Control Theory in Biology: From MCA to Chemotaxis

1. Control Theory in Biology: From MCA to Chemotaxis

2. What is Control Theory? �Principles and methods used to design engineering systems that maintain desirable performance by automatically adapting to changes in the environment.� More specifically, control theory is concerned with designing strategies that ensure the robust performance of a system. Examples of control systems are everywhere. Read the slide. Uncertainty in environment and components. Meet performance objectives in the presence of uncertainty.Read the slide. Uncertainty in environment and components. Meet performance objectives in the presence of uncertainty.

3. Basic Feedback Control System Here we have a feedback control system in which the variable being controlled (speed) is measured, the controller decides whether the speed needs to be increased or decreased, sends the signal to the actuator (gas pedal) that implements an action on the plant (car) that alters the speed. Here we have a feedback control system in which the variable being controlled (speed) is measured, the controller decides whether the speed needs to be increased or decreased, sends the signal to the actuator (gas pedal) that implements an action on the plant (car) that alters the speed.

4. Biological Example of Simple Feedback Control System Examples of feedback control in biological systems are everywhere. Here we have a simple metabolic pathway turning glucose into ATP. ATP is an allosteric regulator of one of the enzymes in the pathway so that the production of ATP is more robust to perturbations. It should be noted that in biological systems, the distinction between plant, controller, and actuator may not be so obvious. Examples of feedback control in biological systems are everywhere. Here we have a simple metabolic pathway turning glucose into ATP. ATP is an allosteric regulator of one of the enzymes in the pathway so that the production of ATP is more robust to perturbations. It should be noted that in biological systems, the distinction between plant, controller, and actuator may not be so obvious.

6. What is the Big Deal about Control? The real world is full of internal and external disturbances. Complex, high-performance systems are difficult to control. Instabilities can have catastrophic consequences. The more complex the system, the more important are issues concerning control. Control structures contribute greatly to the complexity of real-world systems. For engineers designing high-performance man-made systems such as jet airplanes or computer networks, issues of control and robustness are of the greatest concern.For engineers designing high-performance man-made systems such as jet airplanes or computer networks, issues of control and robustness are of the greatest concern.

7. Control Theory and Biology Biological systems are extremely complex, efficient, robust, and high-performance. Issues of control are paramount. Biological networks are dominated by feedback loops. Control theory is important for both engineering and reverse-engineering feedback systems. Likewise, we expect issues of control to be paramount in biology. Of course, the perspective will be different: engineers are trying forward engineer a robust system, whereas biologists are reverse-engineering robust systems. This difference in perspective has impeded communication between the two groups.Likewise, we expect issues of control to be paramount in biology. Of course, the perspective will be different: engineers are trying forward engineer a robust system, whereas biologists are reverse-engineering robust systems. This difference in perspective has impeded communication between the two groups.

8. Feedback Control and Disturbance Attenuation

9. Robustness and Sensitivity Function Measure of inverse robustness (fragility). Sensitivity of output to disturbance at all frequencies: S(w). Manipulating S(w) forms the essence of control design. As defined in the previous slide sensitivity is most intuitively thought of as the sensitivity of the output to a disturbance d. But, it can also be thought of as the scaled sensitivity of the output to a change in the plant gain under certain conditions. Many control engineers design systems by manipulating this sensitivity function. Not as easy as it may seem because there are tradeoffs which we will describe in more detail in Section 4. As defined in the previous slide sensitivity is most intuitively thought of as the sensitivity of the output to a disturbance d. But, it can also be thought of as the scaled sensitivity of the output to a change in the plant gain under certain conditions. Many control engineers design systems by manipulating this sensitivity function. Not as easy as it may seem because there are tradeoffs which we will describe in more detail in Section 4.

10. Outline Section 1: A Control Theoretic Approach to Metabolic Control Analysis (1 hour) Section 2: Integral Feedback Control: From Homeostasis to Chemotaxis (1 hour) Section 3: Intercellular Communication: Uses of Positive and Negative Feedback (1 hour)