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

This ebook provides new arithmetic for the outline of constitution and dynamics in molecular and mobile biology. On an exponential scale it really is attainable to mix features describing internal supplier, together with finite periodicity, with services for outdoor 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 on the topic of atomic and molecular forces and supply details on structural mechanisms. The calculations were focussed on lipid membranes forming the skin layers of cellphone organelles. Calculated surfaces characterize the mid-surface of the lipid bilayer. Membrane dynamics similar to vesicle delivery are defined during this new language. Periodic membrane assemblies convey conformations in keeping with the status wave oscillations of the bilayer, thought of to mirror the genuine dynamic nature of periodic membrane constructions. 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 company of the lipid bilayer of nerve cells is analyzed, bearing in mind an previous saw lipid bilayer part transition linked to the depolarisation of the membrane. facts is given for a brand new constitution of the alveolar floor, bearing on the mathematical floor defining the bilayer employer to new experimental information. the outside layer is proposed to encompass a coherent part, which includes a lipid-protein bilayer curved in response to a classical floor - the CLP floor. with out using this new arithmetic it'll now not be attainable to provide an analytical description of this constitution and its deformation throughout 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 details on the way to comprehend the mechanisms governing form of dwelling organisms.

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5 Projection of the gyroid along the a-axis. 7 Projection of D along a cubic space diagonal. 6 Projection of the gyroid along a space diagonal. 8 Projection of D along a cubic face diagonal. 4. 9 but with larger boundaries. 2 Nodal Surfaces and Planes The w a y we describe the nodal surfaces is particularly useful to study some of their properties. 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.

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]. We show how the cubic nodal surfaces are derived from the permutation of variables in space. We study how parallel planes transform into surfaces.

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. 6. 2. 7 we demonstrate that it is possible to use a plane that does not belong to the surface. These mathematics are used to describe the structural changes in the Endoplasmic Reticulum in chapter 8. 6. 6. 6. 6. 6. 7. 7. 7. 7. We redo the calculations with the D-surface and the plane, cos(x+y+z).