1 Complex Systems Biophysics
1.1 Introduction
Complex Systems Biophysics (CSB) or Complex systems biology (CSB) 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 systems biology in entries that should be
described in fact as complex systems biology.
1.2 Categorical ontology: theories of existence levels
Definition 1.1. A categorical ontology theory of levels is often defined as the classification
of ontology, or theory of existence of items (objects–in the mathematical 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, categories of (M,R)-systems and organismic supercategories.
From a categorical ontology theory of levels viewpoint, however, the term complex is 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; CSB 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 CSB 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.
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