Estimating model parameters from experimental data is a crucial technique for working with computational models in systems biology. Since stochastic models are increasingly important, parameter estimation methods for stochastic modelling are also of increasing interest. This study presents an extension to the ‘multiple shooting for stochastic systems (MSS)’ method for parameter estimation. The transition probabilities of the likelihood function are approximated with normal distributions. Means and variances are calculated with a linear noise approximation on the interval between succeeding measurements. The fact that the system is only approximated on intervals which are short in comparison with the total observation horizon allows to deal with effects of the intrinsic stochasticity. The study presents scenarios in which the extension is essential for successfully estimating the parameters and scenarios in which the extension is of modest benefit. Furthermore, it compares the estimation results with reversible jump techniques showing that the approximation does not lead to a loss of accuracy. Since the method is not based on stochastic simulations or approximative sampling of distributions, its computational speed is comparable with conventional least-squares parameter estimation methods.

In computational systems biology, the general aim is to derive regulatory models from multivariate readouts, thereby generating predictions for novel experiments. In the past, many such models have been formulated for different biological applications. The authors consider the scenario where a given model fails to predict a set of observations with acceptable accuracy and ask the question whether this is because of the model lacking important external regulations. Real-world examples for such entities range from microRNAs to metabolic fluxes. To improve the prediction, they propose an algorithm to systematically extend the network by an additional latent dynamic variable which has an exogenous effect on the considered network. This variable's time course and influence on the other species is estimated in a two-step procedure involving spline approximation, maximum-likelihood estimation and model selection. Simulation studies show that such a hidden influence can successfully be inferred. The method is also applied to a signalling pathway model where they analyse real data and obtain promising results. Furthermore, the technique can be employed to detect incomplete network structures.

The authors developed a mathematical model of arachidonic acid (AA) degradation to prostaglandins (PGs) and leukotrienes (LTs), which are implicated in the processes of inflammation and hypersensitivity to non-steroidal anti-inflammatory drugs (NSAIDs). The model focuses on two PGs (PGE₂ and PGD₂) and one LT (LTC₄), their % increases and their ratios. Results are compared with experimental studies obtained from non-asthmatics (NAs), and asthmatics tolerant (ATA) or intolerant (AIA) to aspirin. Simulations are carried out for predefined model populations NA, ATA and three AIA, based on the differences of two enzymes, PG E synthase and/or LTC₄-synthase in two states, that is, no-inflammation and inflammation. Their model reveals that the model population with concomitant malfunctions in both enzymes is the most sensitive to NSAIDs, since the duration and the capacity for bronchoconstriction risk are highest after simulated oral dosing of indomethacin. Furthermore, inflammation prolongs the duration of the bronchoconstriction risk in all AIA model populations, and the sensitivity analysis reveals multiple possible scenarios leading to hypersensitivity, especially if inflammatory processes affect the expression of multiple enzymes of the AA metabolic pathway. Their model estimates the expected fold-changes in enzyme activities and gives valuable information for further targeted transcriptomic/proteomic and metabolomic studies.