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The data for provide evidences of the multi steady state of the human cell line HEK 293 was obtained from 2 L bioreactor continuous culture. A HEK 293 cell line transfected to produce soluble HER1 receptor was used. The bioreactor was operated at three different dilution rates in sequential manner. Daily samples of culture broth were collected, a total of 85 samples were processed. Viable cell concentration and culture viability was addressing by trypan blue exclusion method using a hemocytometer. Heterologous HER1 supernatant concentration was quantified by a specific ELISA and the metabolites by mass spectrometry coupled to a liquid chromatography. The primary data were collected in excel files, where it was calculated the kinetic and other variables by using mass balance and mathematical principles. It was compared the steady states behavior each other's to find out the existence of steady states' multiplicity, taking into account the stationary phase with respect to the cell density (which means its coefficient of variation is less than 20 %). From the metabolic measurements by using Liquid Chromatography coupled to mass spectrometry (LC-MS), it was also built the data matrix with the specific rates of the 76 metabolites obtained. The data were processed and analyzed, using multivariate data asssnalysis (MVDA) to reduce the complexity and to find the main patterns present in the data. We describe also the full data of the metabolites not only for steady states but also in the time evolution, which could help others in terms of modeling and deep understanding of HEK293 metabolism, especially under different culture conditions.

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The study of cellular metabolism is limited by the amount of experimental data available. Formulations able to extract relevant predictions from accessible measurements are needed. Maximum Entropy (ME) inference has been successfully applied to genome-scale models of cellular metabolism, and recent data-driven studies have suggested that in chemostat cultures of Escherichia coli (E. coli), the growth rate and uptake rates of limiting nutrients are the most informative observables. We propose the thesis that this can be explained by the chemostat dynamics, which typically drives nutrient-limited cultures toward observable metabolic states maximally restricted in the dimensions of those fluxes. A practical consequence is that relevant flux observables can now be replaced by culture parameters usually controlled. We test our model by using simulations, and then we apply it to E. coli experimental data where we evaluate the quality of the inference, comparing it to alternative formulations that rest on convex optimization.

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The cell culture is the central piece of a biotechnological industrial process. It includes upstream (e.g. media preparation, fixed costs, etc.) and downstream steps (e.g. product purification, waste disposal, etc.). In the continuous mode of cell culture, a constant flow of fresh media replaces culture fluid until the system reaches a steady state. This steady state is the standard operation mode which, under very general conditions, is a function of the ratio between the cell density and the dilution rate and depends on the media supplied to the culture. To optimize the production process it is widely accepted that the concentration of the metabolites in this media should be carefully tuned. A poor media may not provide enough nutrients to the culture, while a media too rich in nutrients may be a waste of resources because, either the cells do not use all of the available nutrients, or worse, they over-consume them producing toxic byproducts. In this study, we show how an in-silico study of a genome scale metabolic network coupled to the dynamics of a chemostat could guide the strategy to optimize the media to be used in a continuous process. Given a known media we model the concentrations of the cells in a chemostat as a function of the dilution rate. Then, we cast the problem of optimizing the production process within a linear programming framework in which the goal is to minimize the cost of the media keeping fixed the cell concentration for a given dilution rate in the chemostat. We evaluate our results in two metabolic models: first a simplified model of mammalian cell metabolism, and then in a realistic genome-scale metabolic network of mammalian cells, the Chinese hamster ovary cell line. We explore the latter in more detail given specific meaning to the predictions of the concentrations of several metabolites.

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The recent technological advances underlying the screening of large combinatorial libraries in high-throughput mutational scans deepen our understanding of adaptive protein evolution and boost its applications in protein design. Nevertheless, the large number of possible genotypes requires suitable computational methods for data analysis, the prediction of mutational effects, and the generation of optimized sequences. We describe a computational method that, trained on sequencing samples from multiple rounds of a screening experiment, provides a model of the genotype-fitness relationship. We tested the method on five large-scale mutational scans, yielding accurate predictions of the mutational effects on fitness. The inferred fitness landscape is robust to experimental and sampling noise and exhibits high generalization power in terms of broader sequence space exploration and higher fitness variant predictions. We investigate the role of epistasis and show that the inferred model provides structural information about the 3D contacts in the molecular fold.

