Stochastic Molecular Replacement. Nicholas M. Glykos MBG, DUTH, Alexandroupolis, Greece

StochasticStochasticMolecular Replacement.Molecular Replacement.

Nicholas M. GlykosMBG, DUTH, Alexandroupolis, Greece.

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Molecular Replacement as a Molecular Replacement as a rigid-body rigid-body refinement problem :refinement problem :

Determine the orientations and positions of the search models for which the agreement between the observed and calculated structure factor amplitudes is maximised. If the structures of the search models are sufficiently accurate, these orientations and positions will correspond to the correct molecular replacement solution.

Molecular Replacement as a Molecular Replacement as a rigid-body rigid-body refinement problem :refinement problem :

1. Systematic search : Examine all unique combinations of positions and orientations of all search models. The best solution will be the molecular replacement solution.

2. Stochastic searches : Use a global optimisation method (usually non-deterministic) to efficiently search the multidimensional parameter space.

Basic equations : Basic equations : The structure factorThe structure factor

Basic equations : Basic equations : The target function(s)The target function(s)

The search algorithms :The search algorithms :

1. Genetic algorithms.

2. Evolutionary programming (EPMR).

3. Simulated annealing (Qs).

The Metropolis algorithm :The Metropolis algorithm :

1. Assign random initial positions & orientations to all molecules present in the asymmetric unit of the target crystal structure. Calculate Fc’s from this arrangement.

2. Calculate the R-factor between the Fo’s and the Fc’s. Call this Rold.

The Metropolis algorithm :The Metropolis algorithm :

3. Randomly chose and alter the orientation and position of one of the molecules. Calculate the R-factor resulting from the new arrangement (Rnew).

4. If Rnew < Rold , then, the new arrangement is accepted and we start again from (3).

5. If the new R-factor is worse, we still accept the move with probability exp[ –(Rnew – Rold) / T ].

Annealing schedules :Annealing schedules :

Constant temperature run. Linear temperature gradient (slow cooling). Boltzmann annealing (logarithmic schedule). “Heating bath” mode.

The temperature is automatically adjusted in such a way as to keep the fraction of moves performed against the gradient of the target function constant and equal to a user-defined value.

Temperature determination :Temperature determination :

At T=0.3125000, average R=0.59937

At T=0.1562500, average R=0.59707

At T=0.0781250, average R=0.59861

At T=0.0390625, average R=0.59028

At T=0.0195312, average R=0.58783

At T=0.0097656, average R=0.57545

At T=0.0048828, average R=0.55527

At T=0.0024414, average R=0.53016

At T=0.0012207, average R=0.52038

At T=0.0006104, average R=0.51799

At T=0.0003052, average R=0.51524

Temperature determination :Temperature determination :

At T=0.3125000, average R=0.59937

At T=0.1562500, average R=0.59707

At T=0.0781250, average R=0.59861

At T=0.0390625, average R=0.59028

At T=0.0195312, average R=0.58783

At T=0.0097656, average R=0.57545

At T=0.0048828, average R=0.55527

At T=0.0024414, average R=0.53016

At T=0.0012207, average R=0.52038

At T=0.0006104, average R=0.51799

At T=0.0003052, average R=0.51524

Scaling & bulk solvent correctionScaling & bulk solvent correction

The default is to scale |Fc|’s to |Fo|’s using both a scale and a temperature factor even at the relatively low resolution used for molecular replacement calculations.

The program implements the exponential scaling model algorithm which allows a computationally efficient and model-independent bulk solvent correction to be applied :

Fcorrected = Fp { 1.0 – ksol exp[ -Bsol / d2 ] }

Speeding it up :Speeding it up :

Avoid FFTs : calculate and store (in core) the molecular transform of the search model.

Keep a table containing the contribution of each molecule to each reflection.

CPU time per step ~ Number of reflections in P1.

Speeding it up : parallelisationSpeeding it up : parallelisation

The program :The program :

Name : “Queen of Spades” (Qs). Availability : free, open source software, BSD-like

license. The distribution includes source code, plenty of

documentation, plus pre-compiled executables for Linux, Irix, OSF, Solaris, VMS & windoze.

