Feedback Control Of Dynamic Systems Franklin 14.pdf
Click Here >>> https://ssurll.com/2sYeze
An introduction to feedback and control in physical, biological, engineering, and information sciences. Basic principles of feedback and its use as a tool for altering the dynamics of systems and managing uncertainty. Key themes throughout the course will include input/output response, modeling and model reduction, linear versus nonlinear models, and local versus global behavior. This course is taught concurrently with CDS 110a, but is intended for students who are interested primarily in the concepts and tools of control theory and not the analytical techniques for design and synthesis of control systems.
Dynamic control of gene expression can have far-reaching implications for biotechnological applications and biological discovery. Thanks to the advantages of light, optogenetics has emerged as an ideal technology for this task. Current state-of-the-art methods for optical expression control fail to combine precision with repeatability and cannot withstand changing operating culture conditions. Here, we present a novel fully automatic experimental platform for the robust and precise long-term optogenetic regulation of protein production in liquid Escherichia coli cultures. Using a computer-controlled light-responsive two-component system, we accurately track prescribed dynamic green fluorescent protein expression profiles through the application of feedback control, and show that the system adapts to global perturbations such as nutrient and temperature changes. We demonstrate the efficacy and potential utility of our approach by placing a key metabolic enzyme under optogenetic control, thus enabling dynamic regulation of the culture growth rate with potential applications in bacterial physiology studies and biotechnology.
A key emerging optogenetic application is the control of gene expression. Such control may be achieved in an open-loop manner by administering light-induced perturbations to a given system with the goal of achieving a prescribed expression profile. State-of-the-art work in this area9 involved the use of a finely tuned mathematical model obtained through a long characterization process and recalibrated daily. While such open-loop operation is effective for parts characterization, as nicely demonstrated in Olson et al.9, the general applicability of this approach in biotechnology is ultimately limited by the fact that the model is only accurate for one specific culture condition, and any alterations or slight disturbances to cultures during the course of an experiment would result in inaccurate tracking. Precision, robustness and repeatability are thus restricted by day-to-day variability in cellular behaviour, changes in the cellular environment, and the typically limited quantitative understanding of the open-loop controlled system. Overcoming these challenges promises to unlock the huge potential of optogenetics for biotechnology applications. An effective and feasible technology for achieving this is in silico automatic feedback control10. This involves measuring the system output in real-time, comparing it against a desired tracking objective, and feeding the difference to a dynamic control system, which in turn uses it to compute the necessary adjustments of the system input. Automatic feedback control of cell populations has been implemented11,12,13 with promising results using microfluidics. However, while microfluidic approaches are well-suited for high-throughput analysis of single-cell behaviour as well as biomedical diagnostics, promising biotechnological applications of optogenetics, such as control of metabolic activity in microbial production strains14,15, require the use of large-volume liquid cell cultures.
Our turbidostat follows a simple and intuitive design18 (see the Methods section and Supplementary Note 1). An infrared sensor measures the amount of light absorbed by the culture and feeds the measurement to a proportional-integral feedback controller implemented on a microcontroller, which computes the necessary dilution rate to maintain a given culture density. The control signal is then fed to two peristaltic pumps, one of which adds fresh medium and the other removes liquid at the same rate.
