Chemometric Approaches for Systems Biology

The present Ph.D. thesis is devoted to study, develop and apply approaches commonly used in chemometrics to the emerging field of systems biology. Existing procedures and new methods are applied to solve research and industrial questions in different multidisciplinary teams. The methodologies developed in this document will enrich the plethora of procedures employed within omic sciences to understand biological organisms and will improve processes in biotechnological industries integrating biological knowledge at different levels and exploiting the software packages derived from the thesis. This dissertation is structured in four parts. The first block describes the framework in which the contributions presented here are based. The objectives of the two research projects related to this thesis are highlighted and the specific topics addressed in this document via conference presentations and research articles are introduced. A comprehensive description of omic sciences and their relationships within the systems biology paradigm is given in this part, jointly with a review of the most applied multivariate methods in chemometrics, on which the novel approaches proposed here are founded. The second part addresses many problems of data understanding within metabolomics, fluxomics, proteomics and genomics. Different alternatives are proposed in this block to understand flux data in steady state conditions. Some are based on applications of multivariate methods previously applied in other chemometrics areas. Others are novel approaches based on a bilinear decomposition using elemental metabolic pathways, from which a GNU licensed toolbox is made freely available for the scientific community. As well, a framework for metabolic data understanding is proposed for non-steady state data, using the same bilinear decomposition proposed for steady state data, but modelling the dynamics of the experiments using novel two and three-way data analysis procedures. Also, the relationships between different omic levels are assessed in this part integrating different sources of information of plant viruses in data fusion models. Finally, an example of interaction between organisms, oranges and fungi, is studied via multivariate image analysis techniques, with future application in food industries. The third block of this thesis is a thoroughly study of different missing data problems related to chemometrics, systems biology and industrial bioprocesses. In the theoretical chapters of this part, new algorithms to obtain multivariate exploratory and regression models in the presence of missing data are proposed, which serve also as preprocessing steps of any other methodology used by practitioners. Regarding applications, this block explores the reconstruction of networks in omic sciences when missing and faulty measurements appear in databases, and how calibration models between near infrared instruments can be transferred, avoiding costs and time-consuming full recalibrations in bioindustries and research laboratories. Finally, another software package, including a graphical user interface, is made freely available for missing data imputation purposes. The last part discusses the relevance of this dissertation for research and biotechnology, including proposals deserving future research.Esta tesis doctoral se centra en el estudio, desarrollo y aplicación de técnicas quimiométricas en el emergente campo de la biología de sistemas. Procedimientos comúnmente utilizados y métodos nuevos se aplican para resolver preguntas de investigación en distintos equipos multidisciplinares, tanto del ámbito académico como del industrial. Las metodologías desarrolladas en este documento enriquecen la plétora de técnicas utilizadas en las ciencias ómicas para entender el funcionamiento de organismos biológicos y mejoran los procesos en la industria biotecnológica, integrando conocimiento biológico a diferentes niveles y explotando los paquetes de software derivados de esta tesis. Esta disertación se estructura en cuatro partes. El primer bloque describe el marco en el cual se articulan las contribuciones aquí presentadas. En él se esbozan los objetivos de los dos proyectos de investigación relacionados con esta tesis. Asimismo, se introducen los temas específicos desarrollados en este documento mediante presentaciones en conferencias y artículos de investigación. En esta parte figura una descripción exhaustiva de las ciencias ómicas y sus interrelaciones en el paradigma de la biología de sistemas, junto con una revisión de los métodos multivariantes más aplicados en quimiometría, que suponen las pilares sobre los que se asientan los nuevos procedimientos aquí propuestos. La segunda parte se centra en resolver problemas dentro de metabolómica, fluxómica, proteómica y genómica a partir del análisis de datos. Para ello se proponen varias alternativas para comprender a grandes rasgos los datos de flujos metabólicos en estado estacionario. Algunas de ellas están basadas en la aplicación de métodos multivariantes propuestos con anterioridad, mientras que otras son técnicas nuevas basadas en descomposiciones bilineales utilizando rutas metabólicas elementales. A partir de éstas se ha desarrollado software de libre acceso para la comunidad científica. A su vez, en esta tesis se propone un marco para analizar datos metabólicos en estado no estacionario. Para ello se adapta el enfoque tradicional para sistemas en