Mathematical and theoretical biology: Difference between revisions

From Wikipedia, the free encyclopedia
Browse history interactively
← Previous editNext edit →
Content deleted Content added
VisualWikitext
Undid revision 328054628 by 98.28.146.15 (talk)Unexplained removal of alternative name
No edit summary
Line 1: Line 1:
{{merge|Theoretical biology|discuss=Talk:Mathematical biology#Merge with Theoretical biology?|date=November 2009}}
{{merge|Theoretical biology|discuss=Talk:Mathematical biology#Merge with Theoretical biology?|date=November 2009}}
'''Mathematical biology''' is also called '''theoretical biology''',<ref>Mathematical Biology and Theoretical Biophysics-An Outline: What is Life? http://planetmath.org/?op=getobj&from=objects&id=10921</ref> and sometimes '''biomathematics'''. It includes at least four major subfields: ''biological mathematical modeling'', ''relational biology/complex systems biology (CSB)'', ''bioinformatics'' and ''computational biomodeling''/''biocomputing''. It is an [[interdisciplinary]] academic research field with a wide range of applications in [[biology]], [[medicine]]<ref>http://www.kli.ac.at/theorylab/EditedVol/W/WittenM1987a.html</ref> and [[biotechnology]].<ref>http://en.scientificcommons.org/1857372</ref>
'''Mathematical biology''' is also called '''theoretical biology''',<ref>Mathematical Biology and Theoretical Biophysics-An Outline: What is Life? http://planetmath.org/?op=getobj&from=objects&id=10921{{MEDRS}}</ref> and sometimes '''biomathematics'''. It includes at least four major subfields: ''biological mathematical modeling'', ''relational biology/complex systems biology (CSB)'', ''bioinformatics'' and ''computational biomodeling''/''biocomputing''. It is an [[interdisciplinary]] academic research field with a wide range of applications in [[biology]], [[medicine]]{{fact}} and [[biotechnology]].<ref>http://en.scientificcommons.org/1857372{{MEDRS}}</ref>


Mathematical biology aims at the mathematical representation, treatment and modeling of [[biology|biological]] processes, using a variety of [[mathematics|applied mathematical]] techniques and tools. It has both theoretical and practical applications in biological, biomedical and biotechnology research. For example, in cell biology, protein interactions are often represented as "cartoon" models, which, although easy to visualize, do not accurately describe the systems studied. In order to do this, precise mathematical models are required. By describing the systems in a quantitative manner, their behavior can be better simulated, and hence properties can be predicted that might not be evident to the experimenter.
Mathematical biology aims at the mathematical representation, treatment and modeling of [[biology|biological]] processes, using a variety of [[mathematics|applied mathematical]] techniques and tools. It has both theoretical and practical applications in biological, biomedical and biotechnology research. For example, in cell biology, protein interactions are often represented as "cartoon" models, which, although easy to visualize, do not accurately describe the systems studied. In order to do this, precise mathematical models are required. By describing the systems in a quantitative manner, their behavior can be better simulated, and hence properties can be predicted that might not be evident to the experimenter.
Line 14: Line 14:


==Areas of research==
==Areas of research==
Several areas of specialized research in mathematical and theoretical biology<ref>http://www.kli.ac.at/theorylab/index.html</ref><ref>http://www.springerlink.com/content/w2733h7280521632/ </ref><ref>http://en.scientificcommons.org/1857371</ref><ref>http://cogprints.org/3687/</ref><ref>{{cite web|url=http://www.maths.gla.ac.uk/research/groups/biology/kal.htm |title=Research in Mathematical Biology |publisher=Maths.gla.ac.uk |date= |accessdate=2008-09-10}}</ref><ref>http://acube.org/volume_23/v23-1p11-36.pdf J. R. Junck. Ten Equations that Changed Biology: Mathematics in Problem-Solving Biology Curricula, ''Bioscene'', (1997), 1-36</ref> as well as external links to related projects in various universities are concisely presented in the following subsections, including also a large number of appropriate validating references from a list of several thousands of published authors contributing to this field. Many of the included examples are characterised by highly complex, nonlinear, and supercomplex mechanisms, as it is being increasingly recognised that the result of such interactions may only be understood through a combination of mathematical, logical, physical/chemical, molecular and computational models. Due to the wide diversity of specific knowledge involved, biomathematical research is often done in collaboration between [[mathematicians]], biomathematicians,
Several areas of specialized research in mathematical and theoretical biology<ref name=s10516-005-3973-8>{{cite journal |doi=10.1007/s10516-005-3973-8}}</ref><ref>http://en.scientificcommons.org/1857371{{MEDRS}}</ref><ref>http://cogprints.org/3687/{{MEDRS}}</ref><ref>{{cite web|url=http://www.maths.gla.ac.uk/research/groups/biology/kal.htm |title=Research in Mathematical Biology |publisher=Maths.gla.ac.uk |date= |accessdate=2008-09-10}}</ref><ref>http://acube.org/volume_23/v23-1p11-36.pdf J. R. Junck. Ten Equations that Changed Biology: Mathematics in Problem-Solving Biology Curricula, ''Bioscene'', (1997), 1-36</ref> as well as external links to related projects in various universities are concisely presented in the following subsections, including also a large number of appropriate validating references from a list of several thousands of published authors contributing to this field. Many of the included examples are characterised by highly complex, nonlinear, and supercomplex mechanisms, as it is being increasingly recognised that the result of such interactions may only be understood through a combination of mathematical, logical, physical/chemical, molecular and computational models. Due to the wide diversity of specific knowledge involved, biomathematical research is often done in collaboration between [[mathematicians]], biomathematicians,
[[theoretical biologist]]s, [[physics|physicists]], [[biophysicists]], [[biochemists]], [[Bioengineering|bioengineers]], engineers, biologists, physiologists, research [[physiology|physicians]], biomedical researchers, [[oncologists]], [[molecular biologists]], [[geneticists]], [[Embryology|embryologists]], [[zoology|zoologists]], [[chemistry|chemists]], etc.
[[theoretical biologist]]s, [[physics|physicists]], [[biophysicists]], [[biochemists]], [[Bioengineering|bioengineers]], engineers, biologists, physiologists, research [[physiology|physicians]], biomedical researchers, [[oncologists]], [[molecular biologists]], [[geneticists]], [[Embryology|embryologists]], [[zoology|zoologists]], [[chemistry|chemists]], etc.


