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What lies behind the complexity of biological networks? Can one make sense of the web of interconnections that result from the myriad of molecular interactions within living cells? If one represents the different constituents of a cell (e.g. DNA, RNA, enzymes) as the nodes of a network and then draws a line between any two nodes whose corresponding constituents interact in a significant way, the complexity of the resulting network representation will be daunting. Is this complexity gratuitous—a kind of a historical accident? Are all these connections necessary? And how can one unravel this complexity to understand how these biological networks carry out their function robustly?
In trying to answer these questions, one key observation is that much of the complexity of cellular networks has to do with regulation of cellular function. In fact, regulation is a running theme throughout all of biology. Various strategies for regulation exist, but none is as ubiquitous as feedback. This is not unlike synthetic engineering systems where feedback control strategies can be found universally. Our approach to studying biological complexity is driven by the methods and techniques of control theory: an inter-disciplinary branch of engineering and mathematics that deals with the regulation of dynamical systems of any type. Control theoretic approaches have been applied profitably in a wide spectrum of disciplines, including economics, engineering, and the physical sciences. Control theory has had less impact on the biological sciences, although this is beginning to change. In this article, we use a control theory approach to explore the exquisite architecture of a well-known cellular stress system—the bacterial heat shock response. Our goal is to demonstrate the effectiveness of this approach and its potential to generate a deeper understanding of biological complexity.
The heat shock response in bacteria is an important mechanism for combating the stress associated with an increase in temperature in the cellular environment (1). The resulting increased heat causes the unfolding or misfolding of cellular proteins and leads to a state of cellular stress. The cell responds to the accumulation of nonfunctional proteins by the heat-induced upregulation of the heat shock proteins (HSPs), including both chaperones and proteases (2). The production of HSPs is regulated directly by alterations in the level, activity, and stability of the alternative sigma factor sigma-32 (3). The logic of the heat shock response is implemented through a hierarchy of feedback and feedforward controls that regulate both the amount of sigma-32 and its functionality. Upon a temperature upshift from 30° to 42°C, sigma-32 levels rapidly increase during what is referred to as the induction phase. Subsequently, sigma-32 levels gradually decrease during the adaptation phase, reaching a new steady state level that is higher than the level prior to the temperature upshift.
Figure 1.
We have developed a computational dynamic model that captures known aspects of the heat shock system (8). With the aid of this model, we discuss the logic of the heat shock response from a control theory perspective, drawing comparisons to synthetic engineering control systems. We begin by exploring the regulation of sigma-32 synthesis. At low temperatures, the sigma-32 messenger RNA (mRNA) has a secondary structure through base pairings, which has the effect of making translation of sigma-32 very inefficient. The increase of temperature leads to a fast melting of the secondary structure opening up the mRNA for a much more efficient translation of sigma-32 (4). This is akin to what control theorists refer to as feedforward control strategy. The heat shock system responds immediately to the disturbance (increased heat) by increasing the synthesis rate of the sigma factor. This direct response to the disturbance ensures a speedy heat shock response by not waiting until the effect of the increased temperature on the cellular proteins is sensed (i.e., no feedback is necessary). Feedforward strategies are very common in control engineering applications. One example is that of a driver on the freeway trying to maintain a constant distance with the car ahead. He or she would depress the brake pedal in response to seeing the brake light of the car ahead in anticipation of the imminent deceleration. This takes place before the driver is able to measure and respond to a decrease in the distance between the two vehicles (feedback control).
