Batch-to-Batch Adaptive Iterative Learning Control-Explicit Model Predictive Control Two-Tier Framework for the Control of Batch Transesterification Process.

To harness energy security and reduce carbon emissions, humankind is trying to switch toward renewable energy resources. To this extent, fatty acid methyl esters, also known as biodiesel, are popularly used as a green fuel. Fatty acid methyl esters can be produced by a batch transesterification reaction between vegetable oil and alcohol. Being a batch process, fatty acid methyl esters production is beset with issues such as uncertainties and unsteady state behavior, and therefore, adequate process control measures are necessitated. In this study, we have proposed a novel two-tier framework for the control of the fatty acid methyl esters production process. The proposed approach combines the constrained batch-to-batch iterative learning control technique and explicit model predictive control to obtain the desired concentration of the fatty acid methyl esters. In particular, the batch-to-batch iterative learning control technique is used to generate reactor temperature set-points, which is further utilized to obtain an optimal coolant flow rate by solving a quadratic objective cost function, with the help of explicit model predictive control. Our simulation results indicate that the fatty acid methyl esters concentration trajectory converges to the desired batch trajectory within four batches for uncertainty in activation energy and six batches for uncertainty in both inlet concentration of triglyceride and in activation energy even in the presence of process disturbances. The proposed approach was compared to the heuristic-based approach and constraint iterative learning control approach to showcase its efficacy.

Dual switch simulated moving bed chromatography: An optimal two-fraction yielding separation process.

Conventional Simulated Moving Bed Chromatography (C-SMBC) characterized by a single operating point comprising of the internal flow rates and switching period, yields a single fraction of the extract and raffinate, at cyclic steady state. In the current work, we deal with two-fraction yielding Dual Switch SMBC (DS-SMBC) characterized by two operating points implemented during alternate switches. The higher degrees of freedom in Dual Switch SMBC give it the potential of obtaining a higher average extract purity, for one of its two fractions, compared to conventional SMBC, at a certain minimum feed flow rate and minimum average extract recovery. This becomes possible with a trade-off in the average purity of the other extract fraction of Dual Switch SMBC, without any addition to the conventional SMBC equipment. We solve a multi-objective optimization problem wherein we maximize the average purity of one of the extract fractions of Dual Switch SMBC, with the requirement of certain minimum feed flow rate, minimum average extract recovery and minimum average purity of the non-objective extract fraction. One of the aims of the current work is deduction of the working principle of Dual Switch SMBC, that facilitates superior average extract purity. Next, we analyze the trade-offs due to the said process bounds on the objective i.e. average purity of objective extract fraction of Dual Switch SMBC. This has been done for the two case studies of separation: 1) linear isotherm based separation of fructose-glucose in deionized water on cation exchange resin 2) non-linear isotherm based separation of enantiomers of Tröger's base in ethanol on microcrystalline cellulose triacetate. The findings from the trade-offs in the multi-objective optimization problem, further corroborate our understanding of the working principle.

Rate and grade transition control using PI controller based supervisory and regulatory layers: Diacetone alcohol process case study.

Product rate and grade transitions are two significant operations undertaken by process plants to operate in uncertain environments. Rate transitions, typically dictated by economic considerations, are often implemented in open loop via a throughput manipulator (TPM). The absence of feedback of product rate to manipulate the TPM results in an offset during rate/grade transitions as well as in presence of feed-side disturbances. In this work, we explore use of a simple PI controller based supervisory control layer that guides the plantwide regulatory layer to achieve product rate targets during grade transition or in the presence of feed grade disturbances. While such a layer cannot incorporate optimal operation and constraint handling explicitly as in model predictive control, it obviates the need for advanced process control elements that medium-to-small scale industries can ill-afford. The PI based supervisory-regulatory control structure is illustrated using simulated case studies on a prototypical process for diacetone alcohol production comprising of a reactor followed by two distillation columns and a recycle.

Low soil moisture predisposes field-grown chickpea plants to dry root rot disease: evidence from simulation modeling and correlation analysis.

