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 e-book provides new arithmetic for the outline of constitution and dynamics in molecular and mobile biology. On an exponential scale it's attainable to mix services describing internal organization, 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 relating to atomic and molecular forces and supply details 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 similar to vesicle delivery are defined during this new language. Periodic membrane assemblies convey conformations in response to the status wave oscillations of the bilayer, thought of to mirror the real dynamic nature of periodic membrane constructions. for example the constitution of an endoplasmatic reticulum has been calculated. The transformation of such mobilephone membrane assemblies into cubosomes turns out to mirror a transition into vegetative states. The supplier of the lipid bilayer of nerve cells is analyzed, taking into consideration 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, concerning the mathematical floor defining the bilayer supplier to new experimental info. the skin layer is proposed to include a coherent section, which include a lipid-protein bilayer curved in accordance with a classical floor - the CLP floor. with out utilizing this new arithmetic it should no longer be attainable to offer 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 presents major new info with a purpose to comprehend the mechanisms governing form of dwelling organisms.

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Sample text

A corresponding hexagonal coordinate system would need four planes. In crystallography such a system is used for this type of symmetry. 2. 3 and 4 show the same monkey saddle but with larger boundaries. 1 Three intersecting planes. 2 Monkey saddle. 3 The monkey saddle with larger boundaries. 4 Different projection of the monkey saddle. 5 Periodic hexagonal planes with cosine. 5. 7, where the latter is the honeycomb packing. 6 Cosine and subtracting a constant gives hexagonal packing of cylinders.

17 Different projection reveals the twin character of the structure. 3 Hexagonal Nodal Surfaces and their Rod Structures The hexagonal symmetry is common in life as the building principle for apatite, in rod systems, and in the arrangements of giant molecules. It is also essential for the description of muscle contraction which we will show below. The best packing for rods is the hexagonal and we derive this again from parallel planes. For the simplest forms of cubic or tetragonal structures we had three intersecting planes after the Cartesian coordinate system.

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.

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