mathematical biology and theoretical biophysics of DNA

mathematical biology and theoretical biophysics of DNA

1

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

[

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 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’

[

1

,

28

]

.

A prominent early example was the famous Erwin

S

⁢

c

⁢

h

⁢

r

⁢

ö

⁢

d

⁢

i

⁢

n

⁢

g

⁢

e

⁢

r

’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 (

[

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 at

http://www.kcl.ac.uk/schools/biohealth/graduate/taught/molbiophysics/

King’s College in London, (see also the websites about

http://www.kcl.ac.uk/college/history/people/franklin_wilkins.html

Rosalind Franklin and Maurice Wilkins), and the last two researchers working at

http://www.phy.cam.ac.uk/

The Cavendish Laboratory of the University of Cambridge(UK), (see also

http://www.admin.cam.ac.uk/news/dp/2004072903

related news at, and also the

http://www.pom.cam.ac.uk/initiative.html

new Biology and Physics of Medicine Laboratory at

http://www.pom.cam.ac.uk/initiative.html

The Cavendish). With the notable exception of Rosalind Franklin and Robert Rosen, the other three mathematical and experimental biophysicists became

http://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.php

DNA G-quadruplexes that can control gene transcription and translation
- especially in cancers.

Erwin

S

⁢

c

⁢

h

⁢

r

⁢

ö

⁢

d

⁢

i

⁢

n

⁢

g

⁢

e

⁢

r

’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

S

⁢

c

⁢

h

⁢

r

⁢

ö

⁢

d

⁢

i

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n

⁢

g

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e

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r

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 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

categories of sets

called

categories

of metabolic–replication systems

, or
category 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

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

“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.

References

1

Erwin Schroedinger.1945.

What is Life?

. Cambridge University Press: Cambridge (UK).

2

Nicolas Rashevsky.1954,

Topology

and life: In search of general mathematical principles in
biology and sociology,

Bull. Math. Biophys.

16: 317-348.

3

Nicolas Rashevsky. 1965. Models and Mathematical Principles in Biology. In: Waterman/Morowitz,

Theoretical and Mathematical Biology

, pp. 36-53.

4

Rosalind E. Franklin and R.G. Gosling. 1953. Evidence for 2-chain helix in crystalline structure
of sodium deoxyribonucleate (DNA).

Nature

177: 928-930.

5

Wilkins, M.H.F. et al. 1953. Helical structure of crystalline deoxypentose nucleic acid (DNA).

Nature

172: 759-762.

6

Francis H.C. Crick. 1953. Fourier transform of a coiled coil.

Acta Cryst

. 6: 685-687

7

H. R. Wilson. 1966.

Diffraction of X-rays by Proteins, Nucleic Acids and Viruses

.
London: Arnold.

8

I. C. Baianu, J. F. Glazebrook, R. Brown and G. Georgescu.: Complex Nonlinear

Biodynamics

in Categories,

Higher dimensional Algebra

and Łukasiewicz-Moisil Topos:

Transformation

of Neural, Genetic and Neoplastic Networks,

Axiomathes

,

16

: 65-122(2006).

http://www.bangor.ac.uk/ mas010/pdffiles/Axio7complx_Printedk7_v17p223_fulltext.pdf

available here as PDF

9

I.C. Baianu. 1974. Ch.4 in

Structural Studies by X-ray Diffraction and Electron Microscopy of Erythrocite and Bacterial Plasma Membranes

. PhD Thesis, London: a University of London Library publication.

10

Baianu, I.C.: 1977, A Logical Model of Genetic Activities in Łukasiewicz

Algebras

: The Non-linear Theory.

Bulletin of Mathematical Biology

,

39

: 249-258.

11

I.C. Baianu. 1978. X-ray Scattering by Partially Disordered Membrane Lattices.

Acta Crystall

.

A34

: 731-753. (

paper contributed from The Cavendish Laboratory, Cambridge in 1979

).

12

I.C. Baianu. 1980. Structural Order and Partial Disorder in Biological Systems.

Bull. Math. Biol.

, 42: 186-191.
(

paper contributed from The Cavendish Laboratory, Cambridge in 1979

).

13

I. C. Baianu, C. Critchley, Govindjee, AND H. S. Gutowsky. 1984.
NMR study of chloride ion interactions with thylakoid membranes

Proced. Natl. Acad. Sci. USA (Biophysics)

., Vol. 81, pp. 3713–3717, June 1984,
(Key words: photosynthesis/oxygen evolution/chloride binding/chlorine–35/halophytes).

14

Baianu, I. C.: 1986-1987a, Computer Models and

Automata Theory

in Biology and Medicine., in M. Witten (ed.),

Mathematical Models in Medicine

, vol. 7., Ch.11 Pergamon Press, New York, 1513 -1577;
available downloads as:

CERN Preprint No. EXT-2004-072

-

http://doe.cern.ch//archive/electronic/other/ext/ext-2004-072.pdf

CERN Preprint as PDF, or

http://en.scientificcommons.org/1857371

as external html document .

15

Baianu, I. C.: 1987b, Molecular Models of Genetic and Organismic Structures, in

Proceed. Relational Biology Symp.

Argentina;

http://doc.cern.ch/archive/electronic/other/ext/extusers/2004
67/MolecularModels-ICB3.doc

CERN Preprint No.EXT-2004-067.

16

Baianu, I. C.: 1983,

Natural Transformation

Models in Molecular Biology., in

Proceedings of the SIAM Natl. Meet

., Denver,CO.;

http://cogprints.org/3675/

Eprint: and

http://cogprints.org/3675/0l/Naturaltransfmolbionu6.pdf

html document.

17

Baianu, I.C.: 1984, A Molecular-Set-Variable Model of Structural and Regulatory Activities in Metabolic and

Genetic Networks

,

FASEB Proceedings

43

, 917.