Dots denote sfGFP measurements, lines are polynomial fits. (a) Constant reference tracking: for each constant reference level, a PI and an MPC controller were used. Grey bands determine a tolerance margin around each setpoint (±5% of the target level). It should be noted that MPC responses achieve the target (that is, stay inside the grey band) much earlier than PI responses. The applied green light inputs, expressed as a percentage of the maximum green LED intensity, are shown for the starred reference. All applied light inputs can be found in Supplementary Note 5. The maximum allowable LED intensity for MPC was limited to 60% since the dose-response curve (Supplementary Note 11) of the system is almost flat above this level. PI gains were set to KP=80 and KI=8. (b) Tracking of a sinusoidal reference: since the reference varies relatively fast with respect to the intrinsic timescales of the system, tracking is impossible for the PI controller (gains as in a). On the other hand, MPC control was still capable of excellent tracking. The grey band denotes a tolerance margin around the reference trajectory (±5% of the reference curve). To determine the repeatability of open-loop input application, the MPC input profile (green line) was applied to a culture grown on a different day, using the same growth protocol and conditions. Day-to-day variability in the dynamical behaviour of the culture is manifested in the deviation of the dark-grey response from the reference trajectory. (c) Tracking of a piecewise linear reference: PI control is known to generate a constant steady-state tracking error for linearly increasing inputs25 (unless the controlled system behaves like an integrator by itself), and was therefore not tested. MPC again achieved very good tracking (grey band depicts ±5% of the final constant level). Repetition of the MPC input profile (green line) on a different day, resulted in the dark-grey response.
Disturbances are unwanted perturbations that can alter the response, the behaviour or the measured output of the controlled system, and consequently lead to gross inaccuracies in the tracking of a given reference. Disturbances in a biochemical system may arise due to unwanted interactions with its cellular environment, or changes in the external environment of the culture. In fact, complete isolation of the controlled system from its intra- and extra-cellular environment is nearly impossible. One of the principal reasons for the use of feedback control is its ability to attenuate the effect of disturbances on the system output25, thereby enabling robust tracking of the desired output reference. On the contrary, open-loop control is completely incapable of disturbance rejection: by their very nature, disturbances are unmodelled inputs that cannot be anticipated, and thus application of pre-computed input sequences cannot compensate for output deviations caused by disturbances.
We have presented an integrated framework for automatic optogenetic feedback of liquid cell cultures that comprises tailor-made hardware and software. With its help, we have been able to achieve excellent precision in the regulation of protein expression driven by a light-switchable two-component system in E. coli. Moreover, we have shown how feedback operation enables the system to function reliably even in the presence of large global perturbations to the culture, such as a change of the growth medium, a temperature shift or an input perturbation. Taken together, these benefits demonstrate the advantages of feedback regulation over open-loop control approaches typically reported in the optogenetics literature.
Our experimental platform also enabled us to explore the accuracy/complexity trade-offs of two different feedback-control schemes, and investigate their interplay with the biological system under study. Our results on the control of continuous cell cultures nicely complement recently presented work36, which compared the performance of three alternative control strategies (PI, MPC and Zero Average Dynamics) for the regulation of fluorescent protein levels using a galactose-inducible system in yeast grown inside a microfluidic device. They also constitute a significant extension, both in terms of complexity and accuracy, of the work presented in ref. 37.
Besides the feedback-control algorithms tested in this work, our experimental platform can be easily used with alternative, possibly more advanced, controllers and serves as a test bed for various control approaches from the rich automatic control literature38.
Our system can be expanded in several directions: the use of parallel continuous cell cultures and multiplexed sampling (for example, with the help of a simple x-y-z robotic arm) will accelerate data collection and speed up the controller-tuning process. On the other hand, more complex feedback-control tasks (such as the simultaneous control of protein mean and variance over a cell population) can be accomplished via the incorporation of multiple orthogonal optogenetic systems within the same cell41, and the use of multivariable control techniques42.
To demonstrate the capabilities and potential of optogenetic feedback, we chose to dynamically regulate the culture growth rate by placing the supply of intracellular methionine under optogenetic control, thus effectively controlling the global protein-synthesis rate in the cells. Despite the increased dynamical complexity of the resulting system, we demonstrated that precise growth-rate regulation is possible and indeed achievable without the use of sophisticated measurement systems, simply by monitoring a control signal in our turbidostat. Furthermore, the ability to control the growth rate can be also be used to study how bacterial physiology responds to dynamic variations in global protein-synthesis rates43, thus overcoming the limitations of studies focusing on steady-state growth. 2b1af7f3a8