Deciphering the regulation of metabolism with dynamic optimization: an overview of recent advances.

Understanding optimality principles shaping the evolution of regulatory networks controlling metabolism is crucial for deriving a holistic picture of how metabolism is integrated into key cellular processes such as growth, adaptation and pathogenicity. While in the past the focus of research in pathway regulation was mainly based on stationary states, more recently dynamic optimization has proved to be an ideal tool to decipher regulatory strategies for metabolic pathways in response to environmental cues. In this short review, we summarize recent advances in the elucidation of optimal regulatory strategies and identification of optimal control points in metabolic pathways. We discuss biological implications of the discovered optimality principles on genome organization and provide examples how the derived knowledge can be used to identify new treatment strategies against pathogens. Furthermore, we briefly discuss the variety of approaches for solving dynamic optimization problems and emphasize whole-cell resource allocation models as an important emerging area of research that will allow us to study the regulation of metabolism on the whole-cell level.

Optimality principles reveal a complex interplay of intermediate toxicity and kinetic efficiency in the regulation of prokaryotic metabolism.

A precise and rapid adjustment of fluxes through metabolic pathways is crucial for organisms to prevail in changing environmental conditions. Based on this reasoning, many guiding principles that govern the evolution of metabolic networks and their regulation have been uncovered. To this end, methods from dynamic optimization are ideally suited since they allow to uncover optimality principles behind the regulation of metabolic networks. We used dynamic optimization to investigate the influence of toxic intermediates in connection with the efficiency of enzymes on the regulation of a linear metabolic pathway. Our results predict that transcriptional regulation favors the control of highly efficient enzymes with less toxic upstream intermediates to reduce accumulation of toxic downstream intermediates. We show that the derived optimality principles hold by the analysis of the interplay between intermediate toxicity and pathway regulation in the metabolic pathways of over 5000 sequenced prokaryotes. Moreover, using the lipopolysaccharide biosynthesis in Escherichia coli as an example, we show how knowledge about the relation of regulation, kinetic efficiency and intermediate toxicity can be used to identify drug targets, which control endogenous toxic metabolites and prevent microbial growth. Beyond prokaryotes, we discuss the potential of our findings for the development of antifungal drugs.

Optimality in the zonation of ammonia detoxification in rodent liver.

The rodent liver eliminates toxic ammonia. In mammals, three enzymes (or enzyme systems) are involved in this process: glutaminase, glutamine synthetase and the urea cycle enzymes, represented by carbamoyl phosphate synthetase. The distribution of these enzymes for optimal ammonia detoxification was determined by numerical optimization. This in silico approach predicted that the enzymes have to be zonated in order to achieve maximal removal of toxic ammonia and minimal changes in glutamine concentration. Using 13 compartments, representing hepatocytes, the following predictions were generated: glutamine synthetase is active only within a narrow pericentral zone. Glutaminase and carbamoyl phosphate synthetase are located in the periportal zone in a non-homogeneous distribution. This correlates well with the paradoxical observation that in a first step glutamine-bound ammonia is released (by glutaminase) although one of the functions of the liver is detoxification by ammonia fixation. The in silico approach correctly predicted the in vivo enzyme distributions also for non-physiological conditions (e.g. starvation) and during regeneration after tetrachloromethane (CCl4) intoxication. Metabolite concentrations of glutamine, ammonia and urea in each compartment, representing individual hepatocytes, were predicted. Finally, a sensitivity analysis showed a striking robustness of the results. These bioinformatics predictions were validated experimentally by immunohistochemistry and are supported by the literature. In summary, optimization approaches like the one applied can provide valuable explanations and high-quality predictions for in vivo enzyme and metabolite distributions in tissues and can reveal unknown metabolic functions.

Footprints of optimal protein assembly strategies in the operonic structure of prokaryotes.

In this work, we investigate optimality principles behind synthesis strategies for protein complexes using a dynamic optimization approach. We show that the cellular capacity of protein synthesis has a strong influence on optimal synthesis strategies reaching from a simultaneous to a sequential synthesis of the subunits of a protein complex. Sequential synthesis is preferred if protein synthesis is strongly limited, whereas a simultaneous synthesis is optimal in situations with a high protein synthesis capacity. We confirm the predictions of our optimization approach through the analysis of the operonic organization of protein complexes in several hundred prokaryotes. Thereby, we are able to show that cellular protein synthesis capacity is a driving force in the dissolution of operons comprising the subunits of a protein complex. Thus, we also provide a tested hypothesis explaining why the subunits of many prokaryotic protein complexes are distributed across several operons despite the presumably less precise co-regulation.

