Group contributions for estimating standard gibbs energies of formation of biochemical compounds in aqueous solution

A method is presented for the estimation of the standard Gibbs energies of formation of biochemical compounds (and hence the Gibbs energies and equilibrium constants of biochemical reactions) from the contributions of groups. The method employs a large set of groups and special corrections. The contributions were estimated via multiple linear regression, using screened and weighted literature data. For most of the data employed, the error is less than 2 kcal/mol. The method provides a useful first approximation to Gibbs energies and equilibrium constants in biochemical systems.     

Thermodynamic properties of enzyme-catalyzed reactions involving guanine, xanthine, and their nucleosides and nucleotides

The standard Gibbs energies of formation of species in the guanosine triphosphate and the xanthosine triphosphate series have been calculated on the basis of the convention that the standard Gibbs energy of formation for the neutral form of guanosine is equal to zero in aqueous solution at 298.15 K and zero ionic strength. This makes it possible to calculate apparent equilibrium constants for a number of enzyme-catalyzed reactions for which apparent equilibrium constants have not been measured or cannot be measured directly because they are too large. The eventual elimination of this convention is discussed. This adds ten reactants to the database BasicBiochemData3 that has 199 reactants. The standard transformed Gibbs energies of formation of these ten reactants are used to calculate apparent equilibrium constants at 298.15 K, 0.25 M ionic strength, and pHs 5, 6, 7, 8, and 9. The pKs, standard Gibbs energies of hydrolysis, and standard Gibbs energies of deamination are given for the reactants in the ATP, IMP, GTP, and XTP series.     

Thermodynamic properties of enzyme-catalyzed reactions involving cytosine, uracil, thymine, and their nucleosides and nucleotides

The standard Gibbs energies of formation of species in the cytidine triphosphate series, uridine triphosphate series, and thymidine triphosphate series have been calculated on the basis of the convention that Delta(f)G=0 for the neutral form of cytidine in aqueous solution at 298.15 K at zero ionic strength. This makes it possible to calculate apparent equilibrium constants for a number of reactions for which apparent equilibrium constants have not been measured or cannot be measured because they are too large. This paper adds fifteen reactants to the database BasicBiochemData3 at MathSource that includes 199 reactants. The standard transformed Gibbs energies of formation of these fifteen reactants are used to calculate apparent equilibrium constants at 298.15 K, ionic strength 0.25 M, and pHs 5, 6, 7, 8, and 9 for thirty two reactions. The pKs, standard Gibbs energies of hydrolysis, and standard Gibbs energies of deamination are given for these fifteen reactants.     

Thermodynamics of the purine nucleotide cycle

Since the standard Gibbs energies of formation are known for all the species in the purine nucleotide cycle at 298.15 K, the functions of pH and ionic strength that yield the standard transformed Gibbs energies of formation of the ten reactants can be calculated. This makes it possible to calculate the standard transformed Gibbs energies of reaction, apparent equilibrium constants, and changes in the binding of hydrogen ions for the three reactions at desired pHs and ionic strengths. These calculations are also made for the net reaction and a reaction that is related to it. The equilibrium concentrations for the cycle are calculated when all the reactants are initially present or only some are present initially. Since the concentrations of GTP, GDP, and P(i) may be in steady states, the equilibrium concentrations are also calculated for the system at specified steady-state concentrations.     

Determination of the standard Gibbs energies of transfer of cations and anions of amino acids and small peptides across the water nitrobenzene interface

The standard Gibbs energies of transfer of anions and cations of amino acids and small peptides across the water nitrobenzene interface were determined with the help of a novel electrochemical technique using three-phase electrodes. This is the first time that reliable data are reported for the anions of amino acids. The main result is that the standard Gibbs energies of transfer of the anion and cation of an amino acid are almost the same.     

