Cellular nonlinear aspects

Although the importance of a systemic perspective on metabolism has only recently attained widespread attention, a formal frameworks for systemic analysis has already been developed since the late 1960s. Biochemical Systems Theory (BST), put forward by Savageau and others [142, 144 147], seeks to provide a unified framework for the analysis of cellular reaction networks. Predating Metabolic Control Analysis, BST emphasizes three main aspects in the analysis of metabolism [319] (i) the importance of the interconnections, rather than the components, for cellular function (ii) the nonlinearity of biochemical rate equations (iii) the need for a unified mathematical treatment. Similar to MCA, the achievements associated with BST would warrant a more elaborate treatment, here we will focus on BST solely as a tool for the approximation and numerical simulation of complex biochemical reaction networks. 

Mechanical forces, stresses, strains, and velocities play a critical role in many important aspects of cell physiology, such as cell adhesion, motility, and signal transduction. The modeling of cell mechanics is a challenging task because of the interconnection of mechanical, electrical, and biochemical processes involvement of different structural cellular components and multiple timescales. It can involve nonlinear mechanics and thermodynamics, and because of its complexity, it is most hkely that it will require the use of computational techniques. Typical steps in the development of a cell modeling include constitutive relations describing the state or evolution of the cell or its components, mathematical solution or transformation of the corresponding equations and boundary conditions, and computational implementation of the model. 

Finally, Fd like to stress the dynamic aspects which are of utmost importance for an understanding of biochemical processes. Biochemical processes are essentially open in nature. This means that all enzymes are constantly, stochastically or periodically activated by substrates which are produced by the cellular environment or by precursor enzymes and transformed so that products are picked up by other enzymes within a reaction sequence. Biochemical processes are controlled by their cyclic design, by allosteric feedback and by electrochemical coupling. The discovery of the principle of cyclic processes induced the notion that the dynamic coupling of networks of integrated biochemical processes must be extremely complex and nonlinear. Indeed, today we observe a large variety of coupled dynamic states and time pattern formations in biochemical processes from simple periodic reactions to the most complex chaotic states of biochemical turnover. 

---