estado estacionario, modelando las dinámicas de los experimentos empleando análisis de datos de dos y tres vías. En esta parte de la tesis también se establecen relaciones entre los distintos niveles ómicos, integrando diferentes fuentes de información en modelos de fusión de datos. Finalmente, se estudia la interacción entre organismos, como naranjas y hongos, mediante el análisis multivariante de imágenes, con futuras aplicaciones a la industria alimentaria. El tercer bloque de esta tesis representa un estudio a fondo de diferentes problemas relacionados con datos faltantes en quimiometría, biología de sistemas y en la industria de bioprocesos. En los capítulos más teóricos de esta parte, se proponen nuevos algoritmos para ajustar modelos multivariantes, tanto exploratorios como de regresión, en presencia de datos faltantes. Estos algoritmos sirven además como estrategias de preprocesado de los datos antes del uso de cualquier otro método. Respecto a las aplicaciones, en este bloque se explora la reconstrucción de redes en ciencias ómicas cuando aparecen valores faltantes o atípicos en las bases de datos. Una segunda aplicación de esta parte es la transferencia de modelos de calibración entre instrumentos de infrarrojo cercano, evitando así costosas re-calibraciones en bioindustrias y laboratorios de investigación. Finalmente, se propone un paquete software que incluye una interfaz amigable, disponible de forma gratuita para imputación de datos faltantes. En la última parte, se discuten los aspectos más relevantes de esta tesis para la investigación y la biotecnología, incluyendo líneas futuras de trabajo.Aquesta tesi doctoral es centra en l'estudi, desenvolupament, i aplicació de tècniques quimiomètriques en l'emergent camp de la biologia de sistemes. Procediments comúnment utilizats i mètodes nous s'apliquen per a resoldre preguntes d'investigació en diferents equips multidisciplinars, tant en l'àmbit acadèmic com en l'industrial. Les metodologies desenvolupades en aquest document enriquixen la plétora de tècniques utilitzades en les ciències òmiques per a entendre el funcionament d'organismes biològics i milloren els processos en la indústria biotecnològica, integrant coneixement biològic a distints nivells i explotant els paquets de software derivats d'aquesta tesi. Aquesta dissertació s'estructura en quatre parts. El primer bloc descriu el marc en el qual s'articulen les contribucions ací presentades. En ell s'esbossen els objectius dels dos projectes d'investigació relacionats amb aquesta tesi. Així mateix, s'introduixen els temes específics desenvolupats en aquest document mitjançant presentacions en conferències i articles d'investigació. En aquesta part figura una descripació exhaustiva de les ciències òmiques i les seues interrelacions en el paradigma de la biologia de sistemes, junt amb una revisió dels mètodes multivariants més aplicats en quimiometria, que supossen els pilars sobre els quals s'assenten els nous procediments ací proposats. La segona part es centra en resoldre problemes dins de la metabolòmica, fluxòmica, proteòmica i genòmica a partir de l'anàlisi de dades. Per a això es proposen diverses alternatives per a compendre a grans trets les dades de fluxos metabòlics en estat estacionari. Algunes d'elles estàn basades en l'aplicació de mètodes multivariants propostos amb anterioritat, mentre que altres són tècniques noves basades en descomposicions bilineals utilizant rutes metabòliques elementals. A partir d'aquestes s'ha desenvolupat software de lliure accés per a la comunitat científica. Al seu torn, en aquesta tesi es proposa un marc per a analitzar dades metabòliques en estat no estacionari. Per a això s'adapta l'enfocament tradicional per a sistemes en estat estacionari, modelant les dinàmiques dels experiments utilizant anàlisi de dades de dues i tres vies. En aquesta part de la tesi també s'establixen relacions entre els distints nivells òmics, integrant diferents fonts d'informació en models de fusió de dades. Finalment, s'estudia la interacció entre organismes, com taronges i fongs, mitjançant l'anàlisi multivariant d'imatges, amb futures aplicacions a la indústria alimentària. El tercer bloc d'aquesta tesi representa un estudi a fons de diferents problemes relacionats amb dades faltants en quimiometria, biologia de sistemes i en la indústria de bioprocessos. En els capítols més teòrics d'aquesta part, es proposen nous algoritmes per a ajustar models multivariants, tant exploratoris com de regressió, en presencia de dades faltants. Aquests algoritmes servixen ademés com a estratègies de preprocessat de dades abans de l'ús de qualsevol altre mètode. Respecte a les aplicacions, en aquest bloc s'explora la reconstrucció de xarxes en ciències òmiques quan apareixen valors faltants o atípics en les bases de dades. Una segona aplicació d'aquesta part es la transferència de models de calibració entre instruments d'infrarroig proper, evitant així costoses re-calibracions en bioindústries i laboratoris d'investigació. Finalment, es proposa un paquet software que inclou una interfície amigable, disponible de forma gratuïta per a imputació de dades faltants. En l'última part, es discutixen els aspectes més rellevants d'aquesta tesi per a la investigació i la biotecnologia, incloent línies futures de treball.Folch Fortuny, A. (2016). Chemometric Approaches for Systems Biology [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/77148TESISPremios Extraordinarios de tesis doctorale

