Biomathematics: Mathematics of Biostructures and Biodynamics by S. Andersson, K. Larsson, M. Larsson, M. Jacob
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's attainable to mix capabilities describing internal 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 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 mobilephone organelles. Calculated surfaces signify the mid-surface of the lipid bilayer. Membrane dynamics equivalent to vesicle shipping are defined during this new language. Periodic membrane assemblies convey conformations according to the status wave oscillations of the bilayer, thought of to mirror the real dynamic nature of periodic membrane buildings. as an example 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 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. proof is given for a brand new constitution of the alveolar floor, pertaining to the mathematical floor defining the bilayer organization to new experimental facts. the skin layer is proposed to encompass a coherent part, including a lipid-protein bilayer curved in line with a classical floor - the CLP floor. with no applying this new arithmetic it can no longer be attainable to provide an analytical description of this constitution and its deformation throughout the respiratory cycle. in additional normal 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 details so as to comprehend the mechanisms governing form of residing organisms.
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Additional resources for Biomathematics: Mathematics of Biostructures and Biodynamics
17. 20, which build the periodic Neovius surface . 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 . 22 Going circular with the monkey saddle gives the Neoviussurface. References 2 Pythagoras from Georg D.
The DNA structure is one case, the apatite structure that is the inorganic part of bones and teeth is another. The filaments do also represent very important examples. 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 .
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].