Ljubisa Miskovic

Towards kinetic modeling of genome-scale metabolic networks without sacrificing stoichiometric, thermodynamic and physiological constraints.

Mathematical modeling is an essential tool for the comprehensive understanding of cell metabolism and its interactions with the environmental and process conditions. Recent developments in the construction and analysis of stoichiometric models made it possible to define limits on steady-state metabolic behavior using flux balance analysis. However, detailed information on enzyme kinetics and enzyme regulation is needed to formulate kinetic models that can accurately capture the dynamic metabolic responses. The use of mechanistic enzyme kinetics is a difficult task due to uncertainty in the kinetic properties of enzymes. Therefore, the majority of recent works considered only mass action kinetics for reactions in metabolic networks. Herein, we applied the optimization and risk analysis of complex living entities (ORACLE) framework and constructed a large-scale mechanistic kinetic model of optimally grown Escherichia coli. We investigated the complex interplay between stoichiometry, thermodynamics, and kinetics in determining the flexibility and capabilities of metabolism. Our results indicate that enzyme saturation is a necessary consideration in modeling metabolic networks and it extends the feasible ranges of metabolic fluxes and metabolite concentrations. Our results further suggest that enzymes in metabolic networks have evolved to function at different saturation states to ensure greater flexibility and robustness of cellular metabolism.

Identification and the Information Matrix: How to Get Just Sufficiently Rich?

In prediction error identification, the information matrix plays a central role. Specifically, when the system is in the model set, the covariance matrix of the parameter estimates converges asymptotically, up to a scaling factor, to the inverse of the information matrix. The existence of a finite covariance matrix thus depends on the positive definiteness of the information matrix, and the rate of convergence of the parameter estimate depends on its ¿size¿. The information matrix is also the key tool in the solution of optimal experiment design procedures, which have become a focus of recent attention. Introducing a geometric framework, we provide a complete analysis, for arbitrary model structures, of the minimum degree of richness required to guarantee the nonsingularity of the information matrix. We then particularize these results to all commonly used model structures, both in open loop and in closed loop. In a closed-loop setup, our results provide an unexpected and precisely quantifiable trade-off between controller degree and required degree of external excitation.

Iterative correlation-based controller tuning with application to a magnetic suspension system

Iterative tuning of the parameters of a restricted-order controller using the data acquired in closed-loop operation seems to be a promising idea, especially for tuning PID controllers in industrial applications. In this paper, a new tuning approach based on decorrelation is proposed. The basic idea is to make the output error between the designed and achieved closed-loop systems uncorrelated with the reference signal. The controller parameters are calculated as the solution of correlation equations involving instrumental variables. Different choices of instrumental variables are proposed and compared via simulation. The stochastic properties of the correlation approach are compared with those of standard IFT using Monte-Carlo simulation. The proposed approach is also implemented on an experimental magnetic suspension system, and excellent performance using only a few real-time experiments is achieved.

Identification of multi-input systems: variance analysis and input design issues

This paper examines the identification of multi-input systems. Motivated by an experiment design problem (should one excite the various inputs simultaneously or separately), we examine the effect of an additional input on the variance of the estimated coefficients of parametrized rational transfer function models, with special emphasis on the commonly used FIR, ARX, ARMAX, OE and BJ model structures. We first show that, for model structures that have common parameters in the input-output and noise models (e.g. ARMAX), any additional input contributes to a reduction of the covariance of all parameter estimates. We then show that the accuracy improvement extends beyond the case of common parameters in all transfer functions, and we show exactly which parameter estimates are improved when a new input is added. We also conclude that it is always better to excite all inputs simultaneously.

Correlation-based tuning of decoupling multivariable controllers

The iterative method labelled correlation-based tuning (CbT) is considered in this paper for tuning linear time-invariant multivariable controllers. The approach allows one to tune some elements of the controller transfer function matrix to satisfy the desired closed-loop performance, while the other elements are tuned to mutually decouple the closed-loop outputs. Decoupling is achieved by decorrelating a given reference with the non-corresponding outputs. The controller parameters are calculated either by solving a correlation equation (decorrelation procedure) or by minimizing a cross-correlation function (correlation reduction). In addition, the preferred way of exciting a 2x2 system for CbT is investigated via the accuracy of the estimated controller parameters. It is shown that simultaneous excitation of both reference signals does not improve the accuracy of the estimated controller parameters compared to the case of sequential excitation. In fact, one must choose between low experimental cost (simultaneous excitation) and better accuracy of the estimated parameters (sequential excitation). The theoretical results are illustrated via three simulation studies.

Production of biofuels and biochemicals: in need of an ORACLE

The engineering of cells for the production of fuels and chemicals involves simultaneous optimization of multiple objectives, such as specific productivity, extended substrate range and improved tolerance - all under a great degree of uncertainty. The achievement of these objectives under physiological and process constraints will be impossible without the use of mathematical modeling. However, the limited information and the uncertainty in the available information require new methods for modeling and simulation that will characterize the uncertainty and will quantify, in a statistical sense, the expectations of success of alternative metabolic engineering strategies. We discuss these considerations toward developing a framework for the Optimization and Risk Analysis of Complex Living Entities (ORACLE) - a computational method that integrates available information into a mathematical structure to calculate control coefficients.

From network models to network responses: integration of thermodynamic and kinetic properties of yeast genome‐scale metabolic networks

Many important problems in cell biology arise from the dense nonlinear interactions between functional modules. The importance of mathematical modelling and computer simulation in understanding cellular processes is now indisputable and widely appreciated. Genome-scale metabolic models have gained much popularity and utility in helping us to understand and test hypotheses about these complex networks. However, there are some caveats that come with the use and interpretation of different types of metabolic models, which we aim to highlight here. We discuss and illustrate how the integration of thermodynamic and kinetic properties of the yeast metabolic networks in network analyses can help in understanding and utilizing this organism more successfully in the areas of metabolic engineering, synthetic biology and disease treatment.

Iterative minimization of H2 control performance criteria

a b s t r a c t Data-based control design methods most often consist of iterative adjustment of the controllers parameters towards the parameter values which minimize an H2 performance criterion. Typically, batches of input-output data collected from the system are used to feed directly a gradient descent optimization — no process model is used. A limiting factor in the application of these methods is the lack of useful conditions guaranteeing convergence to the global minimum; several adaptive control algorithmssufferfromthesamelimitation.InthispapertheH2 performancecriterionisanalyzedinorder to characterize and enlarge the set of initial parameter values from which a gradient descent algorithm can converge to its global minimum.

Closed-Loop Identification of MIMO Systems: A New Look at Identifiability and Experiment Design

This paper addresses a question raised by a leading expert in the identification of multivariable systems: “Is it necessary to excite all reference signals for the identification of a multivariable system operating in closed loop with a linear time-invariant controller?” On the basis of earlier results on identifiability of closed-loop systems, he conjectured that this was necessary. We show that it is not, on the basis of a careful re-examination of the notions of identifiability and informative experiments for closed-loop systems.

Control of an active suspension system as a benchmark for design and optimisation of restricted-complexity controllers

A benchmark problem for restricted complexity controller design is introduced. The objective is to design the lowest-order controller which meets the control specifications for an active suspension system. The input-output data of the plant are provided on the benchmark site and the final controllers are evaluated using the closed-loop data. Thirteen solutions proposed to solve the benchmark problem are briefly presented and classified in terms of methodology and compared with respect to their complexity and performance.