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

This booklet offers new arithmetic for the outline of constitution and dynamics in molecular and mobile biology. On an exponential scale it really is attainable to mix services describing internal corporation, together with finite periodicity, with features 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 with regards to atomic and molecular forces and supply details on structural mechanisms. The calculations were focussed on lipid membranes forming the outside layers of telephone organelles. Calculated surfaces characterize the mid-surface of the lipid bilayer. Membrane dynamics resembling vesicle delivery are defined during this new language. Periodic membrane assemblies show conformations in keeping with the status wave oscillations of the bilayer, thought of to mirror the real 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 enterprise of the lipid bilayer of nerve cells is analyzed, bearing in mind an past saw lipid bilayer part transition linked to the depolarisation of the membrane. facts is given for a brand new constitution of the alveolar floor, referring to the mathematical floor defining the bilayer organization to new experimental information. the skin layer is proposed to include a coherent section, along with a lipid-protein bilayer curved in accordance with a classical floor - the CLP floor. with out utilising this new arithmetic it should now not be attainable to provide an analytical description of this constitution and its deformation through the breathing 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 offers major new info which will comprehend the mechanisms governing form of dwelling organisms.

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But we shall do just one more tetragonal and use the saddle concept again. 12. 11 The rods of CLP. 12 Four intersecting planes. 13 Periodicity also gives two intersecting planes. 13. 14. 14 The saddle from four intersecting planes. 15 Periodicity shows the rod structure. The rods are liberated with a constant, as before, and we continue to make them connect by catenoids with a z term as in equation. 12. 15. 12 Careful inspection of this surface reveals that it is really composed of units of the first tetragonal surface, twinned in a cyclic way.

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. ) = 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.

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