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.

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.

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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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.

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.

In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem ill-defined: the model is consistent with the data for many values of its parameters. The objective is to find the probability distribution of parameter values consistent with the data, a problem that can be cast as the exploration of a high dimensional convex polytope.In this work we introduce a novel algorithm to solve this problem efficiently. It provides results that are statistically indistinguishable from currently used numerical techniques while its running time scales linearly with the system size. We show that the algorithm performs robustly in many abstract and practical applications. As working examples we simulate the effects of restricting reaction fluxes on the space of feasible phenotypes of a genome scale E. Coli metabolic network and infer the traffic flow between origin and destination nodes in a real communication network.

Formate is a precursor for the de novo synthesis of purine and deoxythymidine nucleotides. Formate also interacts with energy metabolism by promoting the synthesis of adenine nucleotides. Here we use theoretical modelling together with metabolomics analysis to investigate the link between formate, nucleotide and energy metabolism. We uncover that endogenous or exogenous formate induces a metabolic switch from low to high adenine nucleotide levels, increasing the rate of glycolysis and repressing the AMPK activity. Formate also induces an increase in the pyrimidine precursor orotate and the urea cycle intermediate argininosuccinate, in agreement with the ATPdependent activities of carbamoyl-phosphate and argininosuccinate synthetase. In vivo data for mouse and human cancers confirms the association between increased formate production, nucleotide and energy metabolism. Finally, the in vitro observations are recapitulated in mice following and intraperitoneal injection of formate. We conclude that formate is a potent regulator of purine, pyrimidine and energy metabolism.