Rhizoctonia bataticola causes dry root rot (DRR), a devastating disease in chickpea (Cicer arietinum). DRR incidence increases under water deficit stress and high temperature. However, the roles of other edaphic and environmental factors remain unclear. Here, we performed an artificial neural network (ANN)-based prediction of DRR incidence considering DRR incidence data from previous reports and weather factors. ANN-based prediction using the backpropagation algorithm showed that the combination of total rainfall from November to January of the chickpea-growing season and average maximum temperature of the months October and November is crucial in determining DRR occurrence in chickpea fields. The prediction accuracy of DRR incidence was 84.6% with the validation dataset. Field trials at seven different locations in India with combination of low soil moisture and pathogen stress treatments confirmed the impact of low soil moisture on DRR incidence under different agroclimatic zones and helped in determining the correlation of soil factors with DRR incidence. Soil phosphorus, potassium, organic carbon, and clay content were positively correlated with DRR incidence, while soil silt content was negatively correlated. Our results establish the role of edaphic and other weather factors in chickpea DRR disease incidence. Our ANN-based model will allow the location-specific prediction of DRR incidence, enabling efficient decision-making in chickpea cultivation to minimize yield loss.

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.

Analysis of osmoadaptation system in budding yeast suggests that regulated degradation of glycerol synthesis enzyme is key to near-perfect adaptation.

In order to maintain its turgor pressure at a desired homeostatic level, budding yeast, Saccharomyces cerevisiae responds to the external variation of the osmotic pressure by varying its internal osmotic pressure through regulation of synthesis and transport of the intracellular glycerol. Hog1PP (dually phosphorylated Hog1), a final effector in the signalling pathway of the hyper osmotic stress, regulates the glycerol synthesis both at transcriptional and non-transcriptional stages. It is known that for a step-change in salt concentration leading to moderate osmotic shock, Hog1PP activity shows a transient response before it returns to the vicinity of pre-stimulus level. It is believed that an integrating process in a negative feedback loop can be a design strategy to yield such an adaptive response. Several negative feedback loops have been identified in the osmoadaptation system in yeast. However, the precise location of the integrating process in the osmoadaptation system which includes signalling, gene regulation, metabolism and biophysical modules is unclear. To address this issue, we developed a reduced model which captures various experimental observations of the osmoadaptation behaviour of wild type and mutant strains. Dynamic simulations and steady state analysis suggested that known information about the osmoadaptation system of budding yeast does not necessarily give a perfect integrating process through the known feedback loops of Hog1PP. On the other hand, regulation of glycerol synthesising enzyme degradation can result in a near integrating process leading to a near-perfect adaptation.

Quantification of metabolism in Saccharomyces cerevisiae under hyperosmotic conditions using elementary mode analysis.

Yeast metabolism under hyperosmotic stress conditions was quantified using elementary mode analysis to obtain insights into the metabolic status of the cell. The fluxes of elementary modes were determined as solutions to a linear program that used the stoichiometry of the elementary modes as constraints. The analysis demonstrated that distinctly different sets of elementary modes operate under normal and hyperosmotic conditions. During the adaptation phase, elementary modes that only produce glycerol are active, while elementary modes that yield biomass, ethanol, and glycerol become active after the adaptive phase. The flux distribution in the metabolic network, calculated using the fluxes in the elementary modes, was employed to obtain the flux ratio at key nodes. At the glucose 6-phosphate (G6P) node, 25% of the carbon influx was diverted towards the pentose phosphate pathway under normal growth conditions, while only 0.3% of the carbon flux was diverted towards the pentose phosphate pathway during growth at 1 M NaCl, indicating that cell growth is arrested under hyperosmotic conditions. Further, objective functions were used in the linear program to obtain optimal solution spaces corresponding to the different accumulation rates. The analysis demonstrated that while biomass formation was optimal under normal growth conditions, glycerol synthesis was closer to optimal during adaptation to osmotic shock.

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.

Mathematical modeling of fission yeast Schizosaccharomyces pombe cell cycle: exploring the role of multiple phosphatases.

UNLABELLED: Cell cycle is the central process that regulates growth and division in all eukaryotes. Based on the environmental condition sensed, the cell lies in a resting phase G0 or proceeds through the cyclic cell division process (G1→S→G2→M). These series of events and phase transitions are governed mainly by the highly conserved Cyclin dependent kinases (Cdks) and its positive and negative regulators. The cell cycle regulation of fission yeast Schizosaccharomyces pombe is modeled in this study. The study exploits a detailed molecular interaction map compiled based on the published model and experimental data. There are accumulating evidences about the prominent regulatory role of specific phosphatases in cell cycle regulations. The current study emphasizes the possible role of multiple phosphatases that governs the cell cycle regulation in fission yeast S. pombe. The ability of the model to reproduce the reported regulatory profile for the wild-type and various mutants was verified though simulations. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s11693-011-9090-7) contains supplementary material, which is available to authorized users.

Dynamic analysis of the KlGAL regulatory system in Kluyveromyces lactis: a comparative study with Saccharomyces cerevisiae.

