Existence of multiple solutions for a quasilinear elliptic problem

In this paper we prove the existence of multiple solutions for a quasilinear elliptic boundary value problem, when the p-derivative at zero and the p-derivative at infinity of the nonlinearity are greater than the first eigenvalue of the p-Laplace operator. Our proof uses bifurcation from infinity and bifurcation from zero to prove the existence of unbounded branches of positive solutions (resp. of negative solutions). We show the existence of multiple solutions and we provide qualitative properties of these solutions

Limits of aerobic metabolism in cancer cells

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

A physical model of cell metabolism

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

Multiple Solutions for a Semilinear Dirichlet Problem

The authors prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. Extensive use is made of Lyapunov–Schmidt reduction arguments, the mountain pass lemma, and characterizations of the local degree of critical points

Characterizing steady states of genome-scale metabolic networks in continuous cell cultures

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. More importantly, we derive a number of consequences from the model that are independent of parameter values. First, that the ratio between cell density and dilution rate is an ideal control parameter to fix a steady state with desired metabolic properties invariant across perfusion systems. This conclusion is robust even in the presence of multi-stability, which is explained in our model by the negative feedback loop on cell growth due to toxic byproduct accumulation. Moreover, a complex landscape of steady states in continuous cell culture 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. Thus, in order to actually reflect the expected behavior in perfusion, performance benchmarks of cell-lines and culture media should be carried out in a chemostat

Existence and Qualitative Properties of Solutions for Nonlinear Dirichlet Problems

Sign-changing solutions to semilinear elliptic problems in connection with their Morse indices. To this end, we first establish a priori bounds for one-sign solutions. Secondly, using abstract saddle point principles we find large augmented Morse index solutions. In this part, extensive use is made of critical groups, Morse index arguments, Lyapunov-Schmidt reduction, and Leray-Schauder degree. Finally, we provide conditions under which these solutions necessarily change sign and we comment about further qualitative properties