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

Partial inhibition and bilevel optimization in flux balance analysis

Motivation: Within Flux Balance Analysis, the investigation of complex subtasks, such as finding the optimal perturbation of the network or finding an optimal combination of drugs, often requires to set up a bilevel optimization problem. In order to keep the linearity and convexity of these nested optimization problems, an ON/OFF description of the effect of the perturbation (i.e. Boolean variable) is normally used. This restriction may not be realistic when one wants, for instance, to describe the partial inhibition of a reaction induced by a drug.Results: In this paper we present a formulation of the bilevel optimization which overcomes the oversimplified ON/OFF modeling while preserving the linear nature of the problem. A case study is considered: the search of the best multi-drug treatment which modulates an objective reaction and has the minimal perturbation on the whole network. The drug inhibition is described and modulated through a convex combination of a fixed number of Boolean variables. The results obtained from the application of the algorithm to the core metabolism of E.coli highlight the possibility of finding a broader spectrum of drug combinations compared to a simple ON/OFF modeling.Conclusions: The method we have presented is capable of treating partial inhibition inside a bilevel optimization, without loosing the linearity property, and with reasonable computational performances also on large metabolic networks. The more fine-graded representation of the perturbation allows to enlarge the repertoire of synergistic combination of drugs for tasks such as selective perturbation of cellular metabolism. This may encourage the use of the approach also for other cases in which a more realistic modeling is required. \ua9 2013 Facchetti and Altafini; licensee BioMed Central Ltd

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)

Computational approaches to complex biological networks

The need of understanding and modeling the biological networks is one of the raisons d'\ueatre and of the driving forces behind the emergence of Systems Biology. Because of its holistic approach and because of the widely different level of complexity of the networks, different mathematical methods have been developed during the years. Some of these computational methods are used in this thesis in order to investigate various properties of different biological systems. The first part deals with the prediction of the perturbation of cellular metabolism induced by drugs. Using Flux Balance Analysis to describe the reconstructed genome-wide metabolic networks, we consider the problem of identifying the most selective drug synergisms for given therapeutic targets. The second part of this thesis considers gene regulatory and large social networks as signed graphs (activation/deactivation or friendship/hostility are rephrased as positive/negative coupling between spins). Using the analogy with an Ising spin glass an analysis of the energy landscape and of the content of \u201cdisorder\u201d 'is carried out. Finally, the last part concerns the study of the spatial heterogeneity of the signaling pathway of rod photoreceptors. The electrophysiological data produced by our collaborators in the Neurobiology laboratory have been analyzed with various dynamical systems giving an insight into the process of ageing of photoreceptors and into the role diffusion in the pathway

Stoichiometric representation of geneproteinreaction associations leverages constraint-based analysis from reaction to gene-level phenotype prediction

Genome-scale metabolic reconstructions are currently available for hundreds of organisms. Constraint-based modeling enables the analysis of the phenotypic landscape of these organisms, predicting the response to genetic and environmental perturbations. However, since constraint-based models can only describe the metabolic phenotype at the reaction level, understanding the mechanistic link between genotype and phenotype is still hampered by the complexity of gene-protein-reaction associations. We implement a model transformation that enables constraint-based methods to be applied at the gene level by explicitly accounting for the individual fluxes of enzymes (and subunits) encoded by each gene. We show how this can be applied to different kinds of constraint-based analysis: flux distribution prediction, gene essentiality analysis, random flux sampling, elementary mode analysis, transcriptomics data integration, and rational strain design. In each case we demonstrate how this approach can lead to improved phenotype predictions and a deeper understanding of the genotype-to-phenotype link. In particular, we show that a large fraction of reaction-based designs obtained by current strain design methods are not actually feasible, and show how our approach allows using the same methods to obtain feasible gene-based designs. We also show, by extensive comparison with experimental 13C-flux data, how simple reformulations of different simulation methods with gene-wise objective functions result in improved prediction accuracy. The model transformation proposed in this work enables existing constraint-based methods to be used at the gene level without modification. This automatically leverages phenotype analysis from reaction to gene level, improving the biological insight that can be obtained from genome-scale models.DM was supported by the Portuguese Foundationfor Science and Technologythrough a post-doc fellowship (ref: SFRH/BPD/111519/ 2015). This study was supported by the PortugueseFoundationfor Science and Technology (FCT) under the scope of the strategic fundingof UID/BIO/04469/2013 unitand COMPETE2020 (POCI-01-0145-FEDER-006684) and BioTecNorte operation (NORTE-01-0145FEDER-000004) fundedby EuropeanRegional Development Fund under the scope of Norte2020Programa Operacional Regional do Norte. This project has received fundingfrom the European Union’s Horizon 2020 research and innovation programme under grant agreementNo 686070. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Reverse engineering of drug induced DNA damage response signalling pathway reveals dual outcomes of ATM kinase inhibition

