Francis J. Doyle

Robustness of cellular functions.

Robustness, the ability to maintain performance in the face of perturbations and uncertainty, is a long-recognized key property of living systems. Owing to intimate links to cellular complexity, however, its molecular and cellular basis has only recently begun to be understood. Theoretical approaches to complex engineered systems can provide guidelines for investigating cellular robustness because biology and engineering employ a common set of basic mechanisms in different combinations. Robustness may be a key to understanding cellular complexity, elucidating design principles, and fostering closer interactions between experimentation and theory.

Dynamic Flux Balance Analysis of Diauxic Growth in Escherichia coli

Flux Balance Analysis (FBA) has been used in the past to analyze microbial metabolic networks. Typically, FBA is used to study the metabolic flux at a particular steady state of the system. However, there are many situations where the reprogramming of the metabolic network is important. Therefore, the dynamics of these metabolic networks have to be studied. In this paper, we have extended FBA to account for dynamics and present two different formulations for dynamic FBA. These two approaches were used in the analysis of diauxic growth in Escherichia coli. Dynamic FBA was used to simulate the batch growth of E. coli on glucose, and the predictions were found to qualitatively match experimental data. The dynamic FBA formalism was also used to study the sensitivity to the objective function. It was found that an instantaneous objective function resulted in better predictions than a terminal-type objective function. The constraints that govern the growth at different phases in the batch culture were also identified. Therefore, dynamic FBA provides a framework for analyzing the transience of metabolism due to metabolic reprogramming and for obtaining insights for the design of metabolic networks.

Intercellular Coupling Confers Robustness against Mutations in the SCN Circadian Clock Network

Molecular mechanisms of the mammalian circadian clock have been studied primarily by genetic perturbation and behavioral analysis. Here, we used bioluminescence imaging to monitor Per2 gene expression in tissues and cells from clock mutant mice. We discovered that Per1 and Cry1 are required for sustained rhythms in peripheral tissues and cells, and in neurons dissociated from the suprachiasmatic nuclei (SCN). Per2 is also required for sustained rhythms, whereas Cry2 and Per3 deficiencies cause only period length defects. However, oscillator network interactions in the SCN can compensate for Per1 or Cry1 deficiency, preserving sustained rhythmicity in mutant SCN slices and behavior. Thus, behavior does not necessarily reflect cell-autonomous clock phenotypes. Our studies reveal previously unappreciated requirements for Per1, Per2, and Cry1 in sustaining cellular circadian rhythmicity and demonstrate that SCN intercellular coupling is essential not only to synchronize component cellular oscillators but also for robustness against genetic perturbations.

A model-based algorithm for blood glucose control in Type I diabetic patients

A model-based-predictive control algorithm is developed to maintain normoglycemia in the Type I diabetic patient using a closed-loop insulin infusion pump. Utilizing compartmental modeling techniques, a fundamental model of the diabetic patient is constructed. The resulting nineteenth-order nonlinear pharmacokinetic-pharmacodynamic representation is used in controller synthesis. Linear identification of an input-output model from noisy patient data is performed by filtering the impulse-response coefficients via projection onto the Laguerre basis. A linear model predictive controller is developed using the identified step response model. Controller performance for unmeasured disturbance rejection (50 g oral glucose tolerance test) is examined. Glucose setpoint tracking performance is improved by designing a second controller which substitutes a more detailed internal model including state-estimation and a Kalman filter for the input-output representation The state-estimating controller maintains glucose within 15 mg/dl of the setpoint in the presence of measurement noise. Under noise-free conditions, the model based predictive controller using state estimation outperforms an internal model controller from literature (49.4% reduction in undershoot and 45.7% reduction in settling time). These results demonstrate the potential use of predictive algorithms for blood glucose control in an insulin infusion pump.

A novel computational model of the circadian clock in Arabidopsis that incorporates PRR7 and PRR9

In plants, as in animals, the core mechanism to retain rhythmic gene expression relies on the interaction of multiple feedback loops. In recent years, molecular genetic techniques have revealed a complex network of clock components in Arabidopsis. To gain insight into the dynamics of these interactions, new components need to be integrated into the mathematical model of the plant clock. Our approach accelerates the iterative process of model identification, to incorporate new components, and to systematically test different proposed structural hypotheses. Recent studies indicate that the pseudo‐response regulators PRR7 and PRR9 play a key role in the core clock of Arabidopsis. We incorporate PRR7 and PRR9 into an existing model involving the transcription factors TIMING OF CAB (TOC1), LATE ELONGATED HYPOCOTYL (LHY) and CIRCADIAN CLOCK ASSOCIATED (CCA1). We propose candidate models based on experimental hypotheses and identify the computational models with the application of an optimization routine. Validation is accomplished through systematic analysis of various mutant phenotypes. We introduce and apply sensitivity analysis as a novel tool for analyzing and distinguishing the characteristics of proposed architectures, which also allows for further validation of the hypothesized structures.

