Babatunde A. Ogunnaike

Nonlinear model-based control using second-order Volterra models

Abstract A nonlinear controller synthesis scheme is presented that retains the original spirit and characteristics of conventional (linear) model predictive control (MPC) while extending its capabilities to nonlinear systems. The scheme employs a Volterra model—a simple and convenient nonlinear extension of the linear convolution model employed by conventional MPC—and gives rise to a controller composed of a conventional linear controller augmented by an auxiliary loop of nonlinear ‘corrections’. Simulation case studies involving two different examples representative of the typical spectrum of nonlinear behavior in real chemical processes—an industrial polymerization reactor and an isothermal reactor exhibiting inverse response—are used to demonstrate the practical utility of the control scheme and to evaluate its performance.

Ligand‐dependent responses of the ErbB signaling network: experimental and modeling analyses

Deregulation of ErbB signaling plays a key role in the progression of multiple human cancers. To help understand ErbB signaling quantitatively, in this work we combine traditional experiments with computational modeling, building a model that describes how stimulation of all four ErbB receptors with epidermal growth factor (EGF) and heregulin (HRG) leads to activation of two critical downstream proteins, extracellular‐signal‐regulated kinase (ERK) and Akt. Model analysis and experimental validation show that (i) ErbB2 overexpression, which occurs in approximately 25% of all breast cancers, transforms transient EGF‐induced signaling into sustained signaling, (ii) HRG‐induced ERK activity is much more robust to the ERK cascade inhibitor U0126 than EGF‐induced ERK activity, and (iii) phosphoinositol‐3 kinase is a major regulator of post‐peak but not pre‐peak EGF‐induced ERK activity. Sensitivity analysis leads to the hypothesis that ERK activation is robust to parameter perturbation at high ligand doses, while Akt activation is not.

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.

Ligand-Specific c-Fos Expression Emerges from the Spatiotemporal Control of ErbB Network Dynamics

Activation of ErbB receptors by epidermal growth factor (EGF) or heregulin (HRG) determines distinct cell-fate decisions, although signals propagate through shared pathways. Using mathematical modeling and experimental approaches, we unravel how HRG and EGF generate distinct, all-or-none responses of the phosphorylated transcription factor c-Fos. In the cytosol, EGF induces transient and HRG induces sustained ERK activation. In the nucleus, however, ERK activity and c-fos mRNA expression are transient for both ligands. Knockdown of dual-specificity phosphatases extends HRG-stimulated nuclear ERK activation, but not c-fos mRNA expression, implying the existence of a HRG-induced repressor of c-fos transcription. Further experiments confirmed that this repressor is mainly induced by HRG, but not EGF, and requires new protein synthesis. We show how a spatially distributed, signaling-transcription cascade robustly discriminates between transient and sustained ERK activities at the c-Fos system level. The proposed control mechanisms are general and operate in different cell types, stimulated by various ligands.

Multi-variate approach to global protein aggregation behavior and kinetics: Effects of pH, NaCl, and temperature for α-chymotrypsinogen A

A global characterization of nonnative aggregation is presented for alpha-chymotrypsinogen A (aCgn) as a function of temperature (T), pH, and [NaCl]. Changes in unfolding free energy, native-state second osmotic virial coefficient (B(22)), and aggregation pathways and kinetics were qualitatively and quantitatively determined using a combination of size-exclusion chromatography, multi-angle laser light scattering, and circular dichroism and fluorescence spectroscopy. Results were analyzed quantitatively using multi-variate statistical models and a recently developed mechanistic model that naturally accounts for changes in aggregation pathway due to competition between unfolding, nucleation, chain polymerization, aggregate condensation, and phase separation. State diagrams are presented that show the natural progression between different aggregation behaviors or pathways. Together, the results show that pH and [NaCl] determine both the rates of aggregation and what aggregation behavior or pathway holds. In contrast, T affects primarily only aggregation rates, in large part due to changes in unfolding free energy. Finally, it is shown that B(22) correlates strongly with which type of aggregation pathway is followed, suggesting a potentially useful approach for predicting and controlling physical properties of the resulting aggregates.

