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Biomathematics - Mathematics of Biostructures and Biodynamics (Hardcover)
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Biomathematics - Mathematics of Biostructures and Biodynamics (Hardcover)
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This book presents new mathematics for the description of structure
and dynamics in molecular and cellular biology. On an exponential
scale it is possible to combine functions describing inner
organisation, including finite periodicity, with functions for
outside morphology into a complete definition of structure. This
mathematics is particularly fruitful to apply at molecular and
atomic distances. The structure descriptions can then be related to
atomic and molecular forces and provide information on structural
mechanisms. The calculations have been focussed on lipid membranes
forming the surface layers of cell organelles. Calculated surfaces
represent the mid-surface of the lipid bilayer. Membrane dynamics
such as vesicle transport are described in this new language.
Periodic membrane assemblies exhibit conformations based on the
standing wave oscillations of the bilayer, considered to reflect
the true dynamic nature of periodic membrane structures. As an
illustration the structure of an endoplasmatic reticulum has been
calculated. The transformation of such cell membrane assemblies
into cubosomes seems to reflect a transition into vegetative
states. The organisation of the lipid bilayer of nerve cells is
analyzed, taking into account an earlier observed lipid bilayer
phase transition associated with the depolarisation of the
membrane. Evidence is given for a new structure of the alveolar
surface, relating the mathematical surface defining the bilayer
organisation to new experimental data. The surface layer is
proposed to consist of a coherent phase, consisting of a
lipid-protein bilayer curved according to a classical surface - the
CLP surface. Without employing this new mathematics it would not be
possible to give an analytical description of this structure and
its deformation during the respiration cycle. In more general terms
this mathematics is applied to the description of the structure and
dynamic properties 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 biological structure and dynamics,
biomathematics, also provides significant new information in order
to understand the mechanisms governing shape of living
organisms.
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