Josephus Hulshof

Lost in Transition: Start-Up of Glycolysis Yields Subpopulations of Nongrowing Cells

Introduction Cells use multilayered regulatory systems to respond adequately to changing environments or perturbations. Failure in regulation underlies cellular malfunctioning, loss of fitness, or disease. How molecular components dynamically interact to give rise to robust and adaptive responses is not well understood. Here, we studied how the model eukaryote Saccharomyces cerevisiae can cope with transition to high glucose levels, a failure of which results in metabolic malfunctioning and growth arrest. Initiation of glycolysis can have two outcomes. Upon glucose availability, glycolysis can end up in either a functional steady state or an unviable imbalanced state with imbalanced fluxes between ATP-consuming (Vupper) and ATP-producing steps (Vlower). In wild-type yeast, the transient activation of trehalose cycling pushes glycolysis toward the viable steady state. Failure to do so results in metabolic malfunctioning, as observed in mutants in trehalose biosynthesis (tps1Δ). Methods We combined experimental and modeling approaches to unravel the mechanisms used by yeast to cope with sudden glucose availability. We studied growth characteristics and metabolic state at population and single-cell levels (through flow cytometry and colony plating) of the wild type and of mutants unable to transit properly to excess glucose; such mutants are defective in trehalose synthesis, a disaccharide associated with stress resistance. Dynamic 13C tracer enrichment was used to estimate dynamic intracellular fluxes immediately after glucose addition. Mathematical modeling was used to interpret and generalize results and to suggest subsequent experiments. Results The failure to cope with glucose is caused by imbalanced reactions in glycolysis, the essential pathway in energy metabolism in most organisms. In the failure mode, the first steps of glycolysis carry more flux than the downstream steps, resulting in accumulating intermediates at constant low levels of adenosine triphosphate (ATP) and inorganic phosphate. We found that cells with such an unbalanced glycolysis coexist with vital cells with normal glycolytic function. Spontaneous, nongenetic metabolic variability among individual cells determines which state is reached and consequently which cells survive. In mutants of trehalose metabolism, only 0.01% of the cells started to grow on glucose; in the wild type, the success rate was still only 93% (i.e., 7% of wild-type yeast did not properly start up glycolysis). Mathematical models predicted that the dynamics of inorganic phosphate is a key determinant in successful transition to glucose, and that phosphate release through ATP hydrolysis reduces the probability of reaching an imbalanced state. 13C-labeling experiments confirmed the hypothesis that trehalose metabolism constitutes a futile cycle that would provide proper phosphate balance: Upon a glucose pulse, almost 30% of the glucose is transiently shuttled into trehalose metabolism. Discussion Our work reveals how cell fate can be determined by glycolytic dynamics combined with cell heterogeneity purely at the metabolic level. Specific regulatory mechanisms are required to initiate the glycolytic pathway; in yeast, trehalose cycling pushes glycolysis transiently into the right direction, after which cycling stops. The coexistence of two modes of glycolysis—an imbalanced state and the normal functional state—arises from the fundamental design of glycolysis. This makes the imbalanced state a generic risk for humans as well, extending our fundamental knowledge of this central pathway that is dysfunctional in diseases such as diabetes and cancer. Metabolic Heterogeneity We commonly think of genetic or epigenetic sources of variation in cells and individuals. However, biochemical regulatory pathways can potentially also exist in multiple stable states and confer variable phenotypes on cells in a population. Van Heerden et al. (10.1126/science.1245114, published online 16 January) demonstrate such a phenomenon in yeast cells. Two distinct types of cell were observed that differed in the state of glycolysis, the central pathway in energy metabolism for these cells. This allowed some members of a population of cells to survive changes in glucose concentrations, whereas most cells did not. One source of nongenetic variation in yeast can be traced to distinct steady-state levels of glycolysis. Cells need to adapt to dynamic environments. Yeast that fail to cope with dynamic changes in the abundance of glucose can undergo growth arrest. We show that this failure is caused by imbalanced reactions in glycolysis, the essential pathway in energy metabolism in most organisms. The imbalance arises largely from the fundamental design of glycolysis, making this state of glycolysis a generic risk. Cells with unbalanced glycolysis coexisted with vital cells. Spontaneous, nongenetic metabolic variability among individual cells determines which state is reached and, consequently, which cells survive. Transient ATP (adenosine 5′-triphosphate) hydrolysis through futile cycling reduces the probability of reaching the imbalanced state. Our results reveal dynamic behavior of glycolysis and indicate that cell fate can be determined by heterogeneity purely at the metabolic level.