Download the latest version via http://www.mbg.duth.gr/~glykos/

or from the various CCP14 mirrors. Current stable version : 1.3.

http://www.mbg.duth.gr/~glykos/

Using the program :Using the program :

Input : .pdb files containing the models, and a formatted (ASCII) file containing h,k,l,F,σ(F).

Output : .pdb files containing the final coordinates for each model, plus a packing diagram for each solution.

Running the program (1) :Running the program (1) :

$ Qs –auto 1or,

$ Qs –auto 2etc.

Running the program (2) :Running the program (2) :##########################################################

# Target function (can be R-FACTOR, CORR-1 or CORR-2) and

# number of minimisations and steps.

#

TARGET R-FACTOR

CYCLES 5

STEPS 100000000

############################################################

# Annealing schedule & move size control.

#

BOLTZMANN

START 0.06800

############################################################

# Reflection selection.

#

KEEP 0.70

AMPLIT_CUTOFF 1.0

SIGMA_CUTOFF 2.0

RESOLUTION 15.0 3.5

. . . . . . .

Examples : A 17D problem.Examples : A 17D problem.

Target structure 1a02, NFAT-Fos-Jun-DNA.

Treated Fos-Jun as one model.

Monoclinic space group (P21), experimental 19-4Å data.

Models deviated by 1.1, 1.5 and 2.2Å.

Three days per run on an Intel PIV at 1.8 GHz.


Target structure 1a02, NFAT-Fos-Jun-DNA.

Treated Fos-Jun as one model.

Monoclinic space group (P21), experimental 19-4Å data.

Models deviated by 1.1, 1.5 and 2.2Å.

Three days per run on an Intel PIV at 1.8 GHz.


Run 1.0-Corr Free

1 0.2437 0.3509

2 0.2465 0.6189

3 0.2466 0.5131

4 0.2557 0.6295

5 0.2227 0.3175

Target structure : monoclinic form of the A31P Rop mutant

Model : one poly-Ala helix (13% of atoms).

Four helices per asymmetric unit.

Space group C2, 15-3.5Å data.

Target function 1.0-Corr(Fo,Fc)

36 hours per run on an Intel PIII at 800MHz.


Target structure : monoclinic form of the A31P Rop mutant

Model : one poly-Ala helix (13% of atoms).

Four helices per asymmetric unit.

Space group C2, 15-3.5Å data.

Target function 1.0-Corr(Fo,Fc)

36 hours per run on an Intel PIII at 800MHz.





Disadvantages :Disadvantages :

In most cases, treating the molecular replacement problem as 6n-dimensional is like shooting a sparrow with a cannon.

The structures of the search models are kept fixed throughout the calculation.

The (putative) evidence from the self-rotation function and/or the native Patterson function are not actively used.

Disadvantages :Disadvantages :

When the starting models deviate significantly from the target structures, (i) there is no guarantee that the global minimum of any chosen statistic will correspond to the correct solution, (ii) traditional methods may be more sensitive in identifying the correct solution.

Advantages :Advantages :

All information (data + structures) is used right from the beginning of the calculations.

If there are just one or two molecules per asymmetric unit and CPU time is not a problem, the method can be used as a last ditch effort to conclusively show that there is no such thing as a pronounced global minimum (or otherwise ?).

The computational procedures differ so much from those used in the other methods, that the results obtained can be considered as independent.

Advantages :Advantages :

The method’s only requirement is that the global minimum of the target function (for the given models and data), corresponds to the correct solution.

The method does not assume that the self- and cross-vectors are topologically segregated in the Patterson function, and is, thus, expected to be more robust in the case of closely-packed structures, or when the molecules deviate significantly from being approximately spherical.

Conclusion :Conclusion :

Substituting computing for thinking will almost certainly fail for nn ≥ 5.

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Stochastic Molecular Replacement. Nicholas M. Glykos MBG, DUTH, Alexandroupolis, Greece