Cell signaling pathways as control modules: complexity for simplicity?

A biology begins to move into the ‘‘postgenomic’’ era, a key emerging question is how to approach the understanding of how complex biomolecular networks function as dynamical systems. Prominent examples include multimolecular protein ‘‘machines,’’ intracellular signal transduction cascades, and cell–cell communication mechanisms. As the proportion of identified components involved in any of these networks continues to increase, in certain instances already asymptotically, the daunting challenge of developing useful models—mathematical as well as conceptual—for how they work is drawing interest. At one extreme is the hope that fundamental relationships will emerge from essentially statistical analyses of large genomic and proteomic databases enumerating correlations among gene expression, protein levelystatey location, and cell behavior. At another extreme is a view that sheer computational power can be harnessed to create comprehensive simulations of the full set of fundamental physicochemical molecular interactions. Recently, an intermediate concept suggests a ‘‘modular’’ framework, treating subsystems of complex molecular networks as functional units that perform identifiable tasks—perhaps even able to be characterized in familiar engineering terms (1). The idea of functional modules as an effective approach to modeling biomolecular systems is quite appealing, because, even in nonbiological applications, engineering design is generally carried out in hierarchical or ‘‘nested’’ fashion. That is, the behavior of a system at the highest (i.e., largest space scale andyor longest time scale) level is typically analyzed and predicted with a model involving properties of the next-lower spaceytime scales; these properties are then analyzed and predicted with another set of models involving further subdivided space andyor time scales and so forth to a most detailed level as limited by current data. Despite its intuitive appeal, however, support for the concept of modular cell biology will demand that actual manifestations be identified that can lead to advances in understanding of cell function in molecular terms. Thus, the contribution by Yi et al. (2) is important in providing a compelling example, based on analysis of adaptation in bacterial chemotaxis (3) as a dynamical systems control process. Chemotaxis, most simply defined as a phenomenon in which cells can bias their locomotion along gradients in concentration of a chemical stimulus, has a well characterized foundation of molecular components involved in its signal transduction cascade in the case of the flagellar bacterium Escherichia coli (4). Indeed, the completeness of its component identification has permitted it to be unusually amenable to full computational simulation (5–7). Accordingly, the molecular network of signaling in bacterial chemotaxis offers a timely test bed for elucidating modular representation. As illustrated schematically in Fig. 1 and outlined by Yi et al. (2), this network comprises six intracellular proteins (designated A, B, R, W, Y, and Z) along with the transmembrane receptor that binds the stimulatory chemotactic ligand. Biologically, the input is the stimulatory ligand concentration, and the output is the frequency of tumbling (the process by which the cell stops swimming in a particular direction and reorients randomly). Because ligand concentration is perceived by receptor binding and the tumbling frequency is governed by the level of phosphorylated Y, a dynamical systems representation can use receptor occupancy and phosphorylated Y as surrogate input and output. A striking previous finding (3) had been that this system of molecular interactions possesses the characteristic of robustness, meaning that the inputyoutput relationship is relatively insensitive to variations in parameter values across a wide range. Robustness is an important property of an engineered system when functional behavior needs to be reliable in the face of external and internal uncertainties and heterogeneities. In the context of bacterial chemotaxis, the inputy output property found to be robust is that of perfect adaptation (8). That is, the output (tumbling frequency) attained at steady state after the transient after a change in input (stimulus concentration) is exactly equal to the prestimulus level regardless of the input value (see Fig. 2). This behavior seems to be necessary for bacteria to respond to stimulus concentration gradients (9). How is this crucial behavior accomplished by the biochemical signaling network of Fig. 1? What Yi et al. (2) have determined is that this network possesses the central characteristics of a process control strategy termed integral feedback control. Process control refers to an engineering operation by which a system makes decisions about how to best manipulate available variables to obtain a desired output. Feedback means that the information on which the decision is based derives from measurement of the output. Diverse types of feedback control are possible, including proportional (P), differential (D), and integral (I) as well as various combinations such as PI, PID, etc. (10). Integral feedback control bases decisions about manipulating system variables on the disparity between the desired output and the actual output integrated over time. A critical feature of integral feedback control, as outlined explicitly by Yi et al. (2), is that the steady-state value ultimately reached after a changed input is indeed the original prestimulus value— i.e., perfect adaptation. Control schemes lacking integral feedback, such as P or PD, in general yield new steady-state values after a changed input that are different from the prestimulus value; in process control parlance, the deviation is known as off-set. In many engineering applications, nonzero off-set is tolerable, but when it is not, implementation of an integral feedback control scheme is required. Hence, in considering models for bacterial chemotaxis, continuing our example, alternative options are available depending on the goal of the modeling effort. One can employ a full computational simulation of the complete set of physi-