By S. Andersson, K. Larsson, M. Larsson, M. Jacob
This booklet 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 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 on the topic of atomic and molecular forces and supply details on structural mechanisms. The calculations were focussed on lipid membranes forming the outside layers of phone organelles. Calculated surfaces characterize the mid-surface of the lipid bilayer. Membrane dynamics comparable to vesicle shipping 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 telephone membrane assemblies into cubosomes turns out to mirror a transition into vegetative states. The employer of the lipid bilayer of nerve cells is analyzed, making an allowance for an past saw lipid bilayer section transition linked to the depolarisation of the membrane. proof is given for a brand new constitution of the alveolar floor, concerning the mathematical floor defining the bilayer supplier to new experimental info. the outside layer is proposed to encompass a coherent section, which includes a lipid-protein bilayer curved in keeping with a classical floor - the CLP floor. with out utilizing this new arithmetic it'll now not be attainable to provide an analytical description of this constitution and its deformation through the respiratory cycle. in additional common phrases this arithmetic is utilized to the outline of the constitution and dynamic homes 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 as a way to comprehend the mechanisms governing form of dwelling organisms.
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Additional info for Biomathematics: Mathematics of Biostructures and Biodynamics
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]. We show how the cubic nodal surfaces are derived from the permutation of variables in space.
Motion is to its nature anisotropic. The structure of the sacromere is hexagonal. A saddle is by itself non-cubic and a good starting point. We will describe a way to derive tetragonal and hexagonal surfaces. 2 Tetragonal Nodal Surfaces and their Rod Structures We have shown before that there is no obvious link or path between 3D non-intersecting rod systems and the fundamental surfaces . However there is a link between one parallel rod system and the surfaces, and we shall in the next chapter show simple transformations.
Andersson, THE NATURE OF MA THEMA TICS AND THE MATHEMATICS OF NATURE, Elsevier, 1998. A. Burkhardt, U. G. von Schnering and A. Savin, Z. anorg. allg. Chem. 619 (1993) 437. G. von Schnering and R. Nesper, Z. Phys. B - Condensed Matter 83, 407 (1991). 27 Nodal Surfaces of Tetragonal and Hexagonal Symmetry, and Rods 3 Nodal Surfaces of Symmetry, and Rods Tetragonal and Hexagonal There are many ways to skin a cat. We have shown that the circular functions, or periodicity, is obtained by counting positive numbers from the algebra.