PLS model building with missing data: New algorithms and a comparative study

[EN] New algorithms to deal with missing values in predictive modelling are presented in this article. Specifically, 2 trimmed scores regression adaptations are proposed, one from principal component analysis model building with missing data (MD) and other from partial least squares regression model exploitation with missing values. Using these methods, practitioners can impute MD both in the explanatory/predictor and the dependent/response variables. Partial least squares is used here to build the multivariate calibration models; however, any regression method can be used after MD imputation. Four case studies, with different latent structures, are analysed here to compare the trimmed scores regression¿based methods against state-of-the-art approaches. The MATLAB code for these methods is also provided for its direct implementation at http://mseg.webs.upv.es, under a GNU license.Spanish Ministry of Science and Innovation; FEDER; European Union, Grant/Award Number: DPI2011-28112-C04-02 and DPI2014-55276-C5-1R; Spanish Ministry of Economy and Competitiveness, Grant/Award Number: ECO2013-43353-RFolch-Fortuny, A.; Arteaga, F.; Ferrer, A. (2017). PLS model building with missing data: New algorithms and a comparative study. Journal of Chemometrics. 31(7):1-12. https://doi.org/10.1002/cem.2897S112317Grung, B., & Manne, R. (1998). Missing values in principal component analysis. Chemometrics and Intelligent Laboratory Systems, 42(1-2), 125-139. doi:10.1016/s0169-7439(98)00031-8Arteaga, F., & Ferrer-Riquelme, A. J. (2009). Missing Data. Comprehensive Chemometrics, 285-314. doi:10.1016/b978-044452701-1.00125-3Folch-Fortuny, A., Arteaga, F., & Ferrer, A. (2015). PCA model building with missing data: New proposals and a comparative study. Chemometrics and Intelligent Laboratory Systems, 146, 77-88. doi:10.1016/j.chemolab.2015.05.006Arteaga, F., & Ferrer, A. (2002). Dealing with missing data in MSPC: several methods, different interpretations, some examples. Journal of Chemometrics, 16(8-10), 408-418. doi:10.1002/cem.750Arteaga, F., & Ferrer, A. (2005). Framework for regression-based missing data imputation methods in on-line MSPC. Journal of Chemometrics, 19(8), 439-447. doi:10.1002/cem.946Nelson, P. R. C., Taylor, P. A., & MacGregor, J. F. (1996). Missing data methods in PCA and PLS: Score calculations with incomplete observations. Chemometrics and Intelligent Laboratory Systems, 35(1), 45-65. doi:10.1016/s0169-7439(96)00007-xWalczak, B., & Massart, D. L. (2001). Dealing with missing data. Chemometrics and Intelligent Laboratory Systems, 58(1), 15-27. doi:10.1016/s0169-7439(01)00131-9Schafer, J. L. (1997). Analysis of Incomplete Multivariate Data. doi:10.1201/9781439821862Folch-Fortuny, A., Arteaga, F., & Ferrer, A. (2016). Missing Data Imputation Toolbox for MATLAB. Chemometrics and Intelligent Laboratory Systems, 154, 