Line 20: Line 20:
{{main|Modelling biological systems}}
{{main|Modelling biological systems}}
A monograph on this topic summarizes an extensive amount of published research
A monograph on this topic summarizes an extensive amount of published research
in this area up to 1987,<ref>http://en.scientificcommons.org/1857371</ref> including subsections in the following areas: [[computer modeling]] in biology and medicine, arterial system models, [[neuron]] models, biochemical and [[oscillation]] [[wikt:network|network]]s, [http://planetphysics.org/encyclopedia/QuantumAutomaton.html quantum automata], [[quantum computers]] in [[molecular biology]] and [[genetics]], cancer modelling, [[neural net]]s, [[genetic network]]s, abstract relational biology, metabolic-replication systems, [[category theory]]<ref>http://planetphysics.org/encyclopedia/BibliographyForCategoryTheoryAndAlgebraicTopologyApplicationsInTheoreticalPhysics.html</ref> applications in biology and medicine,<ref>http://planetphysics.org/encyclopedia/BibliographyForMathematicalBiophysicsAndMathematicalMedicine.html</ref> [[automata theory]],[[cellular automata]], [[tessallation]] models<ref>''Modern Cellular Automata'' by Kendall Preston and M. J. B. Duff http://books.google.co.uk/books?id=l0_0q_e-u_UC&dq=cellular+automata+and+tessalation&pg=PP1&ots=ciXYCF3AYm&source=citation&sig=CtaUDhisM7MalS7rZfXvp689y-8&hl=en&sa=X&oi=book_result&resnum=12&ct=result</ref><ref>http://mathworld.wolfram.com/DualTessellation.html</ref> and [http://planetphysics.org/encyclopedia/ETACAxioms.html complete self-reproduction], [[chaotic system]]s in [[organism]]s, relational biology and organismic theories.<ref>Baianu, I. C. 1987, 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. http://cogprints.org/3687/</ref><ref>http://www.kli.ac.at/theorylab/EditedVol/W/WittenM1987a.html</ref> This published report also includes 390 references to peer-reviewed articles by a large number of authors.<ref>http://www.springerlink.com/content/w2733h7280521632/</ref><ref>Currently available for download as an updated PDF: http://cogprints.ecs.soton.ac.uk/archive/00003718/01/COMPUTER_SIMULATIONCOMPUTABILITYBIOSYSTEMSrefnew.pdf</ref><ref>http://planetphysics.org/encyclopedia/BibliographyForMathematicalBiophysics.html</ref>
in this area up to 1987,<ref>http://en.scientificcommons.org/1857371{{rs}}</ref> including subsections in the following areas: [[computer modeling]] in biology and medicine, arterial system models, [[neuron]] models, biochemical and [[oscillation]] [[wikt:network|network]]s, [http://planetphysics.org/encyclopedia/QuantumAutomaton.html quantum automata], [[quantum computers]] in [[molecular biology]] and [[genetics]], cancer modelling, [[neural net]]s, [[genetic network]]s, abstract relational biology, metabolic-replication systems, [[category theory]]<ref>http://planetphysics.org/encyclopedia/BibliographyForCategoryTheoryAndAlgebraicTopologyApplicationsInTheoreticalPhysics.html</ref> applications in biology and medicine,<ref>http://planetphysics.org/encyclopedia/BibliographyForMathematicalBiophysicsAndMathematicalMedicine.html</ref> [[automata theory]],[[cellular automata]], [[tessallation]] models<ref>''Modern Cellular Automata'' by Kendall Preston and M. J. B. Duff http://books.google.co.uk/books?id=l0_0q_e-u_UC&dq=cellular+automata+and+tessalation&pg=PP1&ots=ciXYCF3AYm&source=citation&sig=CtaUDhisM7MalS7rZfXvp689y-8&hl=en&sa=X&oi=book_result&resnum=12&ct=result</ref><ref>http://mathworld.wolfram.com/DualTessellation.html</ref> and [http://planetphysics.org/encyclopedia/ETACAxioms.html complete self-reproduction], [[chaotic system]]s in [[organism]]s, relational biology and organismic theories.<ref>Baianu, I. C. 1987, 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. http://cogprints.org/3687/</ref><ref>http://www.kli.ac.at/theorylab/EditedVol/W/WittenM1987a.html</ref> This published report also includes 390 references to peer-reviewed articles by a large number of authors.<ref name=s10516-005-3973-8/><ref>Currently available for download as an updated PDF: http://cogprints.ecs.soton.ac.uk/archive/00003718/01/COMPUTER_SIMULATIONCOMPUTABILITYBIOSYSTEMSrefnew.pdf</ref><ref>http://planetphysics.org/encyclopedia/BibliographyForMathematicalBiophysics.html</ref>