Strongly indefinite systems with critical Sobolev exponents

We consider an elliptic system of Hamiltonian type on a bounded domain. In the superlinear case with critical growth rates we obtain existence and positivity results for solutions under suitable conditions on the linear terms. Our proof is based on an adaptation of the dual variational method as applied before to the scalar case. INTRODUCTION Existence and non-existence of solutions of semilinear elliptic srstems has been a subject of active research recently; see for example [FF], [L3], [PS]. Such systems are called variational if solutions can be viewed as critical points of an associated functional defined on a suitable function space. Restricting our attention to systems with two unknowns, we distinguish two classes of variational elliptic systems: (a) potential systems; (b) Hamiltonian systems. Potential systems are of the form (A) -Llu = ,,> (u, v), ztL2v = ,,> (u, v), where L1 and L2 are second order selfadjoint elliptic operators. Formally these are the Euler-Lagrange equations of the functional f (u, v) = (L1u, u) i (L2v, v)-tH(u, v) . Here (, ) is the L2 inner product for functions defined on the underlying domain, and tt(u, v) = S H(u(x), v(x))dx. The functional f is often called the Lagrangian. Its critical points correspond to weak soltbtions of (A). The appropr:;ate choice of the function spaces for u and v follows by requiring that the quadratic part of f be well defined. This naturally leads to Sobolev spaces with square irltegrable first derivatives. Since also A(, ) must be well defined, by virtue of the embedding theorems, some growth restrictions on this latter function are required. An extra difficulty appears if we consider system (A) with a plus sign in the second equation, for then the corresponding functiorl f has a strongly indefinite quadratic part. For systems of superlinear type and with sllbcritical growth the Mountain Pass Theorem [AR] or, in the strongly indefinite case, the Benci-Rabinowitz Theorem Received by the editors June 5, 1996. 1991 Mathematics Subject Classification. Primary 35J50, 35J55, 35J65.

Asymptotic behaviour of ground states

We derive the asymptotic behaviour of the ground states of a system of two coupled semilinear Poisson equations with a strongly indefinite variational structure in the critical Sobolev growth case.

Formal asymptotics of bubbling in the harmonic map heat flow

The harmonic map heat flow is a model for nematic liquid crystals and also has origins in geometry. We present an analysis of the asymptotic behavior of singularities arising in this flow for a special class of solutions which generalizes a known (radially symmetric) reduction. Specifically, the rate at which blowup occurs is investigated in settings with certain symmetries, using the method of matched asymptotic expansions. We identify a range of blowup scenarios in both finite and infinite time, including degenerate cases.

A note on the quenching rate

We examine the quenching rate near a quenching point of a solution of a semilinear heat equation with singular powerlike absorption. A selfcontained result on similarity profiles allows us to improve a previous quenching theorem by Guo.

Amplitude saturation of MEMS resonators explained by autoparametric resonance

This paper describes a phenomenon that limits the power handling of MEMS resonators. It is observed that above a certain driving level, the resonance amplitude becomes independent of the driving level. In contrast to previous studies of power handling of MEMS resonators, it is found that this amplitude saturation cannot be explained by nonlinear terms in the spring constant or electrostatic force. Instead we show that the amplitude in our experiments is limited by nonlinear terms in the equation of motion which couple the in-plane length-extensional resonance mode to one or more out-of-plane (OOP) bending modes. We present experimental evidence for the autoparametric excitation of these OOP modes using a vibrometer. The measurements are compared to a model that can be used to predict a power-handling limit for MEMS resonators. (Some figures in this article are in colour only in the electronic version)