93-100. doi:10.1016/j.chemolab.2016.03.019ProSensus Multivariate release 16.02 2016SIMCA release 14 2015The Unscrambler X Release 10.4 2016PLS_Toolbox Release 8.1 2016Liu, Y., & Brown, S. D. (2013). Comparison of five iterative imputation methods for multivariate classification. Chemometrics and Intelligent Laboratory Systems, 120, 106-115. doi:10.1016/j.chemolab.2012.11.010White, I. R., Royston, P., & Wood, A. M. (2010). Multiple imputation using chained equations: Issues and guidance for practice. Statistics in Medicine, 30(4), 377-399. doi:10.1002/sim.4067Schneider, T. (2001). Analysis of Incomplete Climate Data: Estimation of Mean Values and Covariance Matrices and Imputation of Missing Values. Journal of Climate, 14(5), 853-871. doi:10.1175/1520-0442(2001)0142.0.co;2Fierro, R. D., Golub, G. H., Hansen, P. C., & O’Leary, D. P. (1997). Regularization by Truncated Total Least Squares. SIAM Journal on Scientific Computing, 18(4), 1223-1241. doi:10.1137/s1064827594263837Puwakkatiya-Kankanamage, E. H., García-Muñoz, S., & Biegler, L. T. (2014). An optimization-based undeflated PLS (OUPLS) method to handle missing data in the training set. Journal of Chemometrics, 28(7), 575-584. doi:10.1002/cem.2618Camacho, J., Picó, J., & Ferrer, A. (2008). Bilinear modelling of batch processes. Part II: a comparison of PLS soft-sensors. Journal of Chemometrics, 22(10), 533-547. doi:10.1002/cem.1179Geladi, P., & Kowalski, B. R. (1986). Partial least-squares regression: a tutorial. Analytica Chimica Acta, 185, 1-17. doi:10.1016/0003-2670(86)80028-9Kubinyi, H. (1996). Evolutionary variable selection in regression and PLS analyses. Journal of Chemometrics, 10(2), 119-133. doi:10.1002/(sici)1099-128x(199603)10:23.0.co;2-4González-Martínez, J. M., Folch-Fortuny, A., Llaneras, F., Tortajada, M., Picó, J., & Ferrer, A. (2014). Metabolic flux understanding of Pichia pastoris grown on heterogenous culture media. Chemometrics and Intelligent Laboratory Systems, 134, 89-99. doi:10.1016/j.chemolab.2014.02.003Folch-Fortuny, A., Vitale, R., de Noord, O. E., & Ferrer, A. (2017). Calibration transfer between NIR spectrometers: New proposals and a comparative study. Journal of Chemometrics, 31(3), e2874. doi:10.1002/cem.2874Arteaga, F., & Ferrer, A. (2010). How to simulate normal data sets with the desired correlation structure. Chemometrics and Intelligent Laboratory Systems, 101(1), 38-42. doi:10.1016/j.chemolab.2009.12.003Arteaga, F., & Ferrer, A. (2013). Building covariance matrices with the desired structure. Chemometrics and Intelligent Laboratory Systems, 127, 80-88. doi:10.1016/j.chemolab.2013.06.003Folch-Fortuny, A., Arteaga, F., & Ferrer, A. (2016). Assessment of maximum likelihood PCA missing data imputation. Journal of Chemometrics, 30(7), 386-393. doi:10.1002/cem.2804Saccenti, E., & Camacho, J. (2015). On the use of the observation-wisek-fold operation in PCA cross-validation. Journal of Chemometrics, 29(8), 467-478. doi:10.1002/cem.272