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Large molecular interaction networks are nowadays assembled in biomedical researches along with important technological advances. Diverse interaction measures, for which input solely consisting of the incidence of causal-factors, with the corresponding outcome of an inquired effect, are formulated without an obvious mathematical unity. Consequently, conceptual and practical ambivalences arise. We identify here a probabilistic requirement consistent with that input, and find, by the rules of probability theory, that it leads to a model multiplicative in the complement of the effect. Important practical properties are revealed along these theoretical derivations, that has not been noticed before.

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We cast the metabolism of interacting cells within a statistical mechanics framework considering both the actual phenotypic capacities of each cell and its interaction with its neighbors. Reaction fluxes will be the components of high-dimensional spin vectors, whose values will be constrained by the stochiometry and the energy requirements of the metabolism. Within this picture, finding the phenotypic states of the population turns out to be equivalent to searching for the equilibrium states of a disordered spin model. We provide a general solution of this problem for arbitrary metabolic networks and interactions. We apply this solution to a simplified model of metabolism and to a complex metabolic network, the central core of Escherichia coli, and demonstrate that the combination of selective pressure and interactions defines a complex phenotypic space. We also present numerical results for cells fixed in a grid. These results reproduce the qualitative picture discussed for the mean-field model. Cells may specialize in producing or consuming metabolites complementing each other, and this is described by an equilibrium phase space with multiple minima, like in a spin-glass model.

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A fundamental question in biology is how cell populations evolve into different subtypes based on homogeneous processes at the single cell level. Here we show that population bimodality can emerge even when biological processes are homogenous at the cell level and the environment is kept constant. Our model is based on the stochastic partitioning of a cell component with an optimal copy number. We show that the existence of unimodal or bimodal distributions depends on the variance of partition errors and the growth rate tolerance around the optimal copy number. In particular, our theory provides a consistent explanation for the maintenance of aneuploid states in a population. The proposed model can also be relevant for other cell components such as mitochondria and plasmids, whose abundances affect the growth rate and are subject to stochastic partition at cell division.

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Continuous cultures of mammalian cells are complex systems displaying hallmark phenomena of nonlinear dynamics, such as multi-stability, hysteresis, as well as sharp transitions between different metabolic states. In this context mathematical models may suggest control strategies to steer the system towards desired states. Although even clonal populations are known to exhibit cell-to-cell variability, most of the currently studied models assume that the population is homogeneous. To overcome this limitation, we use the maximum entropy principle to model the phenotypic distribution of cells in a chemostat as a function of the dilution rate. We consider the coupling between cell metabolism and extracellular variables describing the state of the bioreactor and take into account the impact of toxic byproduct accumulation on cell viability. We present a formal solution for the stationary state of the chemostat and show how to apply it in two examples. First, a simplified model of cell metabolism where the exact solution is tractable, and then a genome-scale metabolic network of the Chinese hamster ovary (CHO) cell line. Along the way we discuss several consequences of heterogeneity, such as: qualitative changes in the dynamical landscape of the system, increasing concentrations of byproducts that vanish in the homogeneous case, and larger population sizes.

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Selection from a phage display library derived from human Interleukin-2 (IL-2) yielded mutated variants with greatly enhanced display levels of the functional cytokine on filamentous phages. Introduction of a single amino acid replacement selected that way (K35E) increased the secretion levels of IL-2-containing fusion proteins from human transfected host cells up to 20-fold. Super-secreted (K35E) IL-2/Fc is biologically active in vitro and in vivo, has anti-tumor activity and exhibits a remarkable reduction in its aggregation propensity- the major manufacturability issue limiting IL-2 usefulness up to now. Improvement of secretion was also shown for a panel of IL-2-engineered variants with altered receptor binding properties, including a selective agonist and a super agonist that kept their unique properties. Our findings will improve developability of the growing family of IL-2-derived immunotherapeutic agents and could have a broader impact on the engineering of structurally related four-alpha-helix bundle cytokines.