Optimal programs of pathway control: dissecting the influence of pathway topology and feedback inhibition on pathway regulation.

BACKGROUND: Adjusting the capacity of metabolic pathways in response to rapidly changing environmental conditions is an important component of microbial adaptation strategies to stochastic environments. In this work, we use advanced dynamic optimization techniques combined with theoretical models to study which reactions in pathways are optimally targeted by regulatory interactions in order to minimize the regulatory effort that is required to adjust the flux through a complex metabolic network. Moreover, we analyze how constraints in the speed at which an organism can respond on a proteomic level influences these optimal targets of pathway control. RESULTS: We find that limitations in protein biosynthetic rates have a strong influence. With increasing protein biosynthetic rates the regulatory effort targeting the initial enzyme in a pathway is reduced while the regulatory effort in the terminal enzyme is increased. Studying the impact of allosteric regulation for different pathway topologies, we find that the presence of feedback inhibition by products of metabolic pathways allows organisms to reduce the regulatory effort that is required to control a metabolic pathway in all cases. In a linear pathway this even leads to the case where the sole transcriptional regulatory control of the terminal enzyme is sufficient to control flux through the entire pathway. We confirm the utilization of these pathway regulation strategies through the large-scale analysis of transcriptional regulation in several hundred prokaryotes. CONCLUSIONS: This work expands our knowledge about optimal programs of pathway control. Optimal targets of pathway control strongly depend on the speed at which proteins can be synthesized. Moreover, post-translational regulation such as allosteric regulation allows to strongly reduce the number of transcriptional regulatory interactions required to control a metabolic pathway across different pathway topologies.

Dynamic optimization identifies optimal programmes for pathway regulation in prokaryotes.

To survive in fluctuating environmental conditions, microorganisms must be able to quickly react to environmental challenges by upregulating the expression of genes encoding metabolic pathways. Here we show that protein abundance and protein synthesis capacity are key factors that determine the optimal strategy for the activation of a metabolic pathway. If protein abundance relative to protein synthesis capacity increases, the strategies shift from the simultaneous activation of all enzymes to the sequential activation of groups of enzymes and finally to a sequential activation of individual enzymes along the pathway. In the case of pathways with large differences in protein abundance, even more complex pathway activation strategies with a delayed activation of low abundance enzymes and an accelerated activation of high abundance enzymes are optimal. We confirm the existence of these pathway activation strategies as well as their dependence on our proposed constraints for a large number of metabolic pathways in several hundred prokaryotes.

Optimal regulatory strategies for metabolic pathways in Escherichia coli depending on protein costs.

While previous studies have shed light on the link between the structure of metabolism and its transcriptional regulation, the extent to which transcriptional regulation controls metabolism has not yet been fully explored. In this work, we address this problem by integrating a large number of experimental data sets with a model of the metabolism of Escherichia coli. Using a combination of computational tools including the concept of elementary flux patterns, methods from network inference and dynamic optimization, we find that transcriptional regulation of pathways reflects the protein investment into these pathways. While pathways that are associated to a high protein cost are controlled by fine-tuned transcriptional programs, pathways that only require a small protein cost are transcriptionally controlled in a few key reactions. As a reason for the occurrence of these different regulatory strategies, we identify an evolutionary trade-off between the conflicting requirements to reduce protein investment and the requirement to be able to respond rapidly to changes in environmental conditions.

Modelling the optimal timing in metabolic pathway activation-use of Pontryagin's Maximum Principle and role of the Golden section.

The time course of enzyme concentrations in metabolic pathways can be predicted on the basis of the optimality criterion of minimizing the time period in which an essential product is generated. This criterion is in line with the widely accepted view that high fitness requires high pathway flux. Here, based on Pontryagin's Maximum Principle, a method is developed to solve the corresponding constrained optimal control problem in an almost exclusively analytical way and, thus, to calculate optimal enzyme profiles, when linear, irreversible rate laws are assumed. Three different problem formulations are considered and the corresponding optimization results are derived. Besides the minimization of transition time, we consider an operation time in which 90% of the substrate has been converted into product. In that case, only the enzyme at the lower end of the pathway rather than all enzymes are active in the last phase. In all cases, biphasic or multiphasic time courses are obtained. The biological meaning of the results in terms of a consecutive just-in-time expression of metabolic genes is discussed. For the special case of two-enzyme systems, the role of the Golden section in the solution is outlined.