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.

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Much of enzyme kinetics builds on simplifications enabled by the quasi‐steady‐state approximation and is highly useful when the concentration of the enzyme is much lower than that of its substrate. However, in vivo, this condition is often violated. In the present study, we show that, under conditions of realistic yet high enzyme concentrations, the quasi‐steady‐state approximation may readily be off by more than a factor of four when predicting concentrations. We then present a novel extension of the quasi‐steady‐state approximation based on the zero‐derivative principle, which requires considerably less theoretical work than did previous such extensions. We show that the first‐order zero‐derivative principle, already describes much more accurately the true enzyme dynamics at enzyme concentrations close to the concentration of their substrates. This should be particularly relevant for enzyme kinetics where the substrate is an enzyme, such as in phosphorelay and mitogen‐activated protein kinase pathways. We illustrate this for the important example of the phosphotransferase system involved in glucose uptake, metabolism and signaling. We find that this system, with a potential complexity of nine dimensions, can be understood accurately using the first‐order zero‐derivative principle in terms of the behavior of a single variable with all other concentrations constrained to follow that behavior.

Cells adapt to changes in their environment by the concerted action of many different regulatory mechanisms. Examples of such mechanisms are feedback inhibition by intermediates of metabolism, covalent modification of enzymes and changes in the abundance of mRNAs and proteins. These mechanisms act in parallel at different levels in the cellular hierarchy while regulating a single process. Existing hierarchical regulation analysis determines the relative importance of these mechanisms when the cell regulates a transition from one steady-state to another. Here, the analysis is extended to the regulation of time-dependent phenomena, for which two methods are introduced and illustrated with a kinetic model incorporating transcription and translation of metabolic enzymes.