A group contribution method for the estimation of equilibrium constants for biochemical reactions

Using Gibbs Energies of compounds, as well as Gibbs Energy changes and equilibrium constants of biochemical reactions, the contributions of functional groups to the Gibbs Energy (in aqueous solution, temperature 25°C, and pH=7) have been estimated. These contributions allow the estimation of the Gibbs Free Energy and the equilibrium constant of a biochemical reaction, given the structure of the reactants and products.     

Calculating apparent equilibrium constants of enzyme-catalyzed reactions at pH 7

Apparent equilibrium constants K' of biochemical reactions at pH 7 and standard apparent reduction potentials of half reactions at pH 7 can be calculated using a table of standard transformed Gibbs energies of formation Delta(f)G'(0) at pH 7. A table is provided for 136 reactants at 25 degrees C, pH 7, and ionic strengths of 0, 0.10, and 0.25 M. Examples are given to illustrate the use of the table.     

Thermodynamics of the reactions of carbamoyl phosphate

Two measurements of equilibrium constants by Marshall and Cohen make it possible to calculate standard Gibbs energies of formation of the species of carbamate and carbamoyl phosphate. Carbamate formation from carbon dioxide and ammonia does not require an enzyme, and the equilibrium concentrations of carbamate in ammonium bicarbonate are calculated. Knowing the values of standard Gibbs energies of formation of species of carbamate and carbamoyl phosphate make it possible to calculate the dependencies of the standard transformed Gibbs energies of formation of these reactants on pH and ionic strength and to calculate apparent equilibrium constants for several enzyme-catalyzed reactions and several chemical reactions. These calculations are sufficiently complicated that computer programs in Mathematica are used to make tables and plots. The dependences of apparent equilibrium constants on pH are consequences of the production or consumption of hydrogen ions, which are shown in plots. As usual the increase in the number of enzyme-catalyzed reactions for which apparent equilibrium constants can be calculated is larger than the number of reactions required to obtain the thermodynamic properties of the species involved.     

Equilibrium calculations on systems of biochemical reactions at specified pH and pMg.

The use of G' in discussing the thermodynamics of biochemical reactions at a specified pH and pMg is justified by use of a Legendre transform of the Gibbs energy G. When several enzymatic reactions occur simultaneously in a system, the standard transformed Gibbs energies of reaction delta rG'0 can be used in a computer program to calculate the equilibrium composition that minimizes the transformed Gibbs energy at the specified pH and pMg. The calculation of standard transformed Gibbs energies of formation of reactants at pH 7 and pMg 3 is described. In addition a method for calculating the equilibrium concentrations of reactants is illustrated for a system with steady state concentrations of some reactants like ATP and NAD.     

Levels of thermodynamic treatment of biochemical reaction systems.

Equilibrium calculations on biochemical reaction systems can be made at three levels. Level 1 is the usual chemical calculation with species at specified temperature and pressure using standard Gibbs energies of formation of species or equilibrium constants K. Level 2 utilizes reactants such as ATP (a sum of species) at specified T, P, pH, and pMg with standard transformed Gibbs energies of formation of reactants or apparent equilibrium constants K'. Calculations at this level can also be made on the enzymatic mechanism for a biochemical reaction. Level 3 utilizes reactants at specified T, P, pH, and pMg, but the equilibrium concentrations of certain reactants are also specified. The fundamental equation of thermodynamics is derived here for Level 3. Equilibrium calculations at this level use standard transformed Gibbs energies of formation of reactants at specified concentrations of certain reactants or apparent equilibrium constants K". Level 3 is useful in calculating equilibrium concentrations of reactants that can be reached in a living cell when some of the reactants are available at steady-state concentrations. Calculations at all three levels are facilitated by the use of conservation matrices and stoichiometric number matrices for systems. Three cases involving glucokinase, glucose-6-phosphatase, and ATPase are discussed.     