UNLABELLED: The GAL regulatory system is highly conserved in yeast species of Saccharomyces cerevisiae and Kluyveromyces lactis. While the GAL system is a well studied system in S. cerevisiae, the dynamic behavior of the KlGAL system in K. lactis has not been characterized. Here, we have characterized the GAL system in yeast K. lactis by developing a dynamic model and comparing its performance to its not-so-distant cousin S. cerevisiae. The present analysis demonstrates the significance of the autoregulatory feedbacks due to KlGal4p, KlGal80p, KlGal1p and Lac12p on the dynamic performance of the KlGAL switch. The model predicts the experimentally observed absence of bistability in the wild type strain of K. lactis, unlike the short term memory of preculturing conditions observed in S. cerevisiae. The performance of the GAL switch is distinct for the two yeast species although they share similarities in the molecular components. The analysis suggests that the whole genome duplication of S. cerevisiae, which resulted in a dedicated inducer protein, Gal3p, may be responsible for the high sensitivity of the system to galactose concentrations. On the other hand, K. lactis uses a bifunctional protein as an inducer in addition to its galactokinase activity, which restricts its regulatory role and hence higher galactose levels in the medium are needed to trigger the GAL system. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s11693-011-9082-7) contains supplementary material, which is available to authorized users.

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.

Experimental and steady-state analysis of the GAL regulatory system in Kluyveromyces lactis.

The galactose uptake mechanism in yeast is a well-studied regulatory network. The regulatory players in the galactose regulatory mechanism (GAL system) are conserved in Saccharomyces cerevisiae and Kluyveromyces lactis, but the molecular mechanisms that occur as a result of the molecular interactions between them are different. The key differences in the GAL system of K. lactis relative to that of S. cerevisiae are: (a) the autoregulation of KlGAL4; (b) the dual role of KlGal1p as a metabolizing enzyme as well as a galactose-sensing protein; (c) the shuttling of KlGal1p between nucleus and cytoplasm; and (d) the nuclear confinement of KlGal80p. A steady-state model was used to elucidate the roles of these molecular mechanisms in the transcriptional response of the GAL system. The steady-state results were validated experimentally using measurements of beta-galactosidase to represent the expression for genes having two binding sites. The results showed that the autoregulation of the synthesis of activator KlGal4p is responsible for the leaky expression of GAL genes, even at high glucose concentrations. Furthermore, GAL gene expression in K. lactis shows low expression levels because of the limiting function of the bifunctional protein KlGal1p towards the induction process in order to cope with the need for the metabolism of lactose/galactose. The steady-state model of the GAL system of K. lactis provides an opportunity to compare with the design prevailing in S. cerevisiae. The comparison indicates that the existence of a protein, Gal3p, dedicated to the sensing of galactose in S. cerevisiae as a result of genome duplication has resulted in a system which metabolizes galactose efficiently.

A model-based study delineating the roles of the two signaling branches of Saccharomyces cerevisiae, Sho1 and Sln1, during adaptation to osmotic stress.

Adaptation to osmotic shock in Saccharomyces cerevisiae is brought about by the activation of two independent signaling pathways, Sho1 and Sln1, which in turn trigger the high osmolarity glycerol (HOG) pathway. The HOG pathway thereby activates the transcription of Gpd1p, an enzyme necessary to synthesize glycerol. The production of glycerol brings about a change in the intracellular osmolarity leading to adaptation. We present a detailed mechanistic model for the response of the yeast to hyperosmotic shock. The model integrates the two branches, Sho1 and Sln1, of the HOG pathway and also includes the mitogen-activated protein kinase cascade, gene regulation and metabolism. Model simulations are consistent with known experimental results for wild-type strain, and Ste11Delta and Ssk1Delta mutant strains subjected to osmotic stress. Simulation results predict that both the branches contribute to the overall wild-type response for moderate osmotic shock, while under severe osmotic shock, the cell responds mainly through the Sln1 branch. The analysis shows that the Sln1 branch helps the cell in preventing cross-talk to other signaling pathways by inhibiting ste11ste50 activation and also by increasing the phosphorylation of Ste50. We show that the negative feedbacks to the Sho1 branch must be faster than those to the Sln1 branch to simultaneously achieve pathway specificity and adaptation during hyperosmotic shock. Sensitivity analysis revealed that the presence of both branches imparts robust behavior to the cell under osmoadaptation to perturbations.

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.

Substrate specificity of lipases in alkoxycarbonylation reaction: QSAR model development and experimental validation.

