Maximum likelihood density modification by pattern recognition of structural motifs

摘要

An electron density for a crystallographic structure having protein regions and solvent regions is improved by maximizing the log likelihood of a set of structures factors {F_h} using a local log-likelihood function:; $PTEXTHILITALICPDATLL/PDAT/ITALIC/HILPDAT(\&rgr;(/PDATHILITALICPDATx,\; \{F/PDAT/ITALIC/HILHILSBPDATh/PDAT/SB/HILPDAT\}))\=ln\[/PDATHILITALICPDATp/PDAT/ITALIC/HILPDAT(\&rgr;(/PDATHILITALICPDATx/PDAT/ITALIC/HILPDAT)\|PROT)/PDATHILITALICPDATp/PDAT/ITALIC/HILHILSBPDATPROT/PDAT/SB/HILPDAT(/PDATHILITALICPDATx/PDAT/ITALIC/HILPDAT)\+/PDATHILITALICPDATp/PDAT/ITALIC/HILPDAT(\&rgr;(/PDATHILITALICPDATx/PDAT/ITALIC/HILPDAT)\|SOLV)/PDATHILITALICPDATp/PDAT/ITALIC/HILHILSBPDATSOLV/PDAT/SB/HILPDAT(/PDATHILITALICPDATx/PDAT/ITALIC/HILPDAT)\+/PDATHILITALICPDATp/PDAT/ITALIC/HILPDAT(\&rgr;(/PDATHILITALICPDATx/PDAT/ITALIC/HILPDAT)\|/PDATHILITALICPDATH/PDAT/ITALIC/HILPDAT)/PDATHILITALICPDATp/PDAT/ITALIC/HILHILSBPDATH/PDAT/SB/HILPDAT(/PDATHILITALICPDATx/PDAT/ITALIC/HILPDAT)\],/PDAT/PTEXT$ ;where p_PROT(x) is the probability that x is in the protein region, p(&rgr;(x)|PROT) is the conditional probability for &rgr;(x) given that x is in the protein region, and p_SOLV(x) and p(&rgr;(x)|SOLV) are the corresponding quantities for the solvent region, p_H(x) refers to the probability that there is a structural motif at a known location, with a known orientation, in the vicinity of the point x; and p(&rgr;(x)|H) is the probability distribution for electron density at this point given that the structural motif actually is present. One appropriate structural motif is a helical structure within the crystallographic structure.