Abstract
BackgroundBiochemical equilibria are usually modeled iteratively: given one or a few fitted models, if there is a lack of fit or over fitting, a new model with additional or fewer parameters is then fitted, and the process is repeated. The problem with this approach is that different analysts can propose and select different models and thus extract different binding parameter estimates from the same data. An alternative is to first generate a comprehensive standardized list of plausible models, and to then fit them exhaustively, or semi-exhaustively.ResultsA framework is presented in which equilibriums are modeled as pairs (g, h) where g = 0 maps total reactant concentrations (system inputs) into free reactant concentrations (system states) which h then maps into expected values of measurements (system outputs). By letting dissociation constants Kd be either freely estimated, infinity, zero, or equal to other Kd, and by letting undamaged protein fractions be either freely estimated or 1, many g models are formed. A standard space of g models for ligand-induced protein dimerization equilibria is given. Coupled to an h model, the resulting (g, h) were fitted to dTTP induced R1 dimerization data (R1 is the large subunit of ribonucleotide reductase). Models with the fewest parameters were fitted first. Thereafter, upon fitting a batch, the next batch of models (with one more parameter) was fitted only if the current batch yielded a model that was better (based on the Akaike Information Criterion) than the best model in the previous batch (with one less parameter). Within batches models were fitted in parallel. This semi-exhaustive approach yielded the same best models as an exhaustive model space fit, but in approximately one-fifth the time.ConclusionComprehensive model space based biochemical equilibrium model selection methods are realizable. Their significance to systems biology as mappings of data into mathematical models warrants their development.
Highlights
Biochemical equilibria are usually modeled iteratively: given one or a few fitted models, if there is a lack of fit or over fitting, a new model with additional or fewer parameters is fitted, and the process is repeated
Ribonucleotide reductase (RNR) has a small subunit R2 that exists almost exclusively as a dimer, and a large subunit R1 that dimerizes when dTTP, dGTP, dATP, or ATP binds to its specificity site, and hexamerizes when dATP or ATP binds to its activity site [1,2,3,4,5,6]
The relationship between the system inputs (Tn), states (Fn) and outputs is modeled by I total concentration constraints g(Fn, Tn, K, p) = 0 that must be solved for the I free reactant concentrations Fn at each n (1
Summary
Biochemical equilibria are usually modeled iteratively: given one or a few fitted models, if there is a lack of fit or over fitting, a new model with additional or fewer parameters is fitted, and the process is repeated. BMC Systems Biology 2008, 2:15 http://www.biomedcentral.com/1752-0509/2/15 data are too weak to rule out a null hypothesis of the form Kd = K′d Model parameters such as the fraction of R1 capable of forming dimers and hexamers, and the enzymatic activities of these R1 states, come with plausible null hypotheses. As modelers traverse a path of reasonable hypotheses until they arrive at a model that provides both a good fit and Kd confidence interval limits that are not too wide, they often stop at different places, and report different Kd values Such Kd estimate extraction differences could be reduced, if a systematic reproducible approach to biochemical equilibria model building was established.
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