Sharad Bhartiya

A novel approach to multiparametric quadratic programming

Multiparametric (mp) programming pre-computes optimal solutions offline which are functions of parameters whose values become apparent online. This makes it particularly well suited for applications that need a rapid solution of online optimization problems. In this work, we propose a novel approach to multiparametric programming problems based on an enumeration of active sets and use it to obtain a parametric solution for a convex quadratic program (QP). To avoid the combinatorial explosion of the enumeration procedure, an active set pruning criterion is presented that makes the enumeration implicit. The method guarantees that all regions of the partition are critical regions without any artificial cuts, and further that no region of the parameter space is left unexplored.

Multiple feedback loops are key to a robust dynamic performance of tryptophan regulation in Escherichia coli

Living systems must adapt quickly and stably to uncertain environments. A common theme in cellular regulation is the presence of multiple feedback loops in the network. An example of such a feedback structure is regulation of tryptophan concentration in Escherichia coli. Here, three distinct feedback mechanisms, namely genetic regulation, mRNA attenuation and enzyme inhibition, regulate tryptophan synthesis. A pertinent question is whether such multiple feedback loops are “a case of regulatory overkill, or do these different feedback regulators have distinct functions?” [Freeman (2000) Nature 295, 313–319]. Another moot question is how robustness to uncertainties can be achieved structurally through biological interactions. Correlation between the feedback structure and robustness can be systematically studied by tools commonly employed in feedback theory. An analysis of feedback strategies in the tryptophan system in E. coli reveals that the network complexity arising due to the distributed feedback structure is responsible for the rapid and stable response observed even in the presence of system uncertainties.

Development of inferential measurements using neural networks

In many industrial processes, the most desirable variables to control are measured infrequently off-line in a quality control laboratory. In these situations, use of advanced control or optimization techniques requires use of inferred measurements generated from correlations. For well-understood processes, the structure of the correlation as well as the choice of inputs may be known a priori. However, many industrial processes are too complex and the appropriate form of the correlation and choice of input measurements are not obvious. Here, process knowledge, operating experience, and statistical methods play an important role in development of correlations. This paper describes a systematic approach to the development of nonlinear correlations for inferential measurements using neural networks. A three-step procedure is proposed. The first step consists of data collection and preprocessing. Next, the process variables are subjected to simple statistical analyses to identify a subset of measurements to be used in the inferential scheme. The third step involves generation of the inferential scheme. We demonstrate the methodology by inferring the ASTM 95% endpoint of a petroleum product using data from a domestic US refinery.

Multiple feedback loop design in the tryptophan regulatory network of Escherichia coli suggests a paradigm for robust regulation of processes in series

Biological networks have evolved through adaptation in uncertain environments. Of the different possible design paradigms, some may offer functional advantages over others. These designs can be quantified by the structure of the network resulting from molecular interactions and the parameter values. One may, therefore, like to identify the design motif present in the evolved network that makes it preferable over other alternatives. In this work, we focus on the regulatory networks characterized by serially arranged processes, which are regulated by multiple feedback loops. Specifically, we consider the tryptophan system present in Escherichia coli, which may be conceptualized as three processes in series, namely transcription, translation and tryptophan synthesis. The multiple feedback loop motif results from three distinct negative feedback loops, namely genetic repression, mRNA attenuation and enzyme inhibition. A framework is introduced to identify the key design components of this network responsible for its physiological performance. We demonstrate that the multiple feedback loop motif, as seen in the tryptophan system, enables robust performance to variations in system parameters while maintaining a rapid response to achieve homeostasis. Superior performance, if arising from a design principle, is intrinsic and, therefore, inherent to any similarly designed system, either natural or engineered. An experimental engineering implementation of the multiple feedback loop design on a two-tank system supports the generality of the robust attributes offered by the design.

Global optimization of mixed-integer nonlinear (polynomial) programming problems: the Bernstein polynomial approach

In this paper, we propose an algorithm for constrained global optimization of mixed-integer nonlinear programming (MINLP) problems. The proposed algorithm uses the Bernstein polynomial form in a branch-and-bound framework. Ingredients such as continuous relaxation, branching for integer decision variables, and fathoming for each subproblem in the branch-and-bound tree are used. The performance of the proposed algorithm is tested and compared with several state-of-the-art MINLP solvers, on two sets of test problems. The results of the tests show the superiority of the proposed algorithm over the state-of-the-art solvers in terms of the chosen performance metrics.