Although lipases are known to catalyze alkoxycarbonylation reactions in organic solvents, the existing knowledge base on their substrate specificity in alkoxycarbonylation reaction is sparse. Moreover, models to predict substrate specificity have not been reported. Here, we report the experimentally measured rate constants for 180 acyl donor-alcohol pairs and demonstrate the two-step synthesis of over 70 disubstituted carbonate products from simple precursors such as diphenyl carbonate and alcohols. The efficiency of synthesis was found to be dependent on the order of alcohol addition. This motivated the need to develop a model to predict lipase specificity in alkoxycarbonylation reactions. A partial least square model has been developed to correlate the reaction rate with (i) descriptors of alcohol for a fixed acyl donor, (ii) descriptors of acyl donor for a fixed alcohol, (iii) descriptors of both the acyl donor and the alcohol. The number of descriptors being far greater than the number of observations was a potential limitation in the model development. This was addressed by selecting a subset of descriptors using a systematic procedure based on (a) correlation among the descriptors and step-wise regression methodology, and (b) variable influence on projection methodology. The model was able to accurately predict the reaction rate and the optimal order of addition of alcohols in the two-step synthesis of disubstituted carbonates using the enzyme mixture. The descriptor subset and the relevant model would benefit the users of lipases in synthetic applications while the modeling strategy presented here can have applications in predicting specificity of other enzymes.

Structured kinetic model to represent the utilization of multiple substrates in complex media during rifamycin B fermentation.

Industrial fermentations typically use media that are balanced with multiple substitutable substrates including complex carbon and nitrogen source. Yet, much of the modeling effort to date has mainly focused on defined media. Here, we present a structured model that accounts for growth and product formation kinetics of rifamycin B fermentation in a multi-substrate complex medium. The phenomenological model considers the organism to be an optimal strategist with an in-built mechanism that regulates the sequential and simultaneous uptake of the substrate combinations. This regulatory process is modeled by assuming that the uptake of a substrate depends on the level of a key enzyme or a set of enzymes, which may be inducible. Further, the fraction of flux through a given metabolic branch is estimated using a simple multi-variable constrained optimization. The model has the typical form of Monod equation with terms incorporating multiple limiting substrates and substrate inhibition. Several batch runs were set up with varying initial substrate concentrations to estimate the kinetic parameters for the rifamycin overproducer strain Amycolatopsis mediterranei S699. Glucose and ammonium sulfate (AMS) demonstrated significant substrate inhibition toward growth as well as product formation. The model correctly predicts the experimentally observed regulated simultaneous uptake of the substitutable substrate combinations under different fermentation conditions. The modeling results may have applications in the optimization and control of rifamycin B fermentation while the modeling strategy presented here would be applicable to other industrially important fermentations.

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.

A steady-state modeling approach to validate an in vivo mechanism of the GAL regulatory network in Saccharomyces cerevisiae.

Cellular regulation is a result of complex interactions arising from DNA-protein and protein-protein binding, autoregulation, and compartmentalization and shuttling of regulatory proteins. Experiments in molecular biology have identified these mechanisms recruited by a regulatory network. Mathematical models may be used to complement the knowledge-base provided by in vitro experimental methods. Interactions identified by in vitro experiments can lead to the hypothesis of multiple candidate models explaining the in vivo mechanism. The equilibrium dissociation constants for the various interactions and the total component concentration constitute constraints on the candidate models. In this work, we identify the most plausible in vivo network by comparing the output response to the experimental data. We demonstrate the methodology using the GAL system of Saccharomyces cerevisiae for which the steady-state analysis reveals that Gal3p neither dimerizes nor shuttles between the cytoplasm and the nucleus.

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?" 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.

Dynamic model of Escherichia coli tryptophan operon shows an optimal structural design.

A mathematical model has been developed to study the effect of external tryptophan on the trp operon. The model accounts for the effect of feedback repression by tryptophan through the Hill equation. We demonstrate that the trp operon maintains an intracellular steady-state concentration in a fivefold range irrespective of extracellular conditions. Dynamic behavior of the trp operon corresponding to varying levels of extracellular tryptophan illustrates the adaptive nature of regulation. Depending on the external tryptophan level in the medium, the transient response ranges from a rapid and underdamped to a sluggish and highly overdamped response. To test model fidelity, simulation results are compared with experimental data available in the literature. We further demonstrate the significance of the biological structure of the operon on the overall performance. Our analysis suggests that the tryptophan operon has evolved to a truly optimal design.