'''Modeling cell and molecular biology'''
'''Modeling cell and molecular biology'''
Line 27: Line 27:
*Mechanics of biological tissues<ref>http://www.maths.gla.ac.uk/~rwo/research_areas.htm</ref>
*Mechanics of biological tissues<ref>http://www.maths.gla.ac.uk/~rwo/research_areas.htm</ref>
*Theoretical enzymology and [[enzyme kinetics]]
*Theoretical enzymology and [[enzyme kinetics]]
*[[Cancer]] modelling and simulation <ref>http://www.springerlink.com/content/71958358k273622q/</ref><ref>http://calvino.polito.it/~mcrtn/</ref>
*[[Cancer]] modelling and simulation<ref>{{cite journal |doi=10.1007/s10516-005-4943-x}}</ref><ref>http://calvino.polito.it/~mcrtn/</ref>
*Modelling the movement of interacting cell populations<ref>http://www.ma.hw.ac.uk/~jas/researchinterests/index.html</ref>
*Modelling the movement of interacting cell populations<ref>http://www.ma.hw.ac.uk/~jas/researchinterests/index.html</ref>
*Mathematical modelling of scar tissue formation<ref>http://www.ma.hw.ac.uk/~jas/researchinterests/scartissueformation.html</ref>
*Mathematical modelling of scar tissue formation<ref>http://www.ma.hw.ac.uk/~jas/researchinterests/scartissueformation.html</ref>
Line 41: Line 41:
===Molecular set theory===
===Molecular set theory===
Molecular set theory was introduced by Anthony Bartholomay, and its applications were developed in mathematical biology and especially in Mathematical Medicine.<ref>http://planetphysics.org/encyclopedia/CategoryOfMolecularSets2.html</ref>
Molecular set theory was introduced by Anthony Bartholomay, and its applications were developed in mathematical biology and especially in Mathematical Medicine.<ref>http://planetphysics.org/encyclopedia/CategoryOfMolecularSets2.html</ref>
Molecular set theory (MST) is a mathematical formulation of the wide-sense chemical kinetics of biomolecular reactions in terms of sets of molecules and their chemical transformations represented by set-theoretical mappings between molecular sets. In a more general sense, MST is the theory of molecular categories defined as categories of molecular sets and their chemical transformations represented as set-theoretical mappings of molecular sets. The theory has also contributed to biostatistics and the formulation of clinical biochemistry problems in mathematical formulations of pathological, biochemical changes of interest to Physiology, Clinical Biochemistry and Medicine.<ref> Representation of Uni-molecular and Multimolecular Biochemical Reactions in terms of Molecular Set Transformations http://planetmath.org/?op=getobj&from=objects&id=10770</ref><ref>http://planetphysics.org/encyclopedia/CategoryOfMolecularSets2.html</ref>
Molecular set theory (MST) is a mathematical formulation of the wide-sense chemical kinetics of biomolecular reactions in terms of sets of molecules and their chemical transformations represented by set-theoretical mappings between molecular sets. In a more general sense, MST is the theory of molecular categories defined as categories of molecular sets and their chemical transformations represented as set-theoretical mappings of molecular sets. The theory has also contributed to biostatistics and the formulation of clinical biochemistry problems in mathematical formulations of pathological, biochemical changes of interest to Physiology, Clinical Biochemistry and Medicine.<ref> Representation of Uni-molecular and Multimolecular Biochemical Reactions in terms of Molecular Set Transformations http://planetmath.org/?op=getobj&from=objects&id=10770{{MEDRS}}</ref><ref>http://planetphysics.org/encyclopedia/CategoryOfMolecularSets2.html</ref>


