizing this new arithmetic it will no longer be attainable to offer an analytical description of this constitution and its deformation in the course of the respiratory cycle. in additional common phrases this arithmetic is utilized to the outline of the constitution and dynamic houses of motor proteins, cytoskeleton proteins, and RNA/DNA. On a macroscopic scale the motions of cilia, sperm and flagella are modelled. This mathematical description of organic constitution and dynamics, biomathematics, additionally presents major new info so one can comprehend the mechanisms governing form of residing organisms.

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Extra info for Biomathematics: Mathematics of Biostructures and Biodynamics

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1 cos A + cos B + cos C + cos E + cos D... = 0, one term, cosA, is an infinite number of parallel planes. 2. ) = 0 Similarly the terms cosA+cosB, or cosA+cosB+cosC, are two sets of intersecting planes that via the addition of a constant become parallel rod systems. ) = 0. 4 To transform a plane or rod system into a surface, N starts as a small number. We illustrate this with examples, and start with the P-surface. 5. 5. 5. 5. 5. 5. 8, and 1. A=I is of course the P-surface. For lower A:s, curvature is given to the plane and gradually, as A increases, the planes are joined via catenoids and the transformation to the P-surface is obvious.

18 and 19. 17 D surface from circular functions. 18 The IWP surface. 19 The gyroid surface. 17. 20, which build the periodic Neovius surface [4]. 21. We see that this is really four cube comers that meet in a non-intersecting figure. 22. 20 Simple multiplication and addition of variables gives a saddle. 21 but with larger boundaries. 18 adds the planes of the D surface with those of the surface of P. These trigonometric equations are the same as those originally derived by von Schnering and Nesper [4].

12. 16. 13 The H surface. 14 Projection of the H surface along c. 15 The H surface at different of c/a. 15. G. von Schnering and R. Nesper, Z. Phys. B - Condensed Matter 83, 407 (1991). M. Jacob and S. Andersson, THE NATURE OF MATHEMATICS AND THE MATHEMATICS OF NATURE, Elsevier, 1998. A. Burkhardt, U. G. von Schnering and A. Savin, Z. allg. Chem. 619 (1993) 437. S. Lidin, and S. T. Hyde, J. Phys. France 48, 15 (1987). S. Lidin, J. Phys. France 49, 421 (1988). anorg. This Page Intentionally Left Blank Nodal Surfaces, Planes, Rods and Transformations 47 4 Nodal Surfaces, Planes, Rods and Transformations In the actual three-dimensional case we have nodal surfaces, nodal planes and spheres, instead of nodal lines [Bom,1].

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Biomathematics: Mathematics of Biostructures and Biodynamics by S. Andersson, K. Larsson, M. Larsson, M. Jacob

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