Towards the systematic simplification of mechanistic models

Mechanistic models used for prediction should be parsimonious, as models which are over-parameterised may have poor predictive performance. Determining whether a model is parsimonious requires comparisons with alternative model formulations with differing levels of complexity. However, creating alternative formulations for large mechanistic models is often problematic, and usually time-consuming. Consequently, few are ever investigated. In this paper, we present an approach which rapidly generates reduced model formulations by replacing a model’s variables with constants. These reduced alternatives can be compared to the original model, using data based model selection criteria, to assist in the identification of potentially unnecessary model complexity, and thereby inform reformulation of the model. To illustrate the approach, we present its application to a published radiocaesium plant-uptake model, which predicts uptake on the basis of soil characteristics (e.g. pH, organic matter content, clay content). A total of 1024 reduced model formulations were generated, and ranked according to five model selection criteria: Residual Sum of Squares (RSS), AICc, BIC, MDL and ICOMP. The lowest scores for RSS and AICc occurred for the same reduced model in which pH dependent model components were replaced. The lowest scores for BIC, MDL and ICOMP occurred for a further reduced model in which model components related to the distinction between adsorption on clay and organic surfaces were replaced. Both these reduced models had a lower RSS for the parameterisation dataset than the original model. As a test of their predictive performance, the original model and the two reduced models outlined above were used to predict an independent dataset. The reduced models have lower prediction sums of squares than the original model, suggesting that the latter may be overfitted. The approach presented has the potential to inform model development by rapidly creating a class of alternative model formulations, which can be compared.

Structure of the N-terminal oligomerization domain of DnaD reveals a unique tetramerization motif and provides insights into scaffold formation

DnaD is a primosomal protein that remodels supercoiled plasmids. It binds to supercoiled forms and converts them to open forms without nicking. During this remodeling process, all the writhe is converted to twist and the plasmids are held around the periphery of large scaffolds made up of DnaD molecules. This DNA-remodeling function is the sum of a scaffold-forming activity on the N-terminal domain and a DNA-dependent oligomerization activity on the C-terminal domain. We have determined the crystal structure of the scaffold-forming N-terminal domain, which reveals a winged-helix architecture, with additional structural elements extending from both N- and C-termini. Four monomers form dimers that join into a tetramer. The N-terminal extension mediates dimerization and tetramerization, with extensive interactions and distinct interfaces. The wings and helices of the winged-helix domains remain exposed on the surface of the tetramer. Structure-guided mutagenesis and atomic force microscopy imaging indicate that these elements, together with the C-terminal extension, are involved in scaffold formation. Based upon our data, we propose a model for the DnaD-mediated scaffold formation.