Protein folding tames chaos

Protein folding produces characteristic and functional three-dimensional structures from unfolded polypeptides or disordered coils. The emergence of extraordinary complexity in the protein folding process poses astonishing challenges to theoretical modeling and computer simulations. The present work introduces molecular nonlinear dynamics (MND), or molecular chaotic dynamics, as a theoretical framework for describing and analyzing protein folding. We unveil the existence of intrinsically low dimensional manifolds (ILDMs) in the chaotic dynamics of folded proteins. Additionally, we reveal that the transition from disordered to ordered conformations in protein folding increases the transverse stability of the ILDM. Stated differently, protein folding reduces the chaoticity of the nonlinear dynamical system, and a folded protein has the best ability to tame chaos. Additionally, we bring to light the connection between the ILDM stability and the thermodynamic stability, which enables us to quantify the disorderliness and relative energies of folded, misfolded and unfolded protein states. Finally, we exploit chaos for protein flexibility analysis and develop a robust chaotic algorithm for the prediction of Debye-Waller factors, or temperature factors, of protein structures

Analytic Models of the ROC Curve: Applications to Credit Rating Model Validation

In this paper, the authors use the concept of the population ROC curve to build analytic models of ROC curves. Information about the population properties can be used to gain greater accuracy of estimation relative to the non-parametric methods currently in vogue. If used properly this is particularly helpful in some situations where the number of sick loans is rather small; a situation frequently met in periods of benign macro-economic background.validation; credit analysis; rating model; ROC; Basel II