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Experimental Phasing. Andrew Howard ACA Summer School 22 July 2005. Experimental Phasing. You can solve a structure with phases derived from experiments; it just may take some thinking. But the results will be statistically and esthetically satisfying. Why don’t we always do this?.
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Experimental Phasing Andrew Howard ACA Summer School 22 July 2005
Experimental Phasing • You can solve a structure with phases derived from experiments; it just may take some thinking. But the results will be statistically and esthetically satisfying.
Why don’t we always do this? • Multiple experiments • Sometimes requires specialized facilities • Requires familiarity with a different set of software • - so - • We’ll often do difference Fouriers or molecular replacement even when we do have resources to do experimental phasing
Categories of Experimental Phasing • Patterson methods • Isomorphous replacement • Single isomorphous replacement • Multiple isomorphous replacement • Anomalous diffraction • Multi-wavelength anomalous diffraction • Single-wavelenth anomalous diffraction • Optimized anomalous • ASIR / AMIR
General Concept • Remember:(r) = (1/V) h Fh exp(ih) exp(-2i h•r) • We can measure Fh • We can’t trivially measure h. • So we seek an experimental probe that will enable us to estimate h
Pattersons • Calculate the following object: • P(u) = (1/V2) h |Fh|2 cos2(h•u) • Note that h is a 3-vector in an integer-valued space, and u is a 3-vector in continuous space • This allows for analysis of interatomic vectors, so if we have n atoms, we will find n(n-1)/2 peaks in the Patterson map in u.
Can we use this to solve structures? • … sure, if n is moderate. • Doesn’t require phase information directly! Whoopie! • BUT • If n=1000, n(n-1)/2 ~ 500000. Eech. • So as a straight-ahead method for doing big molecular structures, this is a non-starter
Isomorphous replacement • Relies on the fact that proteins and nucleic acids are almost entirely constructed from atoms with Z < 16, and mostly Z < 9. • Scattering power for X-rays increases rapidly with Z • Therefore if we have a small number of heavy atoms, our diffraction pattern will be significantly perturbed relative to the light-atom-only pattern
How does it work? • Measure native data • Measure data with heavy atom bound • We rely on the fact that the Fourier transform is a linear transform: • (r) = (1/V) h(Fh exp(ih)) exp(-2i h•r) • The inverse of that concept is applied to the problem we’re really trying to deal with.