===Population dynamics===
===Population dynamics===
Line 174: Line 174:
* [[Biologically inspired computing]]
* [[Biologically inspired computing]]
* [[Biostatistics]]
* [[Biostatistics]]
* [[Cellular automata]]<ref name=s10516-005-3973-8/>
* [[Cellular automata]]<ref>Baianu, I. C. 1987, 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. http://www.springerlink.com/content/w2733h7280521632/ </ref>
* [[Coalescent theory]]
* [[Coalescent theory]]
* [[Systems biology|Complex systems biology]]<ref>http://www.springerlink.com/content/v1rt05876h74v607/?p=2bd3993c33644512ba7069ed7fad0046&pi=1</ref><ref>http://www.springerlink.com/content/j7t56r530140r88p/?p=2bd3993c33644512ba7069ed7fad0046&pi=3</ref><ref>http://www.springerlink.com/content/98303486x3l07jx3/</ref>
* [[Systems biology|Complex systems biology]]<ref>{{cite journal |doi=10.1007/s10516-007-9011-2}}</ref><ref name=s10516-007-9010-3>{{cite journal |doi=10.1007/s10516-007-9010-3}}</ref><ref name=BF02476770>{{cite journal |doi=10.1007/BF02476770}}</ref>
* [[Computational biology]]
* [[Computational biology]]
* [[Dynamical system]]s in biology<ref>Robert Rosen, ''Dynamical system theory in biology.'' New York, Wiley-Interscience (1970) ISBN 0471735507 http://www.worldcat.org/oclc/101642 </ref><ref>http://www.springerlink.com/content/j7t56r530140r88p/?p=2bd3993c33644512ba7069ed7fad0046&pi=3</ref><ref>http://cogprints.org/3674/</ref><ref>http://cogprints.org/3829/</ref><ref>http://www.ncbi.nlm.nih.gov/pubmed/4327361</ref><ref>http://www.springerlink.com/content/98303486x3l07jx3/</ref>
* [[Dynamical system]]s in biology<ref>Robert Rosen, ''Dynamical system theory in biology.'' New York, Wiley-Interscience (1970) ISBN 0471735507 http://www.worldcat.org/oclc/101642 </ref><ref name=s10516-007-9010-3/><ref>http://cogprints.org/3674/{{MEDRS}}</ref><ref>http://cogprints.org/3829/{{MEDRS}}</ref><ref>{{cite journal |author=Băianu I |title=Organismic supercategories. II. On multistable systems |journal=The Bulletin of Mathematical Biophysics |volume=32 |issue=4 |pages=539–61 |year=1970 |month=December |pmid=4327361}}</ref><ref name=BF02476770/>
* [[Epidemiology]]
* [[Epidemiology]]
* [[Evolution|Evolution theories and Population Genetics]]
* [[Evolution|Evolution theories and Population Genetics]]
Line 189: Line 189:
** [[Molecular modeling on GPU|Molecular modelling on GPU]]
** [[Molecular modeling on GPU|Molecular modelling on GPU]]
** [[List of software for molecular mechanics modeling|Software for molecular modeling]]
** [[List of software for molecular mechanics modeling|Software for molecular modeling]]
** [http://planetphysics.org/encyclopedia/RSystemsCategoryOfM.html Metabolic-replication systems]<ref>http://www.kli.ac.at/theorylab/ALists/Authors_R.html</ref>
** Metabolic-replication systems<ref>http://planetphysics.org/encyclopedia/RSystemsCategoryOfM.html</ref>
** [[D'Arcy Thompson|Models of Growth and Form]]
** [[D'Arcy Thompson|Models of Growth and Form]]
** [[Neighbour-sensing model]]
** [[Neighbour-sensing model]]
* [[Morphometrics]]
* [[Morphometrics]]
* [http://planetphysics.org/encyclopedia/OrganismicSetTheory.html Organismic systems (OS)]<ref>Organisms as Super-complex Systems http://planetmath.org/?op=getobj&from=objects&id=10890</ref>
* [http://planetphysics.org/encyclopedia/OrganismicSetTheory.html Organismic systems (OS)]<ref>Organisms as Super-complex Systems http://planetmath.org/?op=getobj&from=objects&id=10890{{MEDRS}}</ref>
* [http://planetphysics.org/encyclopedia/OrganismicSetTheory.html Organismic supercategories]<ref>http://www.springerlink.com/content/98303486x3l07jx3/</ref><ref>http://planetmath.org/encyclopedia/SupercategoriesOfComplexSystems.html</ref>
* [http://planetphysics.org/encyclopedia/OrganismicSetTheory.html Organismic supercategories]<ref name=BF02476770/><ref>http://planetmath.org/encyclopedia/SupercategoriesOfComplexSystems.html{{MEDRS}}</ref>
* [[Population dynamics of fisheries]]
* [[Population dynamics of fisheries]]
* [[Protein folding]], also [[blue Gene]] and [[folding@home]]
* [[Protein folding]], also [[blue Gene]] and [[folding@home]]
* [[Quantum computer]]s
* [[Quantum computer]]s
* [[DNA computing|Quantum genetics]]
* [[DNA computing|Quantum genetics]]
* [http://planetmath.org/?op=getobj&from=objects&id=10921 Relational biology]
* Relational biology<ref>http://planetmath.org/?op=getobj&from=objects&id=10921{{MEDRS}}</ref>
* [[DNA|Self-reproduction]]<ref>http://planetmath.org/?method=l2h&from=objects&name=NaturalTransformationsOfOrganismicStructures&op=getobj</ref>(also called [[self-replication]] in a more general context).
* [[DNA|Self-reproduction]]<ref>http://planetmath.org/?method=l2h&from=objects&name=NaturalTransformationsOfOrganismicStructures&op=getobj{{MEDRS}}</ref>(also called [[self-replication]] in a more general context).
* [[Computational gene|Computational gene models]]
* [[Computational gene|Computational gene models]]
* [[Systems biology]]<ref>http://www.kli.ac.at/theorylab/ALists/Authors_R.html</ref>
* [[Systems biology]]<ref>http://www.kli.ac.at/theorylab/ALists/Authors_R.html</ref>
Line 227: Line 227:


==References==
==References==

* Nicolas Rashevsky. (1938)., ''Mathematical Biophysics''. Chicago: University of Chicago Press.
* Nicolas Rashevsky. (1938)., ''Mathematical Biophysics''. Chicago: University of Chicago Press.
* Robert Rosen, Dynamical system theory in biology. New York, Wiley-Interscience (1970) ISBN 0471735507 <ref>http://www.worldcat.org/oclc/101642 </ref>
* Robert Rosen, Dynamical system theory in biology. New York, Wiley-Interscience (1970) ISBN 0471735507 <ref>http://www.worldcat.org/oclc/101642 </ref>
* Israel, G., 2005, "Book on mathematical biology" in [[Ivor Grattan-Guinness|Grattan-Guinness, I.]], ed., ''Landmark Writings in Western Mathematics''. Elsevier: 936-44.
* Israel, G., 2005, "Book on mathematical biology" in [[Ivor Grattan-Guinness|Grattan-Guinness, I.]], ed., ''Landmark Writings in Western Mathematics''. Elsevier: 936-44.
* {{cite journal |author=Israel G |title=On the contribution of Volterra and Lotka to the development of modern biomathematics |journal=History and Philosophy of the Life Sciences |volume=10 |issue=1 |pages=37–49 |year=1988 |pmid=3045853}}
* {{Citation
*{{cite journal |author=Scudo FM |title=Vito Volterra and theoretical ecology |journal=Theoretical Population Biology |volume=2 |issue=1 |pages=1–23 |year=1971 |month=March |pmid=4950157}}
|id = [[PMID]]:3045853
|url= http://www.ncbi.nlm.nih.gov/pubmed/3045853
|last=Israel
|first=G
|publication-date=1988
|year=1988
|title=On the contribution of Volterra and Lotka to the development of modern biomathematics.
|volume=10
|issue=1
|periodical=History and philosophy of the life sciences
|pages=37-49
}}
* {{Citation
|id = [[PMID]]:4950157
|url= http://www.ncbi.nlm.nih.gov/pubmed/4950157
|last=Scudo
|first=F M
|publication-date=1971 Mar
|year=1971
|title=Vito Volterra and theoretical ecology.
|volume=2
|issue=1
|periodical=Theoretical population biology
|pages=1-23
}}

