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Under ideal conditions, Escherichia coli cells divide after adding a fixed cell size, a strategy known as the adder. This concept applies to various microbes and is often explained as the division that occurs after a certain number of stages, associated with the accumulation of precursor proteins at a rate proportional to cell size. However, under poor media conditions, E. coli cells exhibit a different size regulation. They are smaller and follow a sizer-like division strategy where the added size is inversely proportional to the size at birth. We explore three potential causes for this deviation: degradation of the precursor protein and two models where the propensity for accumulation depends on the cell size: a nonlinear accumulation rate, and accumulation starting at a threshold size termed the commitment size. These models fit the mean trends but predict different distributions given the birth size. To quantify the precision of the models to explain the data, we used the Akaike information criterion and compared them to open datasets of slow-growing E. coli cells in different media. We found that none of the models alone can consistently explain the data. However, the degradation model better explains the division strategy when cells are larger, whereas size-related models (power-law and commitment size) account for smaller cells. Our methodology proposes a data-based method in which different mechanisms can be tested systematically.

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BACKGROUND: How small, fast-growing bacteria ensure tight cell-size distributions remains elusive. High-throughput measurement techniques have propelled efforts to build modeling tools that help to shed light on the relationships between cell size, growth and cycle progression. Most proposed models describe cell division as a discrete map between size at birth and size at division with stochastic fluctuations assumed. However, such models underestimate the role of cell size transient dynamics by excluding them. RESULTS: We propose an efficient approach for estimation of cell size transient dynamics. Our technique approximates the transient size distribution and statistical moment dynamics of exponential growing cells following an adder strategy with arbitrary precision. CONCLUSIONS: We approximate, up to arbitrary precision, the distribution of division times and size across time for the adder strategy in rod-shaped bacteria cells. Our approach is able to compute statistical moments like mean size and its variance from such distributions efficiently, showing close match with numerical simulations. Additionally, we observed that these distributions have periodic properties. Our approach further might shed light on the mechanisms behind gene product homeostasis.

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Una de las técnicas más utilizadas para la predicción de producción de bioproductos y distribución intracelular de flujos de microorganismos es el Análisis de Balance de Flujos - FBA por sus siglas en inglés. El FBA requiere de una función objetivo que represente el objetivo biológico del microorganismo estudiado. En este trabajo se propone un nuevo tipo de funciones objetivo basada en la combinación de objetivos de compartimentos físicos presentes en el microorganismo estudiado. Este tipo de funciones objetivo son examinadas junto con un modelo estequiométrico extraído de la reconstrucción iMM904 del microorganismo S. cerevisiae. Su desempeño se compara con la función objetivo más usada en la literatura, la maximización de biomasa, en condiciones experimentales anaeróbicas en cultivos continuos y aeróbicas en cultivos tipo lote. La función objetivo propuesta en este trabajo mejora las predicciones de crecimiento en un 10% y las predicciones de producción de etanol en un 75% respecto a las obtenidas por la función objetivo de maximización de biomasa, en condiciones anaeróbicas. En condiciones aeróbicas tipo lote la función objetivo propuesta mejora en un 98% las predicciones de crecimiento y en un 70% las predicciones de etanol con respecto a la función objetivo de biomasa.

Flux Balance Analysis - FBA - is one of the most used techniques in prediction of microorganism bioproducts. It requires an objective function that represents biological objective of the studied microorganism. This paper presents a new kind of objective functions based on individual physical compartment objetives in the studied microorganism. These kind of functions was tested with a stoichiometric model extracted from iMM904 reconstruction of S. cerevisiae and its performance is compared with the most used objective function in literature, growth maximization, in anaerobic and aerobic batch conditions. The presented objective function outperform growth predictions in 10% and ethanol predictions in 75% compared with obtained by maximization of growth objective function, in anaerobic conditions. In aerobic batch conditions the presented objective function outperforms in 98% growth preditions and 70% ethanol predictions compared with growth maximization.

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BACKGROUND: The main objective of flux balance analysis (FBA) is to obtain quantitative predictions of metabolic fluxes of an organism, and it is necessary to use an appropriate objective function to guarantee a good estimation of those fluxes. METHODOLOGY: In this study, the predictive performance of FBA was evaluated, using objective functions arising from the linear combination of different cellular objectives. This approach is most suitable for eukaryotic cells, owing to their multiplicity of cellular compartments. For this reason, Saccharomyces cerevisiae was used as model organism, and its metabolic network was represented using the genome-scale metabolic model iMM904. As the objective was to evaluate the predictive performance from the FBA using the kind of objective function previously described, substrate uptake and oxygen consumption were the only input data used for the FBA. Experimental information about microbial growth and exchange of metabolites with the environment was used to assess the quality of the predictions. CONCLUSIONS: The quality of the predictions obtained with the FBA depends greatly on the knowledge of the oxygen uptake rate. For the most of studied classifications, the best predictions were obtained with "maximization of growth", and with some combinations that include this objective. However, in the case of exponential growth with unknown oxygen exchange flux, the objective function "maximization of growth, plus minimization of NADH production in cytosol, plus minimization of NAD(P)H consumption in mitochondrion" gave much more accurate estimations of fluxes than the obtained with any other objective function explored in this study.

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El microorganismo Saccharomyces cerevisiae cuenta con gran número de modelos biológicos conocidos como reconstrucciones, las cuales pueden ser a escala genómica. De estas reconstrucciones a escala genómica provienen los modelos matemáticos, también llamados modelos estequiométricos. Una de las técnicas más usadas para estudiar estos modelos es el Análisis de Balance de Flujos (FBA). El proposito del FBA es predecir el crecimiento del microorganismo bajo estudio, y la producción y consumo de componentes como el etanol, CO2 glicerol, sucinato, acetato y piruvato. Para determinar si las predicciones obtenidas mediante FBA son únicas se utiliza la técnica de Análisis de Variabilidad Flujos (FVA). El presente trabajo muestra los resultados de aplicar el FBA a la reconstrucción reciente del microorganismo S. cerevisiae, la denominada iMM904 y los compara con un conjunto de datos experimentales presente en la literatura. Este trabajo también estudia la existencia de múltiples predicciones FBA utilizando la técnica FVA. Los resultados ilustran que es posible predecir el crecimiento del microorganimo S. cerevisiae, con errores entre el 11% y 28%; la producción de CO2, con errores entre el 0.3% y 4.5% y la producción de etanol, con errores entre el 11% y 13%.

Several biological models, named reconstructions, are used for the study of the S. cerevisiae microorganism. The reconstructions can be genomic scaled. Mathematical models are generated from the reconstructions and they are called stoichiometric models. The flux balance analysis (FBA) is one of the tools used for the analysis of these models. The FBA attempts to predict the evolution of the microorganism and the consumption and production of components like glucose, ethanol, glycerol, succinate, acetate and pyruvate. A Flux variability analysis (FVA) is used to determine the uniqueness of the FBA predictions. This paper shows the results of applying FBA to the iMM904 reconstruction of S. cerevisiae and compares them with experimental data from literature. The results in this paper show that it is possible to predict the evolution with errors between 11% and 28% ; the production of CO2 with errors between 0.3% and 4.5%; and the production of ethanol with errors between 11% and 13%, using FBA for the iMM904 model.

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