Global optimization in systems biology: stochastic methods and their applications

Mathematical optimization is at the core of many problems in systems biology: (1) as the underlying hypothesis for model development, (2) in model identification, or (3) in the computation of optimal stimulation procedures to synthetically achieve a desired biological behavior. These problems are usually formulated as nonlinear programing problems (NLPs) with dynamic and algebraic constraints. However the nonlinear and highly constrained nature of systems biology models, together with the usually large number of decision variables, can make their solution a daunting task, therefore calling for efficient and robust optimization techniques. Here, we present novel global optimization methods and software tools such as cooperative enhanced scatter search (eSS), AMIGO, or DOTcvpSB, and illustrate their possibilities in the context of modeling including model identification and stimulation design in systems biology.This work was supported by the Spanish MICINN project ”MultiSysBio” (ref. DPI2008-06880-C03-02), and by CSIC intramural project ”BioREDES” (ref. PIE-201170E018).Peer reviewe

Towards predictive models in food engineering: Parameter estimation dos and don'ts

1 póster.-- 29th EFFoST International Conference, 10-12 November 2015, Athens, GreeceRigorous, physics based, modeling is at the core of computer aided food process engineering. Models often require the values of some, typically unknown, parameters (thermo-physical properties, kinetic constants, etc). Therefore, parameter estimation from experimental data is critical to achieve desired model predictive properties. Unfortunately, it must be admitted that often experiment design and modeling are fully separated tasks: experiments are not designed for the purpose of modeling and models are usually derived without paying especial attention to available experimental data or experimentation capabilities. When, at some point, the parameter estimation problem is put on the table, modelers use available experimental data to ``manually'' tune the unknown parameters. This results in inaccurate parameter estimates, usually experiment dependent, with the implications this has in model validation. This work takes a new look into the parameter estimation problem in food process modeling. First the common pitfalls in parameter estimation are described. Second we present the theoretical background and the numerical techniques to define a parameter estimation protocol to iteratively improve model predictive capabilities. This protocol includes: reduced order modeling, structural and practical identifiability analyses, data fitting with global optimization methods and optimal experimental design. And, to finish, we illustrate the performance of the proposed protocol with an example related to the thermal processing of packaged foods. The model was experimentally validated in the IIM-CSIC pilot plantThe authors acknowledge financial support from the EU (Project SPECTRAFISH), Spanish Ministry of Science and Innovation (Project ISFORQUALITY) and CSIC (Project CONTROLA)Peer reviewe

Identifiability of large nonlinear biochemical networks

Dynamic models formulated as a set of ordinary differential equations provide a detailed description of the time-evolution of a system. Such models of (bio)chemical reaction networks have contributed to important advances in biotechnology and biomedical applications, and their impact is foreseen to increase in the near future. Hence, the task of dynamic model building has attracted much attention from scientists working at the intersection of biochemistry, systems theory, mathematics, and computer science, among other disciplines-an area sometimes called systems biology. Before a model can be effectively used, the values of its unknown parameters have to be estimated from experimental data. A necessary condition for parameter estimation is identifiability, the property that, for a certain output, there exists a unique (or finite) set of parameter values that produces it. Identifiability can be analysed from two complementary points of view: structural (which searches for symmetries in the model equations that may prevent parameters from being uniquely determined) or practical (which focuses on the limitations introduced by the quantity and quality of the data available for parameter estimation). Both types of analyses are often difficult for nonlinear models, and their complexity increases rapidly with the problem size. Hence, assessing the identifiability of realistic dynamic models of biochemical networks remains a challenging task. Despite the fact that many methods have been developed for this purpose, it is still an open problem and an active area of research. Here we review the theory and tools available for the study of identifiability, and discuss some closely related concepts such as sensitivity to parameter perturbations, observability, distinguishability, and optimal experimental design, among others.This work was funded by the Galician government (Xunta de Galiza) through the I2C postdoctoral program (fellowship ED481B2014/133-0), and by the Spanish Ministry of Economy and Competitiveness (grant DPI2013-47100-C2-2-P)