Autoregulation of regulatory proteins is key for dynamic operation of GAL switch in Saccharomyces cerevisiae

Autoregulation and nucleocytoplasmic shuttling play important roles in the operation of the GAL regulatory system. However, the significance of these mechanisms in the overall operation of the switch is unclear. In this work, we develop a dynamic model for the GAL system and further validate the same using steady‐state and dynamic experimental expression data. Next, the model is used to delineate the relevance of shuttling and autoregulation in response to inducing, repressing, and non‐inducing–non‐repressing media. The analysis indicates that autoregulation of the repressor, Gal80p, is key in obtaining three distinct steady states in response to the three media. In particular, the analysis rationalizes the intuitively paradoxical observation that the concentration of repressor, Gal80p, actually increases in response to an increase in the inducer concentration. On the other hand, although nucleocytoplasmic shuttling does not affect the dynamics of the system, it plays a dominant role in obtaining a sensitive response to galactose. The dynamic model was also used to obtain insights on the preculturing effect on the system behavior.

Characterization of the adaptive response and growth upon hyperosmotic shock in Saccharomyces cerevisiae

Molecular and physiological details of osmoadaptation in yeast Saccharomyces cerevisiae are well characterized. It is well known that a cell, upon osmotic shock, delays its growth, produces a compatible solute like glycerol in yeast to maintain the osmotic equilibrium. Many genes are regulated by the hyperosmolarity glycerol (HOG) singling pathway, some of which in turn control the carbon flux in the glycolytic pathway for glycerol synthesis and reduced growth. The whole process of survival of cells under hyperosmotic stress is controlled at multiple levels in signaling and metabolic pathways. To better understand the multi-level regulations in yeast to osmotic shock, a mathematical model is formulated which integrates the growth and the osmoadaptation process. The model included the HOG pathway which consists of Sho1 and Sln1 signaling branches, gene regulation, metabolism and cell growth on glucose and ethanol. Experiments were performed to characterize the effect of various concentrations of salt on the wild-type and mutant strains. The model was able to successfully predict the experimental observations for both the wild-type and mutant strains. Further, the model was used to analyze the effects of various regulatory mechanisms prevalent in the signaling and metabolic pathways which are essential in achieving optimum growth in a saline medium. The analysis demonstrated the relevance of the combined effects of regulation at several points in the signaling and metabolic pathways including activation of GPD1 and GPD2, inhibition of PYK and PDC1, closure of the Fps1 channel, volume effect on the glucose uptake rate, downregulation of ethanol synthesis and upregulation of ALD6 for acetate synthesis. The analysis demonstrated that these combined effects orchestrated the phenomena of adaptation to osmotic stress in yeast.

Systems biology of GAL regulon in Saccharomyces cerevisiae

Evolutionary success of an organism depends on its ability to express or adapt to constantly changing environmental conditions. Saccharomyces cerevisiae has evolved an elaborate genetic circuit to regulate the expression of galactose‐metabolizing enzymes in the presence of galactose but in the absence of glucose. The circuit possesses molecular mechanisms such as multiple binding sites, cooperativity, autoregulation, nucleocytoplasmic shuttling, and substrate sensing mechanism. Furthermore, the GAL system consists of two positive (activating) feedback and one negative (repressing) feedback loops. These individual mechanisms, elucidated through experimental approach, can be integrated to obtain a system‐wide behavior. Mathematical models in conjunction with guided experiments have demonstrated system‐level properties such as ultrasensitivity, memory, noise attenuation, rapid response, and sensitive response arising out of the molecular interactions. These system‐level properties allow S. cerevisiae to adapt and grow in a galactose medium under noisy and changing environments. This review focuses on system‐level models and properties of the GAL regulon Copyright

PROFILE CONTROL IN DISTRIBUTED PARAMETER SYSTEMS USING LEXICOGRAPHIC OPTIMIZATION BASED MPC

Abstract We have studied control of spatial property in distributed parameter systems using a lexicographic optimization based MPC formulation to prioritize the different sections of the profile. We demonstrate using a hypothetical plug flow reactor that the proposed method has significant benefits when the target profile as a whole is unachievable but parts of which can be satisfied. We have also applied the proposed control strategy for property profile control in a continuous pulp digester of industrial size, which represents a large scale distributed parameter system.

Implementation of integral feedback control in biological systems

Integral control design ensures that a key variable in a system is tightly maintained within acceptable levels. This approach has been widely used in engineering systems to ensure offset free operation in the presence of perturbations. Several biological systems employ such an integral control design to regulate cellular processes. An integral control design motif requires a negative feedback and an integrating process in the network loop. This review describes several biological systems, ranging from bacteria to higher organisms in which the presence of integral control principle has been hypothesized. The review highlights that in addition to the negative feedback, occurrence of zero‐order kinetics in the process is a key element to realize the integral control strategy. Although the integral control motif is common to these systems, the mechanisms involved in achieving it are highly specific and can be incorporated at the level of signaling, metabolism, or at the phenotypic levels. WIREs Syst Biol Med 2015, 7:301–316. doi: 10.1002/wsbm.1307