Metabolic states with maximal specific rate carry flux through an elementary flux mode

Specific product formation rates and cellular growth rates are important maximization targets in biotechnology and microbial evolution. Maximization of a specific rate (i.e. a rate expressed per unit biomass amount) requires the expression of particular metabolic pathways at optimal enzyme concentrations. In contrast to the prediction of maximal product yields, any prediction of optimal specific rates at the genome scale is currently computationally intractable, even if the kinetic properties of all enzymes are available. In the present study, we characterize maximal‐specific‐rate states of metabolic networks of arbitrary size and complexity, including genome‐scale kinetic models. We report that optimal states are elementary flux modes, which are minimal metabolic networks operating at a thermodynamically‐feasible steady state with one independent flux. Remarkably, elementary flux modes rely only on reaction stoichiometry, yet they function as the optimal states of mathematical models incorporating enzyme kinetics. Our results pave the way for the optimization of genome‐scale kinetic models because they offer huge simplifications to overcome the concomitant computational problems.

Similarity solutions of the porous medium equation with sign changes

with m > 1. Here u is a function of x and t. For nonnegative u Eq. (1.1) arises in the theory of gas flow through a one-dimensional porous medium, and an extensive theory has been developed over the last decades (see, e.g., [l, 3, 151). More recently [4, 5, 12, 131 applied and pure mathematicians have also become interested in solutions of (1.1) with sign changes. The most striking property of (1.1) is that solutions may have compact support whose (free) boundaries (or interfaces) move outwards with a finite, possibly zero speed proportional to the one-sided x-derivative of 1~1”~ ’ at the free boundary, taken from the interior of the support. This is usually called the interface condition. The expression between brackets in (l.l), i.e., 1~1~~’ uX= ((l/m) Iu)“--’ u),, which we shall think of as theflux because of the divergence form of (l.l), is continuous with respect to x in zeros of U. If it is nonzero we shall call this the sign change condition. We observe that for u bounded away from zero and infinity Eq. (1.1) is uniformly parabolic and local smoothness follows from standard regularity theory. For the development of the theory of (1.1) similarity solutions play an important role. Essentially these are solutions whose profiles remain the same as t varies. In the nonnegative case they were studied extensively in [7-91. The most familiar of them are of course the Burenblatt-Pattle solutions, given by

Extinction and focusing behaviour of spherical and annular flames described by a free boundary problem

Abstract We consider a free-boundary problem for the heat equation which arises in the description of premixed equi-diffusional flames in the limit of high activation energy. It consists of the heat equation u t = Δu, u > o, posed in an a priori unknown set Ω ⊂ QT = RN × (0,T) for some T > 0 with boundary conditions on the free lateral boundary τ = ∂Ω∩ QT (the flame front): u = o and ∂u ∂v = − 1. We impose initial condition u0(x) ≥ 0 on the known initial domain Ω 0 = Ω ∩ {t = 0} . The paper establishes a theory of existence, uniqueness and regularity for radial symmetric solutions having bounded support. We remark that such solutions vanish in finite time (extinction phenomenon). In the paper we analyze the different types of possible extinction behaviour. We also investigate the focusing behaviour for solutions whose support expands in finite time to fill a hole. In all the cases the asymptotic behaviour is shown to be self-similar.

An elliptic-parabolic free boundary problem

in which c is a continuous nondecreas~Rg function defined on R such that C(U) is strictly increasing when u 0, Ui = 1 if bi = 0 and bi = 1 if ai = 0 for i = 0 and i = 1 and fO, fi and t’. are prescribed functions. Problem I arises in the theory of fluid Aow through parGaIly saturated media. Then t6 denotes the potential due to capiitary suction and c the moisture content. The dependence of c on IE is found empirically to be as in Fig. I, c being bounded above by the saturation value c, = 1. Thus, in regions where the medium is saturated, the flow is of potential type, and described by an ehiptic equation, and in regions where the medium is unsaturated, the flow is of diffusive type and described by a parabolic equation. At the boundary between these regions-the interface-one expects U’= 0 and u, continuous.