mathematical biology and theoretical biophysics of DNA

1 Introduction

Mathematical biology (also known as theoretical biology) is the study of biologicalprinciples and laws, together with the formulation of mathematical models– and also the logical and mathematical representation [3]– of complex biological systems at all levels of biological organization, from the quantum/molecular level to the physiological, systemic and the whole organism levels.

2 Mathematical biophysics

2.1 History

Mathematical biophysics has dominated for over half a century developments in mathematical biologyas theoretical or mathematical physicists have expanded their interests to applying mathematical andphysical concepts to studying living organisms and in repeated attempts to ‘define life itself’ [1, 28].

A prominent early example was the famous Erwin ’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 thedouble helical, molecular structures of A- and B- DNA crystals/paracrystals ([26, 9, 12, 25]) 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 athttp://www.kcl.ac.uk/schools/biohealth/graduate/taught/molbiophysics/King’s College in London, (see also the websites abouthttp://www.kcl.ac.uk/college/history/people/franklin_wilkins.htmlRosalind Franklin and Maurice Wilkins), and the last two researchers working athttp://www.phy.cam.ac.uk/The Cavendish Laboratory of the University of Cambridge(UK), (see alsohttp://www.admin.cam.ac.uk/news/dp/2004072903related news at, and also thehttp://www.pom.cam.ac.uk/initiative.htmlnew Biology and Physics of Medicine Laboratory athttp://www.pom.cam.ac.uk/initiative.htmlThe Cavendish). With the notable exception of Rosalind Franklin and Robert Rosen, the other three mathematical and experimental biophysicists becamehttp://nobelprize.org/nobel_prizes/medicine/laureates/1962/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 ([26, 9, 12]), 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 [27], as well as a recent update review [25] and earlier generalizations [14, 15]), such as the http://www.phy.cam.ac.uk/research/bss/molbiophysics.phpDNA G-quadruplexes that can control gene transcription and translation- especially in cancers.

Erwin ’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 equations the“Hamiltonian operator” (http://planetmath.org/HamiltonianOperatorOfAQuantumSystem) - 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, Schrödinger 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.

3 Recent developments

Robert Rosen (1937-1998) was a prominent relational biologist who completed his PhD studies withNicolas Rashevsky, the former Head of the Committee for Mathematical Biology at theUniversity 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 categories of sets called categories of metabolic–replication systems, orcategory of $(M,R)$-systems (http://planetmath.org/CategoryOfMRSystems3).

To quote Robert Rosen:

“Ironically, the idea that life requires an explanation is a relatively new one. To the ancients life simply 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 reductionto genes, nucleic acids, enzymes and small biomolecules’, i.e. some sort of ordered ‘bag’ of biochemicals mostly filledwith 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 characterizedby flows–relational/material, energetic and informational processes– perhaps closer to the injunction by Heraclitus of “panta rhei”-everything flows, but with the very important addition that life flows in a uniquely complex relational pattern that is observed only in living systems, thus perhaps uniquely defining Life as a special, super-complex process ([8]. 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.