Dynamical compensation and structural identifiability: analysis, implications, and reconciliation

The concept of dynamical compensation has been recently introduced to describe the ability of a biological system to keep its output dynamics unchanged in the face of varying parameters. Here we show that, according to its original definition, dynamical compensation is equivalent to lack of structural identifiability. This is relevant if model parameters need to be estimated, which is often the case in biological modelling. This realization prompts us to warn that care should we taken when using an unidentifiable model to extract biological insight: the estimated values of structurally unidentifiable parameters are meaningless, and model predictions about unmeasured state variables can be wrong. Taking this into account, we explore alternative definitions of dynamical compensation that do not necessarily imply structural unidentifiability. Accordingly, we show different ways in which a model can be made identifiable while exhibiting dynamical compensation. Our analyses enable the use of the new concept of dynamical compensation in the context of parameter identification, and reconcile it with the desirable property of structural identifiability

Multicriteria global optimization for biocircuit design

One of the challenges in Synthetic Biology is to design circuits with increasing levels of complexity. While circuits in Biology are complex and subject to natural tradeoffs, most synthetic circuits are simple in terms of the number of regulatory regions, and have been designed to meet a single design criterion. In this contribution we introduce a multiobjective formulation for the design of biocircuits. We set up the basis for an advanced optimization tool for the modular and systematic design of biocircuits capable of handling high levels of complexity and multiple design criteria. Our methodology combines the efficiency of global Mixed Integer Nonlinear Programming solvers with multiobjective optimization techniques. Through a number of examples we show the capability of the method to generate non intuitive designs with a desired functionality setting up a priori the desired level of complexity. The presence of more than one competing objective provides a realistic design setting where every design solution represents a trade-off between different criteria. The tool can be useful to explore and identify different design principles for synthetic gene circuits

Design Principles of Biological Oscillators through Optimization: Forward and Reverse Analysis

26 páginas, 10 figuras, 1 tabla.-- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are creditedFrom cyanobacteria to human, sustained oscillations coordinate important biological functions. Although much has been learned concerning the sophisticated molecular mechanisms underlying biological oscillators, design principles linking structure and functional behavior are not yet fully understood. Here we explore design principles of biological oscillators from a multiobjective optimization perspective, taking into account the trade-offs between conflicting performance goals or demands. We develop a comprehensive tool for automated design of oscillators, based on multicriteria global optimization that allows two modes: (i) the automatic design (forward problem) and (ii) the inference of design principles (reverse analysis problem). From the perspective of synthetic biology, the forward mode allows the solution of design problems that mimic some of the desirable properties appearing in natural oscillators. The reverse analysis mode facilitates a systematic exploration of the design space based on Pareto optimality concepts. The method is illustrated with two case studies: the automatic design of synthetic oscillators from a library of biological parts, and the exploration of design principles in 3-gene oscillatory systemsThis work was supported by MINECO (and the European Regional Development Fund) project ªSYNBIOFACTORYº (grant number DPI2014-55276-C5-2-R).Peer reviewe

Reverse engineering of logic-based differential equation models using a mixed-integer dynamic optimization approach

9 páginas, 6 figuras.-- This is an Open Access article distributed under the terms of the Creative Commons Attribution LicenseMotivation: Systems biology models can be used to test new hypotheses formulated on the basis of previous knowledge or new experimental data, contradictory with a previously existing model. New hypotheses often come in the shape of a set of possible regulatory mechanisms. This search is usually not limited to finding a single regulation link, but rather a combination of links subject to great uncertainty or no information about the kinetic parameters. Results: In this work, we combine a logic-based formalism, to describe all the possible regulatory structures for a given dynamic model of a pathway, with mixed-integer dynamic optimization (MIDO). This framework aims to simultaneously identify the regulatory structure (represented by binary parameters) and the real-valued parameters that are consistent with the available experimental data, resulting in a logic-based differential equation model. The alternative to this would be to perform real-valued parameter estimation for each possible model structure, which is not tractable for models of the size presented in this work. The performance of the method presented here is illustrated with several case studies: a synthetic pathway problem of signaling regulation, a two-component signal transduction pathway in bacterial homeostasis, and a signaling network in liver cancer cellsD.H., J.R.B. and J.S.R. acknowledge funding from the EU FP7 projects ‘NICHE’ (ITN Grant number 289384) and ‘BioPreDyn’ (KBBE grant number 289434). J.R.B. also acknowledges funding from the Spanish Ministerio de Economía y Competitividad (and the FEDER) through the project MultiScales (DPI2011-28112-C04-03).Peer reviewe

Reverse engineering of logic-based differential equation models using a mixed-integer dynamic optimisation approach

