Books by Rafael Muñoz-Tamayo
Papers by Rafael Muñoz-Tamayo
International Dairy Journal, 2011
Lactic acid bacteria possess extracellular proteases that hydrolyze milk proteins. This work aime... more Lactic acid bacteria possess extracellular proteases that hydrolyze milk proteins. This work aimed to describe mathematically the hydrolysis of intact b-casein by the P I -type protease of Lactococcus lactis, using a mutant strain that lacks the oligopeptide transport system. Experiments were performed under a broad range of initial protein concentrations (17e196 mM), at constant enzyme concentration or at constant initial enzyme/substrate ratio. Hydrolysis of the intact b-casein was monitored and quantified. Four kinetic functions were evaluated to describe the hydrolysis: First-order, nth-order, MichaeliseMenten, and competitive inhibition kinetics. The hydrolysis rate was found to depend on the initial protein concentration, due to the micellisation behaviour of b-casein. This effect was accounted for by modifying the kinetic functions. The modified competitive inhibition model provided the lowest mean square error. This model has only three parameters and described the hydrolysis of intact b-casein effectively for a broad range of initial conditions.
Process Biochemistry, 2012
Hydrolysis of milk proteins by lactic acid bacteria leads to the formation of a large number of p... more Hydrolysis of milk proteins by lactic acid bacteria leads to the formation of a large number of peptides. In this work, the hydrolysis of -casein by the protease PrtP I of Lactococcus lactis was studied. Experiments were carried out at different initial enzyme/substrate ratios. Identification and quantification of peptides were performed by MS and RP-UHPLC analyses. Nine low molecular weight (LMW) peptides were quantified absolutely. Additionally, semi-quantification of six high molecular weight peptides (HMW) was provided. To describe the dynamics of peptides concentrations, an aggregated model was developed. This model links peptide formation to the breakdown of intact protein by introducing the concept of virtual intermediate peptides (VIP). The model represented the experimental data with an average error of 14% (comparable with the experimental error). By using the model, three dynamic pools of peptides were identified. The model suggests that LMW peptides have similar dynamic characteristics as their counterpart HMW peptides in the -casein sequence. This study indicates that the presence and structure of micelles affect the hydrolysis dynamics and that, for some peptides, the enzyme/substrate ratio appears to affect the hydrolysis stoichiometry. The model developed is parsimonious and has a basic mechanistic component. It allows for a rational study of protein hydrolysis.
Current opinion in biotechnology, Jan 26, 2015
The conversion of microalgae lipids and cyanobacteria carbohydrates into biofuels appears to be a... more The conversion of microalgae lipids and cyanobacteria carbohydrates into biofuels appears to be a promising source of renewable energy. This requires a thorough understanding of their carbon metabolism, supported by mathematical models, in order to optimize biofuel production. However, unlike heterotrophic microorganisms that utilize the same substrate as sources of energy and carbon, photoautotrophic microorganisms require light for energy and CO2 as carbon source. Furthermore, they are submitted to permanent fluctuating light environments due to outdoor cultivation or mixing inducing a flashing effect. Although, modeling these nonstandard organisms is a major challenge for which classical tools are often inadequate, this step remains a prerequisite towards efficient optimization of outdoor biofuel production at an industrial scale.
En este artículo se presenta el diseño de un controlador predictivo lineal basado en modelo para ... more En este artículo se presenta el diseño de un controlador predictivo lineal basado en modelo para regular la remoción de materia orgánica en un reactor anaerobio de manto de lodos de flujo ascendente (UASB) a escala piloto, en el que se lleva a cabo la degradación de una corriente de lixiviado diluido proveniente del Relleno Sanitario La Esmeralda de la ciudad de Manizales (Colombia). El trabajo se desarrolla a través de simulaciones numéricas, con el ánimo de establecer la viabilidad de aplicar este tipo de control para el sistema de estudio, partiendo del modelo fenomenológico del proceso.
En este artículo se presentan resultados a nivel teórico, obtenidos de modelar y controlar un rea... more En este artículo se presentan resultados a nivel teórico, obtenidos de modelar y controlar un reactor UASB para el tratamiento de lixiviados. Inicialmente se desarrolla el modelo matemático para representar la dinámica del reactor en relación a las ecuaciones de consumo de sustrato y crecimiento biológico. Debido a que la configuración del UASB, en relación a la biomasa, no permite caracterizarlo como un reactor continuo de mezcla completa CSTR ni como reactor de flujo pistón (PFR), se hace una modificación sobre las ecuaciones dinámicas del CSTR. El modelo obtenido se basa en la cinética de Monod y fue determinado a partir de los datos operacionales de un reactor piloto UASB de 1.3681 m 3 , que alcanzó la estabilidad para un tiempo de residencia hidráulico de 0.4073 d y una carga orgánica de 27.56 kg/m 3 d. Posteriormente, se muestran los resultados de controlar el sistema, a nivel de simulación, en un prototipo a escala de laboratorio (11.7810 l). El controlador diseñado corresponde a un control de temperatura proporcional para regular la remoción de materia orgánica a través de la variación de temperatura, la cual permite ajustar la velocidad de reacción sin alterar el tiempo de residencia hidráulico. La temperatura de reacción es controlada por efecto de un baño termostático, al cual se le proporciona energía por medio de una resistencia eléctrica de 70W. El sistema así diseñado se proyecta como una alternativa adecuada para mejorar el rendimiento de sistemas de alta carga.