*S.H. Strogatz, ''Nonlinear dynamics and Chaos: Applications to Physics, Biology, Chemistry, and Engineering.'' Perseus, 2001, ISBN 0-7382-0453-6
*S.H. Strogatz, ''Nonlinear dynamics and Chaos: Applications to Physics, Biology, Chemistry, and Engineering.'' Perseus, 2001, ISBN 0-7382-0453-6
*N.G. van Kampen, ''Stochastic Processes in Physics and Chemistry'', North Holland., 3rd ed. 2001, ISBN 0-444-89349-0
*N.G. van Kampen, ''Stochastic Processes in Physics and Chemistry'', North Holland., 3rd ed. 2001, ISBN 0-444-89349-0
Line 278: Line 252:
* A general list of Theoretical biology/Mathematical biology references, including an updated list of actively contributing authors<ref>http://www.kli.ac.at/theorylab/index.html</ref>.
* A general list of Theoretical biology/Mathematical biology references, including an updated list of actively contributing authors<ref>http://www.kli.ac.at/theorylab/index.html</ref>.
*A list of references for applications of category theory in relational biology<ref>http://planetmath.org/?method=l2h&from=objects&id=10746&op=getobj</ref>.
*A list of references for applications of category theory in relational biology.<ref>http://planetmath.org/?method=l2h&from=objects&id=10746&op=getobj{{MEDRS}}</ref>


*An updated list of publications of theoretical biologist Robert Rosen<ref>Publications list for Robert Rosen http://www.people.vcu.edu/~mikuleck/rosen.htm</ref>
*An updated list of publications of theoretical biologist Robert Rosen<ref>Publications list for Robert Rosen http://www.people.vcu.edu/~mikuleck/rosen.htm</ref>

Revision as of 09:29, 30 November 2009

Mathematical biology is also called theoretical biology,[1] and sometimes biomathematics. It includes at least four major subfields: biological mathematical modeling, relational biology/complex systems biology (CSB), bioinformatics and computational biomodeling/biocomputing. It is an interdisciplinary academic research field with a wide range of applications in biology, medicine[citation needed] and biotechnology.[2]

Mathematical biology aims at the mathematical representation, treatment and modeling of biological processes, using a variety of applied mathematical techniques and tools. It has both theoretical and practical applications in biological, biomedical and biotechnology research. For example, in cell biology, protein interactions are often represented as "cartoon" models, which, although easy to visualize, do not accurately describe the systems studied. In order to do this, precise mathematical models are required. By describing the systems in a quantitative manner, their behavior can be better simulated, and hence properties can be predicted that might not be evident to the experimenter.

Importance

Applying mathematics to biology has a long history, but only recently has there been an explosion of interest in the field. Some reasons for this include:

  • the explosion of data-rich information sets, due to the genomics revolution, which are difficult to understand without the use of analytical tools,
  • recent development of mathematical tools such as chaos theory to help understand complex, nonlinear mechanisms in biology,
  • an increase in computing power which enables calculations and simulations to be performed that were not previously possible, and
  • an increasing interest in in silico experimentation due to ethical considerations, risk, unreliability and other complications involved in human and animal research.
For use of statistics in biology, see Biostatistics.
For use of basic arithmetics in biology, see relevant topic, such as Serial dilution.

Areas of research

Several areas of specialized research in mathematical and theoretical biology[3][4][5][6][7] as well as external links to related projects in various universities are concisely presented in the following subsections, including also a large number of appropriate validating references from a list of several thousands of published authors contributing to this field. Many of the included examples are characterised by highly complex, nonlinear, and supercomplex mechanisms, as it is being increasingly recognised that the result of such interactions may only be understood through a combination of mathematical, logical, physical/chemical, molecular and computational models. Due to the wide diversity of specific knowledge involved, biomathematical research is often done in collaboration between mathematicians, biomathematicians, theoretical biologists, physicists, biophysicists, biochemists, bioengineers, engineers, biologists, physiologists, research physicians, biomedical researchers, oncologists, molecular biologists, geneticists, embryologists, zoologists, chemists, etc.

Computer models and automata theory

Main article: Modelling biological systems

A monograph on this topic summarizes an extensive amount of published research in this area up to 1987,[8] including subsections in the following areas: computer modeling in biology and medicine, arterial system models, neuron models, biochemical and oscillation networks, quantum automata, quantum computers in molecular biology and genetics, cancer modelling, neural nets, genetic networks, abstract relational biology, metabolic-replication systems, category theory[9] applications in biology and medicine,[10] automata theory,cellular automata, tessallation models[11][12] and complete self-reproduction, chaotic systems in organisms, relational biology and organismic theories.[13][14] This published report also includes 390 references to peer-reviewed articles by a large number of authors.[3][15][16]

Modeling cell and molecular biology

This area has received a boost due to the growing importance of molecular biology.[17]

  • Mechanics of biological tissues[18]
  • Theoretical enzymology and enzyme kinetics
  • Cancer modelling and simulation[19][20]
  • Modelling the movement of interacting cell populations[21]
  • Mathematical modelling of scar tissue formation[22]
  • Mathematical modelling of intracellular dynamics[23]
  • Mathematical modelling of the cell cycle[24]