18

Baianu, I.C.: 2004a. Łukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models (2004). Eprint. Cogprints–Sussex Univ.

19

Baianu, I.C.: 2004b Łukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamics). CERN Preprint EXT-2004-059.

Health Physics and Radiation Effects

(June 29, 2004).

20

Baianu, I. C., Glazebrook, J. F. and G. Georgescu: 2004, Categories of

Quantum Automata

and N-Valued Łukasiewicz Algebras in

Relation

to Dynamic Bionetworks,

(M,R)

–Systems and Their Higher Dimensional Algebra,

http://www.ag.uiuc.edu/fs401/QAuto.pdf

Abstract and Preprint of Report as PDF or
as

http://www.medicalupapers.com/quantum+automata+math+categories+baianu/

an html document.

21

Baianu, I. C.: 2004b, Quantum Interactomics and Cancer Mechanisms,

http: bioline.utsc.utoronto.ca/archive/00001978/01/

Quantum Interactomics In Cancer--Sept13k4E-- cuteprt.pdf

Preprint No. 00001978.

22

Baianu, I. C.: 2006, Robert Rosen’s Work and Complex Systems Biology,

Axiomathes

16

(1–2):25–34.

23

Baianu I. C., Brown R., Georgescu G. and J. F. Glazebrook: 2006, Complex Nonlinear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz-Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks.,

Axiomathes

,

16

Nos. 1-2: 65-122.

24

Baianu, I.C., R. Brown and J.F. Glazebrook. : 2007,

Categorical Ontology

of Complex Spacetime Structures: The Emergence of Life and Human Consciousness,

Axiomathes

,

17

: 35-168.

25

Baianu, I.C. et al. 2009.

http://planetphysics.org/?op=getobj&from=books&id=220

“DNA Molecular Structure, Dynamics and Spectroscopy.” (Free GNUL download.)

26

R. Hosemann and S. N. Bagchi. 1962.

Direct

Analysis

of Diffraction by Matter

. Amsterdam: North Holland.

27

D. Voet and J.G. Voet. 1995.

Biochemistry

. 2nd Edition, New York, Chichester, Brisbone, Toronto,
Singapore: J. Wiley and Sons, INC., 1,361 pages, over 3,000 high-resolution molecular models in color – (

an excellently illustrated textbook

)

28

Robert Rosen. 1997 and 2002.

Essays on Life Itself

.

29

Rosen, R.: 1958a, A Relational Theory of Biological Systems

Bulletin of Mathematical Biophysics

20

: 245-260.

30

Rosen, R.: 1958b, The Representation of Biological Systems from the Standpoint of the Theory of Categories.,

Bulletin of Mathematical Biophysics

20

: 317-341.

31

Rosen, R. 1960. A quantum-theoretic approach to genetic problems.

Bulletin of Mathematical Biophysics

22: 227-255.

32

Rosen, R.: 1987, On

Complex Systems

,

European Journal of Operational Research

30

, 129-134.

33

Rosen,R. 1970,

Dynamical Systems Theory in Biology

. New York: Wiley Interscience.

34

Rosen,R. 1970,

Optimality Principles in Biology

, New York and London: Academic Press.

35

Rosen,R. 1978,

Fundamentals of Measurement and Representation of Natural Systems

, Elsevier Science Ltd,

36

Rosen,R. 1985,

Anticipatory Systems: Philosophical, Mathematical and Methodological

Foundations

. Pergamon Press.

37

Rosen,R. 1991,

Life Itself: A Comprehensive Inquiry into the Nature, Origin, and Fabrication of Life

, Columbia University Press

38

Ehresmann, C.: 1984,

Oeuvres complètes et commentées: Amiens, 1980-84

, edited and commented
by Andrée Ehresmann.

39

Ehresmann, A. C. and J.-P. Vanbremersch: 2006, The Memory Evolutive Systems as a Model of Rosen’s Organisms,
in

Complex Systems Biology

, I.C. Baianu, Editor,

Axiomathes

16

(1–2), pp. 13-50.

40

Eilenberg, S. and Mac Lane, S.: 1942,

Natural Isomorphisms

in

Group Theory

.,

American Mathematical Society

43

: 757-831.

41

Eilenberg, S. and Mac Lane, S.: 1945, The General Theory of Natural Equivalences,

Transactions of the American Mathematical Society

58: 231-294.

42

Elsasser, M.W.: 1981, A Form of Logic Suited for Biology., In: Robert, Rosen, ed.,

Progress in Theoretical Biology

, Volume 6, Academic Press, New York and London, pp 23-62.

Title

mathematical biology and theoretical biophysics of DNA

Canonical name

MathematicalBiologyAndTheoreticalBiophysicsOfDNA

Date of creation

2013-03-22 18:18:09

Last modified on

2013-03-22 18:18:09

Owner

bci1 (20947)

Last modified by

bci1 (20947)

Numerical id

110

Author

bci1 (20947)

Entry type

Topic

Classification

msc 93A05

Classification

msc 92B20

Classification

msc 92B05

Classification

msc 18-00

Classification

msc 18D35

Synonym

theoretical biology

Synonym

mathematical biophysics

Related topic

ComplexSystemsBiology

Related topic

CategoryOfSets

Related topic

HamiltonianOperatorOfAQuantumSystem

Related topic

BibliographyForMathematicalBiophysics

Related topic

CategoryOfMRSystems3

Related topic

RobertRosen

Related topic

NicolasRashevsky

Related topic

Quaternions

Related topic

SimilarityAndAnalogousSystemsDynamicAdjointness2

Related topic

PhysicalMathematicsAndEng

Defines

A- and B- DNA paracrystals

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