BackgroundDeterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function.ResultsOur results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops.ConclusionsHC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems.

BackgroundStriking a balance between the degree of model complexity and parameter identifiability, while still producing biologically feasible simulations using modelling is a major challenge in computational biology. While these two elements of model development are closely coupled, parameter fitting from measured data and analysis of model mechanisms have traditionally been performed separately and sequentially. This process produces potential mismatches between model and data complexities that can compromise the ability of computational frameworks to reveal mechanistic insights or predict new behaviour. In this study we address this issue by presenting a generic framework for combined model parameterisation, comparison of model alternatives and analysis of model mechanisms.ResultsThe presented methodology is based on a combination of multivariate metamodelling (statistical approximation of the input–output relationships of deterministic models) and a systematic zooming into biologically feasible regions of the parameter space by iterative generation of new experimental designs and look-up of simulations in the proximity of the measured data. The parameter fitting pipeline includes an implicit sensitivity analysis and analysis of parameter identifiability, making it suitable for testing hypotheses for model reduction. Using this approach, under-constrained model parameters, as well as the coupling between parameters within the model are identified. The methodology is demonstrated by refitting the parameters of a published model of cardiac cellular mechanics using a combination of measured data and synthetic data from an alternative model of the same system. Using this approach, reduced models with simplified expressions for the tropomyosin/crossbridge kinetics were found by identification of model components that can be omitted without affecting the fit to the parameterising data. Our analysis revealed that model parameters could be constrained to a standard deviation of on average 15% of the mean values over the succeeding parameter sets.ConclusionsOur results indicate that the presented approach is effective for comparing model alternatives and reducing models to the minimum complexity replicating measured data. We therefore believe that this approach has significant potential for reparameterising existing frameworks, for identification of redundant model components of large biophysical models and to increase their predictive capacity.

Protein Alpha Shape (PAS) Dock is a new empirical score function suitable for virtual library screening using homology modelled protein structures. Here, the score function is used in combination with the geometry search method Tabu search. A description of the protein binding site is generated using gaussian property fields like in Protein Alpha Shape Similarity Analysis (PASSA). Gaussian property fields are also used to describe the ligand properties. The overlap between the receptor and ligand hydrophilicity and lipophilicity fields is maximised, while minimising steric clashes. Gaussian functions introduce a smoothing of the property fields. This makes the score function robust against small structural variations, and therefore suitable for use with homology models. This also makes it less critical to include protein flexibility in the docking calculations. We use a fast and simplified version of the score function in the geometry search, while a more detailed version is used for the final prediction of the binding free energies. This use of a two-level scoring makes PAS-Dock computationally efficient, and well suited for virtual screening. The PAS-Dock score function is trained on 218 X-ray structures of protein- ligand complexes with experimental binding affinities. The performance of PAS-Dock is compared to two other docking methods, AutoDock and MOE-Dock, with respect to both accuracy and computational efficiency. According to this study, PAS-Dock is more computationally efficient than both AutoDock and MOE-Dock, and gives a better prediction of the free energies of binding. PAS-Dock is also more robust against structural variations than AutoDock.