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Cell metabolism is characterized by three fundamental energy demands: to sustain cell maintenance, to trigger aerobic fermentation and to achieve maximum metabolic rate. The transition to aerobic fermentation and the maximum metabolic rate are currently understood based on enzymatic cost constraints. Yet, we are lacking a theory explaining the maintenance energy demand. Here we report a physical model of cell metabolism that explains the origin of these three energy scales. Our key hypothesis is that the maintenance energy demand is rooted on the energy expended by molecular motors to fluidize the cytoplasm and counteract molecular crowding. Using this model and independent parameter estimates we make predictions for the three energy scales that are in quantitative agreement with experimental values. The model also recapitulates the dependencies of cell growth with extracellular osmolarity and temperature. This theory brings together biophysics and cell biology in a tractable model that can be applied to understand key principles of cell metabolism.

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In the continuous mode of cell culture, a constant flow carrying fresh media replaces culture fluid, cells, nutrients and secreted metabolites. Here we present a model for continuous cell culture coupling intra-cellular metabolism to extracellular variables describing the state of the bioreactor, taking into account the growth capacity of the cell and the impact of toxic byproduct accumulation. We provide a method to determine the steady states of this system that is tractable for metabolic networks of arbitrary complexity. We demonstrate our approach in a toy model first, and then in a genome-scale metabolic network of the Chinese hamster ovary cell line, obtaining results that are in qualitative agreement with experimental observations. We derive a number of consequences from the model that are independent of parameter values. The ratio between cell density and dilution rate is an ideal control parameter to fix a steady state with desired metabolic properties. This conclusion is robust even in the presence of multi-stability, which is explained in our model by a negative feedback loop due to toxic byproduct accumulation. A complex landscape of steady states emerges from our simulations, including multiple metabolic switches, which also explain why cell-line and media benchmarks carried out in batch culture cannot be extrapolated to perfusion. On the other hand, we predict invariance laws between continuous cell cultures with different parameters. A practical consequence is that the chemostat is an ideal experimental model for large-scale high-density perfusion cultures, where the complex landscape of metabolic transitions is faithfully reproduced.

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Cancer cells exhibit high rates of glycolysis and glutaminolysis. Glycolysis can provide energy and glutaminolysis can provide carbon for anaplerosis and reductive carboxylation to citrate. However, all these metabolic requirements could be in principle satisfied from glucose. Here we investigate why cancer cells do not satisfy their metabolic demands using aerobic biosynthesis from glucose. Based on the typical composition of a mammalian cell we quantify the energy demand and the OxPhos burden of cell biosynthesis from glucose. Our calculation demonstrates that aerobic growth from glucose is feasible up to a minimum doubling time that is proportional to the OxPhos burden and inversely proportional to the mitochondria OxPhos capacity. To grow faster cancer cells must activate aerobic glycolysis for energy generation and uncouple NADH generation from biosynthesis. To uncouple biosynthesis from NADH generation cancer cells can synthesize lipids from carbon sources that do not produce NADH in their catabolism, including acetate and the amino acids glutamate, glutamine, phenylalanine and tyrosine. Finally, we show that cancer cell lines have an OxPhos capacity that is insufficient to support aerobic biosynthesis from glucose. We conclude that selection for high rate of biosynthesis implies a selection for aerobic glycolysis and uncoupling biosynthesis from NADH generation.

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We introduce an in silico model for the initial spread of an aberrant phenotype with Warburg-like overflow metabolism within a healthy homeostatic tissue in contact with a nutrient reservoir (the blood), aimed at characterizing the role of the microenvironment for aberrant growth. Accounting for cellular metabolic activity, competition for nutrients, spatial diffusion and their feedbacks on aberrant replication and death rates, we obtain a phase portrait where distinct asymptotic whole-tissue states are found upon varying the tissue-blood turnover rate and the level of blood-borne primary nutrient. Over a broad range of parameters, the spreading dynamics is bistable as random fluctuations can impact the final state of the tissue. Such a behaviour turns out to be linked to the re-cycling of overflow products by non-aberrant cells. Quantitative insight on the overall emerging picture is provided by a spatially homogeneous version of the model.

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We derive a new efficient algorithm for the computation of the isotopic peak center-mass distribution of a molecule. With the use of Fourier transform techniques, the algorithm accurately computes the total abundance and average mass of all the isotopic species with the same number of nucleons. We evaluate the performance of the method with 10 benchmark proteins and other molecules; results are compared with BRAIN, a recently reported polynomial method. The new algorithm is comparable to BRAIN in accuracy and superior in terms of speed and memory, particularly for large molecules. An implementation of the algorithm is available for download.

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