Microbial communities, complex ecological networks crucial for human and planetary health, remain poorly understood in terms of the quantitative principles governing their composition, assembly, and function. Dynamic modeling using ordinary differential equations (ODEs) is a powerful framework for understanding and predicting microbiome behaviors. However, developing reliable ODE models is severely hampered by their nonlinear nature and the presence of significant challenges, particularly critical issues related to identifiability. Here, we address the identification problem in dynamic microbial community models by proposing an integrated methodology to tackle key challenges. Focusing on nonlinear ODE-based models, we examine four critical pitfalls: identifiability issues (structural and practical), unstable dynamics (potentially leading to numerical blow-up), underfitting (convergence to suboptimal solutions), and overfitting (fitting noise rather than signal). These pitfalls yield unreliable parameter estimates, unrealistic model behavior, and poor generalization. Our study presents a comprehensive workflow incorporating structural and practical identifiability analysis, robust global optimization for calibration, stability checks, and rigorous predictive power assessment. The methodology's effectiveness and versatility in mitigating these pitfalls are demonstrated through case studies of increasing complexity, paving the way for more reliable and mechanistically insightful models of microbial communities.

Synthetic biology is predicated upon the paradigm of rationally engineering biological systems to enrich them with new functions. Departing from the path outlined by other engineering disciplines, synthetic biology has made limited use of mathematical models so far. Indeed, their laborious inference leverages on noisy data that often provide partial insights into the system behaviour. If the quality of data generated via a perturbation is a road-block to inference, how should we analyse the informativeness of a stimulus? Which are the factors that contribute to it? Here we combine ideas from System Identification and Bayesian inference to quantify the information content of in vivo experiments for the calibration of a deterministic model of the genetic toggle switch. Beyond establishing a link between Bayes- and Fisher Information-based inference approaches, we find a ~ 40% gain can be ascribed to the dynamical properties of the perturbation scheme. Our results hint at the importance of including Bayesian experimental design in the characterisation of synthetic circuits.

Motivation: Mathematical modeling using ordinary differential equations is used in systems biology to improve the understanding of dynamic biological processes. The parameters of ordinary differential equation models are usually estimated from experimental data. To analyze a priori the uniqueness of the solution of the estimation problem, structural identifiability analysis methods have been developed. Results: We introduce GenSSI 2.0, an advancement of the software toolbox GenSSI (Generating Series for testing Structural Identifiability). GenSSI 2.0 is the first toolbox for structural identifiability analysis to implement Systems Biology Markup Language import, state/parameter transformations and multi-experiment structural identifiability analysis. In addition, GenSSI 2.0 supports a range of MATLAB versions and is computationally more efficient than its previous version, enabling the analysis of more complex models. Availability and implementation: GenSSI 2.0 is an open-source MATLAB toolbox and available at https://github.com/genssi-developer/GenSSI. Contact: [email protected] or [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

Motivation: Optimality principles have been used to explain many biological processes and systems. However, the functions being optimized are in general unknown a priori. Here we present an inverse optimal control framework for modeling dynamics in systems biology. The objective is to identify the underlying optimality principle from observed time-series data and simultaneously estimate unmeasured time-dependent inputs and time-invariant model parameters. As a special case, we also consider the problem of optimal simultaneous estimation of inputs and parameters from noisy data. After presenting a general statement of the inverse optimal control problem, and discussing special cases of interest, we outline numerical strategies which are scalable and robust. Results: We discuss the existence, relevance and implications of identifiability issues in the above problems. We present a robust computational approach based on regularized cost functions and the use of suitable direct numerical methods based on the control-vector parameterization approach. To avoid convergence to local solutions, we make use of hybrid global-local methods. We illustrate the performance and capabilities of this approach with several challenging case studies, including simulated and real data. We pay particular attention to the computational scalability of our approach (with the objective of considering large numbers of inputs and states). We provide a software implementation of both the methods and the case studies. Availability and implementation: The code used to obtain the results reported here is available at https://zenodo.org/record/1009541. Supplementary information: Supplementary data are available at Bioinformatics online.

MOTIVATION: Many problems of interest in dynamic modeling and control of biological systems can be posed as non-linear optimization problems subject to algebraic and dynamic constraints. In the context of modeling, this is the case of, e.g. parameter estimation, optimal experimental design and dynamic flux balance analysis. In the context of control, model-based metabolic engineering or drug dose optimization problems can be formulated as (multi-objective) optimal control problems. Finding a solution to those problems is a very challenging task which requires advanced numerical methods. RESULTS: This work presents the AMIGO2 toolbox: the first multiplatform software tool that automatizes the solution of all those problems, offering a suite of state-of-the-art (multi-objective) global optimizers and advanced simulation approaches. AVAILABILITY AND IMPLEMENTATION: The toolbox and its documentation are available at: sites.google.com/site/amigo2toolbox CONTACT: [email protected] information: Supplementary data are available at Bioinformatics online.