Motivation: Systems biology models can be used to test new hypotheses formulated on the basis of previous knowledge or new experimental data, contradictory with a previously existing model. New hypotheses often come in the shape of a set of possible regulatory mechanisms. This search is usually not limited to finding a single regulation link, but rather a combination of links subject to great uncertainty or no information about the kinetic parameters.Results: In this work, we combine a logic-based formalism, to describe all the possible regulatory structures for a given dynamic model of a pathway, with mixed-integer dynamic optimization (MIDO). This framework aims to simultaneously identify the regulatory structure (represented by binary parameters) and the real-valued parameters that are consistent with the available experimental data, resulting in a logic-based differential equation model. The alternative to this would be to perform real-valued parameter estimation for each possible model structure, which is not tractable for models of the size presented in this work. The performance of the method presented here is illustrated with several case studies: a synthetic pathway problem of signaling regulation, a two component signal transduction pathway in bacterial homeostasis, and a signaling network in liver cancer cells.D.H., J.R.B. and J.S.R. acknowledge funding from the EU FP7 projects 'NICHE' (ITN Grant number 289384) and 'BioPreDyn' (KBBE grant number 289434). J.R.B. also acknowledges funding from the Spanish Ministerio de Economia y Competitividad (and the FEDER) through the project MultiScales (DPI2011-28112-C04-03)

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

[Background] Kinetic models of biochemical systems usually consist of ordinary differential equations that have many unknown parameters. Some of these parameters are often practically unidentifiable, that is, their values cannot be uniquely determined from the available data. Possible causes are lack of influence on the measured outputs, interdependence among parameters, and poor data quality. Uncorrelated parameters can be seen as the key tuning knobs of a predictive model. Therefore, before attempting to perform parameter estimation (model calibration) it is important to characterize the subset(s) of identifiable parameters and their interplay. Once this is achieved, it is still necessary to perform parameter estimation, which poses additional challenges.[Methods] We present a methodology that (i) detects high-order relationships among parameters, and (ii) visualizes the results to facilitate further analysis. We use a collinearity index to quantify the correlation between parameters in a group in a computationally efficient way. Then we apply integer optimization to find the largest groups of uncorrelated parameters. We also use the collinearity index to identify small groups of highly correlated parameters. The results files can be visualized using Cytoscape, showing the identifiable and non-identifiable groups of parameters together with the model structure in the same graph.[Results] Our contributions alleviate the difficulties that appear at different stages of the identifiability analysis and parameter estimation process. We show how to combine global optimization and regularization techniques for calibrating medium and large scale biological models with moderate computation times. Then we evaluate the practical identifiability of the estimated parameters using the proposed methodology. The identifiability analysis techniques are implemented as a MATLAB toolbox called VisId, which is freely available as open source from GitHub ( https://github.com/gabora/visid ).[Conclusions] Our approach is geared towards scalability. It enables the practical identifiability analysis of dynamic models of large size, and accelerates their calibration. The visualization tool allows modellers to detect parts that are problematic and need refinement or reformulation, and provides experimentalists with information that can be helpful in the design of new experiments.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 686282 (“CANPATHPRO”), from the EU FP7 project "NICHE" (ITN Grant number 289384), and from the Spanish MINECO project "SYNBIOFACTORY" (grant number DPI2014-55276-C5-2-R).Peer reviewe

PREMER: Parallel reverse engineering of biological networks with information theory

A common approach for reverse engineering biological networks from data is to deduce the existence of interactions among nodes from information theoretic measures. Estimating these quantities in a multidimensional space is computationally demanding for large datasets. This hampers the application of elaborate algorithms which are crucial for discarding spurious interactions and determining causal relationships  to large-scale network inference problems. To alleviate this issue we have developed PREMER, a software tool which can automatically run in parallel and sequential environments, thanks to its implementation of OpenMP directives. It recovers network topology and estimates the strength and causality of interactions using information theoretic criteria, and allowing the incorporation of prior knowledge. A preprocessing module takes care of imputing missing data and correcting outliers if needed. PREMER (https://sites.google.com/site/premertoolbox/) runs on Windows, Linux and OSX, it is implemented in Matlab/Octave and Fortran 90, and it does not require any commercial software.AFV acknowledges funding from the Galician government (Xunta de Galiza) through the I2C fellowship ED481B2014/133-0. KB was supported by the German Federal Ministry of Research and Education (BMBF, OncoPath consortium). JRB acknowledges funding from the Spanish government (MINECO) and the European Regional Development Fund (ERDF) through the project “SYNBIOFACTORY” (grant number DPI2014-55276-C5-2-R). This project has received funding from the European Unions Horizon 2020 research and innovation programme under grant agreement No 686282 (CanPathPro). We thank David R. Penas and David Henriques for assistance with the implementation

DOTcvpSB, a software toolbox for dynamic optimization in systems biology

<p>Abstract</p> <p>Background</p> <p>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.</p> <p>Results</p> <p>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.</p> <p>Conclusion</p> <p>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.</p