PEtab -- interoperable specification of parameter estimation problems in systems biology

Reproducibility and reusability of the results of data-based modeling studies are essential. Yet, there has been -- so far -- no broadly supported format for the specification of parameter estimation problems in systems biology. Here, we introduce PEtab, a format which facilitates the specification of parameter estimation problems using Systems Biology Markup Language (SBML) models and a set of tab-separated value files describing the observation model and experimental data as well as parameters to be estimated. We already implemented PEtab support into eight well-established model simulation and parameter estimation toolboxes with hundreds of users in total. We provide a Python library for validation and modification of a PEtab problem and currently 20 example parameter estimation problems based on recent studies. Specifications of PEtab, the PEtab Python library, as well as links to examples, and all supporting software tools are available at https://github.com/PEtab-dev/PEtab, a snapshot is available at https://doi.org/10.5281/zenodo.3732958. All original content is available under permissive licenses

A parallel metaheuristic for large mixed-integer dynamic optimization problems, with applications in computational biology

[Abstract] Background: We consider a general class of global optimization problems dealing with nonlinear dynamic models. Although this class is relevant to many areas of science and engineering, here we are interested in applying this framework to the reverse engineering problem in computational systems biology, which yields very large mixed-integer dynamic optimization (MIDO) problems. In particular, we consider the framework of logic-based ordinary differential equations (ODEs). Methods: We present saCeSS2, a parallel method for the solution of this class of problems. This method is based on an parallel cooperative scatter search metaheuristic, with new mechanisms of self-adaptation and specific extensions to handle large mixed-integer problems. We have paid special attention to the avoidance of convergence stagnation using adaptive cooperation strategies tailored to this class of problems. Results: We illustrate its performance with a set of three very challenging case studies from the domain of dynamic modelling of cell signaling. The simpler case study considers a synthetic signaling pathway and has 84 continuous and 34 binary decision variables. A second case study considers the dynamic modeling of signaling in liver cancer using high-throughput data, and has 135 continuous and 109 binaries decision variables. The third case study is an extremely difficult problem related with breast cancer, involving 690 continuous and 138 binary decision variables. We report computational results obtained in different infrastructures, including a local cluster, a large supercomputer and a public cloud platform. Interestingly, the results show how the cooperation of individual parallel searches modifies the systemic properties of the sequential algorithm, achieving superlinear speedups compared to an individual search (e.g. speedups of 15 with 10 cores), and significantly improving (above a 60%) the performance with respect to a non-cooperative parallel scheme. The scalability of the method is also good (tests were performed using up to 300 cores). Conclusions: These results demonstrate that saCeSS2 can be used to successfully reverse engineer large dynamic models of complex biological pathways. Further, these results open up new possibilities for other MIDO-based large-scale applications in the life sciences such as metabolic engineering, synthetic biology, drug scheduling.Ministerio de Economía y Competitividad; DPI2014-55276-C5-2-RMinisterio de Economía y Competitividad; TIN2016-75845-PGalicia. Consellería de Cultura, Educación e Ordenación Universitaria; R2016/045Galicia. Consellería de Cultura, Educación e Ordenación Universitaria; GRC2013/05

Review: to be or not to be an identifiable model. Is this a relevant question in animal science modelling?

International audienceWhat is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODE) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and highly informative experiments. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design

CADLIVE Optimizer: Web-based Parameter Estimation for Dynamic Models

Computer simulation has been an important technique to capture the dynamics of biochemical networks. In most networks, however, few kinetic parameters have been measured in vivo because of experimental complexity. We develop a kinetic parameter estimation system, named the CADLIVE Optimizer, which comprises genetic algorithms-based solvers with a graphical user interface. This optimizer is integrated into the CADLIVE Dynamic Simulator to attain efficient simulation for dynamic models