PlanetPhysics/Mathematical Biology and Theoretical Biophysics

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Introduction
Mathematical Biology (also known as theoretical biology ) is the study of biological principles and laws, together with the formulation of mathematical models-- and also the logical and mathematical representation -- of complex biological systems at all levels of biological organization, from the quantum/molecular level to the physiological, systemic and the whole organism levels.

History
Mathematical biophysics has dominated for over half a century developments in mathematical biology as theoretical or mathematical physicists have expanded their interests to applying mathematical and physical concepts to studying living organisms and in repeated attempts to `define life itself'.

A prominent early example was the famous Erwin Schr\"odinger's book (published in 1945 in Cambridge, UK) entitled suggestively ``What is Life?", and that was perhaps too critically re-evaluated a decade ago by Robert Rosen. This interesting and concise book appears to have inspired a decade later the discovery of the double helical, molecular structures of A- and B- DNA crystals/paracrystals by Maurice Wilkins, Rosalind Franklin, Francis Crick and James D. Watson, with the first two (bio)physical chemists working at that time with X-ray diffraction of DNA crystals at King's College in London, (see also the websites about Rosalind Franklin and Maurice Wilkins), and the last two researchers working at The Cavendish Laboratory of the University of Cambridge(UK), (see also related news, and also the new Biology and Physics of Medicine Laboratory at The Cavendish). With the notable exception of Rosalind Franklin and Robert Rosen, the other three mathematical and experimental biophysicists became Nobel Laureates in Physiology and Medicine.

Notably DNA configurations in vivo include a significant amount of dynamic, partial disorder and may be defined at best as paracrystals , a fact which has important consequences for functional biology and in vivo  molecular genetics. Moreover, other structures (such as Z-DNA) were discovered in certain organisms, and other configurations were found under physiological conditions (see, for example, the excellent, DNA structure representations rendered by computers on pp. 852-854 in Voet and Voet, 1995, as well as a recent update review and earlier generalizations ), such as the \htmladdnormallink{DNA G-quadruplexes that can control gene transcription and translation - especially in cancers}{http://www.phy.cam.ac.uk/research/bss/molbiophysics.php}.

Erwin Schr\"odinger's fundamental contribution to quantum mechanics preceded the others discussed in the previous paragraph by more than two decades when he formulated the fundamental equations of Quantum Mechanics which bear his name, and modestly called the operator appearing in the Schr\"odinger equations the "Hamiltonian operator" - a term universally employed in the Theoretical and mathematical physics literature that now bears the name of the distinguished Irish physicist, Sir William Rowan Hamilton. Hamilton is now also considered to be one of the world's greatest mathematicians (see for example, his introduction of the concept of quaternions in 1835), and he was also the first foreign Member to be elected to the US National Academy of Sciences in 1865. Subsequently, Schr\"odinger was awarded a Nobel Prize for his fundamental, theoretical (and mathematical) physics contribution by the Stockholm Nobel Committee, and soon thereafter in 1941 became the Director of the (Dublin) Institute for Advanced Studies (DIAS) in Ireland, instead of joining Albert Einstein on the staff at Princeton's Institute for Advanced Studies.

Recent developments
Robert Rosen (1937-1998) was a prominent relational biologist who completed his PhD studies with Nicolas Rashevsky, the former Head of the Committee for Mathematical Biology at the University of Chicago, USA, with a Thesis on relational biology (Metabolic-Replication Systems, or $$(M,R)$$-systems). His publications (see bibliography) include an impressive number of volumes and textbooks on Theoretical Biology, Relational Biology, Anticipation, Ageing, Complex Dynamical Systems in Biology, (Bio) Chemical Morphogenesis and Quantum Genetics. He also reported in 1958 the first abstract representation of living organisms in special, small \htmladdnormallink{categories {http://planetphysics.us/encyclopedia/Cod.html} of sets} called categories of metabolic--replication systems, or category of $$(M,R)$$-systems.

To quote Robert Rosen:

"Ironically, the idea that life requires an explanation is a relatively new one. To the ancients life simply \emph {was" ; it was a given; a first principle...}

One might add also that to most biologists Life is still a given, but something that might be `explained by reduction to genes, nucleic acids, enzymes and small biomolecules', i.e. some sort of ordered 'bag' of biochemicals mostly filled with aqueous solutions inside selective biomembranes, etc. Robert Rosen's viewpoint was quite different from this: he saw life as a dynamic, relational pattern in categories of metabolic-repair (open) systems characterized by flows--relational/material, energetic and informational processes-- perhaps closer to the injunction by Heraclitus of \emph {"panta rhei"-everything flows}, but with the very important addition that life flows in a \emph {uniquely complex relational pattern} that is observed only in living systems, thus perhaps uniquely defining Life as a special, super-complex process  ( . Once life stops-- even though the material structure is still there-- the essential relational flow (related to energetic, informational as well as material) patterns are gone forever, with the possible exceptions of the `raising from the dead in the Egyptian myths about Osiris', and also in certain well-known sections of the New Testament.