complex systems biology (CSB)

complex systems biology (CSB)

0.1

Introduction

Complex systems biology (

C

⁢

S

⁢

B

)

is generally described as a non-reductionist, mathematical theory
of emergent living organisms or biosystems in terms of a

network

, graph or

category

of integrated interactions between their structural and

functional

components

or subsystems. This is often abbreviated to

http://planetphysics.org/?op=getobj&from=books&id=248

systems biology

in entries that should be described in fact as

complex systems biology

. Notably, several mathematical physicists or mathematicians,
such as von Neumann believed that all

complex systems

can be ultimately ‘decomposed’ or disassembled into their simpler, physical components, whereas others, such as Elsasser argued that the heterogeneous logical class of biosystems makes them

irreducible

to their physical components of logically

homogeneous

classes; the latter view was
also shared by

Robert Rosen

who also produced encoding and dynamic reasons for which reductionism would not work
for biosystems. Thus, it would seem that there is a fundamental, physical and mathematical controvercy regarding the
essential nature of Life.

Resolution

of this fundamental controvercy in terms of mathematics is denied by many biologists who argue that the dynamics and physiology of biosystems is not formalizable in either mathematical terms or physical theory. The key question:

“What is Life?”

is also the title of the widely-read book published in 1945 by the famous quantum theoretician Erwin

S

⁢

c

⁢

h

⁢

r

⁢

ö

⁢

d

⁢

i

⁢

n

⁢

g

⁢

e

⁢

r

, Nobel laureate and inventor of the equation that carries his name.

To address this fundamental question of life, applied mathematicians, as well as mathematical and theoretical biologists have been developing for over a century precise mathematical models of biosystems or organisms of increasing sophistication and generality. One can select the birth of cybernetics, biocybernetics, and the application of

category theory

, as well as

set theory

, to biosystems as the starting point of

C

⁢

S

⁢

B

which is currently the branch of inter-disciplinary science, between mathematics and biology, as well as sociology, that aims to define in precise, mathematical terms the nature of dynamic and organizational complexity both in living organisms and in societies.
The famous topologist and Fields medalist René Thom was one of the more recent contributors to this field from the
viewpoint of

topology

and Poincaré’ s

Qualitative Dynamics

. Grothendieck is also said to have a keen interest in such complexity problems related to living organisms. Defining the main problems and approaches in

C

⁢

S

⁢

B

remains
a monumental task for multi-disciplinary teams of applied mathematicians, biologists, biochemists, physicists, biophysicists, sociologists, computer scientists, and so on. The underlying logical problems are also formidable
as most complexity problems do not have easy, or simple, Boolean logic solutions,
and are not amenable to linear engineering

analysis

, either direct or reverse.

0.2

Complex systems biology

Definition 0.1

.

The

categorical ontology

theory of levels

is often defined as the classification theory in

ontology

, or the theory of

existence

of items (or objects–defined in the mathematical or logical sense) by means of the mathematical theory of categories into three levels of dynamic systems pertaining to: the physical/chemical level, the biological level, and the psychological level (or human mind).

Connections

between the three levels of reality and their

transformations

are represented, respectively, by

morphisms

/

functors

and

natural transformations

defined for

categories of molecular sets

,

http://planetmath.org/CategoryOfMRSystems3

categories of

(

M

,

R

)

-systems and

organismic supercategories

.

From a categorical ontology theory of levels viewpoint, however, the term complex may appear to be misplaced because

systems with chaos

, or chaotic dynamics, are currently defined by physicists as

‘complex systems’

, which may have placed a role in the emergence of living systems that are, in fact,

super-complex

. Therefore, the more appropriate

classification

of this relatively new area in mathematical or

theoretical biology

and Biophysics is

super-complex systems

biology,

s

-complex systems biology, or simply “systems biology”–as a more general approach where the focus may be not on the super-complexity aspects of living systems but on computer modeling of physiological, or functional genomics, integration of physiological flows, signaling pathways or interactomics. However, unlike the case of purely functional

(

M

,

R

)

-systems theory in

abstract relational biology

(ARB), complex systems biology (or systems biology) proponents are primarily concerned with the integration of data from a multitude of bioinformatics and genomic/proteomic/post-genomic (primarily structural) data;

C

⁢

S

⁢

B

scientists also aim to study

interactomics

or

metabolomics

primarily through computer-based data analysis, and often Bayesian-based attempts at integration. branches of mathematics that find applications in

C

⁢

S

⁢

B

are, for example: computer modeling,

colored graphs

, graph-theoretical based approaches, biotopology, genetic, metabolic and signaling network theories,

Bayesian models

, biostatistics, correlation techniques, and less frequently: abstract algebra, group theory,

groupoid

and category theory modeling of cell-cell interactions and biodynamics.

Title

complex systems biology (CSB)

Canonical name

ComplexSystemsBiologyCSB

Date of creation

2013-03-22 18:11:43

Last modified on

2013-03-22 18:11:43

Owner

bci1 (20947)

Last modified by

bci1 (20947)

Numerical id

44

Author

bci1 (20947)

Entry type

Topic

Classification

msc 00A30

Classification

msc 18A40

Classification

msc 37F99

Classification

msc 11Y16

Classification

msc 18A05

Classification

msc 03D15

Synonym

systems biology

Synonym

CSB

Synonym

abstract relational biology

Related topic

Category

Related topic

SystemDefinitions

Related topic

CategoryOfMRSystems3

Related topic

CategoricalOntology

Related topic

OrganismicSets2

Related topic

FunctionalBiology

Related topic

RosettaGroupoids

Related topic

NaturalTransformationsOfOrganismicStructures

Related topic

MolecularSetVariable

Related topic

CategoryOfMolecularSets

Related topic

SupercategoryOfVariableMolecularSets

Related topic

Mat

Defines

categorical ontology of levels

Defines

complex system biology modeling and ontology

Defines

CSB

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