Assessment of maximum likelihood PCA missing data imputation

Maximum likelihood principal component analysis (MLPCA) was originally proposed to incorporate measurement error variance information in principal component analysis (PCA) models. MLPCA can be used to fit PCA models in the presence of missing data, simply by assigning very large variances to the non-measured values. An assessment of maximum likelihood missing data imputation is performed in this paper, analysing the algorithm of MLPCA and adapting several methods for PCA model building with missing data to its maximum likelihood version. In this way, known data regression (KDR), KDR with principal component regression (PCR), KDR with partial least squares regression (PLS) and trimmed scores regression (TSR) methods are implemented within the MLPCA method to work as different imputation steps. Six data sets are analysed using several percentages of missing data, comparing the performance of the original algorithm, and its adapted regression-based methods, with other state-of-the-art methods.Research in this study was partially supported by the Spanish Ministry of Science and Innovation and FEDER funds from the European Union through grant DPI2011-28112-C04-02 and DPI2014-55276-C5-1R, and the Spanish Ministry of Economy and Competitiveness through grant ECO2013-43353-R.Folch Fortuny, A.; Arteaga Moreno, FJ.; Ferrer, A. (2016). Assessment of maximum likelihood PCA missing data imputation. Journal of Chemometrics. 30(7):386-393. https://doi.org/10.1002/cem.280438639330

Missing Data Imputation Toolbox for MATLAB

[EN] Here we introduce a graphical user-friendly interface to deal with missing values called Missing Data Imputation (MDI) Toolbox. This MATLAB toolbox allows imputing missing values, following missing completely at random patterns, exploiting the relationships among variables. In this way, principal component anal- ysis (PCA) models are fitted iteratively to impute the missing data until convergence. Different methods, using PCA internally, are included in the toolbox: trimmed scores regression (TSR), known data regres- sion (KDR), KDR with principal component regression (KDR-PCR), KDR with partial least squares regression (KDR-PLS), projection to the model plane (PMP), iterative algorithm (IA), modified nonlinear iterative partial least squares regression algorithm (NIPALS) and data augmentation (DA). MDI Toolbox presents a general procedure to impute missing data, thus can be used to infer PCA models with missing data, to estimate the covariance structure of incomplete data matrices, or to impute the missing values as a preprocessing step of other methodologies.Research in this study was partially supported by the Spanish Ministry of Science and Innovation and FEDER funds from the European Union through grant DPI2011-28112-C04-02 and DPI2014-55276-C5-1 R, and the Spanish Ministry of Economy and Competitiveness through grant ECO2013-43353-R.Folch Fortuny, A.; Arteaga Moreno, FJ.; Ferrer, A. (2016). Missing Data Imputation Toolbox for MATLAB. Chemometrics and Intelligent Laboratory Systems. 154:93-100. https://doi.org/10.1016/j.chemolab.2016.03.019S9310015

Calibration transfer between NIR spectrometers: new proposals and a comparative study

[EN] Calibration transfer between near-infrared (NIR) spectrometers is a subtle issue in chemometrics and process industry. In fact, as even very similar instruments may generate strongly different spectral responses, regression models developed on a first NIR system can rarely be used with spectra collected by a second apparatus. In this work, two novel methods to perform calibration transfer between NIR spectrometers are proposed. Both of them permit to exploit the specific relationships between instruments for imputing new unmeasured spectra, which will be then resorted to for building an improved predictive model, suitable for the analysis of future incoming data. Specifically, the two approaches are based on trimmed scores regression and joint-Y partial least squares regression, respectively. The performance of these novel strategies will be assessed and compared to that of well-established techniques such as maximum likelihood principal component analysis and piecewise direct standardisation in two real case studies.This research work was partially supported by the Spanish Ministry of Economy and Competitiveness under the project DPI2014-55276-C5-1R and Shell Global Solutions International B.V. (Amsterdam, the Netherlands).Folch-Fortuny, A.; Vitale, R.; De Noord, OE.; Ferrer, A. (2017). Calibration transfer between NIR spectrometers: new proposals and a comparative study. Journal of Chemometrics. 31(3):1-11. doi:10.1002/cem.2874S11131

VIS/NIR hyperspectral imaging and N-way PLS-DA models for detection of decay lesions in citrus fruits

