Proteins Wriggle

We propose an algorithmic strategy for improving the efficiency of Monte Carlo searches for the low-energy states of proteins. Our strategy is motivated by a model of how proteins alter their shapes. In our model when proteins fold under physiological conditions, their backbone dihedral angles change synchronously in groups of four or more so as to avoid steric clashes and respect the kinematic conservation laws. They wriggle; they do not thrash. We describe a simple algorithm that can be used to incorporate wriggling in Monte Carlo simulations of protein folding. We have tested this wriggling algorithm against a code in which the dihedral angles are varied independently (thrashing). Our standard of success is the average root-mean-square distance (rmsd) between the alpha-carbons of the folding protein and those of its native structure. After 100,000 Monte Carlo sweeps, the relative decrease in the mean rmsd, as one switches from thrashing to wriggling, rises from 11% for the protein 3LZM with 164 amino acids (aa) to 40% for the protein 1A1S with 313 aa and 47% for the protein 16PK with 415 aa. These results suggest that wriggling is useful and that its utility increases with the size of the protein. One may implement wriggling on a parallel computer or a computer farm.Comment: 12 pages, 2 figures, JHEP late

Supersymmetry without Grassmann Variables

Supersymmetry transformations may be represented by unitary operators in a formulation of supersymmetry without numbers that anti-commute. The physical relevance of this formulation hinges on whether or not one may add states of even and odd fermion number, a question which soon may be settled by experiment.Comment: 8 pages, JHEP styl

Neutrinos Are Nearly Dirac Fermions

Neutrino masses and mixings are analyzed in terms of left-handed fields and a 6x6 complex symmetric mass matrix whose singular values are the neutrino masses. An angle x_nu characterizes the kind of the neutrinos, with x_nu = 0 for Dirac neutrinos and x_nu = pi/2 for Majorana neutrinos. If x_nu = 0, then baryon-minus-lepton number is conserved. When x_nu is approximately zero, the six neutrino masses coalesce into three nearly degenerate pairs. Thus the smallness of the differences in neutrino masses exhibited in the solar and atmospheric neutrino experiments and the stringent limits on neutrinoless double beta decay are naturally explained if B-L is approximately conserved and neutrinos are nearly Dirac fermions. If one sets sin(x_nu) = 0.003, suppresses inter-generational mixing, and imposes a quark-like mass hierarchy, then one may fit the essential features of the solar, reactor, and atmospheric neutrino experiments with otherwise random mass matrices in the eV range. This B-L model leads to these predictions: neutrinos oscillate mainly between flavor eigenfields and sterile eigenfields, and so the probabilities of the appearance of neutrinos or antineutrinos are very small; neutrinos may well be of cosmological importance; in principle the disappearance of the tau neutrino should be observable; and neutrinoless double beta decay is suppressed by an extra factor of < 10^(-5) and hence will not be seen in the Heidelberg/Moscow, IGEX, GENIUS, or CUORE experiments.Comment: 38 pages, 12 figures; uses Takagi's factorization and the Bartol fluxes; contains a new analysis of the solar, atmospheric, LSND, KARMEN2, and neutrinoless double beta decay data; and presents a better treatment of CP violation and of cosmological issue