BACKGROUND: Adjusting the capacity of metabolic pathways in response to rapidly changing environmental conditions is an important component of microbial adaptation strategies to stochastic environments. In this work, we use advanced dynamic optimization techniques combined with theoretical models to study which reactions in pathways are optimally targeted by regulatory interactions in order to minimize the regulatory effort that is required to adjust the flux through a complex metabolic network. Moreover, we analyze how constraints in the speed at which an organism can respond on a proteomic level influences these optimal targets of pathway control. RESULTS: We find that limitations in protein biosynthetic rates have a strong influence. With increasing protein biosynthetic rates the regulatory effort targeting the initial enzyme in a pathway is reduced while the regulatory effort in the terminal enzyme is increased. Studying the impact of allosteric regulation for different pathway topologies, we find that the presence of feedback inhibition by products of metabolic pathways allows organisms to reduce the regulatory effort that is required to control a metabolic pathway in all cases. In a linear pathway this even leads to the case where the sole transcriptional regulatory control of the terminal enzyme is sufficient to control flux through the entire pathway. We confirm the utilization of these pathway regulation strategies through the large-scale analysis of transcriptional regulation in several hundred prokaryotes. CONCLUSIONS: This work expands our knowledge about optimal programs of pathway control. Optimal targets of pathway control strongly depend on the speed at which proteins can be synthesized. Moreover, post-translational regulation such as allosteric regulation allows to strongly reduce the number of transcriptional regulatory interactions required to control a metabolic pathway across different pathway topologies.

Systems biology proceeds through repeated cycles of experiment and modeling. One way to implement this is reverse engineering, where models are fit to data to infer and analyse regulatory mechanisms. This requires rigorous methods to determine whether model parameters can be properly identified. Applying such methods in a complex biological context remains challenging. We use reverse engineering to study post-transcriptional regulation in pattern formation. As a case study, we analyse expression of the gap genes Krüppel, knirps, and giant in Drosophila melanogaster. We use detailed, quantitative datasets of gap gene mRNA and protein expression to solve and fit a model of post-transcriptional regulation, and establish its structural and practical identifiability. Our results demonstrate that post-transcriptional regulation is not required for patterning in this system, but is necessary for proper control of protein levels. Our work demonstrates that the uniqueness and specificity of a fitted model can be rigorously determined in the context of spatio-temporal pattern formation. This greatly increases the potential of reverse engineering for the study of development and other, similarly complex, biological processes.

MOTIVATION: Mathematical models of complex biological systems usually consist of sets of differential equations which depend on several parameters which are not accessible to experimentation. These parameters must be estimated by fitting the model to experimental data. This estimation problem is very challenging due to the non-linear character of the dynamics, the large number of parameters and the frequently poor information content of the experimental data (poor practical identifiability). The design of optimal (more informative) experiments is an associated problem of the highest interest. RESULTS: This work presents AMIGO, a toolbox which facilitates parametric identification by means of advanced numerical techniques which cover the full iterative identification procedure putting especial emphasis on robust methods for parameter estimation and practical identifiability analyses, plus flexible capabilities for optimal experimental design. AVAILABILITY: The toolbox and the corresponding documentation may be downloaded from: http://www.iim.csic.es/~amigo CONTACT: [email protected].

SUMMARY: Mathematical modeling has a key role in systems biology. Model building is often regarded as an iterative loop involving several tasks, among which the estimation of unknown parameters of the model from a certain set of experimental data is of central importance. This problem of parameter estimation has many possible pitfalls, and modelers should be very careful to avoid them. Many of such difficulties arise from a fundamental (yet often overlooked) property: the so-called structural (or a priori) identifiability, which considers the uniqueness of the estimated parameters. Obviously, the structural identifiability of any tentative model should be checked at the beginning of the model building loop. However, checking this property for arbitrary non-linear dynamic models is not an easy task. Here we present a software toolbox, GenSSI (Generating Series for testing Structural Identifiability), which enables non-expert users to carry out such analysis. The toolbox runs under the popular MATLAB environment and is accompanied by detailed documentation and relevant examples. AVAILABILITY: The GenSSI toolbox and the related documentation are available at http://www.iim.csic.es/%7Egenssi. CONTACT: [email protected].

BACKGROUND: Mathematical optimization aims to make a system or design as effective or functional as possible, computing the quality of the different alternatives using a mathematical model. Most models in systems biology have a dynamic nature, usually described by sets of differential equations. Dynamic optimization addresses this class of systems, seeking the computation of the optimal time-varying conditions (control variables) to minimize or maximize a certain performance index. Dynamic optimization can solve many important problems in systems biology, including optimal control for obtaining a desired biological performance, the analysis of network designs and computer aided design of biological units. RESULTS: Here, we present a software toolbox, DOTcvpSB, which uses a rich ensemble of state-of-the-art numerical methods for solving continuous and mixed-integer dynamic optimization (MIDO) problems. The toolbox has been written in MATLAB and provides an easy and user friendly environment, including a graphical user interface, while ensuring a good numerical performance. Problems are easily stated thanks to the compact input definition. The toolbox also offers the possibility of importing SBML models, thus enabling it as a powerful optimization companion to modelling packages in systems biology. It serves as a means of handling generic black-box models as well. CONCLUSION: Here we illustrate the capabilities and performance of DOTcvpSB by solving several challenging optimization problems related with bioreactor optimization, optimal drug infusion to a patient and the minimization of intracellular oscillations. The results illustrate how the suite of solvers available allows the efficient solution of a wide class of dynamic optimization problems, including challenging multimodal ones. The toolbox is freely available for academic use.