Modelling physiological systems

Molecular set theory

Molecular set theory was introduced by Anthony Bartholomay, and its applications were developed in mathematical biology and especially in Mathematical Medicine.[27] Molecular set theory (MST) is a mathematical formulation of the wide-sense chemical kinetics of biomolecular reactions in terms of sets of molecules and their chemical transformations represented by set-theoretical mappings between molecular sets. In a more general sense, MST is the theory of molecular categories defined as categories of molecular sets and their chemical transformations represented as set-theoretical mappings of molecular sets. The theory has also contributed to biostatistics and the formulation of clinical biochemistry problems in mathematical formulations of pathological, biochemical changes of interest to Physiology, Clinical Biochemistry and Medicine.[28][29]

Population dynamics

Population dynamics has traditionally been the dominant field of mathematical biology. Work in this area dates back to the 19th century. The Lotka–Volterra predator-prey equations are a famous example. In the past 30 years, population dynamics has been complemented by evolutionary game theory, developed first by John Maynard Smith. Under these dynamics, evolutionary biology concepts may take a deterministic mathematical form. Population dynamics overlap with another active area of research in mathematical biology: mathematical epidemiology, the study of infectious disease affecting populations. Various models of viral spread have been proposed and analyzed, and provide important results that may be applied to health policy decisions.

Mathematical methods

A model of a biological system is converted into a system of equations, although the word 'model' is often used synonymously with the system of corresponding equations. The solution of the equations, by either analytical or numerical means, describes how the biological system behaves either over time or at equilibrium. There are many different types of equations and the type of behavior that can occur is dependent on both the model and the equations used. The model often makes assumptions about the system. The equations may also make assumptions about the nature of what may occur.

Mathematical biophysics

The earlier stages of mathematical biology were dominated by mathematical biophysics, described as the application of mathematics in biophysics, often involving specific physical/mathematical models of biosystems and their components or compartments.

The following is a list of mathematical descriptions and their assumptions.

Deterministic processes (dynamical systems)

A fixed mapping between an initial state and a final state. Starting from an initial condition and moving forward in time, a deterministic process will always generate the same trajectory and no two trajectories cross in state space.

Stochastic processes (random dynamical systems)

A random mapping between an initial state and a final state, making the state of the system a random variable with a corresponding probability distribution.

Spatial modelling

One classic work in this area is Alan Turing's paper on morphogenesis entitled The Chemical Basis of Morphogenesis, published in 1952 in the Philosophical Transactions of the Royal Society.

Phylogenetics

Phylogenetics is an area that deals with the reconstruction and analysis of phylogenetic (evolutionary) trees and networks based on inherited characteristics[35]

Model example: the cell cycle

Main article: Cellular model

The eukaryotic cell cycle is very complex and is one of the most studied topics, since its misregulation leads to cancers. It is possibly a good example of a mathematical model as it deals with simple calculus but gives valid results. Two research groups [36][37] have produced several models of the cell cycle simulating several organisms. They have recently produced a generic eukaryotic cell cycle model which can represent a particular eukaryote depending on the values of the parameters, demonstrating that the idiosyncrasies of the individual cell cycles are due to different protein concentrations and affinities, while the underlying mechanisms are conserved (Csikasz-Nagy et al., 2006).
By means of a system of ordinary differential equations these models show the change in time (dynamical system) of the protein inside a single typical cell; this type of model is called a deterministic process (whereas a model describing a statistical distribution of protein concentrations in a population of cells is called a stochastic process).
To obtain these equations an iterative series of steps must be done: first the several models and observations are combined to form a consensus diagram and the appropriate kinetic laws are chosen to write the differential equations, such as rate kinetics for stoichiometric reactions, Michaelis-Menten kinetics for enzyme substrate reactions and Goldbeter–Koshland kinetics for ultrasensitive transcription factors, afterwards the parameters of the equations (rate constants, enzyme efficiency coefficients and Michealis constants) must be fitted to match observations; when they cannot be fitted the kinetic equation is revised and when that is not possible the wiring diagram is modified. The parameters are fitted and validated using observations of both wild type and mutants, such as protein half-life and cell size.
In order to fit the parameters the differential equations need to be studied. This can be done either by simulation or by analysis.
In a simulation, given a starting vector (list of the values of the variables), the progression of the system is calculated by solving the equations at each time-frame in small increments.

In analysis, the proprieties of the equations are used to investigate the behavior of the system depending of the values of the parameters and variables. A system of differential equations can be represented as a vector field, where each vector described the change (in concentration of two or more protein) determining where and how fast the trajectory (simulation) is heading. Vector fields can have several special points: a stable point, called a sink, that attracts in all directions (forcing the concentrations to be at a certain value), an unstable point, either a source or a saddle point which repels (forcing the concentrations to change away from a certain value), and a limit cycle, a closed trajectory towards which several trajectories spiral towards (making the concentrations oscillate).
A better representation which can handle the large number of variables and parameters is called a bifurcation diagram(Bifurcation theory): the presence of these special steady-state points at certain values of a parameter (e.g. mass) is represented by a point and once the parameter passes a certain value, a qualitative change occurs, called a bifurcation, in which the nature of the space changes, with profound consequences for the protein concentrations: the cell cycle has phases (partially corresponding to G1 and G2) in which mass, via a stable point, controls cyclin levels, and phases (S and M phases) in which the concentrations change independently, but once the phase has changed at a bifurcation event (Cell cycle checkpoint), the system cannot go back to the previous levels since at the current mass the vector field is profoundly different and the mass cannot be reversed back through the bifurcation event, making a checkpoint irreversible. In particular the S and M checkpoints are regulated by means of special bifurcations called a Hopf bifurcation and an infinite period bifurcation.

