Biomathematics: mathematics of biostructures and biodynamics

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Titel: Biomathematics : mathematics of biostructures and biodynamics

Enthält: Front Cover; Biomathematics: Mathematics of Biostructures and Biodynamics; Copyright Page; Contents; Chapter 1. Introduction; References; Chapter 2. Counting, Algebra and Periodicity - the Roots of Mathematics are the Roots of Life; 2.1 Counting and Sine; 2.2 Three Dimensions; Planes and Surfaces, and Surface Growth; 2.3 The Growth of Nodal Surfaces - Molecules and Cubosomes; References 2; Chapter 3. Nodal Surfaces of Tetragonal and Hexagonal Symmetry, and Rods; 3.1 Non Cubic Surfaces; 3.2 Tetragonal Nodal Surfaces and their Rod Structures
3.3 Hexagonal Nodal Surfaces and their Rod StructuresReferences 3; Chapter 4. Nodal Surfaces, Planes, Rods and Transformations; 4.1 Cubic Nodal Surfaces; 4.2 Nodal Surfaces and Planes; 4.3 Cubic Nodal Surfaces and Parallel Rods; 4.4 Transformations of Nodal Surfaces; References 4; Chapter 5. Motion in Biology; 5.1 Background and Essential Functions; 5.2 The Control of Shape - the Natural Exponential or cosh in 3D; 5.3 The Gauss Distribution (GD) Function and Simple Motion; 5.4 More Motion in 3D; References 5; Chapter 6. Periodicity in Biology - Periodic Motion; 6.1 The Hermite Function
6.2 Flagella- Snake and Screw Motion6.3 Periodic Motion with Particles in 2D or 3D; 6.4 Periodic Motion with Rotation of Particles in 2D; References 6; Chapter 7. Finite Periodicity and the Cubosomes; 7.1 Periodicity and the Hermite Function; 7.2 Cubosomes and the Circular Functions; 7.3 Cubosomes and the GD-Function - Finite Periodicity and Symmetry P; 7.4 Cubosomes and the GD-Function - Symmetry G; 7.5 Cubosomes and the GD Function - Symmetry D; 7.6 Cubosomes and the Handmade Function; References 7
Chapter 8. Cubic Cell Membrane Systems/Cell Organelles and Periodically Curved Single Membranes8.0 Introduction; 8.1 Cubic Membranes; 8.2 The Endoplasmatic Reticulum; 8.3 Protein Crystallisation in Cubic Lipid Bilayer Phases and Cubosomes - Colloidal Dispersions of Cubic Phases; 8.4 From a Minimal Surface Description to a Standing Wave Dynamic Model of Cubic Membranes; 8.5 Periodical Curvature in Single Membranes; References 8; Chapter 9. Cells and their Division - Motion in Muscles and in DNA; 9.1 The Roots and Simple Cell Division; 9.2 Cell Division with Double Membranes
9.3 Motion in Muscle Cells9.4 RNA and DNA Modelling; References 9; Chapter 10. Concentration Gradients, Filaments, Motor Proteins and again- Flagella; 10.1 Background and Essential Functions; 10.2 Filaments; 10.3 Microtubulus and Axonemes; 10.4 Motor Proteins and the Power Stroke; 10.5 Algebraic Roots Give Curvature to Flagella; References 10; Chapter 11. Transportation; 11.1 Background - Examples of Docking and Budding with Single Plane Layers, and Other Simple Examples; 11.2 Docking and Budding with Curved Single Layers; 11.3 Transport Through Double Layers; References 11
Chapter 12. Icosahedral Symmetry, Clathrin Structures, Spikes, Axons, the Tree, and Solitary Waves

Beteiligte: Andersson, Sten [Sonstige Person, Familie und Körperschaft]

Erschienen: Amsterdam; New York: Elsevier, 1999
Online-Ausg.

Ausgabe: 1st ed

Umfang: Online Ressource (525 p.); ill

Sprache: Englisch

ISBN: 0444502734; 9780080528076; 0080528074; 9780444502735; 9786611050023; 6611050027

Schlagwörter: Molecular biology Mathematics ; Cytoskeleton Mathematics ; Cells Morphology Mathematics ; Biologie moléculaire Mathématiques ; Biomathématiques ; Cytosquelette Mathématiques ; Cellules Morphologie Mathématiques ; Biologia molecular ; Biomatemática ; Citoesqueleto ; Biomathematics ; Mathematics ; Cells cytology ; Molecular Biology ; Cytoskeleton ; Electronic books ; Molecular biology ; Mathematics ; SCIENCE ; Life Sciences ; Molecular Biology ; Math�ematiques ; Biologie mol�eculaire - Math�ematiques ; Biomath�ematiques ; Biomatem�atica ; Cytosquelette - Math�ematiques ; Cellules - Morphologie - Math�ematiques

Art der Reproduktion: Online-Ausg.

Entstehung:

Anmerkungen: Includes bibliographical references and index. - Description based on print version record

Beschreibung: Chapter headings: Introduction. Counting, algebra and periodicity -- the roots of mathematics are the roots of life. Nodal surfaces of tetragonal and hexagonal symmetry, and rods. Nodal surfaces, planes, rods and transformations. Motion in biology. Periodicity in biology -- periodic motion. Finite periodicity and the cubosomes. Cubic cell membrane systems/cell organelles. Cells and their division -- motion in muscles and in DNA. Concentration gradients, filaments, motor proteins and again -- flagella. Transportation. Icosahedral symmetry, chathrin structures, spikes, axons, the tree, and solitary waves. Axon membranes and synapses -- a role of lipid bilayer structure in nerve signals. The lung surface structure and respiration. Epilogue. Appendices

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

Biomathematics - [1st ed]

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