The identification of nonlinear models for process control using tailored “plant-friendly” input sequences

Abstract This paper considers certain practical aspects of the identification of nonlinear empirical models for chemical process dynamics. The primary focus is the identification of second-order Volterra models using input sequences that offer the following three advantages: (1) they are “plant friendly;” (2) they simplify the required computations; (3) they can emphasize certain model parameters over others. To provide a quantitative basis for discussing the first of these advantages, this paper defines a friendliness index f that relates to the number of changes that occur in the sequence. For convenience, this paper also considers an additional nonlinear model structure: the Volterra–Laguerre model. To illustrate the practical utility of the input sequences considered here, second-order Volterra and Volterra–Laguerre models are developed that approximate the dynamics of a first-principles model of methyl methacrylate polymerization.

Control of product quality for batch nylon 6,6 autoclaves

The focus of this paper is on improving the monitoring and control of end-use quality variables in batch nylon 6,6 autoclaves. Relatively few on-line measurements and frequent disturbances often result in a significant amount of variability in the product quality variables for this system. To lessen the sensitivity to these disturbances, a fundamental model of the nylon autoclave process is developed from first principles and is subsequently used to develop and test practical reactor control configurations. Various PID implementations are evaluated according to their robustness to typical process disturbances. The model is also used to formulate strategies designed to detect process disturbances and monitor the development of the quality variables on-line. The process monitoring results are then used in conjunction with inferential quality control strategies to improve robustness to typical process disturbances.

Quantitative Modeling and Analysis of the Transforming Growth Factor β Signaling Pathway

Transforming growth factor beta (TGF-beta) signaling, which regulates multiple cellular processes including proliferation, apoptosis, and differentiation, plays an important but incompletely understood role in normal and cancerous tissues. For instance, although TGF-beta functions as a tumor suppressor in the premalignant stages of tumorigenesis, paradoxically, it also seems to act as a tumor promoter in advanced cancer leading to metastasis. The mechanisms by which TGF-beta elicits such diverse responses during cancer progression are still not entirely clear. As a first step toward understanding TGF-beta signaling quantitatively, we have developed a comprehensive, dynamic model of the canonical TGF-beta pathway via Smad transcription factors. By describing how an extracellular signal of the TGF-beta ligand is sensed by receptors and transmitted into the nucleus through intracellular Smad proteins, the model provides quantitative insight into how TGF-beta-induced responses are modulated and regulated. Subsequent model analysis shows that mechanisms associated with Smad activation by ligand-activated receptor, nuclear complex formation among Smad proteins, and inactivation of ligand-activated Smad (e.g., degradation, dephosphorylation) may be critical for regulating TGF-beta-targeted functional responses. The model was also used to predict dynamic characteristics of the Smad-mediated pathway in abnormal cells, from which we generated four testable hypotheses regarding potential mechanisms by which TGF-betas tumor-suppressive roles may appear to morph into tumor-promotion during cancer progression.

Emergence of bimodal cell population responses from the interplay between analog single-cell signaling and protein expression noise

BackgroundCell-to-cell variability in protein expression can be large, and its propagation through signaling networks affects biological outcomes. Here, we apply deterministic and probabilistic models and biochemical measurements to study how network topologies and cell-to-cell protein abundance variations interact to shape signaling responses.ResultsWe observe bimodal distributions of extracellular signal-regulated kinase (ERK) responses to epidermal growth factor (EGF) stimulation, which are generally thought to indicate bistable or ultrasensitive signaling behavior in single cells. Surprisingly, we find that a simple MAPK/ERK-cascade model with negative feedback that displays graded, analog ERK responses at a single cell level can explain the experimentally observed bimodality at the cell population level. Model analysis suggests that a conversion of graded input–output responses in single cells to digital responses at the population level is caused by a broad distribution of ERK pathway activation thresholds brought about by cell-to-cell variability in protein expression.ConclusionsOur results show that bimodal signaling response distributions do not necessarily imply digital (ultrasensitive or bistable) single cell signaling, and the interplay between protein expression noise and network topologies can bring about digital population responses from analog single cell dose responses. Thus, cells can retain the benefits of robustness arising from negative feedback, while simultaneously generating population-level on/off responses that are thought to be critical for regulating cell fate decisions.