Metabolic synchronization by traveling waves in yeast cell layers

Kinetic modelling of glycolytic oscillations

Glycolytic oscillations have been studied for well over 60 years, but aspects of their function, and mechanisms of regulation and synchronisation remain unclear. Glycolysis is amenable to mechanistic mathematical modelling, as its components have been well characterised, and the system can be studied at many organisational levels: in vitro reconstituted enzymes, cell free extracts, individual cells, and cell populations. In recent years, the emergence of individual cell analysis has opened new ways of studying this intriguing system.

Synchronisation of glycolytic activity in yeast cells

Glycolysis is the central metabolic pathway of almost every cell and organism. Under appropriate conditions, glycolytic oscillations may occur in individual cells as well as in entire cell populations or tissues. In many biological systems, glycolytic oscillations drive coherent oscillations of other metabolites, for instance in cardiomyocytes near anorexia, or in pancreas where they lead to a pulsatile release of insulin. Oscillations at the population or tissue level require the cells to synchronize their metabolism. We review the progress achieved in studying a model organism for glycolytic oscillations, namely yeast. Oscillations may occur on the level of individual cells as well as on the level of the cell population. In yeast, the cell-to-cell interaction is realized by diffusion-mediated intercellular communication via a messenger molecule. The present mini-review focuses on the synchronisation of glycolytic oscillations in yeast. Synchronisation is a quorum-sensing phenomenon because the collective oscillatory behaviour of a yeast cell population ceases when the cell density falls below a threshold. We review the question, under which conditions individual cells in a sparse population continue or cease to oscillate. Furthermore, we provide an overview of the pathway leading to the onset of synchronized oscillations. We also address the effects of spatial inhomogeneities (e.g., the formation of spatial clusters) on the collective dynamics, and also review the emergence of travelling waves of glycolytic activity. Finally, we briefly review the approaches used in numerical modelling of synchronized cell populations.

Intercellular communication induces glycolytic synchronization waves between individually oscillating cells

Many organs have internal structures with spatially differentiated and sometimes temporally synchronized groups of cells. The mechanisms leading to such differentiation and coordination are not well understood. Here we design a diffusion-limited microfluidic system to mimic a multicellular organ structure with peripheral blood flow and test whether a group of individually oscillating yeast cells could form subpopulations of spatially differentiated and temporally synchronized cells. Upon substrate addition, the dynamic response at single-cell level shows glycolytic oscillations, leading to wave fronts traveling through the monolayered population and to synchronized communities at well-defined positions in the cell chamber. A detailed mechanistic model with the architectural structure of the flow chamber incorporated successfully predicts the spatial-temporal experimental data, and allows for a molecular understanding of the observed phenomena. The intricate interplay of intracellular biochemical reaction networks leading to the oscillations, combined with intercellular communication via metabolic intermediates and fluid dynamics of the reaction chamber, is responsible for the generation of the subpopulations of synchronized cells. This mechanism, as analyzed from the model simulations, is experimentally tested using different concentrations of cyanide stress solutions. The results are reproducible and stable, despite cellular heterogeneity, and the spontaneous community development is reminiscent of a zoned cell differentiation often observed in multicellular organs.

Partial synchronisation of glycolytic oscillations in yeast cell populations

The transition between synchronized and asynchronous behaviour of immobilized yeast cells of the strain Saccharomyces carlsbergensis was investigated by monitoring the autofluorescence of the coenzyme NADH. In populations of intermediate cell densities the individual cells remained oscillatory, whereas on the level of the cell population both a partially synchronized and an asynchronous state were accessible for experimental studies. In the partially synchronized state, the mean oscillatory frequency was larger than that of the cells in the asynchronous state. This suggests that synchronisation occurred due to entrainment by the cells that oscillated more rapidly. This is typical for synchronisation due to phase advancement. Furthermore, the synchronisation of the frequency of the glycolytic oscillations preceded the synchronisation of their phases. However, the cells did not synchronize completely, as the distribution of the oscillatory frequencies only narrowed but did not collapse to a unique frequency. Cells belonging to spatially denser clusters showed a slightly enhanced local synchronisation during the episode of partial synchronisation. Neither the clusters nor a transition from partially synchronized glycolytic oscillations to travelling glycolytic waves did substantially affect the degree of partial synchronisation. Chimera states, i.e., the coexistence of a synchronized and an asynchronous part of the population, could not be found.