Mathematical/theoretical biologists

Mathematical, theoretical and computational biophysicists

See also

For use of statistics in biology, see Biostatistics.
For use of basic arithmetics in biology, see relevant topic, such as Serial dilution.

Mathematical and Theoretical Biology Societies and Institutes

References

  • Nicolas Rashevsky. (1938)., Mathematical Biophysics. Chicago: University of Chicago Press.
  • Robert Rosen, Dynamical system theory in biology. New York, Wiley-Interscience (1970) ISBN 0471735507 [54]
  • Israel, G., 2005, "Book on mathematical biology" in Grattan-Guinness, I., ed., Landmark Writings in Western Mathematics. Elsevier: 936-44.
  • Israel G (1988). "On the contribution of Volterra and Lotka to the development of modern biomathematics". History and Philosophy of the Life Sciences. 10 (1): 37–49. PMID 3045853.
  • Scudo FM (1971). "Vito Volterra and theoretical ecology". Theoretical Population Biology. 2 (1): 1–23. PMID 4950157. {{cite journal}}: Unknown parameter |month= ignored (help)
  • S.H. Strogatz, Nonlinear dynamics and Chaos: Applications to Physics, Biology, Chemistry, and Engineering. Perseus, 2001, ISBN 0-7382-0453-6
  • N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North Holland., 3rd ed. 2001, ISBN 0-444-89349-0
  • I. C. Baianu., Computer Models and Automata Theory in Biology and Medicine., Monograph, Ch.11 in M. Witten (Editor), Mathematical Models in Medicine, vol. 7., Vol. 7: 1513-1577 (1987),Pergamon Press:New York, (updated by Hsiao Chen Lin in 2004[55],[56],[57] ISBN 0080363776 [58].
  • P.G. Drazin, Nonlinear systems. C.U.P., 1992. ISBN 0-521-40668-4
  • L. Edelstein-Keshet, Mathematical Models in Biology. SIAM, 2004. ISBN 0-07-554950-6
  • G. Forgacs and S. A. Newman, Biological Physics of the Developing Embryo. C.U.P., 2005. ISBN 0-521-78337-2
  • A. Goldbeter, Biochemical oscillations and cellular rhythms. C.U.P., 1996. ISBN 0-521-59946-6
  • L.G. Harrison, Kinetic theory of living pattern. C.U.P., 1993. ISBN 0-521-30691-4
  • F. Hoppensteadt, Mathematical theories of populations: demographics, genetics and epidemics. SIAM, Philadelphia, 1975 (reprinted 1993). ISBN 0-89871-017-0
  • D.W. Jordan and P. Smith, Nonlinear ordinary differential equations, 2nd ed. O.U.P., 1987. ISBN 0-19-856562-3
  • J.D. Murray, Mathematical Biology. Springer-Verlag, 3rd ed. in 2 vols.: Mathematical Biology: I. An Introduction, 2002 ISBN 0-387-95223-3; Mathematical Biology: II. Spatial Models and Biomedical Applications, 2003 ISBN 0-387-95228-4.
  • E. Renshaw, Modelling biological populations in space and time. C.U.P., 1991. ISBN 0-521-44855-7
  • S.I. Rubinow, Introduction to mathematical biology. John Wiley, 1975. ISBN 0-471-74446-8
  • L.A. Segel, Modeling dynamic phenomena in molecular and cellular biology. C.U.P., 1984. ISBN 0-521-27477-X
  • L. Preziosi, Cancer Modelling and Simulation. Chapman Hall/CRC Press, 2003. ISBN 1-58488-361-8.

Lists of references

  • A general list of Theoretical biology/Mathematical biology references, including an updated list of actively contributing authors[59].
  • A list of references for applications of category theory in relational biology.[60]
  • An updated list of publications of theoretical biologist Robert Rosen[61]

