complex systems biophysics ComplexSystemsBiophysics 2009-01-14 02:50:04 2009-06-09 19:51:40 Topic overview of the content of PlanetPhysics {\em Complex systems biology ($CSB$)} complex system modeling and ontology complex systems biology systems biology complex system biophysics complex system biodynamics % this is the default PlanetPhysics preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % there are many more packages, add them here as you need them % define commands here \usepackage{amsmath, amssymb, amsfonts, amsthm, amscd, latexsym} \usepackage{xypic} \usepackage[mathscr]{eucal} \theoremstyle{plain} \newtheorem{lemma}{Lemma}[section] \newtheorem{proposition}{Proposition}[section] \newtheorem{theorem}{Theorem}[section] \newtheorem{corollary}{Corollary}[section] \theoremstyle{definition} \newtheorem{definition}{Definition}[section] \newtheorem{example}{Example}[section] %\theoremstyle{remark} \newtheorem{remark}{Remark}[section] \newtheorem*{notation}{Notation} \newtheorem*{claim}{Claim} \renewcommand{\thefootnote}{\ensuremath{\fnsymbol{footnote%%@ }}} \numberwithin{equation}{section} \newcommand{\Ad}{{\rm Ad}} \newcommand{\Aut}{{\rm Aut}} \newcommand{\Cl}{{\rm Cl}} \newcommand{\Co}{{\rm Co}} \newcommand{\DES}{{\rm DES}} \newcommand{\Diff}{{\rm Diff}} \newcommand{\Dom}{{\rm Dom}} \newcommand{\Hol}{{\rm Hol}} \newcommand{\Mon}{{\rm Mon}} \newcommand{\Hom}{{\rm Hom}} \newcommand{\Ker}{{\rm Ker}} \newcommand{\Ind}{{\rm Ind}} \newcommand{\IM}{{\rm Im}} \newcommand{\Is}{{\rm Is}} \newcommand{\ID}{{\rm id}} \newcommand{\GL}{{\rm GL}} \newcommand{\Iso}{{\rm Iso}} \newcommand{\Sem}{{\rm Sem}} \newcommand{\St}{{\rm St}} \newcommand{\Sym}{{\rm Sym}} \newcommand{\SU}{{\rm SU}} \newcommand{\Tor}{{\rm Tor}} \newcommand{\U}{{\rm U}} \newcommand{\A}{\mathcal A} \newcommand{\Ce}{\mathcal C} \newcommand{\D}{\mathcal D} \newcommand{\E}{\mathcal E} \newcommand{\F}{\mathcal F} \newcommand{\G}{\mathcal G} \newcommand{\Q}{\mathcal Q} \newcommand{\R}{\mathcal R} \newcommand{\cS}{\mathcal S} \newcommand{\cU}{\mathcal U} \newcommand{\W}{\mathcal W} \newcommand{\bA}{\mathbb{A}} \newcommand{\bB}{\mathbb{B}} \newcommand{\bC}{\mathbb{C}} \newcommand{\bD}{\mathbb{D}} \newcommand{\bE}{\mathbb{E}} \newcommand{\bF}{\mathbb{F}} \newcommand{\bG}{\mathbb{G}} \newcommand{\bK}{\mathbb{K}} \newcommand{\bM}{\mathbb{M}} \newcommand{\bN}{\mathbb{N}} \newcommand{\bO}{\mathbb{O}} \newcommand{\bP}{\mathbb{P}} \newcommand{\bR}{\mathbb{R}} \newcommand{\bV}{\mathbb{V}} \newcommand{\bZ}{\mathbb{Z}} \newcommand{\bfE}{\mathbf{E}} \newcommand{\bfX}{\mathbf{X}} \newcommand{\bfY}{\mathbf{Y}} \newcommand{\bfZ}{\mathbf{Z}} \renewcommand{\O}{\Omega} \renewcommand{\o}{\omega} \newcommand{\vp}{\varphi} \newcommand{\vep}{\varepsilon} \newcommand{\diag}{{\rm diag}} \newcommand{\grp}{{\mathbb G}} \newcommand{\dgrp}{{\mathbb D}} \newcommand{\desp}{{\mathbb D^{\rm{es}}}} \newcommand{\Geod}{{\rm Geod}} \newcommand{\geod}{{\rm geod}} \newcommand{\hgr}{{\mathbb H}} \newcommand{\mgr}{{\mathbb M}} \newcommand{\ob}{{\rm Ob}} \newcommand{\obg}{{\rm Ob(\mathbb G)}} \newcommand{\obgp}{{\rm Ob(\mathbb G')}} \newcommand{\obh}{{\rm Ob(\mathbb H)}} \newcommand{\Osmooth}{{\Omega^{\infty}(X,*)}} \newcommand{\ghomotop}{{\rho_2^{\square}}} \newcommand{\gcalp}{{\mathbb G(\mathcal P)}} \newcommand{\rf}{{R_{\mathcal F}}} \newcommand{\glob}{{\rm glob}} \newcommand{\loc}{{\rm loc}} \newcommand{\TOP}{{\rm TOP}} \newcommand{\wti}{\widetilde} \newcommand{\what}{\widehat} \renewcommand{\a}{\alpha} \newcommand{\be}{\beta} \newcommand{\ga}{\gamma} \newcommand{\Ga}{\Gamma} \newcommand{\de}{\delta} \newcommand{\del}{\partial} \newcommand{\ka}{\kappa} \newcommand{\si}{\sigma} \newcommand{\ta}{\tau} \newcommand{\lra}{{\longrightarrow}} \newcommand{\ra}{{\rightarrow}} \newcommand{\rat}{{\rightarrowtail}} \newcommand{\oset}[1]{\overset {#1}{\ra}} \newcommand{\osetl}[1]{\overset {#1}{\lra}} \newcommand{\hr}{{\hookrightarrow}} \section{Complex Systems Biophysics ($CSB$)} \subsection{Introduction} {\em Complex Systems Biophysics ($CSB$)} or {\em 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 \PMlinkexternal{systems biology}{http://planetphysics.org/?op=getobj&from=books&id=248} in entries that should be described in fact as {\em complex systems biology}. \subsection{Categorical ontology: theories of existence levels} \begin{definition} A {\em 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, \PMlinkname{categories of $(M,R)$-systems}{CategoryOfMRSystems3} and organismic supercategories. \end{definition} From a categorical ontology theory of levels viewpoint, however, the term complex is misplaced because {\em systems with chaos}, or chaotic dynamics, are currently defined by physicists as {\em `complex systems'}, which may have placed a role in the emergence of living systems that are, in fact, {\em 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 {\em interactomics} or {\em 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.