Standard transformed Gibbs energies of coenzyme A derivatives as functions of pH and ionic strength

The best way to store data on apparent equilibrium constants for enzyme-catalyzed reactions is to calculate the standard Gibbs energies of formation of the species involved at 298.15 K and zero ionic strength so that equilibrium constants can be calculated at the desired pH and ionic strength. These calculations are described for CoA, acetyl-CoA, oxalyl-CoA, succinyl-CoA, methylmalonyl-CoA, malyl-CoA and CoA-glutathione. The species properties are then used to calculate standard transformed Gibbs energies of formation for these reactants as functions of pH at ionic strength 0.25 M. The species data also make it possible to calculate apparent equilibrium constants of 23 enzyme-catalyzed reactions as a function of pH, including some that cannot be determined directly because they are so large.     

Standard thermodynamic formation properties for the adenosine 5'-triphosphate series.

The criterion for chemical equilibrium at specified temperature, pressure, pH, concentration of free magnesium ion, and ionic strength is the transformed Gibbs energy, which can be calculated from the Gibbs energy. The apparent equilibrium constant (written in terms of the total concentrations of reactants like adenosine 5'-triphosphate, rather than in terms of species) yields the standard transformed Gibbs energy of reaction, and the effect of temperature on the apparent equilibrium constant at specified pressure, pH, concentration of free magnesium ion, and ionic strength yields the standard transformed enthalpy of reaction. From the apparent equilibrium constants and standard transformed enthalpies of reaction that have been measured in the adenosine 5'-triphosphate series and the dissociation constants of the weak acids and magnesium complexes involved, it is possible to calculate standard Gibbs energies of formation and standard enthalpies of formation of the species involved at zero ionic strength. This requires the convention that the standard Gibbs energy of formation and standard enthalpy of formation for adenosine in dilute aqueous solutions be set equal to zero. On the basis of this convention, standard transformed Gibbs energies of formation and standard transformed enthalpies of formation of adenosine 5'-trisphosphate, adenosine 5'-diphosphate, adenosine 5'-monophosphate, and adenosine at 298.15 K, 1 bar, pH = 7, a concentration of free magnesium ions of 10(-3) M, and an ionic strength of 0.25 M have been calculated.     

The thermodynamic meaning of metabolic exchange fluxes

Metabolic flux analysis (MFA) deals with the experimental determination of steady-state fluxes in metabolic networks. An important feature of the ¹³C MFA method is its capability to generate information on both directions of bidirectional reaction steps given by exchange fluxes. The biological interpretation of these exchange fluxes and their relation to thermodynamic properties of the respective reaction steps has never been systematically investigated. As a central result, it is shown here that for a general class of enzyme reaction mechanisms the quotients of net and exchange fluxes measured by ¹³C MFA are coupled to Gibbs energies of the reaction steps. To establish this relation the concept of apparent flux ratios of enzymatic isotope-labeling networks is introduced and some computing rules for these flux ratios are given. Application of these rules reveals a conceptional pitfall of ¹³C MFA, which is the inherent dependency of measured exchange fluxes on the chosen tracer atom. However, it is shown that this effect can be neglected for typical biochemical reaction steps under physiological conditions. In this situation, the central result can be formulated as a two-sided inequality relating fluxes, pool sizes, and standard Gibbs energies. This relation has far-reaching consequences for metabolic flux analysis, quantitative metabolomics, and network thermodynamics.     

