By S. Andersson, K. Larsson, M. Larsson, M. Jacob
This publication 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 company, together with finite periodicity, with features for outdoor morphology right into a entire definition of constitution. This arithmetic is especially 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 outside layers of phone organelles. Calculated surfaces signify the mid-surface of the lipid bilayer. Membrane dynamics comparable to vesicle shipping are defined during this new language. Periodic membrane assemblies convey conformations in line with 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 cellphone membrane assemblies into cubosomes turns out to mirror a transition into vegetative states. The organization of the lipid bilayer of nerve cells is analyzed, making an allowance for 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 info. the skin layer is proposed to include a coherent section, together with a lipid-protein bilayer curved in response to a classical floor - the CLP floor. with no utilizing this new arithmetic it'll now not be attainable to offer an analytical description of this constitution and its deformation in the course of the breathing cycle. in additional basic 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 as a way to comprehend the mechanisms governing form of residing organisms.
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Additional info for Biomathematics
15 A piece of the D surface. 15, but with larger boundaries. The translation above corresponds to a phase shift from sine to cosine in the circular functions. We do the simplest, and most important, of the surfaces here. 14. 17. 18 and 19. 17 D surface from circular functions. 18 The IWP surface. 19 The gyroid surface. 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.
We have shown that the circular functions, or periodicity, is obtained by counting positive numbers from the algebra. We use the saddle mathematics from chapter 2 and describe hexagonal and tetragonal surfaces, and how they are formed from their rod packings. We can do it all by counting, but as a short-cut we use the trigonometry for the circular functions. For a description of symmetries we refer to appendix 6. 1 Non Cubic Surfaces In biology it is important to realise that cubic symmetry is by no means common.
The translation above corresponds to a phase shift from sine to cosine in the circular functions. We do the simplest, and most important, of the surfaces here. 14. 17. 18 and 19. 17 D surface from circular functions. 18 The IWP surface. 19 The gyroid surface. 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.
Biomathematics by S. Andersson, K. Larsson, M. Larsson, M. Jacob