Enzyme activities predicted by metabolite concentrations and solvent capacity in the cell

Experimental measurements or computational model predictions of the post-translational regulation of enzymes needed in a metabolic pathway is a difficult problem. Consequently, regulation is mostly known only for well-studied reactions of central metabolism in various model organisms. In this study, we use two approaches to predict enzyme regulation policies and investigate the hypothesis that regulation is driven by the need to maintain the solvent capacity in the cell. The first predictive method uses a statistical thermodynamics and metabolic control theory framework while the second method is performed using a hybrid optimization–reinforcement learning approach. Efficient regulation schemes were learned from experimental data that either agree with theoretical calculations or result in a higher cell fitness using maximum useful work as a metric. As previously hypothesized, regulation is herein shown to control the concentrations of both immediate and downstream product concentrations at physiological levels. Model predictions provide the following two novel general principles: (1) the regulation itself causes the reactions to be much further from equilibrium instead of the common assumption that highly non-equilibrium reactions are the targets for regulation; and (2) the minimal regulation needed to maintain metabolite levels at physiological concentrations maximizes the free energy dissipation rate instead of preserving a specific energy charge. The resulting energy dissipation rate is an emergent property of regulation which may be represented by a high value of the adenylate energy charge. In addition, the predictions demonstrate that the amount of regulation needed can be minimized if it is applied at the beginning or branch point of a pathway, in agreement with common notions. The approach is demonstrated for three pathways in the central metabolism of E. coli (gluconeogenesis, glycolysis-tricarboxylic acid (TCA) and pentose phosphate-TCA) that each require different regulation schemes. It is shown quantitatively that hexokinase, glucose 6-phosphate dehydrogenase and glyceraldehyde phosphate dehydrogenase, all branch points of pathways, play the largest roles in regulating central metabolism.

Machine Learning and Optimal Control of Enzyme Activities to Preserve Solvent Capacity in the Cell

ABSTRACTExperimental measurements or computational model predictions of the post-translational regulation of enzymes needed in a metabolic pathway is a difficult problem. Consequently, regulation is mostly known only for well-studied reactions of central metabolism in various model organisms. In this study, we utilize two approaches to predict enzyme regulation policies and investigate the hypothesis that regulation is driven by the need to maintain the solvent capacity in the cell. The first predictive method uses a statistical thermodynamics and metabolic control theory framework while the second method is performed using a hybrid optimization-reinforcement learning approach. Efficient regulation schemes were learned from experimental data that either agree with theoretical calculations or result in a higher cell fitness using maximum useful work as a metric. Model predictions provide the following novel general principles: (1) the regulation itself causes the reactions to be much further from equilibrium instead of the common assumption that highly non-equilibrium reactions are the targets for regulation; (2) regulation is used to maintain the concentrations of both immediate and downstream product concentrations rather than to maintain a specific energy charge; and (3) the minimal regulation needed to maintain metabolite levels at physiological concentrations also results in the maximal energy production rate that can be obtained at physiological conditions. The resulting energy production rate is an emergent property of regulation which may be represented by a high value of the adenylate energy charge. In addition, the predictions demonstrate that the amount of regulation needed can be minimized if it is applied at the beginning or branch point of a pathway, in agreement with common notions. The approach is demonstrated for three pathways in the central metabolism of E. coli (gluconeogenesis, glycolysis-TCA and Pentose Phosphate-TCA) that each require different regulation schemes. It is shown quantitatively that hexokinase, glucose 6-phosphate dehydrogenase and glyceraldehyde phosphate dehydrogenase, all branch points of pathways, play the largest roles in regulating central metabolism.

The pelagic microbial food web structure in Sanggou Bay, Yellow Sea: Spatial variation over four successive seasons

Sanggou Bay (Yellow Sea, China) is a small semi-closed bay in the eastern part of the Shandong Peninsula. In order to characterise the Sanggou Bay microbial food web (MFW) structure, we first documented, over four successive seasons, the distributions of environmental variables and abundances and biomasses of heterotrophic prokaryotes (HP), Synechococcus (SYN), picoeukaryrotes (PEUK), heterotrophic and pigmented nanoflagellates (HNF & PNF) and ciliates. The four season distributions in the Sanggou Bay of environmental variables and MFW components were submitted to cluster analysis, leading to distinguish Inner Bay and Outer Bay clusters at each season. In addition, Outer Bay MFW was found identical to the Inner Bay one but with a delay of one season, thus limiting to 4 the number of MFW characterising Sanggou Bay in that survey. We confirmed the existence of a strong relationship between HNF and HP, and extended this empirical relationship to the other MFW components: SYN, PEUK, PNF and ciliates. We also established upper and lower empirical linear boundaries for all the MFW component relationships with HP. The existence of these boundaries in the complex system made by the MFW stresses the need for systemic studies like the ones conducted for multi-enzyme systems and metabolic pathways that lead to the metabolic control theory. To better determine the MFW structure, we normalised for each sample, the biomass of the MFW components by that of HP. The normalised biomasses of SYN, PEUK, PNF and HNF had obvious seasonal variations with high values in summer or autumn, while ciliate normalised biomasses were low in summer and exhibited high values in winter. The main MFW-structure difference between Inner and Outer Bay clusters came from biomass differences for SYN, PEUK and PNF, whereas other component biomass-values were similar between Inner and Outer Bay clusters. Our study showed that the normalisation method could be used in other marine area to study the microbial food web structure. Indeed, the efficiency of this approach to determine MFW structure was demonstrated by successfully applying it to a similar data set from the literature and related to the Arabian Sea.

A metabolic control analysis of kinetic controls in ATP free energy metabolism in contracting skeletal muscle

A system analysis of ATP free energy metabolism in skeletal muscle was made using the principles of metabolic control theory. We developed a network model of ATP free energy metabolism in muscle consisting of actomyosin ATPase, sarcoplasmic reticulum (SR) Ca2+-ATPase, and mitochondria. These components were sufficient to capture the major aspects of the regulation of the cytosolic ATP-to-ADP concentration ratio (ATP/ADP) in muscle contraction and had inherent homeostatic properties regulating this free energy potential. As input for the analysis, we used ATP metabolic flux and the cytosolic ATP/ADP at steady state at six contraction frequencies between 0 and 2 Hz measured in human forearm flexor muscle by 31P-NMR spectroscopy. We used the mathematical formalism of metabolic control theory to analyze the distribution of fractional kinetic control of ATPase flux and the ATP/ADP in the network at steady state among the components over this experimental range and an extrapolated range of stimulation frequencies (up to 10 Hz). The control analysis showed that the contractile actomyosin ATPase has dominant kinetic control of ATP flux in forearm flexor muscle over the 0- to 1.6-Hz range of contraction frequencies that resulted in steady states, as determined by 31P-NMR. However, flux control begins to shift toward mitochondria at >1 Hz. This inversion of flux control from ATP demand to ATP supply control hierarchy progressed as the contraction frequency increased past 2 Hz and was nearly complete at 10 Hz. The functional significance of this result is that, at steady state, ATP free energy consumption cannot outstrip the ATP free energy supply. Therefore, this reduced, three-component muscle ATPase system is inherently homeostatic.