Identification of Small Molecule Activators of Cryptochrome

Modulating the Clock Because of the close association of the circadian clock with a wide range of physiological processes, identification of clock-modulating small molecules may prove useful for the treatment of circadian-related disorders, which include circadian sleep disorders, cardiovascular disease, cancer, and metabolic disease. Hirota et al. (p. 1094, published online 12 July) screened for chemical compounds that affected the period of the circadian clock in a human osteosarcoma cell line. A carbazole derivative named KL001 appeared to act by inhibiting proteolytic degradation of the cryptochrome proteins, which in turn caused a lengthening of the circadian period. KL001 also inhibited glucagon-induced gluconeogenesis in primary cultures of mouse hepatocytes. A small molecule binds to a core protein in the circadian clock and slows down time. Impairment of the circadian clock has been associated with numerous disorders, including metabolic disease. Although small molecules that modulate clock function might offer therapeutic approaches to such diseases, only a few compounds have been identified that selectively target core clock proteins. From an unbiased cell-based circadian phenotypic screen, we identified KL001, a small molecule that specifically interacts with cryptochrome (CRY). KL001 prevented ubiquitin-dependent degradation of CRY, resulting in lengthening of the circadian period. In combination with mathematical modeling, our studies using KL001 revealed that CRY1 and CRY2 share a similar functional role in the period regulation. Furthermore, KL001-mediated CRY stabilization inhibited glucagon-induced gluconeogenesis in primary hepatocytes. KL001 thus provides a tool to study the regulation of CRY-dependent physiology and aid development of clock-based therapeutics of diabetes.

Fully Integrated Artificial Pancreas in Type 1 Diabetes: Modular Closed-Loop Glucose Control Maintains Near Normoglycemia

Integrated closed-loop control (CLC), combining continuous glucose monitoring (CGM) with insulin pump (continuous subcutaneous insulin infusion [CSII]), known as artificial pancreas, can help optimize glycemic control in diabetes. We present a fundamental modular concept for CLC design, illustrated by clinical studies involving 11 adolescents and 27 adults at the Universities of Virginia, Padova, and Montpellier. We tested two modular CLC constructs: standard control to range (sCTR), designed to augment pump plus CGM by preventing extreme glucose excursions; and enhanced control to range (eCTR), designed to truly optimize control within near normoglycemia of 3.9–10 mmol/L. The CLC system was fully integrated using automated data transfer CGM→algorithm→CSII. All studies used randomized crossover design comparing CSII versus CLC during identical 22-h hospitalizations including meals, overnight rest, and 30-min exercise. sCTR increased significantly the time in near normoglycemia from 61 to 74%, simultaneously reducing hypoglycemia 2.7-fold. eCTR improved mean blood glucose from 7.73 to 6.68 mmol/L without increasing hypoglycemia, achieved 97% in near normoglycemia and 77% in tight glycemic control, and reduced variability overnight. In conclusion, sCTR and eCTR represent sequential steps toward automated CLC, preventing extremes (sCTR) and further optimizing control (eCTR). This approach inspires compelling new concepts: modular assembly, sequential deployment, testing, and clinical acceptance of custom-built CLC systems tailored to individual patient needs.

Identification and control using Volterra models

1. Introduction.- 2. Qualitative Behavior.- 3. Restrietions & Extensions.- 4. Determination of Volterra Model Parameters.- 5. Practical Considerations in Volterra Model Identification.- 6. Model-Based Controller Synthesis.- 7. Advanced Direct Synthesis Controller Design.- 8. Model Predictive Control Using Volterra Series.- 9. Application Case Studies.- 10. Summary.

Nonlinear model predictive control of a simulated multivariable polymerization reactor using second-order volterra models

Abstract Two formulations of a nonlinear model predictive control scheme based on the second-order Volterra series model are presented. The first formulation determines the control action using successive substitution, and the second method directly solves a fourth-order nonlinear programming problem on-line. One case study is presented for the SISO control of an isothermal reactor which utilizes the first controller formulation. A second case study is presented for the multivariable control of a large reactor, and uses the nonlinear programming formulation for the controller. The model coefficients for both examples are obtained by discretizing the bilinear Taylor series approximation of the fundamental model and calculating Markov parameters. The relationships between discrete and continuous-time bilinear model matrices using an explicit fourth-order Runge-Kutta method are also included. The responses to setpoint changes of both reactors controlled with a linear model predictive control scheme and the second-order Volterra model predictive control scheme are compared to desired, linear reference trajectories. In the majority of the cases examined, the responses obtained by the Volterra controller followed the reference trajectories more closely. Practical issues, including the reduction of the number of model parameters, are addressed in both case studies.

Model-based blood glucose control for type 1 diabetes via parametric programming

An advanced model-based control technique for regulating the blood glucose for patients with Type 1 diabetes is presented. The optimal insulin delivery rate is obtained off-line as an explicit function of the current blood glucose concentration of the patient by using novel parametric programming algorithms, developed at Imperial College London. The implementation of the optimal insulin delivery rate, therefore, requires simple function evaluation and minimal on-line computations. The proposed framework also addresses the uncertainty in the model due to interpatient and intrapatient variability by identifying the model parameters which ensure that a feasible control law can be obtained. The developments reported in this paper are expected to simplify the insulin delivery mechanism, thereby enhancing the quality of life of the patient