Prediction of Metabolite Concentrations, Rate Constants and Post-Translational Regulation Using Maximum Entropy-Based Simulations with Application to Central Metabolism of Neurospora crassa

Probabilistic and maximum entropy modeling of chemical reaction systems: Characteristics and comparisons to mass action kinetic models

We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with standard chemical potentials, we derive and compare the free energy dissipation and the entropy production rates. We express the relation between entropy production and the chemical master equation for modeling metabolism, which unifies chemical kinetics and chemical thermodynamics. Because prediction uncertainty with respect to parameter variability is frequently a concern with mass action models utilizing rate constants, we compare and contrast the maximum entropy model, which has its own set of rate parameters, to a population of standard mass action models in which the rate constants are randomly chosen. We show that a maximum entropy model is characterized by a high probability of free energy dissipation rate and likewise entropy production rate, relative to other models. We then characterize the variability of the maximum entropy model predictions with respect to uncertainties in parameters (standard free energies of formation) and with respect to ionic strengths typically found in a cell.

Metabolomics and modelling approaches for systems metabolic engineering

Metabolic engineering involves the manipulation of microbes to produce desirable compounds through genetic engineering or synthetic biology approaches. Metabolomics involves the quantitation of intracellular and extracellular metabolites, where mass spectrometry and nuclear magnetic resonance based analytical instrumentation are often used. Here, the experimental designs, sample preparations, metabolite quenching and extraction are essential to the quantitative metabolomics workflow. The resultant metabolomics data can then be used with computational modelling approaches, such as kinetic and constraint-based modelling, to better understand underlying mechanisms and bottlenecks in the synthesis of desired compounds, thereby accelerating research through systems metabolic engineering. Constraint-based models, such as genome scale models, have been used successfully to enhance the yield of desired compounds from engineered microbes, however, unlike kinetic or dynamic models, constraint-based models do not incorporate regulatory effects. Nevertheless, the lack of time-series metabolomic data generation has hindered the usefulness of dynamic models till today. In this review, we show that improvements in automation, dynamic real-time analysis and high throughput workflows can drive the generation of more quality data for dynamic models through time-series metabolomics data generation. Spatial metabolomics also has the potential to be used as a complementary approach to conventional metabolomics, as it provides information on the localization of metabolites. However, more effort must be undertaken to identify metabolites from spatial metabolomics data derived through imaging mass spectrometry, where machine learning approaches could prove useful. On the other hand, single-cell metabolomics has also seen rapid growth, where understanding cell-cell heterogeneity can provide more insights into efficient metabolic engineering of microbes. Moving forward, with potential improvements in automation, dynamic real-time analysis, high throughput workflows, and spatial metabolomics, more data can be produced and studied using machine learning algorithms, in conjunction with dynamic models, to generate qualitative and quantitative predictions to advance metabolic engineering efforts.

The formulation of chemical potentials and free energy changes in biochemical reactions

In 1994, an IUBMB-IUPAC joint committee recommended a revised formulation for standard chemical potentials and reaction free energies motivated by the fact that, in biochemistry, the reactants and products often exist in multiple charge states depending on the pH and pMg of the solution environment. The recommendation involved both the use of (1) a mathematical transform with the intent to hold the pH constant, and (2) the formulation of reference chemical potentials of ionized isomeric species based on the log sum of the individual standard chemical potentials of each isomeric species. Recently, several reports including a 2020 IUPAC report have appeared that challenged the need for such summary formulations, arguing that the standard chemical potentials were sufficient with full accounting of each of the different charge state isomers involved in a biochemical reaction. This work critically evaluates both the use of thermodynamic transforms and the different chemical potential formulations. It is shown that (1) transforms are not necessary to hold the pH constant and (2) demonstrates that the two chemical potential formulations are not equivalent. Which formulation is appropriate depends on what species are measured experimentally or whether an assumption of equilibrium among the charge state isomers is reasonable and desirable.

