Systems biology towards life in silico: mathematics of the control of living cells

Abstract

Systems Biology is the science that aims to understand how biological function absent from macromolecules in isolation, arises when they are components of their system. Dedicated to the memory of Reinhart Heinrich, this paper discusses the origin and evolution of the new part of systems biology that relates to met- abolic and signal-transduction pathways and extends mathematical biology so as to address postgenomic experimental reality. Various approaches to modeling the dynamics generated by metabolic and signal-transduction pathways are compared. The silicon cell approach aims to describe the intracellular network of interest precisely, by numerically integrating the precise rate equations that characterize the ways macromolecules' interact with each other. The non-equilibrium thermodynamic or 'lin-log' approach approximates the enzyme rate equations in terms of linear functions of the logarithms of the concentrations. Biochemical Systems Analysis approximates in terms of power laws. Importantly all these approaches link system behavior to molecular interaction properties. The latter two do this less precisely but enable analytical solutions. By limiting the questions asked, to optimal flux patterns, or to control of fluxes and concentrations around the (patho)physiological state, Flux Balance Analysis and Metabolic/Hierarchical Control Analysis again enable analytical solutions. Both the silicon cell approach and Metabolic/Hierarchical Control Analysis are able to highlight where and how system function derives from molecular interactions. The latter approach has also discovered a set of fundamental principles underlying the control of biological systems. The new law that relates concentration control to control by time is illustrated for an important signal transduction pathway, i.e. nuclear hormone receptor signaling such as relevant to bone formation. It is envisaged that there is much more Mathematical Biology to be discovered in the area between molecules and Life.

Systems Biology: The elements and principles of Life

“…A new such law, which we present here without its proof (which is analogous to the proofs given in [20]), is the summation law with reference to the control of noise by the catalytic processes:…”

Synthetic biology and regulatory networks: where metabolic systems biology meets control engineering

“…This magnitude however does not indicate whether an enzyme or a kinase of a specific reaction step is actually activated by the network components (i.e. self-regulation) or modulated by an experimenter in a synthetic design [84], or not modulated at all. To describe such regulatory information, Sauro [85] proposed a so-called 'partitioned regulatory coefficient' which describes how a perturbation in the rate of reaction i affects the enzyme activity of another reaction step j in terms of the change in the flux J j and the altered concentrations of the metabolites that interact directly with that enzyme.…”

Computing life: Add logos to biology and bios to physics

“…With respect to a human organism, this approach would lead to a mechanism-based computer replica of a whole body e the so-called silicon human (Westerhoff, 2001;Snoep et al, 2006;Hunter et al, 2008;Westerhoff et al, 2009a;Kolodkin et al, 2011a,b;Kolodkin et al, 2011a,b;Westerhoff et al, 2011).…”