Parameter identifiability analysis and visualization in large-scale kinetic models of biosystems

Mechanistic Models of Inducible Synthetic Circuits for Joint Description of DNA Copy Number, Regulatory Protein Level, and Cell Load

Accurate predictive mathematical models are urgently needed in synthetic biology to support the bottom-up design of complex biological systems, minimizing trial-and-error approaches. The majority of models used so far adopt empirical Hill functions to describe activation and repression in exogenously-controlled inducible promoter systems. However, such equations may be poorly predictive in practical situations that are typical in bottom-up design, including changes in promoter copy number, regulatory protein level, and cell load. In this work, we derived novel mechanistic steady-state models of the lux inducible system, used as case study, relying on different assumptions on regulatory protein (LuxR) and cognate promoter (Plux) concentrations, inducer-protein complex formation, and resource usage limitation. We demonstrated that a change in the considered model assumptions can significantly affect circuit output, and preliminary experimental data are in accordance with the simulated activation curves. We finally showed that the models are identifiable a priori (in the analytically tractable cases) and a posteriori, and we determined the specific experiments needed to parametrize them. Although a larger-scale experimental validation is required, in the future the reported models may support synthetic circuits output prediction in practical situations with unprecedented details.

Parameter estimation in models of biological oscillators: an automated regularised estimation approach

BACKGROUND

Dynamic modelling is a core element in the systems biology approach to understanding complex biosystems. Here, we consider the problem of parameter estimation in models of biological oscillators described by deterministic nonlinear differential equations. These problems can be extremely challenging due to several common pitfalls: (i) a lack of prior knowledge about parameters (i.e. massive search spaces), (ii) convergence to local optima (due to multimodality of the cost function), (iii) overfitting (fitting the noise instead of the signal) and (iv) a lack of identifiability. As a consequence, the use of standard estimation methods (such as gradient-based local ones) will often result in wrong solutions. Overfitting can be particularly problematic, since it produces very good calibrations, giving the impression of an excellent result. However, overfitted models exhibit poor predictive power. Here, we present a novel automated approach to overcome these pitfalls. Its workflow makes use of two sequential optimisation steps incorporating three key algorithms: (1) sampling strategies to systematically tighten the parameter bounds reducing the search space, (2) efficient global optimisation to avoid convergence to local solutions, (3) an advanced regularisation technique to fight overfitting. In addition, this workflow incorporates tests for structural and practical identifiability.

RESULTS

We successfully evaluate this novel approach considering four difficult case studies regarding the calibration of well-known biological oscillators (Goodwin, FitzHugh-Nagumo, Repressilator and a metabolic oscillator). In contrast, we show how local gradient-based approaches, even if used in multi-start fashion, are unable to avoid the above-mentioned pitfalls.

CONCLUSIONS

Our approach results in more efficient estimations (thanks to the bounding strategy) which are able to escape convergence to local optima (thanks to the global optimisation approach). Further, the use of regularisation allows us to avoid overfitting, resulting in more generalisable calibrated models (i.e. models with greater predictive power).

Identifiability Analysis of Three Control-Oriented Models for Use in Artificial Pancreas Systems

OBJECTIVE

Our aim is to analyze the identifiability of three commonly used control-oriented models for glucose control in patients with type 1 diabetes (T1D).

METHODS

Structural and practical identifiability analysis were performed on three published control-oriented models for glucose control in patients with type 1 diabetes (T1D): the subcutaneous oral glucose minimal model (SOGMM), the intensive control insulin-nutrition-glucose (ICING) model, and the minimal model control-oriented (MMC). Structural identifiability was addressed with a combination of the generating series (GS) approach and identifiability tableaus whereas practical identifiability was studied by means of (1) global ranking of parameters via sensitivity analysis together with the Latin hypercube sampling method (LHS) and (2) collinearity analysis among parameters. For practical identifiability and model identification, continuous glucose monitor (CGM), insulin pump, and meal records were selected from a set of patients (n = 5) on continuous subcutaneous insulin infusion (CSII) that underwent a clinical trial in an outpatient setting. The performance of the identified models was analyzed by means of the root mean square (RMS) criterion.