En el presente artículo se analizan algunos de los modelos matemáticos desarrollados en torno a l... more En el presente artículo se analizan algunos de los modelos matemáticos desarrollados en torno a los sistemas de degradación anaerobia para el tratamiento de aguas residuales. Se muestran diversas formas de abordar el problema de modelado, como lo son el estudio fenomenológico del proceso (modelo de caja blanca) y el desarrollo de modelos híbridos (caja gris). También se desarrolla un método para la observación de estados por medio de sensórica virtual, con el objeto de establecer una alternativa para el seguimiento de la operación del sistema, todo esto apuntando al establecimiento de herramientas que brinden información sobre condiciones de operación adecuadas y que permitan realizar análisis e implementación de estrategias de control para tal fin.
Journal of Theoretical Biology, 2010
Mathematical modelling of carbohydrate degradation by human colonic microbiota, Journal of Theore... more Mathematical modelling of carbohydrate degradation by human colonic microbiota, Journal of Theoretical Biology,
FEMS Microbiology Ecology, 2011
Butyrate is the preferred energy source for colonocytes and has an important role in gut health; ... more Butyrate is the preferred energy source for colonocytes and has an important role in gut health; in contrast, accumulation of high concentrations of lactate is detrimental to gut health. The major butyrate-producing bacterial species in the human colon belong to the Firmicutes. Eubacterium hallii and a new species, Anaerostipes coli SS2/1, members of clostridial cluster XIVa, are able to utilize lactate and acetate via the butyryl CoA : acetate CoA transferase route, the main metabolic pathway for butyrate synthesis in the human colon. Here we provide a mathematical model to analyse the production of butyrate by lactate-utilizing bacteria from the human colon. The model is an aggregated representation of the fermentation pathway. The parameters of the model were estimated using total least squares and maximum likelihood, based on in vitro experimental data with E. hallii L2-7 and A. coli SS2/1. The findings of the mathematical model adequately match those from the bacterial batch culture experiments. Such an in silico approach should provide insight into carbohydrate fermentation and short-chain fatty acid cross-feeding by dominant species of the human colonic microbiota.
This paper presents a description of the model structure for the anaerobic digestion of carbohydr... more This paper presents a description of the model structure for the anaerobic digestion of carbohydrates in the human colon. Since anaerobic digestion occurs similarly in both digesters and animal gastrointestinal tracts, a parallel between these systems is presented. Hydraulic behaviour, reaction mechanisms and transport phenomena of the process are identified as key preliminary step for the construction of a mathematical model. On this basis, the obstacles to validate the model are presented and a preliminary approach is proposed to evaluate the adequacy of the structure obtained, in terms of the construction of a minimal microbiota model. The mathematical model will be further validated on animal model, consisting of axenic rodents inoculated with a model microbial consortium from human large bowel. This approach would be very useful for a better understanding of the human digestive tract, as a complex system, and the role of the microbiota on human health.
2008 16th Mediterranean Conference on Control and Automation, 2008
A nonlinear ODE model for in vitro homoacetogenesis by human-colon bacteria is proposed and analy... more A nonlinear ODE model for in vitro homoacetogenesis by human-colon bacteria is proposed and analysed. This model takes into account the biological and physical features of the experiment under consideration and the measurement process. An identifiability analysis is carried out, and the parameters of the model are identified using four different statistical description of the errors on the measurements. The estimated values will be used as prior estimates in a more ambitious modelling project of the carbohydrate trophic chain in the human colon.
15th IFAC Symposium on System Identification, 2009, 2009
IDEAS (IDEntification and Analysis of Sensitivity) is a Matlab toolbox that automatically estimat... more IDEAS (IDEntification and Analysis of Sensitivity) is a Matlab toolbox that automatically estimates parameters of ODE models and assesses their uncertainty, via a symbolic computation of the sensitivity functions. The use of the toolbox is illustrated on a reallife biological model, in the field of microbiology. IDEAS helped improving the model structure, by revealing a lack of practical identifiability that may have not been noticed otherwise.
