Cross-validated maximum likelihood enhances crystallographic simulated annealing refinement

Recently, the target function for crystallographic refinement has been improved through a maximum likelihood analysis, which makes proper allowance for the effects of data quality, model errors, and incompleteness. The maximum likelihood target reduces the significance of false local minima during the refinement process, but it does not completely eliminate them, necessitating the use of stochastic optimization methods such as simulated annealing for poor initial models. It is shown that the combination of maximum likelihood with cross-validation, which reduces overfitting, and simulated annealing by torsion angle molecular dynamics, which simplifies the conformational search problem, results in a major improvement of the radius of convergence of refinement and the accuracy of the refined structure. Torsion angle molecular dynamics and the maximum likelihood target function interact synergistically, the combination of both methods being significantly more powerful than each method individually. This is demonstrated in realistic test cases at two typical minimum Bragg spacings (dmin = 2.0 and 2.8 Å, respectively), illustrating the broad applicability of the combined method. In an application to the refinement of a new crystal structure, the combined method automatically corrected a mistraced loop in a poor initial model, moving the backbone by 4 Å.

Transforming neural computations and representing time

Motifs of neural circuitry seem surprisingly conserved over different areas of neocortex or of paleocortex, while performing quite different sensory processing tasks. This apparent paradox may be resolved by the fact that seemingly different problems in sensory information processing are related by transformations (changes of variables) that convert one problem into another. The same basic algorithm that is appropriate to the recognition of a known odor quality, independent of the strength of the odor, can be used to recognize a vocalization (e.g., a spoken syllable), independent of whether it is spoken quickly or slowly. To convert one problem into the other, a new representation of time sequences is needed. The time that has elapsed since a recent event must be represented in neural activity. The electrophysiological hallmarks of cells that are involved in generating such a representation of time are discussed. The anatomical relationships between olfactory and auditory pathways suggest relevant experiments. The neurophysiological mechanism for the psychophysical logarithmic encoding of time duration would be of direct use for interconverting olfactory and auditory processing problems. Such reuse of old algorithms in new settings and representations is related to the way that evolution develops new biochemistry.