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Cannon WR, Britton S, Banwarth-Kuhn M, Alber M. Probabilistic and maximum entropy modeling of chemical reaction systems: Characteristics and comparisons to mass action kinetic models. J Chem Phys 2024; 160:214123. [PMID: 38842085 DOI: 10.1063/5.0180417] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2023] [Accepted: 05/13/2024] [Indexed: 06/07/2024] Open
Abstract
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.
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Affiliation(s)
- William R Cannon
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, USA
- Department of Mathematics, University of California, Riverside, California 92505, USA
- Center for Quantitative Modeling in Biology, University of California Riverside, Riverside, California 92505, USA
| | - Samuel Britton
- Department of Mathematics, University of California, Riverside, California 92505, USA
- Center for Quantitative Modeling in Biology, University of California Riverside, Riverside, California 92505, USA
| | - Mikahl Banwarth-Kuhn
- Center for Quantitative Modeling in Biology, University of California Riverside, Riverside, California 92505, USA
- Department of Mathematics, California State University East Bay, Hayward, California 94542, USA
| | - Mark Alber
- Department of Mathematics, University of California, Riverside, California 92505, USA
- Center for Quantitative Modeling in Biology, University of California Riverside, Riverside, California 92505, USA
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Vergara RC, Jaramillo-Riveri S, Luarte A, Moënne-Loccoz C, Fuentes R, Couve A, Maldonado PE. Corrigendum: The Energy Homeostasis Principle: Neuronal Energy Regulation Drives Local Network Dynamics Generating Behavior. Front Comput Neurosci 2020; 14:599670. [PMID: 33192429 PMCID: PMC7658562 DOI: 10.3389/fncom.2020.599670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2020] [Accepted: 09/11/2020] [Indexed: 11/20/2022] Open
Affiliation(s)
- Rodrigo C Vergara
- Neurosystems Laboratory, Faculty of Medicine, Biomedical Neuroscience Institute, Universidad de Chile, Santiago, Chile
| | - Sebastián Jaramillo-Riveri
- School of Biological Sciences, Institute of Cell Biology, University of Edinburgh, Edinburgh, United Kingdom
| | - Alejandro Luarte
- Cellular and Molecular Neurobiology Laboratory, Faculty of Medicine, Biomedical Neuroscience Institute, Universidad de Chile, Santiago, Chile
| | - Cristóbal Moënne-Loccoz
- Motor Control Laboratory, Faculty of Medicine, Biomedical Neuroscience Institute, Universidad de Chile, Santiago, Chile.,Department of Health Sciences, Faculty of Medicine, Pontificia Universidad Católica de Chile, Santiago, Chile
| | - Rómulo Fuentes
- Motor Control Laboratory, Faculty of Medicine, Biomedical Neuroscience Institute, Universidad de Chile, Santiago, Chile
| | - Andrés Couve
- Cellular and Molecular Neurobiology Laboratory, Faculty of Medicine, Biomedical Neuroscience Institute, Universidad de Chile, Santiago, Chile
| | - Pedro E Maldonado
- Neurosystems Laboratory, Faculty of Medicine, Biomedical Neuroscience Institute, Universidad de Chile, Santiago, Chile
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Chanda P, Costa E, Hu J, Sukumar S, Van Hemert J, Walia R. Information Theory in Computational Biology: Where We Stand Today. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E627. [PMID: 33286399 PMCID: PMC7517167 DOI: 10.3390/e22060627] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/30/2020] [Revised: 05/31/2020] [Accepted: 06/03/2020] [Indexed: 12/30/2022]
Abstract
"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.
