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.

Numerous top-down kinetic models have been constructed to describe the cell cycle. These models have typically been constructed, validated and analyzed using model species (molecular intermediates and proteins) and phenotypic observations, and therefore do not focus on the individual model processes (reaction steps). We have developed a method to: (a) quantify the importance of each of the reaction steps in a kinetic model for the positioning of a switch point [i.e. the restriction point (RP)]; (b) relate this control of reaction steps to their effects on molecular species, using sensitivity and co-control analysis; and thereby (c) go beyond a correlation towards a causal relationship between molecular species and effects. The method is generic and can be applied to responses of any type, but is most useful for the analysis of dynamic and emergent responses such as switch points in the cell cycle. The strength of the analysis is illustrated for an existing mammalian cell cycle model focusing on the RP [Novak B, Tyson J (2004) J Theor Biol 230, 563-579]. The reactions in the model with the highest RP control were those involved in: (a) the interplay between retinoblastoma protein and E2F transcription factor; (b) those synthesizing the delayed response genes and cyclin D/Cdk4 in response to growth signals; (c) the E2F-dependent cyclin E/Cdk2 synthesis reaction; as well as (d) p27 formation reactions. Nine of the 23 intermediates were shown to have a good correlation between their concentration control and RP control. Sensitivity and co-control analysis indicated that the strongest control of the RP is mediated via the cyclin E/Cdk2:p27 complex concentration. Any perturbation of the RP could be related to a change in the concentration of this complex; apparent effects of other molecular species were indirect and always worked through cyclin E/Cdk2:p27, indicating a causal relationship between this complex and the positioning of the RP. Abbreviations DRG, delayed response genes; ERG, early response genes; MCA, metabolic control analysis; Rb, retinoblastoma protein; RP, restriction point.

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