Complex chaos in conditional qubit dynamics and purification protocols

Selection of an ensemble of equally prepared quantum systems, based on measurements on it, is a basic step in quantum state purification. For an ensemble of single qubits, iterative application of selective dynamics has been shown to lead to complex chaos, which is a novel form of quantum chaos with true sensitivity to the initial conditions. The Julia set of initial valuse with no convergence shows a complicated structre on the complex plane. The shape of the Julia set varies with the parameter of the dynamics. We present here results for the two qubit case demonstrating how a purification process can be destroyed with chaotic oscillations

Complex chaos in the conditional dynamics of qubits

We analyze the consequences of iterative measurement-induced nonlinearity on the dynamical behavior of qubits. We present a one-qubit scheme where the equation governing the time evolution is a complex-valued nonlinear map with one complex parameter. In contrast to the usual notion of quantum chaos, exponential sensitivity to the initial state occurs here. We calculate analytically the Lyapunov exponent based on the overlap of quantum states, and find that it is positive. We present a few illustrative examples of the emerging dynamics.Comment: 4 pages, 3 figure

The Impact of Small Molecule Binding on the Energy Landscape of the Intrinsically Disordered Protein C-Myc

Intrinsically disordered proteins are attractive therapeutic targets owing to their prevalence in several diseases. Yet their lack of well-defined structure renders ligand discovery a challenging task. An intriguing example is provided by the oncoprotein c-Myc, a transcription factor that is over expressed in a broad range of cancers. Transcriptional activity of c-Myc is dependent on heterodimerization with partner protein Max. This protein-protein interaction is disrupted by the small molecule 10058-F4 (1), that binds to monomeric and disordered c-Myc. To rationalize the mechanism of inhibition, structural ensembles for the segment of the c-Myc domain that binds to 1 were computed in the absence and presence of the ligand using classical force fields and explicit solvent metadynamics molecular simulations. The accuracy of the computed structural ensembles was assessed by comparison of predicted and measured NMR chemical shifts. The small molecule 1 was found to perturb the composition of the apo equilibrium ensemble and to bind weakly to multiple distinct c-Myc conformations. Comparison of the apo and holo equilibrium ensembles reveals that the c-Myc conformations binding 1 are already partially formed in the apo ensemble, suggesting that 1 binds to c-Myc through an extended conformational selection mechanism. The present results have important implications for rational ligand design efforts targeting intrinsically disordered proteins

Evidence for a single loss of mineralized teeth in the common avian ancestor

Edentulism, the absence of teeth, has evolved convergently among vertebrates, including birds, turtles, and several lineages of mammals. Instead of teeth, modern birds (Neornithes) use a horny beak (rhamphotheca) and a muscular gizzard to acquire and process food. We performed comparative genomic analyses representing lineages of nearly all extant bird orders and recovered shared, inactivating mutations within genes expressed in both the enamel and dentin of teeth of other vertebrate species, indicating that the common ancestor of modern birds lacked mineralized teeth. We estimate that tooth loss, or at least the loss of enamel caps that provide the outer layer of mineralized teeth, occurred about 116 million years ago