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Affiliation(s)
- Pritam Chanda
- Corteva Agriscience™, Indianapolis, IN 46268, USA
- Computer and Information Science, Indiana University-Purdue University, Indianapolis, IN 46202, USA
| | - Eduardo Costa
- Corteva Agriscience™, Mogi Mirim, Sao Paulo 13801-540, Brazil
| | - Jie Hu
- Corteva Agriscience™, Indianapolis, IN 46268, USA
| | | | | | - Rasna Walia
- Corteva Agriscience™, Johnston, IA 50131, USA
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Vergara RC, Jaramillo-Riveri S, Luarte A, Moënne-Loccoz C, Fuentes R, Couve A, Maldonado PE. The Energy Homeostasis Principle: Neuronal Energy Regulation Drives Local Network Dynamics Generating Behavior. Front Comput Neurosci 2019; 13:49. [PMID: 31396067 PMCID: PMC6664078 DOI: 10.3389/fncom.2019.00049] [Citation(s) in RCA: 55] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2019] [Accepted: 07/01/2019] [Indexed: 01/12/2023] Open
Abstract
A major goal of neuroscience is understanding how neurons arrange themselves into neural networks that result in behavior. Most theoretical and experimental efforts have focused on a top-down approach which seeks to identify neuronal correlates of behaviors. This has been accomplished by effectively mapping specific behaviors to distinct neural patterns, or by creating computational models that produce a desired behavioral outcome. Nonetheless, these approaches have only implicitly considered the fact that neural tissue, like any other physical system, is subjected to several restrictions and boundaries of operations. Here, we proposed a new, bottom-up conceptual paradigm: The Energy Homeostasis Principle, where the balance between energy income, expenditure, and availability are the key parameters in determining the dynamics of neuronal phenomena found from molecular to behavioral levels. Neurons display high energy consumption relative to other cells, with metabolic consumption of the brain representing 20% of the whole-body oxygen uptake, contrasting with this organ representing only 2% of the body weight. Also, neurons have specialized surrounding tissue providing the necessary energy which, in the case of the brain, is provided by astrocytes. Moreover, and unlike other cell types with high energy demands such as muscle cells, neurons have strict aerobic metabolism. These facts indicate that neurons are highly sensitive to energy limitations, with Gibb's free energy dictating the direction of all cellular metabolic processes. From this activity, the largest energy, by far, is expended by action potentials and post-synaptic potentials; therefore, plasticity can be reinterpreted in terms of their energy context. Consequently, neurons, through their synapses, impose energy demands over post-synaptic neurons in a close loop-manner, modulating the dynamics of local circuits. Subsequently, the energy dynamics end up impacting the homeostatic mechanisms of neuronal networks. Furthermore, local energy management also emerges as a neural population property, where most of the energy expenses are triggered by sensory or other modulatory inputs. Local energy management in neurons may be sufficient to explain the emergence of behavior, enabling the assessment of which properties arise in neural circuits and how. Essentially, the proposal of the Energy Homeostasis Principle is also readily testable for simple neuronal networks.
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Affiliation(s)
- Rodrigo C Vergara
- Neurosystems Laboratory, Faculty of Medicine, Biomedical Neuroscience Institute, Universidad de Chile, Santiago, Chile
| | - Sebastián Jaramillo-Riveri
- School of Biological Sciences, Institute of Cell Biology, University of Edinburgh, Edinburgh, United Kingdom
| | - Alejandro Luarte
- Cellular and Molecular Neurobiology Laboratory, Faculty of Medicine, Biomedical Neuroscience Institute, Universidad de Chile, Santiago, Chile
| | - Cristóbal Moënne-Loccoz
- Motor Control Laboratory, Faculty of Medicine, Biomedical Neuroscience Institute, Universidad de Chile, Santiago, Chile.,Department of Health Sciences, Faculty of Medicine, Pontificia Universidad Católica de Chile, Santiago, Chile
| | - Rómulo Fuentes
- Motor Control Laboratory, Faculty of Medicine, Biomedical Neuroscience Institute, Universidad de Chile, Santiago, Chile
| | - Andrés Couve
- Cellular and Molecular Neurobiology Laboratory, Faculty of Medicine, Biomedical Neuroscience Institute, Universidad de Chile, Santiago, Chile
| | - Pedro E Maldonado
- Neurosystems Laboratory, Faculty of Medicine, Biomedical Neuroscience Institute, Universidad de Chile, Santiago, Chile
