By S. Andersson, K. Larsson, M. Larsson, M. Jacob
This ebook 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 features describing internal corporation, together with finite periodicity, with capabilities 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 mobilephone organelles. Calculated surfaces symbolize the mid-surface of the lipid bilayer. Membrane dynamics comparable to vesicle shipping are defined during this new language. Periodic membrane assemblies express conformations according to the status wave oscillations of the bilayer, thought of to mirror the real dynamic nature of periodic membrane buildings. for example 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 organization of the lipid bilayer of nerve cells is analyzed, considering an past 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 corporation to new experimental information. the skin layer is proposed to encompass a coherent part, which includes a lipid-protein bilayer curved in accordance with a classical floor - the CLP floor. with out making use of this new arithmetic it can no longer 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 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 for you to comprehend the mechanisms governing form of residing organisms.
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Additional resources for Biomathematics: Mathematics of Biostructures and Biodynamics
8 Addition of a z-term gives catenoids between rods. 9 The honeycomb surface. 10. 11. 10 Hexagonal sine gives intersecting planes. 11 Sine and the rods. 12a. 12a With a z-term there are catenoids between rods. This surface, and the next one shown below, are of interest in consideration of hexagonal structures of membrane lipids and cell membranes. The common liquid-crystalline phase is termed reverse hexagonal (HII). It is two-dimensional and the lipid bilayer centre has a honeycomb structure. However, the possibility of the occurrence of hexagonal structures free from self-intersections, so that one bilayer can form the whole phase, should be kept in mind.
2. 1. 1 for zero constant. 2. 1 Intersecting planes. 2 Tetragonal rod packing. 3. 4. This surface is topologically right between the Psurface and the hexagonal H-surface (shown below). 6. 3 Simple tetragonal surface. 4 The simple tetragonal surface chosen to show relationships with the P- surface. 5 Different projection of the tetragonal surface. 6 The simple tetragonal surface for zero constant. 7 CLP saddle. 8 Different projection of the CLP saddle. 5. The Weierstrass parametrisation of this minimal surface was first derived by Lidin and Hyde .
2. 1 Hexagonally parallel rods along a cubic space diagonal. 2 Projection along the cubic space diagonal.