Semiconductor quantum dots (QDs) provide an essential link between light and matter in emerging fields such as light-harvesting [1,2], all-solid-state quantum communication [3], and quantum computing [4]. QDs are excellent single-photon sources [5] and can store quantum bits for extended periods [6] making them promising interconnects between light and matter in integrated quantum information networks [7]. To this end the light-matter interaction strength must be strongly enhanced using nanophotonic structures such as photonic crystal cavities [8] and waveguides [9] or plasmonic nanowires [10][11][12][13]. So far it has been assumed that QDs can be treated just like atomic photon emitters where the spatial properties of the wavefunction can be safely ignored. Here we demonstrate that the point-emitter description for QDs near plasmonic nanostructures breaks down. We observe that the QDs can excite plasmons eight times more efficiently depending on their orientation due to their mesoscopic character. Either enhancement or suppresion of the rate of plasmon excitation is observed depending on the geometry of the plasmonic nanostructure in full agreement with a new theory. This discovery has no equivalence in atomic systems and paves the way for novel nanophotonic devices that exploit the extended size of QDs as a resource for increasing the light-matter interaction strength.

Interfacial enzyme reactions are ubiquitous both in vivo and in technical applications, but analysis of their kinetics remains controversial. In particular, it is unclear whether conventional Michaelis–Menten theory, which requires a large excess of substrate, can be applied. Here, an extensive experimental study of the enzymatic hydrolysis of insoluble cellulose indeed showed that the conventional approach had a limited applicability. Instead we argue that, unlike bulk reactions, interfacial enzyme catalysis may reach a steady-state condition in the opposite experimental limit, where the concentration of enzyme far exceeded the molar concentration of accessible surface sites. Under this condition, an “inverse Michaelis–Menten equation”, where the roles of enzyme and substrate had been swapped, proved to be readily applicable. We suggest that this inverted approach provides a general tool for kinetic analyses of interfacial enzyme reactions and that its analogy to established theory provides a bridge to the accumulated understanding of steady-state enzyme kinetics. Finally, we show that the ratio of parameters from conventional and inverted Michaelis–Menten analysis reveals the density of enzyme attack sites on the substrate surface as probed by one specific enzyme. This density, which is an analogue to a molar substrate concentration for interfacial reactions, was shown to vary strongly even among related enzymes. This difference reflects how the enzyme discriminates between local differences in surface structure on the substrate.

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This paper concerns ODE modeling of the hypothalamic-pituitary- adrenal axis (HPA axis) using an analytical and numerical approach, combined with biological knowledge regarding physiological mechanisms and parameters. The three hormones, CRH, ACTH, and cortisol, which interact in the HPA axis are modeled as a system of three coupled, nonlinear differential equations. Experimental data shows the circadian as well as the ultradian rhythm. This paper focuses on the ultradian rhythm. The ultradian rhythm can mathematically be explained by oscillating solutions. Oscillating solutions to an ODE emerges from an unstable fixed point with complex eigenvalues with a positive real parts and a non-zero imaginary parts. The first part of the paper describes the general considerations to be obeyed for a mathematical model of the HPA axis. In this paper we only include the most widely accepted mechanisms that influence the dynamics of the HPA axis, i.e. a negative feedback from cortisol on CRH and ACTH. Therefore we term our model the minimal model. The minimal model, encompasses a wide class of different realizations, obeying only a few physiologically reasonable demands. The results include the existence of a trapping region guaranteeing that concentrations do not become negative or tend to infinity. Furthermore, this treatment guarantees the existence of a unique fixed point. A change in local stability of the fixed point, from stable to unstable, implies a Hopf bifurcation; thereby, oscillating solutions may emerge from the model. Sufficient criteria for local stability of the fixed point, and an easily applicable sufficient criteria guaranteeing global stability of the fixed point, is formulated. If the latter is fulfilled, ultradian rhythm is an impossible outcome of the minimal model and all realizations thereof. The second part of the paper concerns a specific realization of the minimal model in which feedback functions are built explicitly using receptor dynamics. Using physiologically reasonable parameter values, along with the results of the general case, it is demonstrated that un-physiological values of the parameters are needed in order to achieve local instability of the fixed point. Small changes in physiologically relevant parameters cause the system to be globally stable using the analytical criteria. All simulations show a globally stable fixed point, ruling out periodic solutions even when an investigation of the 'worst case parameters' is performed.

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