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Ritchie ME. Reaction and diffusion thermodynamics explain optimal temperatures of biochemical reactions. Sci Rep 2018; 8:11105. [PMID: 30038415 PMCID: PMC6056565 DOI: 10.1038/s41598-018-28833-9] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2017] [Accepted: 06/28/2018] [Indexed: 01/18/2023] Open
Abstract
Ubiquitous declines in biochemical reaction rates above optimal temperatures (Topt) are normally attributed to enzyme state changes, but such mechanisms appear inadequate to explain pervasive Topt well below enzyme deactivation temperatures (Tden). Here, a meta-analysis of 92 experimental studies shows that product formation responds twice as strongly to increased temperature than diffusion or transport. This response difference has multiple consequences for biochemical reactions, such as potential shifts in the factors limiting reactions as temperature increases and reaction-diffusion dynamics that predict potential product inhibition and limitation of the reaction by entropy production at temperatures below Tden. Maximizing entropy production by the reaction predicts Topt that depend on enzyme concentration and efficiency as well as reaction favorability, which are patterns not predicted by mechanisms of enzyme state change. However, these predictions are strongly supported by patterns in a meta-analysis of 121 enzyme kinetic studies. Consequently, reaction-diffusion thermodynamics and entropy production may constrain organism performance at higher temperatures, yielding temperature optima of life that may depend on reaction characteristics and environmental features rather than just enzyme state changes.
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Affiliation(s)
- Mark E Ritchie
- Department of Biology, Syracuse University, 107 College Place, Syracuse, NY, 13244, USA.
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Cannon WR, Zucker JD, Baxter DJ, Kumar N, Baker SE, Hurley JM, Dunlap JC. Prediction of Metabolite Concentrations, Rate Constants and Post-Translational Regulation Using Maximum Entropy-Based Simulations with Application to Central Metabolism of Neurospora crassa. Processes (Basel) 2018; 6. [PMID: 33824861 PMCID: PMC8020867 DOI: 10.3390/pr6060063] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
We report the application of a recently proposed approach for modeling biological systems using a maximum entropy production rate principle in lieu of having in vivo rate constants. The method is applied in four steps: (1) a new ordinary differential equation (ODE) based optimization approach based on Marcelin’s 1910 mass action equation is used to obtain the maximum entropy distribution; (2) the predicted metabolite concentrations are compared to those generally expected from experiments using a loss function from which post-translational regulation of enzymes is inferred; (3) the system is re-optimized with the inferred regulation from which rate constants are determined from the metabolite concentrations and reaction fluxes; and finally (4) a full ODE-based, mass action simulation with rate parameters and allosteric regulation is obtained. From the last step, the power characteristics and resistance of each reaction can be determined. The method is applied to the central metabolism of Neurospora crassa and the flow of material through the three competing pathways of upper glycolysis, the non-oxidative pentose phosphate pathway, and the oxidative pentose phosphate pathway are evaluated as a function of the NADP/NADPH ratio. It is predicted that regulation of phosphofructokinase (PFK) and flow through the pentose phosphate pathway are essential for preventing an extreme level of fructose 1,6-bisphophate accumulation. Such an extreme level of fructose 1,6-bisphophate would otherwise result in a glassy cytoplasm with limited diffusion, dramatically decreasing the entropy and energy production rate and, consequently, biological competitiveness.
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Affiliation(s)
- William R. Cannon
- Biological Sciences Division, Pacific Northwest National Laboratory, Richland, WA 99352, USA
- Correspondence: ; Tel.: +1-509-375-6732
| | - Jeremy D. Zucker
- Biological Sciences Division, Pacific Northwest National Laboratory, Richland, WA 99352, USA
| | - Douglas J. Baxter
- Research Computing Group, Pacific Northwest National Laboratory, Richland, WA 99352, USA
| | - Neeraj Kumar
- Biological Sciences Division, Pacific Northwest National Laboratory, Richland, WA 99352, USA
| | - Scott E. Baker
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, WA 99352, USA
| | - Jennifer M. Hurley
- Department of Biological Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
| | - Jay C. Dunlap
- Department of Molecular and Systems Biology, Geisel School of Medicine at Dartmouth, Hanover, NH 03755, USA
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