Numerical framework to model temporally resolved multi-stage dynamic systems

A consensus approach for estimating the predictive accuracy of dynamic models in biology

Mathematical models that predict the complex dynamic behaviour of cellular networks are fundamental in systems biology, and provide an important basis for biomedical and biotechnological applications. However, obtaining reliable predictions from large-scale dynamic models is commonly a challenging task due to lack of identifiability. The present work addresses this challenge by presenting a methodology for obtaining high-confidence predictions from dynamic models using time-series data. First, to preserve the complex behaviour of the network while reducing the number of estimated parameters, model parameters are combined in sets of meta-parameters, which are obtained from correlations between biochemical reaction rates and between concentrations of the chemical species. Next, an ensemble of models with different parameterizations is constructed and calibrated. Finally, the ensemble is used for assessing the reliability of model predictions by defining a measure of convergence of model outputs (consensus) that is used as an indicator of confidence. We report results of computational tests carried out on a metabolic model of Chinese Hamster Ovary (CHO) cells, which are used for recombinant protein production. Using noisy simulated data, we find that the aggregated ensemble predictions are on average more accurate than the predictions of individual ensemble models. Furthermore, ensemble predictions with high consensus are statistically more accurate than ensemble predictions with large variance. The procedure provides quantitative estimates of the confidence in model predictions and enables the analysis of sufficiently complex networks as required for practical applications.

A multi-step, dynamic allosteric model of testosterone's binding to sex hormone binding globulin

PURPOSE

Circulating free testosterone (FT) levels have been used widely in the diagnosis and treatment of hypogonadism in men. Due to experimental complexities in FT measurements, the Endocrine Society has recommended the use of calculated FT (cFT) as an appropriate approach for estimating FT. We show here that the prevailing model of testosterone's binding to SHBG, which assumes that each SHBG dimer binds two testosterone molecules and that the two binding sites on SHBG have similar binding affinity is erroneous and provides FT values that differ substantially from those obtained using equilibrium dialysis.

METHODS

We characterized testosterone's binding to SHBG using binding isotherms, ligand depletion curves, and isothermal titration calorimetry (ITC). We derived a new model of testosterone's binding to SHBG from these experimental data and used this model to determine FT concentrations and compare these values with those derived from equilibrium dialysis.

RESULTS

Experimental data on testosterone's association with SHBG generated using binding isotherms including equilibrium binding, ligand depletion experiments, and ITC provide evidence of a multi-step dynamic process, encompassing at least two inter-converting microstates in unliganded SHBG, readjustment of equilibria between unliganded states upon binding of the first ligand molecule, and allosteric interaction between two binding sites of SHBG dimer. FT concentrations in men determined using the new multistep dynamic model with complex allostery did not differ from those measured using equilibrium dialysis. Systematic error in calculated FT vales in females using Vermeulen's model was also significantly reduced. In European Male Aging Study, the men deemed to have low FT (<2.5th percentile) by the new model were at increased risk of sexual symptoms and elevated LH.

CONCLUSION

Testosterone's binding to SHBG is a multi-step dynamic process that involves complex allostery within SHBG dimer. FT values obtained using the new model have close correspondence with those measured using equilibrium dialysis.