RESULTS

A reliable set of identifiable parameters was found for every studied model after analyzing the possible identifiability issues of the original parameter sets. According to an importance factor ([Formula: see text]), it was shown that insulin sensitivity is not the most influential parameter from the dynamical point of view, that is, is not the parameter impacting the outputs the most of the three models, contrary to what is assumed in the literature. For the test data, the models demonstrated similar performance with most RMS values around 20 mg/dl (min: 15.64 mg/dl, max: 51.32 mg/dl). However, MMC failed to identify the model for patient 4. Also, considering the three models, the MMC model showed the higher parameter variability when reidentified every 6 hours.

CONCLUSION

This study shows that both structural and practical identifiability analysis need to be considered prior to the model identification/individualization in patients with T1D. It was shown that all the studied models are able to represent the CGM data, yet their usefulness in a hypothetical artificial pancreas could be a matter of debate. In spite that the three models do not capture all the dynamics and metabolic effects as a maximal model (ie, our FDA-accepted UVa/Padova simulator), SOGMM and ICING appear to be more appealing than MMC regarding both the performance and parameter variability after reidentification. Although the model predictions of ICING are comparable to the ones of the SOGMM model, the large parameter set makes the model prone to overfitting if all parameters are identified. Moreover, the existence of a high nonlinear function like [Formula: see text] prevents the use of tools from the linear systems theory.

Deciphering microbial interactions in synthetic human gut microbiome communities

The ecological forces that govern the assembly and stability of the human gut microbiota remain unresolved. We developed a generalizable model-guided framework to predict higher-dimensional consortia from time-resolved measurements of lower-order assemblages. This method was employed to decipher microbial interactions in a diverse human gut microbiome synthetic community. We show that pairwise interactions are major drivers of multi-species community dynamics, as opposed to higher-order interactions. The inferred ecological network exhibits a high proportion of negative and frequent positive interactions. Ecological drivers and responsive recipient species were discovered in the network. Our model demonstrated that a prevalent positive and negative interaction topology enables robust coexistence by implementing a negative feedback loop that balances disparities in monospecies fitness levels. We show that negative interactions could generate history-dependent responses of initial species proportions that frequently do not originate from bistability. Measurements of extracellular metabolites illuminated the metabolic capabilities of monospecies and potential molecular basis of microbial interactions. In sum, these methods defined the ecological roles of major human-associated intestinal species and illuminated design principles of microbial communities.

Use of transcriptomic data for extending a model of the AppA/PpsR system in Rhodobacter sphaeroides

Background

Photosynthetic (PS) gene expression in Rhodobacter sphaeroides is regulated in response to changes in light and redox conditions mainly by PrrB/A, FnrL and AppA/PpsR systems. The PrrB/A and FnrL systems activate the expression of them under anaerobic conditions while the AppA/PpsR system represses them under aerobic conditions. Recently, two mathematical models have been developed for the AppA/PpsR system and demonstrated how the interaction between AppA and PpsR could lead to a phenotype in which PS genes are repressed under semi-aerobic conditions. These models have also predicted that the transition from aerobic to anaerobic growth mode could occur via a bistable regime. However, they lack experimentally quantifiable inputs and outputs. Here, we extend one of them to include such quantities and combine all relevant micro-array data publically available for a PS gene of this bacterium and use that to parameterise the model. In addition, we hypothesise that the AppA/PpsR system alone might account for the observed trend of PS gene expression under semi-aerobic conditions.

Results

Our extended model of the AppA/PpsR system includes the biological input of atmospheric oxygen concentration and an output of photosynthetic gene expression. Following our hypothesis that the AppA/PpsR system alone is sufficient to describe the overall trend of PS gene expression we parameterise the model and suggest that the rate of AppA reduction in vivo should be faster than its oxidation. Also, we show that despite both the reduced and oxidised forms of PpsR binding to the PS gene promoters in vitro, binding of the oxidised form as a repressor alone is sufficient to reproduce the observed PS gene expression pattern. Finally, the combination of model parameters which fit the biological data well are broadly consistent with those which were previously determined to be required for the system to show (i) the repression of PS genes under semi-aerobic conditions, and (ii) bistability.

Conclusion

We found that despite at least three pathways being involved in the regulation of photosynthetic genes, the AppA/PpsR system alone is capable of accounting for the observed trends in photosynthetic gene expression seen at different oxygen levels.

Electronic supplementary material

The online version of this article (10.1186/s12918-017-0489-y) contains supplementary material, which is available to authorized users.