Recommendations for terminology and databases for biochemical thermodynamics

Chemical equations are normally written in terms of specific ionic and elemental species and balance atoms of elements and electric charge. However, in a biochemical context it is usually better to write them with ionic reactants expressed as totals of species in equilibrium with each other. This implies that atoms of elements assumed to be at fixed concentrations, such as hydrogen at a specified pH, should not be balanced in a biochemical equation used for thermodynamic analysis. However, both kinds of equations are needed in biochemistry. The apparent equilibrium constant K' for a biochemical reaction is written in terms of such sums of species and can be used to calculate standard transformed Gibbs energies of reaction Δ(r)G'°. This property for a biochemical reaction can be calculated from the standard transformed Gibbs energies of formation Δ(f)G(i)'° of reactants, which can be calculated from the standard Gibbs energies of formation of species Δ(f)G(j)° and measured apparent equilibrium constants of enzyme-catalyzed reactions. Tables of Δ(r)G'° of reactions and Δ(f)G(i)'° of reactants as functions of pH and temperature are available on the web, as are functions for calculating these properties. Biochemical thermodynamics is also important in enzyme kinetics because apparent equilibrium constant K' can be calculated from experimentally determined kinetic parameters when initial velocities have been determined for both forward and reverse reactions. Specific recommendations are made for reporting experimental results in the literature.     

Accurate gas phase acidities of carboxylic acids estimated by scaling the vibrational contribution of ab initio gibbs free energies

The gas phase Gibbs free energies deltaG(T) of dissociation reaction of 14 carboxylic acids were calculated on the SCF, as well as G3 and CBS-Q levels. Corresponding accuracies were critically compared with experimental data. Since all of the results suffer from systematic errors, the procedure of scaling of thermal contribution to Gibbs free energy was applied for minimizing differences between theoretical and experimental values of deltaG(T). Two parameters were adjusted, namely the scaling of thermal contribution to Gibbs free energy of neutral and anionic forms. The presented results suggest the great effectiveness of such a procedure since for all applied basis sets within the SCF framework the achieved accuracy was below the experimental error. Besides, the proposed low-cost approximation method leads to precision comparable to or even exceeding the quality offered by more sophisticated composite quantum chemistry methods. The extension of the set of training molecules up to 82 has an insignificant impact on the overall quality of deltaG(T) estimation, which suggests that a wisely chosen set of reference data may be used for the characteristics of the whole class of compounds. There is a straightforward way for the analysis of acidities/basicities of other classes of chemicals such as DNA bases, alcohols, phenols, amines, amino acids, etc.     

Energetics of overall metabolic reactions of thermophilic and hyperthermophilic Archaea and bacteria

Thermophilic and hyperthermophilic Archaea and Bacteria have been isolated from marine hydrothermal systems, heated sediments, continental solfataras, hot springs, water heaters, and industrial waste. They catalyze a tremendous array of widely varying metabolic processes. As determined in the laboratory, electron donors in thermophilic and hyperthermophilic microbial redox reactions include H2, Fe(2+), H2S, S, S2O3(2-), S4O6(2-), sulfide minerals, CH4, various mono-, di-, and hydroxy-carboxylic acids, alcohols, amino acids, and complex organic substrates; electron acceptors include O2, Fe(3+), CO2, CO, NO3(-), NO2(-), NO, N2O, SO4(2-), SO3(2-), S2O3(2-), and S. Although many assimilatory and dissimilatory metabolic reactions have been identified for these groups of microorganisms, little attention has been paid to the energetics of these reactions. In this review, standard molal Gibbs free energies (DeltaGr(0)) as a function of temperature to 200 degrees C are tabulated for 370 organic and inorganic redox, disproportionation, dissociation, hydrolysis, and solubility reactions directly or indirectly involved in microbial metabolism. To calculate values of DeltaGr(0) for these and countless other reactions, the apparent standard molal Gibbs free energies of formation (DeltaG(0)) at temperatures to 200 degrees C are given for 307 solids, liquids, gases, and aqueous solutes. It is shown that values of DeltaGr(0) for many microbially mediated reactions are highly temperature dependent, and that adopting values determined at 25 degrees C for systems at elevated temperatures introduces significant and unnecessary errors. The metabolic processes considered here involve compounds that belong to the following chemical systems: H-O, H-O-N, H-O-S, H-O-N-S, H-O-C(inorganic), H-O-C, H-O-N-C, H-O-S-C, H-O-N-S-C(amino acids), H-O-S-C-metals/minerals, and H-O-P. For four metabolic reactions of particular interest in thermophily and hyperthermophily (knallgas reaction, anaerobic sulfur and nitrate reduction, and autotrophic methanogenesis), values of the overall Gibbs free energy (DeltaGr) as a function of temperature are calculated for a wide range of chemical compositions likely to be present in near-surface and deep hydrothermal and geothermal systems.     

