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We study travelling chimera states in a ring of nonlocally coupled heterogeneous (with Lorentzian distribution of natural frequencies) phase oscillators. These states are coherence-incoherence patterns moving in the lateral direction because of the broken reflection symmetry of the coupling topology. To explain the results of direct numerical simulations we consider the continuum limit of the system. In this case travelling chimera states correspond to smooth travelling wave solutions of some integro-differential equation, called the Ott–Antonsen equation, which describes the long time coarse-grained dynamics of the oscillators. Using the Lyapunov–Schmidt reduction technique we suggest a numerical approach for the continuation of these travelling waves. Moreover, we perform their linear stability analysis and show that travelling chimera states can lose their stability via fold and Hopf bifurcations. Some of the Hopf bifurcations turn out to be supercritical resulting in the observation of modulated travelling chimera states.
Yeast hexokinase isoenzyme ScHxk2 stability of a two-domain protein with discontinuous domains
(2011)
The hexokinase isoenzyme 2 of Saccharomyces cerevisiae (ScHxk2) represents an archetype of a two-domain protein with the active site located in a cleft between the two domains. Binding of the substrate glucose results in a rigid body movement of the two domains leading to a cleft closure of the active site. Both domains of this enzyme are composed of discontinuous peptide sequences. This structural feature is reflected in the stability and folding of the ScHxk2 protein. Structural transitions induced by urea treatment resulted in the population of a thermodynamically stable folding intermediate, which, however, does not correspond to a molecule with one domain folded and the other unfolded. As demonstrated by different spectroscopic techniques, both domains are structurally affected by the partial denaturation. The intermediate possesses only 40% of the native secondary structural content and a substantial increase in the Stokes radius as judged by circular dichroism and dynamic light scattering analyses. One-dimensional H-1 NMR data prove that all tryptophan residues are in a non-native environment in the intermediate, indicating substantial changes in the tertiary structure. Still, the intermediate possesses quite a high stability for a transition intermediate of about Delta G = -22 kJ mol(-1).