The DNA Damage Response (DDR) pathway represents a signalling mechanism that is activated in eukaryotic cells following DNA damage and comprises of proteins involved in DNA damage detection, DNA repair, cell cycle arrest and apoptosis. This pathway consists of an intricate network of signalling interactions driving the cellular ability to recognise DNA damage and recruit specialised proteins to take decisions between DNA repair or apoptosis. ATM and ATR are central components of the DDR pathway. The activities of these kinases are vital in DNA damage induced phosphorylational induction of DDR substrates. Here, firstly we have experimentally determined DDR signalling network surrounding the ATM/ATR pathway induced following double stranded DNA damage by monitoring and quantifying time dependent inductions of their phosphorylated forms and their key substrates. We next involved an automated inference of unsupervised predictive models of time series data to generate in silico (molecular) interaction maps. We characterized the complex signalling network through system analysis and gradual utilisation of small time series measurements of key substrates through a novel network inference algorithm. Furthermore, we demonstrate an application of an assumption-free reverse engineering of the intricate signalling network of the activated ATM/ATR pathway. We next studied the consequences of such drug induced inductions as well as of time dependent ATM kinase inhibition on cell survival through further biological experiments. Intermediate and temporal modelling outcomes revealed the distinct signaling profile associated with ATM kinase activity and inhibition and explained the underlying signalling mechanism for dual ATM functionality in cytotoxic and cytoprotective pathways

Unifying metabolic networks, regulatory constraints, and resource allocation

Metabolic and gene regulatory networks are two classic models of systems biology. Biologically, gene regulatory networks are the control system of protein expression while metabolic networks, especially the genome-scale reconstructions consist of thousands of enzymatic reactions breaking down nutrients into precursors and energy to support the cellular survival. Metabolic-genetic networks, in addition, include the translational processes as an integrated model of classical metabolic networks and the gene expression machinery. Conversely, genetic regulation is also affected by the metabolic activities that provide feedbacks and precursors to the regulatory system. Thus, the two systems are highly interactive and depend on each other. Up to now, various efforts have been made to bridge the two network types. Yet, the dynamic integration of metabolic networks and genetic regulation remains a major challenge in computational systems biology. This PhD thesis is a contribution to mathematical modeling approaches for studying metabolic-regulatory systems. Inspired by regulatory flux balance analysis (rFBA), we first propose an analytic pipeline to explore the optimal solution space in rFBA. Then, our efforts focus on the dynamic combination of metabolic networks together with enzyme production costs and genetic regulation. For this purpose, we first explore the intuitive idea that incorporates Boolean regulatory rules while iterating resource balance analysis. However, with the iterative strategy, the gene expression states are only updated in discrete time steps. Furthermore, formalizing the metabolic-regulatory networks (MRNs) by hybrid automata provides a new mathematical framework that allows the quantitative integration of the metabolic-genetic network with the genetic regulation in a hybrid discrete-continuous system. For the application of this theoretical formalization, we develop a constraint-based approach regulatory dynamic enzyme-cost flux balance analysis (r-deFBA) as an optimal control strategy for the hybrid automata representing MRNs. This allows the prediction of optimal regulatory state transitions, dynamics of metabolism, and resource allocation capable of achieving a maximal biomass production over a time interval. Finally, this PhD project ends with a chapter on perspectives; we apply the theory of product automata to model the dynamics at population-level, integrating continuous metabolism and discrete regulatory states