Environmental Microbiology, 2009
The paradox of a host specificity of the human faecal microbiota otherwise acknowledged as charac... more The paradox of a host specificity of the human faecal microbiota otherwise acknowledged as characterized by global functionalities conserved between humans led us to explore the existence of a phylogenetic core. We investigated the presence of a set of bacterial molecular species that would be altogether dominant and prevalent within the faecal microbiota of healthy humans. A total of 10 456 non-chimeric bacterial 16S rRNA sequences were obtained after cloning of PCRamplified rDNA from 17 human faecal DNA samples. Using alignment or tetranucleotide frequency-based methods, 3180 operational taxonomic units (OTUs) were detected. The 16S rRNA sequences mainly belonged to the phyla Firmicutes (79.4%), Bacteroidetes (16.9%), Actinobacteria (2.5%), Proteobacteria (1%) and Verrumicrobia (0.1%). Interestingly, while most of OTUs appeared individual-specific, 2.1% were present in more than 50% of the samples and accounted for 35.8% of the total sequences. These 66 dominant and prevalent OTUs included members of the genera Faecalibacterium, Ruminococcus, Eubacterium, Dorea, Bacteroides, Alistipes and Bifidobacterium. Furthermore, 24 OTUs had cultured type strains representatives which should be subjected to genome sequence with a high degree of priority. Strikingly, 52 of these 66 OTUs were detected in at least three out of four recently published human faecal microbiota data sets, obtained with very different experimental procedures. A statistical model confirmed these OTUs prevalence. Despite the species richness and a high individual specificity, a limited number of OTUs is shared among individuals and might represent the phylogenetic core of the human intestinal microbiota. Its role in human health deserves further study.
Journal of Process Control, 2004
Mathematical models are expected to play a pivotal role for driving microalgal production towards... more Mathematical models are expected to play a pivotal role for driving microalgal production towards aprofitable process of renewable energy generation. To render models of microalgae growth useful toolsfor prediction and process optimization, reliable parameters need to be provided. This reliability impliesa careful design of experiments that can be exploited for parameter estimation. In this paper, we provideguidelines for the design of experiments with high informative content based on optimal experimenttechniques to attain an accurate parameter estimation. We study a real experimental device devotedto evaluate the effect of temperature and light on microalgae growth. On the basis of a mathematicalmodel of the experimental system, the optimal experiment design problem was formulated and solvedwith both static (constant light and temperature) and dynamic (time varying light and temperature)approaches. Simulation results indicated that the optimal experiment design allows for a more accurateparameter estimation than that provided by the existing experimental protocol. For its efficacy in termsof the maximum likelihood properties and its practical aspects of implementation, the dynamic approachis recommended over the static approach.
Biotechnology progress, Mar 2013
The industrial exploitation of microalgae is characterized by the production of high-value compou... more The industrial exploitation of microalgae is characterized by the production of high-value compounds. Optimization of the performance of microalgae culture systems is essential to
render the process economically viable. For raceway systems, the optimization based on optimal control theory is rather challenging, because the process is by essence periodically
forced and, as a consequence, optimization must be carried out in a periodic framework. In this article, we propose a simple operational criterion for raceway systems that when integrated
in a strategy of closed-loop control allows attaining biomass productivities very near to the theoretical maximal productivities. The strategy developed was tested numerically using a mathematical model of microalgae growth in raceways. The model takes into account the temporal variation of the environmental variables temperature and light intensity and their influence on microalgae growth.
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Books by Rafael Muñoz-Tamayo
Papers by Rafael Muñoz-Tamayo
render the process economically viable. For raceway systems, the optimization based on optimal control theory is rather challenging, because the process is by essence periodically
forced and, as a consequence, optimization must be carried out in a periodic framework. In this article, we propose a simple operational criterion for raceway systems that when integrated
in a strategy of closed-loop control allows attaining biomass productivities very near to the theoretical maximal productivities. The strategy developed was tested numerically using a mathematical model of microalgae growth in raceways. The model takes into account the temporal variation of the environmental variables temperature and light intensity and their influence on microalgae growth.
render the process economically viable. For raceway systems, the optimization based on optimal control theory is rather challenging, because the process is by essence periodically
forced and, as a consequence, optimization must be carried out in a periodic framework. In this article, we propose a simple operational criterion for raceway systems that when integrated
in a strategy of closed-loop control allows attaining biomass productivities very near to the theoretical maximal productivities. The strategy developed was tested numerically using a mathematical model of microalgae growth in raceways. The model takes into account the temporal variation of the environmental variables temperature and light intensity and their influence on microalgae growth.