The affinities of hosts—ranging from small synthetic cavitands to large proteins—for organic molecules are well documented. The average association constants for the binding of organic molecules by cyclodextrins, synthetic hosts, and albumins in water, as well as of catalytic antibodies or enzymes for substrates are 103.5±2.5 M−1. Binding affinities are elevated to 108±2 M−1 for the complexation of transition states and biological antigens by antibodies or inhibitors by enzymes, and to 1016±4 M−1 for transition states with enzymes. The origins of the distributions of association constants observed for the broad range of host–guest systems are explored in this Review, and typical approaches to compute and analyze host–guest binding in solution are discussed. In many classes of complexes a rough correlation is found between the binding affinity and the surface area that is buried upon complexation. Enzymes transcend this effect and achieve transition‐state binding much greater than is expected from the surface areas.

Explosive synchronization (ES) is nowadays a hot topic of interest in nonlinear science and complex networks. So far, it is conjectured that ES is rooted in the setting of specific microscopic correlation features between the natural frequencies of the networked oscillators and their effective coupling strengths. We show that ES, in fact, is far more general, and can occur in adaptive and multilayer networks also in the absence of such correlation properties. Precisely, we first report evidence of ES in the absence of correlation for networks where a fraction f of the nodes have links adaptively controlled by a local order parameter, and then we extend the study to a variety of two-layer networks with a fraction f of their nodes coupled each other by means of dependency links. In this latter case, we even show that ES sets in, regardless of the differences in the frequency distribution and/or in the topology of connections between the two layers. Finally, we provide a rigorous, analytical, treatment to properly ground all the observed scenario, and to facilitate the understanding of the actual mechanisms at the basis of ES in real-world systems. 05.45.Xt

Explosive synchronization (ES) has recently attracted much attention, where its two necessary conditions are found to be a scale-free network topology and a positive correlation between the natural frequencies of the oscillators and their degrees. Here we present a framework for ES to be observed in a general complex network, where a positive correlation between coupling strengths of the oscillators and the absolute of their natural frequencies is assumed and the previous studies are included as specific cases. In the framework, the previous two necessary conditions are replaced by another one, thus fundamentally deepening the understanding of the microscopic mechanism toward synchronization. A rigorous analytical treatment by a mean field is provided to explain the mechanism of ES in this alternate framework.

No abstract