A two-dimensional histogram-matching method for protein phase refinement and extension

Nieh, Y.-P.; Zhang, K.Y.J.

doi:10.1107/S0907444999010987

Figure 1
The 2D histogram-matching procedure. 2D histogram matching is achieved through alternating application of 1D histogram matching on electron density and 1D histogram matching on density gradients in a sequential mode. The ideal 1D density histogram and 1D gradient histogram are obtained from the projection of the ideal 2D histogram along the gradient and density, respectively. Starting from an initial structure-factor set F₀, an electron-density map ρ₀ is calculated by a fast Fourier transform F. The initial map is modified by 1D histogram matching to produce a new map ρ′, the density histogram of which conforms to the ideal density histogram. The modified map ρ′ is Fourier transformed to give a new structure-factor set F₁, from which three gradient maps, g_x, g_y and g_z, are calculated along each crystal axis. The three gradient maps are transformed from the crystal axes system to the orthogonal axes system. The transformed gradient maps, g_u, g_v and g_w, are modified by 1D histogram matching on gradients similar to that on density to produce new gradient maps, the gradient distribution of which matches the ideal gradient distribution. The new gradient maps are then transformed from the orthogonal axes to the fractional axes. Three sets of structure factors, $[F_{x}'']$ , $[F_{y}'']$ and $[F_{z}'']$ , are calculated from each of the three new gradient maps, $[g_{x}']$ , $[g_{y}']$ and $[g_{z}']$ by fast Fourier transforms. The three sets of structure factors, $[F_{x}'']$ , $[F_{y}'']$ and $[F_{z}'']$ , are combined to produce a new set of structure factors, F₂, from which a new map ρ₀ is calculated. The process is iterated until the 2D histogram of the modified map matches that of the ideal 2D histogram.

BIOLOGICAL
CRYSTALLOGRAPHY

ISSN: 1399-0047

Volume 55| Part 11| November 1999| Pages 1893-1900

doi:10.1107/S0907444999010987

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