Group contribution method for thermodynamic analysis of complex metabolic networks

Abstract

A new, to our knowledge, group contribution method based on the group contribution method of Mavrovouniotis is introduced for estimating the standard Gibbs free energy of formation (Delta(f)G'(o)) and reaction (Delta(r)G'(o)) in biochemical systems. Gibbs free energy contribution values were estimated for 74 distinct molecular substructures and 11 interaction factors using multiple linear regression against a training set of 645 reactions and 224 compounds. The standard error for the fitted values was 1.90 kcal/mol. Cross-validation analysis was utilized to determine the accuracy of the methodology in estimating Delta(r)G'(o) and Delta(f)G'(o) for reactions and compounds not included in the training set, and based on the results of the cross-validation, the standard error involved in these estimations is 2.22 kcal/mol. This group contribution method is demonstrated to be capable of estimating Delta(r)G'(o) and Delta(f)G'(o) for the majority of the biochemical compounds and reactions found in the iJR904 and iAF1260 genome-scale metabolic models of Escherichia coli and in the Kyoto Encyclopedia of Genes and Genomes and University of Minnesota Biocatalysis and Biodegradation Database. A web-based implementation of this new group contribution method is available free at http://sparta.chem-eng.northwestern.edu/cgi-bin/GCM/WebGCM.cgi.

FIGURE 1

Decomposition of molecular structures into structural groups and interaction factors. When assigning atoms in a molecular structure to structural groups, atoms should always be assigned to the structural group with the lowest search priority number (A). Phosphate chains such as ATP and NADH are the only exceptions to this rule; a phosphate chain of size n should be decomposed into (n − 1) groups and one or group (B). Although each atom in the molecular structure may only participate in a single structural group, atoms can participate in multiple interaction factors. All but one of the interaction factors included in this group contribution method are found within the structure of the example molecule in (C) (the hydrocarbon factor is not included). Note that conjugated double bonds contained entirely within an aromatic or heteroaromatic ring are not counted. However, double bonds outside the ring conjugated to double bonds within the ring are counted. Also note that nitrogen atoms neighboring two carbonyl groups are only counted as a single amide.

FIGURE 2

Distribution of residuals from the MLR fitting of the training set cumulative distribution (A) and histogram (B) of the deviations between calculated using the fitted values and the values in the training set. The cumulative probability for the deviations between and (solid gray line in A) nearly overlaps with the cumulative probability for a normal distribution (dashed line in A). The points of intersection between the cumulative probability line for the residuals of the fitting with the SE_MLR lines (solid vertical gray lines) and 2 SE_MLR lines (dashed vertical gray lines) indicate that ∼85% and 96% of the values will fall within one and two standard deviations, respectively, of The distribution of deviations (shaded bars in B) between and is more compact than a normal distribution (dashed line in B) with the same standard deviation (1.90 kcal/mol). This confirms that uncertainty estimations based on standard deviations will be more conservative than expected for normally distributed errors.

FIGURE 3

pH, temperature, and distributions for the data within the training set. The distributions of pH (A), T (B), and (C) values for the 3153 measurements used in the training set to determine the group contribution energies are shown. The most prevalent condition for the measurements included in the training set was pH 7.0–7.1 and 298–299 K, which is the reference state selected for this group contribution method. Interestingly, most of the values used in the fitting have an absolute value of <10 kcal/mol.

FIGURE 4

Characterization of residuals from the cross-validation analysis. Characterization of residuals for the data associated with the 10% of the reactions and compounds removed from the training set during each cross-validation run. The standard deviation of − for the training set (solid line and squares) varies little over the 200 different samplings performed. The standard deviation of − for the data removed from the training set (gray dashed line and diamonds) varies far more over the 200 different samples performed (A). The distribution of all the − values for the data removed from the training sets over the 200 cross-validation runs (shaded bars) is very similar to the distribution for the data included in the data set, indicating that the accuracy of calculated using the group contribution method is similar in magnitude to the accuracy of the fit of the group contribution model to the training set (B).

FIGURE 5

Variation of group energy values during cross-validation analysis. The differences between the final reported value and the median of the values () calculated during the 200 cross-validation runs for each structural group and interaction factor included in the new group contribution method are indicated. The error bars also capture the extent to which the value of each group varied from the median value during the cross-validation runs. The error bars left of each point extend through the first quartile of calculated values, and the error bars right of each point extend through the third quartile of calculated values.