Nonreciprocity as a generic route to traveling states

We examine a nonreciprocally coupled dynamical model of a mixture of two diffusing species. We demonstrate that nonreciprocity, which is encoded in the model via antagonistic cross-diffusivities, provides a generic mechanism for the emergence of traveling patterns in purely diffusive systems with conservative dynamics. In the absence of nonreciprocity, the binary fluid mixture undergoes a phase transition from a homogeneous mixed state to a demixed state with spatially separated regions rich in one of the two components. Above a critical value of the parameter tuning nonreciprocity, the static demixed pattern acquires a finite velocity, resulting in a state that breaks both spatial and time-reversal symmetry, as well as the reflection parity of the static pattern. We elucidate the generic nature of the transition to traveling patterns using a minimal model that can be studied analytically. Our work has direct relevance to nonequilibrium assembly in mixtures of chemically interacting colloids that are known to exhibit nonreciprocal effective interactions, as well as to mixtures of active and passive agents where traveling states of the type predicted here have been observed in simulations. It also provides insight on transitions to traveling and oscillatory states seen in a broad range of nonreciprocal systems with nonconservative dynamics, from reaction-diffusion and prey-predators models to multispecies mixtures of microorganisms with antagonistic interactions.

Selection of spatiotemporal patterns in arrays of spatially distributed oscillators indirectly coupled via a diffusive environment

Emergence of self-organized behaviors in diverse living systems often depends on population density. In these systems, cell-cell communications are usually mediated by the surrounding environment. Collective behaviors (e.g., synchrony and dynamical quorum sensing) of such systems with stirred environment have been extensively studied, but the spatiotemporal dynamics of the oscillators coupled via a diffusive environment (without stirring) is rather understudied. We here perform a computational study on the selection and competition of wave patterns in arrays of spatially distributed oscillators immersed in a diffusive medium. We find that population density plays a crucial role in the selection of wave patterns: (i) for a single spiral in the system, its rotation either inward or outward could be controlled by population density, and (ii) for spiral and target waves coexisting initially in the system, wave competition happens and population density decides which type of wave will finally survive. The latter phenomenon is further confirmed in a system whose individual element is excitable rather than self-sustained oscillatory. The mechanism underlying all these observations is attributed to the frequency competition. Our results in the excitable case may have implications on the experimental results.

Spiral wave chimeras in locally coupled oscillator systems

The recently discovered chimera state involves the coexistence of synchronized and desynchronized states for a group of identical oscillators. In this work, we show the existence of (inwardly) rotating spiral wave chimeras in the three-component reaction-diffusion systems where each element is locally coupled by diffusion. A transition from spiral waves with the smooth core to spiral wave chimeras is found as we change the local dynamics of the system or as we gradually increase the diffusion coefficient of the activator. Our findings on the spiral wave chimera in the reaction-diffusion systems suggest that spiral chimera states may be found in chemical and biological systems that can be modeled by a large population of oscillators indirectly coupled via a diffusive environment.

Noise facilitates transcriptional control under dynamic inputs

Cells must respond sensitively to time-varying inputs in complex signaling environments. To understand how signaling networks process dynamic inputs into gene expression outputs and the role of noise in cellular information processing, we studied the immune pathway NF-κB under periodic cytokine inputs using microfluidic single-cell measurements and stochastic modeling. We find that NF-κB dynamics in fibroblasts synchronize with oscillating TNF signal and become entrained, leading to significantly increased NF-κB oscillation amplitude and mRNA output compared to non-entrained response. Simulations show that intrinsic biochemical noise in individual cells improves NF-κB oscillation and entrainment, whereas cell-to-cell variability in NF-κB natural frequency creates population robustness, together enabling entrainment over a wider range of dynamic inputs. This wide range is confirmed by experiments where entrained cells were measured under all input periods. These results indicate that synergy between oscillation and noise allows cells to achieve efficient gene expression in dynamically changing signaling environments.

pH wave-front propagation in the urea-urease reaction

The urease-catalyzed hydrolysis of urea displays feedback that results in a switch from acid (pH ~3) to base (pH ~9) after a controllable period of time (from 10 to >5000 s). Here we show that the spatially distributed reaction can support pH wave fronts propagating with a speed of the order of 0.1-1 mm min(-1). The experimental results were reproduced qualitatively in reaction-diffusion simulations including a Michaelis-Menten expression for the urease reaction with a bell-shaped rate-pH dependence. However, this model fails to predict that at lower enzyme concentrations, the unstirred reaction does not always support fronts when the well-stirred reaction still rapidly switches to high pH.

Desynchronisation of glycolytic oscillations in yeast cell populations

Glycolytic oscillations of intact yeast cells of the strain Saccharomyces carlsbergensis were investigated at both the levels of cell populations and of individual cells. Individual cells showed glycolytic oscillations even at very low cell densities (e.g. 1.010⁵ cells/ml). By contrast, the collective behaviour on the population level was cell density-dependent: at high cell densities it is oscillatory, but below the threshold density of 1.010⁶ cells/ml the collective dynamics becomes quiescent. We demonstrate that the transition in the collective dynamics is caused by the desynchronisation of the oscillations of individual cells. This is characteristic for a Kuramoto transition. Spatially resolved measurements at low cell densities revealed that even cells that adhere to their neighbours oscillated with their own, independent frequencies and phases.