Reinforcement learning for robot research: A comprehensive review and open issues

Applying the learning mechanism of natural living beings to endow intelligent robots with humanoid perception and decision-making wisdom becomes an important force to promote the revolution of science and technology in robot domains. Advances in reinforcement learning (RL) over the past decades have led robotics to be highly automated and intelligent, which ensures safety operation instead of manual work and implementation of more intelligence for many challenging tasks. As an important branch of machine learning, RL can realize sequential decision-making under uncertainties through end-to-end learning and has made a series of significant breakthroughs in robot applications. In this review article, we cover RL algorithms from theoretical background to advanced learning policies in different domains, which accelerate to solving practical problems in robotics. The challenges, open issues, and our thoughts on future research directions of RL are also presented to discover new research areas with the objective to motivate new interest.

Flexibility of enzymatic transitions as a hallmark of optimized enzyme steady-state kinetics and thermodynamics

We investigate the relations between the enzyme kinetic flexibility, the rate of entropy production, and the Shannon information entropy in a steady-state enzyme reaction. All these quantities are maximized with respect to enzyme rate constants. We show that the steady-state, which is characterized by the most flexible enzymatic transitions between the enzyme conformational states, coincides with the global maxima of the Shannon information entropy and the rate of entropy production. This steady-state of an enzyme is referred to as globally optimal. This theoretical approach is then used for the analysis of the kinetic and the thermodynamic performance of the enzyme triose-phosphate isomerase. The analysis reveals that there exist well-defined maxima of the kinetic flexibility, the rate of entropy production, and the Shannon information entropy with respect to any arbitrarily chosen rate constant of the enzyme and that these maxima, calculated from the measured kinetic rate constants for the triose-phosphate isomerase are lower, however of the same order of magnitude, as the maxima of the globally optimal state of the enzyme. This suggests that the triose-phosphate isomerase could be a well, but not fully evolved enzyme, as it was previously claimed. Herein presented theoretical investigations also provide clear evidence that the flexibility of enzymatic transitions between the enzyme conformational states is a requirement for the maximal Shannon information entropy and the maximal rate of entropy production.

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.

Information Theory in Computational Biology: Where We Stand Today

"A Mathematical Theory of Communication" was published in 1948 by Claude Shannon to address the problems in the field of data compression and communication over (noisy) communication channels. Since then, the concepts and ideas developed in Shannon's work have formed the basis of information theory, a cornerstone of statistical learning and inference, and has been playing a key role in disciplines such as physics and thermodynamics, probability and statistics, computational sciences and biological sciences. In this article we review the basic information theory based concepts and describe their key applications in multiple major areas of research in computational biology-gene expression and transcriptomics, alignment-free sequence comparison, sequencing and error correction, genome-wide disease-gene association mapping, metabolic networks and metabolomics, and protein sequence, structure and interaction analysis.

Continuous in vivo Metabolism by NMR

Dense time-series metabolomics data are essential for unraveling the underlying dynamic properties of metabolism. Here we extend high-resolution-magic angle spinning (HR-MAS) to enable continuous in vivo monitoring of metabolism by NMR (CIVM-NMR) and provide analysis tools for these data. First, we reproduced a result in human chronic lymphoid leukemia cells by using isotope-edited CIVM-NMR to rapidly and unambiguously demonstrate unidirectional flux in branched-chain amino acid metabolism. We then collected untargeted CIVM-NMR datasets for Neurospora crassa, a classic multicellular model organism, and uncovered dynamics between central carbon metabolism, amino acid metabolism, energy storage molecules, and lipid and cell wall precursors. Virtually no sample preparation was required to yield a dynamic metabolic fingerprint over hours to days at ~4-min temporal resolution with little noise. CIVM-NMR is simple and readily adapted to different types of cells and microorganisms, offering an experimental complement to kinetic models of metabolism for diverse biological systems.

Special Issue on Feature Papers for Celebrating the Fifth Anniversary of the Founding of Processes

The Special Issue “Feature Papers for Celebrating the Fifth Anniversary of the Founding of Processes” represents a landmark for this open access journal covering chemical, biological, materials, pharmaceutical, and environmental systems as well as general computational methods for process and systems engineering. [...]