[EN] In this work an N-way partial least squares regression discriminant analysis (NPLS-DA) methodology is developed to detect symptoms of disease caused by Penicillium digitatum in citrus fruits (green mould) using visible/near infrared (VIS/NIR) hyperspectral images. To build the discriminant model a set of oranges and mandarins was infected by the fungus and another set was infiltrated just with water for control purposes. A double cross-validation strategy is used to validate the discriminant models. Finally, permutation testing is used to select a few bands offering the best correct classification rates in the validation set. The discriminant models developed here can be potentially implemented in a fruit packinghouse to detect infected citrus fruits at their arrival from the field with affordable multispectral (3 5 channels) cameras installed in the packinglines.This research was partially funded by the Spanish Ministry of Science and Innovation through grants DPI2011-28112-C04-02 and DPI2014-55276-C05-1R, and by INIA through grant RTA2012-00062-C04-01. In all cases with the support of European FEDER funds. Authors thank Lluis Palou from the Centro de Tecnologia Postcosecha at the IVIA for the help and supervision in the innoculation process of the fruits.Folch Fortuny, A.; Prats-Montalbán, JM.; Cubero-García, S.; Blasco Ivars, J.; Ferrer, A. (2016). VIS/NIR hyperspectral imaging and N-way PLS-DA models for detection of decay lesions in citrus fruits. Chemometrics and Intelligent Laboratory Systems. 156:241-248. https://doi.org/10.1016/j.chemolab.2016.05.005S24124815

Principal elementary mode analysis (PEMA)

Principal component analysis (PCA) has been widely applied in fluxomics to compress data into a few latent structures in order to simplify the identification of metabolic patterns. These latent structures lack a direct biological interpretation due to the intrinsic constraints associated with a PCA model. Here we introduce a new method that significantly improves the interpretability of the principal components with a direct link to metabolic pathways. This method, called principal elementary mode analysis (PEMA), establishes a bridge between a PCA-like model, aimed at explaining the maximum variance in flux data, and the set of elementary modes (EMs) of a metabolic network. It provides an easy way to identify metabolic patterns in large fluxomics datasets in terms of the simplest pathways of the organism metabolism. The results using a real metabolic model of Escherichia coli show the ability of PEMA to identify the EMs that generated the different simulated flux distributions. Actual flux data of E. coli and Pichia pastoris cultures confirm the results observed in the simulated study, providing a biologically meaningful model to explain flux data of both organisms in terms of the EM activation. The PEMA toolbox is freely available for non-commercial purposes on http://mseg.webs.upv.es.Research in this study was partially supported by the Spanish Ministry of Economy and Competitiveness and FEDER funds from the European Union through grants DPI2011-28112-C04-02 and DPI2014-55276-C5-1R. We would also acknowledge Fundacao para a Ciencia e Tecnologia for PhD fellowships with references SFRH/BD/67033/2009, SFRH/BD/70768/2010 and PTDC/BBB-BSS/2800/2012.Folch Fortuny, A.; Marques, R.; Isidro, IA.; Oliveira, R.; Ferrer, A. (2016). Principal elementary mode analysis (PEMA). Molecular BioSystems. 12(3):737-746. doi:10.1039/c5mb00828jS73774612