External

Notes: inline and online

  1. ^ Mathematical Biology and Theoretical Biophysics-An Outline: What is Life? http://planetmath.org/?op=getobj&from=objects&id=10921[unreliable medical source?]
  2. ^ http://en.scientificcommons.org/1857372[unreliable medical source?]
  3. ^ a b c . doi:10.1007/s10516-005-3973-8. {{cite journal}}: Cite journal requires |journal= (help); Missing or empty |title= (help)
  4. ^ http://en.scientificcommons.org/1857371[unreliable medical source?]
  5. ^ http://cogprints.org/3687/[unreliable medical source?]
  6. ^ "Research in Mathematical Biology". Maths.gla.ac.uk. Retrieved 2008-09-10.
  7. ^ http://acube.org/volume_23/v23-1p11-36.pdf J. R. Junck. Ten Equations that Changed Biology: Mathematics in Problem-Solving Biology Curricula, Bioscene, (1997), 1-36
  8. ^ http://en.scientificcommons.org/1857371[unreliable source?]
  9. ^ http://planetphysics.org/encyclopedia/BibliographyForCategoryTheoryAndAlgebraicTopologyApplicationsInTheoreticalPhysics.html
  10. ^ http://planetphysics.org/encyclopedia/BibliographyForMathematicalBiophysicsAndMathematicalMedicine.html
  11. ^ Modern Cellular Automata by Kendall Preston and M. J. B. Duff http://books.google.co.uk/books?id=l0_0q_e-u_UC&dq=cellular+automata+and+tessalation&pg=PP1&ots=ciXYCF3AYm&source=citation&sig=CtaUDhisM7MalS7rZfXvp689y-8&hl=en&sa=X&oi=book_result&resnum=12&ct=result
  12. ^ http://mathworld.wolfram.com/DualTessellation.html
  13. ^ Baianu, I. C. 1987, 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. http://cogprints.org/3687/
  14. ^ http://www.kli.ac.at/theorylab/EditedVol/W/WittenM1987a.html
  15. ^ Currently available for download as an updated PDF: http://cogprints.ecs.soton.ac.uk/archive/00003718/01/COMPUTER_SIMULATIONCOMPUTABILITYBIOSYSTEMSrefnew.pdf
  16. ^ http://planetphysics.org/encyclopedia/BibliographyForMathematicalBiophysics.html
  17. ^ "Research in Mathematical Biology". Maths.gla.ac.uk. Retrieved 2008-09-10.
  18. ^ http://www.maths.gla.ac.uk/~rwo/research_areas.htm
  19. ^ . doi:10.1007/s10516-005-4943-x. {{cite journal}}: Cite journal requires |journal= (help); Missing or empty |title= (help)
  20. ^ http://calvino.polito.it/~mcrtn/
  21. ^ http://www.ma.hw.ac.uk/~jas/researchinterests/index.html
  22. ^ http://www.ma.hw.ac.uk/~jas/researchinterests/scartissueformation.html
  23. ^ http://www.sbi.uni-rostock.de/dokumente/p_gilles_paper.pdf
  24. ^ http://mpf.biol.vt.edu/Research.html
  25. ^ http://www.maths.gla.ac.uk/~nah/research_interests.html
  26. ^ http://www.integrativebiology.ox.ac.uk/heartmodel.html
  27. ^ http://planetphysics.org/encyclopedia/CategoryOfMolecularSets2.html
  28. ^ Representation of Uni-molecular and Multimolecular Biochemical Reactions in terms of Molecular Set Transformations http://planetmath.org/?op=getobj&from=objects&id=10770[unreliable medical source?]
  29. ^ http://planetphysics.org/encyclopedia/CategoryOfMolecularSets2.html
  30. ^ http://www.maths.ox.ac.uk/~maini/public/gallery/twwha.htm
  31. ^ http://www.math.ubc.ca/people/faculty/keshet/research.html
  32. ^ http://www.maths.ox.ac.uk/~maini/public/gallery/mctom.htm
  33. ^ http://www.maths.ox.ac.uk/~maini/public/gallery/bpf.htm
  34. ^ http://links.jstor.org/sici?sici=0030-1299%28199008%2958%3A3%3C257%3ASDOTMU%3E2.0.CO%3B2-S&size=LARGE&origin=JSTOR-enlargePage
  35. ^ Charles Semple (2003), Phylogenetics, Oxford University Press, ISBN 9780198509424
  36. ^ "The JJ Tyson Lab". Virginia Tech. Retrieved 2008-09-10.
  37. ^ "The Molecular Network Dynamics Research Group". Budapest University of Technology and Economics.
  38. ^ http://planetphysics.org/encyclopedia/AbstractRelationalBiologyARB.html
  39. ^ http://www.kli.ac.at/theorylab/EditedVol/M/MatsunoKDose_84.html
  40. ^ . doi:10.1007/s10516-007-9011-2. {{cite journal}}: Cite journal requires |journal= (help); Missing or empty |title= (help)
  41. ^ a b . doi:10.1007/s10516-007-9010-3. {{cite journal}}: Cite journal requires |journal= (help); Missing or empty |title= (help)
  42. ^ a b c . doi:10.1007/BF02476770. {{cite journal}}: Cite journal requires |journal= (help); Missing or empty |title= (help)
  43. ^ Robert Rosen, Dynamical system theory in biology. New York, Wiley-Interscience (1970) ISBN 0471735507 http://www.worldcat.org/oclc/101642
  44. ^ http://cogprints.org/3674/[unreliable medical source?]
  45. ^ http://cogprints.org/3829/[unreliable medical source?]
  46. ^ Băianu I (1970). "Organismic supercategories. II. On multistable systems". The Bulletin of Mathematical Biophysics. 32 (4): 539–61. PMID 4327361. {{cite journal}}: Unknown parameter |month= ignored (help)
  47. ^ http://planetphysics.org/encyclopedia/RSystemsCategoryOfM.html
  48. ^ Organisms as Super-complex Systems http://planetmath.org/?op=getobj&from=objects&id=10890[unreliable medical source?]
  49. ^ http://planetmath.org/encyclopedia/SupercategoriesOfComplexSystems.html[unreliable medical source?]
  50. ^ http://planetmath.org/?op=getobj&from=objects&id=10921[unreliable medical source?]
  51. ^ http://planetmath.org/?method=l2h&from=objects&name=NaturalTransformationsOfOrganismicStructures&op=getobj[unreliable medical source?]
  52. ^ http://www.kli.ac.at/theorylab/ALists/Authors_R.html
  53. ^ http://www.kli.ac.at/theorylab/index.html
  54. ^ http://www.worldcat.org/oclc/101642
  55. ^ http://cogprints.org/3718/1/COMPUTER_SIMULATIONCOMPUTABILITYBIOSYSTEMSrefnew.pdf
  56. ^ http://www.springerlink.com/content/w2733h7280521632/
  57. ^ http://www.springerlink.com/content/n8gw445012267381/
  58. ^ http://www.bookfinder.com/dir/i/Mathematical_Models_in_Medicine/0080363776/
  59. ^ http://www.kli.ac.at/theorylab/index.html
  60. ^ http://planetmath.org/?method=l2h&from=objects&id=10746&op=getobj[unreliable medical source?]
  61. ^ Publications list for Robert Rosen http://www.people.vcu.edu/~mikuleck/rosen.htm

External links

Retrieved from "https://en.wikipedia.org/w/index.php?title=Mathematical_and_theoretical_biology&oldid=328768325"