Prostaglandins and oxylipins of corals

Literature data for the period from 1969 to 2010 on the distribution and chemical structures of prostaglandins, prostanoids, eicosanoids, and other cyclic and acyclic oxylipins from corals are summarized. The chemical structures of 97 compounds are given.     

Consistent Estimation of Gibbs Energy Using Component Contributions

Standard Gibbs energies of reactions are increasingly being used in metabolic modeling for applying thermodynamic constraints on reaction rates, metabolite concentrations and kinetic parameters. The increasing scope and diversity of metabolic models has led scientists to look for genome-scale solutions that can estimate the standard Gibbs energy of all the reactions in metabolism. Group contribution methods greatly increase coverage, albeit at the price of decreased precision. We present here a way to combine the estimations of group contribution with the more accurate reactant contributions by decomposing each reaction into two parts and applying one of the methods on each of them. This method gives priority to the reactant contributions over group contributions while guaranteeing that all estimations will be consistent, i.e. will not violate the first law of thermodynamics. We show that there is a significant increase in the accuracy of our estimations compared to standard group contribution. Specifically, our cross-validation results show an 80% reduction in the median absolute residual for reactions that can be derived by reactant contributions only. We provide the full framework and source code for deriving estimates of standard reaction Gibbs energy, as well as confidence intervals, and believe this will facilitate the wide use of thermodynamic data for a better understanding of metabolism.     

HMM sampling and applications to gene finding and alternative splicing

The standard method of applying hidden Markov models to biological problems is to find a Viterbi (maximal weight) path through the HMM graph. The Viterbi algorithm reduces the problem of finding the most likely hidden state sequence that explains given observations, to a dynamic programming problem for corresponding directed acyclic graphs. For example, in the gene finding application, the HMM is used to find the most likely underlying gene structure given a DNA sequence. In this note we discuss the applications of sampling methods for HMMs. The standard sampling algorithm for HMMs is a variant of the common forward-backward and backtrack algorithms, and has already been applied in the context of Gibbs sampling methods. Nevetheless, the practice of sampling state paths from HMMs does not seem to have been widely adopted, and important applications have been overlooked. We show how sampling can be used for finding alternative splicings for genes, including alternative splicings that are conserved between genes from related organisms. We also show how sampling from the posterior distribution is a natural way to compute probabilities for predicted exons and gene structures being correct under the assumed model. Finally, we describe a new memory efficient sampling algorithm for certain classes of HMMs which provides a practical sampling alternative to the Hirschberg algorithm for optimal alignment. The ideas presented have applications not only to gene finding and HMMs but more generally to stochastic context free grammars and RNA structure prediction.     

Computational Identification of Conjugate Paths for Estimation of Properties of Organic Compounds

Abstract

We have developed and implemented a computer-based method to generate and enumerate all conjugate forms of acyclic organic compounds. These algorithms are used in a new approach for the estimation of thermodynamic and physical properties of acyclic organic compounds from their molecular structure. The approach is based on the contributions of Atoms and Bonds in the properties of Conjugate forms (ABC) of a compound and has produced more accurate results than group-contribution methods. Generating all conjugate forms of the molecule whose properties we wish to estimate is necessary in the application of this technique. The use of symbolic computing environments allows the flexible representation and manipulation of molecular structures. Atoms, bonds, molecules, and other entities are represented as interconnected objects. The generation, comparison, and analysis of conjugates are carried out through computer-based manipulation of the objects and their interconnections.