Enabling network inference methods to handle missing data and outliers

© 2015 Folch-Fortuny et al. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.[EN] Background: The inference of complex networks from data is a challenging problem in biological sciences, as well as in a wide range of disciplines such as chemistry, technology, economics, or sociology. The quantity and quality of the data greatly affect the results. While many methodologies have been developed for this task, they seldom take into account issues such as missing data or outlier detection and correction, which need to be properly addressed before network inference. Results: Here we present an approach to (i) handle missing data and (ii) detect and correct outliers based on multivariate projection to latent structures. The method, called trimmed scores regression (TSR), enables network inference methods to analyse incomplete datasets by imputing the missing values coherently with the latent data structure. Furthermore, it substitutes the faulty values in a dataset by proper estimations. We provide an implementation of this approach, and show how it can be integrated with any network inference method as a preliminary data curation step. This functionality is demonstrated with a state of the art network inference method based on mutual information distance and entropy reduction, MIDER. Conclusion: The methodology presented here enables network inference methods to analyse a large number of incomplete and faulty datasets that could not be reliably analysed so far. Our comparative studies show the superiority of TSR over other missing data approaches used by practitioners. Furthermore, the method allows for outlier detection and correction.Research in this study was partially supported by the European Union through project BioPreDyn (FP7-KBBE 289434), and the Spanish Ministry of Science and Innovation and FEDER funds from the European Union through grants MultiScales (DPI2011-28112-C04-02, DPI2011-28112-C04-03), and SynBioFactory (DPI2014-55276-C5-1-R, DPI2014-55276-C5-2-R). AF Villaverde also acknowledges funding from the Xunta de Galicia through an I2C postdoctoral fellowship (I2C ED481B 2014/133-0). We also gratefully acknowledge Associate Professor Francisco Arteaga for his help in the adaptation of TSR to the PCA model building context.Folch-Fortuny, A.; Fernández Villaverde, A.; Ferrer Riquelme, AJ.; Rodríguez Banga, J. (2015). Enabling network inference methods to handle missing data and outliers. BMC Bioinformatics. 16(283):1-12. https://doi.org/10.1186/s12859-015-0717-711216283Albert R, Barabási AL. Statistical mechanics of complex networks. Rev Mod Phys. 2002; 74(1):47–97.Newman MEJ. The structure and function of complex networks. SIAM Rev. 2003; 45(2):167–256.De Smet R, Marchal K. Advantages and limitations of current network inference methods. Nat Rev Microbiol. 2010; 8(10):717–29.Marbach D, Prill RJ, Schaffter T, Mattiussi C, Floreano D, Stolovitzky G. Revealing strengths and weaknesses of methods for gene network inference. Proc Natl Acad Sci. 2010; 107(14):6286–291.Prill RJ, Saez-Rodriguez J, Alexopoulos LG, Sorger PK, Stolovitzky G. 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Fusion of genomic, proteomic and phenotypic data: the case of potyviruses

Data fusion has been widely applied to analyse different sources of information, combining all of them in a single multivariate model. This methodology is mandatory when different omic data sets must be integrated to fully understand an organism using a systems biology approach. Here, a data fusion procedure is presented to combine genomic, proteomic and phenotypic data sets gathered for Tobacco etch virus (TEV). The genomic data correspond to random mutations inserted in most viral genes. The proteomic data represent both the effect of these mutations on the encoded proteins and the perturbation induced by the mutated proteins to their neighbours in the protein protein interaction net- work (PPIN). Finally, the phenotypic trait evaluated for each mutant virus is replicative fitness. To analyse these three sources of information a Partial Least Squares (PLS) regression model is fitted in order to extract the latent variables from data that explain (and relate) the significant variables to the fitness of TEV. The final output of this methodology is a set of functional modules of the PPIN relating topology and mutations with fitness. Throughout the re-analysis of these diverse TEV data, we generated valuable information on the mechanism of action of certain mutations and how they translate into organismal fitness. Results show that the effect of some mutations goes beyond the protein they directly affect and spreads on the PPIN to neighbour proteins, thus defining functional modules.This work was supported by the Spanish Ministerio de Economia y Competitividad grants BFU2012-30805 (to SFE), and DPI2011-28112-C04-02, DPI2011-28112-C04-01, DPI2014-55276-C5-1-R (to AF and JP) and by Generalitat Valenciana grant PROMETEOII/2014/021 (to SFE). The first two authors are recipients of fellowships from the Spanish Ministerio de Economia y Competitividad: BES-2012-053772 (to GB) and BES-2012-057812 (to AF-F).Folch-Fortuny, A.; Bosque-Chacon, G.; Picó, J.; Ferrer, A.; Elena, S. (2016). Fusion of genomic, proteomic and phenotypic data: the case of potyviruses. Molecular BioSystems. 12(1):253-261. https://doi.org/10.1039/c5mb00507hS25326112

Dynamic elementary mode modelling of non-steady state flux data

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