ModelingBiochemicalNetworks:ACellular-AutomataApproach by LemontB.Kier, Danail Bonchev*, and GregoryA.Buck Center for the Study of Biological Complexity, Virginia Commonwealth University, P.O. Box 842030, Richmond, VA 23284-2030, USA (phone:  1-804-827-7375,  1-804-827-0026; e-mail: lbkier@vcu.edu, dgbonchev@vcu.edu, gabuck@vcu.edu) The potential of the cellular-automata (CA) method for modeling biological networks is demonstrated for the mitogen-activated protein kinase (MAPK) signaling cascade. The models derived reproduced the high signal amplification through the cascade and the deviation of the cascade enzymes from the Michaelis±Menten kinetics, evidencing cooperativity effects. The patterns of pathway change upon varying substrate concentra- tions and enzyme efficiencies were identified and used to show the ways for controlling pathway processes. Guidance in the selection of enzyme inhibition targets with minimum side effects is one outcome of the study. 1.Introduction. ± Since its introduction 50 years ago, cellular automata (CA) have been used to conduct studies of various dynamical systems [1]. Of interest to us is the emerging role played by CA in the area of dynamic biological systems. Some applications to the modeling of physical systems, such as kinetic and thermodynamic control of chemical reactions, have been reported [2]. These studies point the way to the application of CA to encode the outcomes of the emerging properties in dynamic biochemical systems resulting from changes due to concentration alteration. Biological cell function is related to the interplay of macromolecules, mostly proteins that function as enzymes, and substrates. The antecedents of these proteins are the genes that program their creation. The totality of these molecules can be displayed as networks to reveal the functional relationships among them. A prominent direction of research today is to identify the ingredients that comprise the structural details of these networks. The next step is to attempt to model a fragment of the network that has a demonstrable biological function, the ultimate goal being the modeling of the entire network. Dynamic evolutionary networks have recently been recognized as a universal approach to complex systems, ranging from quantum gravity to biological cells and organisms, ecosystems, social groups, and market economy. The network approach is a non-reductionist approach enabling analysis of the systems as a whole, which makes it an ideal tool for system biology. Network topology is generally used in characterizing networks, focusing on their connectivity, neighborhood, and distance relationships. Network complexity has also been recently quantitatively characterized [3]. This abundance of cellular-network data ± produced by microarrays, two-dimensional gel chromatography, mass spectroscopy, and other techniques ± brings about another dimension of the network approach, allowing the tracing of the continuous changes of CHEMISTRY & BIODIVERSITY ± Vol. 2 (2005) 233  2005 Verlag Helvetica Chimica Acta AG, Zürich