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Open Access Research

Automated mass action model space generation and analysis methods for two-reactant combinatorially complex equilibriums: An analysis of ATP-induced ribonucleotide reductase R1 hexamerization data

Tomas Radivoyevitch

Author Affiliations

Department of Epidemiology and Biostatistics, Case Western Reserve University, Cleveland, Ohio 44106, USA

Biology Direct 2009, 4:50  doi:10.1186/1745-6150-4-50

Published: 9 December 2009



Ribonucleotide reductase is the main control point of dNTP production. It has two subunits, R1, and R2 or p53R2. R1 has 5 possible catalytic site states (empty or filled with 1 of 4 NDPs), 5 possible s-site states (empty or filled with ATP, dATP, dTTP or dGTP), 3 possible a-site states (empty or filled with ATP or dATP), perhaps two possible h-site states (empty or filled with ATP), and all of this is folded into an R1 monomer-dimer-tetramer-hexamer equilibrium where R1 j-mers can be bound by variable numbers of R2 or p53R2 dimers. Trillions of RNR complexes are possible as a result. The problem is to determine which are needed in models to explain available data. This problem is intractable for 10 reactants, but it can be solved for 2 and is here for R1 and ATP.


Thousands of ATP-induced R1 hexamerization models with up to three (s, a and h) ATP binding sites per R1 subunit were automatically generated via hypotheses that complete dissociation constants are infinite and/or that binary dissociation constants are equal. To limit the model space size, it was assumed that s-sites are always filled in oligomers and never filled in monomers, and to interpret model terms it was assumed that a-sites fill before h-sites. The models were fitted to published dynamic light scattering data. As the lowest Akaike Information Criterion (AIC) of the 3-parameter models was greater than the lowest of the 2-parameter models, only models with up to 3 parameters were fitted. Models with sums of squared errors less than twice the minimum were then partitioned into two groups: those that contained no occupied h-site terms (508 models) and those that contained at least one (1580 models). Normalized AIC densities of these two groups of models differed significantly in favor of models that did not include an h-site term (Kolmogorov-Smirnov p < 1 × 10-15); consistent with this, 28 of the top 30 models (ranked by AICs) did not include an h-site term and 28/30 > 508/2088 with p < 2 × 10-15. Finally, 99 of the 2088 models did not have any terms with ATP/R1 ratios >1.5, but of the top 30, there were 14 such models (14/30 > 99/2088 with p < 3 × 10-16), i.e. the existence of R1 hexamers with >3 a-sites occupied by ATP is also not supported by this dataset.


The analysis presented suggests that three a-sites may not be occupied by ATP in R1 hexamers under the conditions of the data analyzed. If a-sites fill before h-sites, this implies that the dataset analyzed can be explained without the existence of an h-site.


This article was reviewed by Ossama Kashlan (nominated by Philip Hahnfeldt), Bin Hu (nominated by William Hlavacek) and Rainer Sachs.