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Multidimensional Multidimensional Molecular Molecular Replacement. Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

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Page 1: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

MultidimensionalMultidimensional Molecular Replacement. Molecular Replacement.

Nicholas M. Glykos & Michael Kokkinidis

IMBB, FORTH, Heraklion, Crete, GREECE

Page 2: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Rigid-body refinement.

Page 3: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE
Page 4: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

2x

Page 5: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE
Page 6: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE
Page 7: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Rigid-body simulated annealing.

Page 8: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

The program :The program :

Name : “Queen of Spades” Availability : absolutely free, open-source software,

no warranties whatsoever. The distribution includes source code, plenty of

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

Download the latest version via http://origin.imbb.forth.gr/software/

Current stable version : ββ , Release 1.0.

Page 9: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Using the program :Using the program :

Input : a .pdb file containing the model, 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.

Page 10: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

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

$ Qs –auto 1or,

$ Qs –auto 2etc.

Page 11: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

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

. . . . . . .

Page 12: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

The algorithm :The 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.

Page 13: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

The algorithm :The 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 ].

Page 14: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

The algorithm :The 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 ].

Page 15: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

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.

Page 16: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Annealing schedules :Annealing schedules :

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

Page 17: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

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.

Page 18: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

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

Page 19: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

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

Page 20: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

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

Page 21: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

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

Page 22: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

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

Page 23: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

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

Page 24: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Move size control :Move size control :

Constant move size : max(Δt) =

dmin/max(a,b,c) ) max(Δκ) =

dmin (in degrees).

Move size linearly dependent on current R-factor and time step :

max(Δt) = 0.5 R (1.0 - t/ttotal )

max(Δκ) = π R (1.0 - t/ttotal )

Page 25: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

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.

Page 26: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

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 correction to be applied : Fcorrected = Fp { 1.0 – ksol exp[ -Bsol / d2 ] }

Page 27: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

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 correction to be applied : Fcorrected = Fp { 1.0 – ksol exp[ -Bsol / d2 ] }

Page 28: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : An 11D problem.Examples : An 11D problem. Target structure 1lys,

model 2ihl (rmsd 1.52 & 1.56Å).

Two molecules of lysozyme per asymmetric unit.

Monoclinic space group (P21), 4Å data.

±20% noise added to error-free data.

Solutions appear after ~3.8 hours of CPU time.

Page 29: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 12D problem. Examples : A 12D problem. Target structure 1b6q. 30% solvent. Search model : one

poly-Alanine helix. One monomer of Rop

per a.u. Orthorhombic space

group (C2221) . Real 15-4Å data. About 120 minutes of

CPU time per run.

Page 30: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 12D problem. Examples : A 12D problem. Target structure 1b6q. 30% solvent. Search model : one

poly-Alanine helix. One monomer of Rop

per a.u. Orthorhombic space

group (C2221) . Real 15-4Å data. About 120 minutes of

CPU time per run.

Page 31: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 12D problem. Examples : A 12D problem. Target structure 1b6q. 30% solvent. Search model : one

poly-Alanine helix. One monomer of Rop

per a.u. Orthorhombic space

group (C2221) . Real 15-4Å data. About 120 minutes of

CPU time per run.

Page 32: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 12D problem. Examples : A 12D problem. Target structure 1b6q. 30% solvent. Search model : one

poly-Alanine helix. One monomer of Rop

per a.u. Orthorhombic space

group (C2221) . Real 15-4Å data. About 120 minutes of

CPU time per run.

Run 1.0-Corr Free

1 0.2778 0.3162

2 0.2744 0.6903

3 0.2407 0.3305

4 0.2639 0.3656

5 0.2632 0.8358

6 0.2473 0.4466

7 0.2590 0.4330

8 0.2937 0.2821

9 0.2725 0.6402

Page 33: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 12D problem. Examples : A 12D problem. Target structure 1b6q. 30% solvent. Search model : one

poly-Alanine helix. One monomer of Rop

per a.u. Orthorhombic space

group (C2221) . Real 15-4Å data. About 120 minutes of

CPU time per run.

Page 34: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 17D problem.Examples : A 17D problem. Target structure 1a2p,

model 2bni. Three molecules of

ribonouclease per asymmetric unit.

Trigonal space group (P32), 15-4Å data.

±10% noise added to error-free data.

2.5 days per run on an Intel PIII at 800MHz.

Page 35: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 17D problem.Examples : A 17D problem. Target structure 1a2p,

model 2bni. Three molecules of

ribonouclease per asymmetric unit.

Trigonal space group (P32), 15-4Å data.

±10% noise added to error-free data.

2.5 days per run on an Intel PIII at 800MHz.

Page 36: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 23D problem.Examples : A 23D problem.

Target structure : monoclinic form of the A31P Rop mutant containing the equivalent of one 4-α-helix bundle in the asymmetric unit (two monomers).

The structure of the orthorhombic form of the same mutant is known (1B6Q.pdb).

Page 37: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 23D problem.Examples : A 23D problem.

Target structure : monoclinic form of the A31P Rop mutant containing the equivalent of one 4-α-helix bundle in the asymmetric unit (two monomers).

The structure of the orthorhombic form of the same mutant is known (1B6Q.pdb).

We had been consistently failing to make any progress since December 1998.

Page 38: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 23D problem.Examples : A 23D problem.

Tried AMoRe & molrep using as search models individual helices, one monomer (helix-turn-helix), or the complete 4-α-helical bundle, with or without side-chains, and at various resolution ranges.

Tried X-plor and CNS with several combinations of models, data and PC-refinement protocols.

Even did an extensive heavy-atom derivative search.

Page 39: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 23D problem.Examples : A 23D problem.

Systematic search with AMoRe using one poly-Ala helix as search model :

1. Keep the best 750 models for the first helix (by combining the best 15 orientations with the best 50 positions).

2. For each of those one-helix models, search with a second helix (562,500 models). Keep only those solutions that simultaneously decrease R and increase correlation (29,638 two-helix models).

3. For each of these, search with a third helix (22.2 million models). Keep only those models for which the addition of the third helix both decreased R and increased correlation (273,258 models).

Page 40: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 23D problem.Examples : A 23D problem.

Systematic search with AMoRe using one poly-Ala helix as search model :

1. Keep the best 750 models for the first helix (by combining the best 15 orientations with the best 50 positions).

2. For each of those one-helix models, search with a second helix (562,500 models). Keep only those solutions that simultaneously decrease R and increase correlation (29,638 two-helix models).

3. For each of these, search with a third helix (22.2 million models). Keep only those models for which the addition of the third helix both decreased R and increased correlation (273,258 models).

Best R=0.583, best Corr=0.37.

Page 41: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 23D problem.Examples : A 23D problem. Target structure :

monoclinic form of 1b6q, 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.

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

Page 42: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 23D problem.Examples : A 23D problem. Target structure :

monoclinic form of 1b6q, 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.

Page 43: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 23D problem.Examples : A 23D problem.

Page 44: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 23D problem.Examples : A 23D problem.

Page 45: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 23D problem.Examples : A 23D problem.

Page 46: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Examples : A 23D problem.Examples : A 23D problem.

Page 47: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE
Page 48: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Disadvantages :Disadvantages :

In most cases, treating the problem as 6n-dimensional is a waste of CPU time.

You can only have one search model (ie you can not search simultaneously with your DNA & protein models).

The structure of the search model is kept fixed throughout the calculation.

Page 49: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Disadvantages :Disadvantages :

The (putative) evidence from the self-rotation function and/or the native Patterson function are ignored.

When the starting model deviates significantly from the target structure, (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.

Page 50: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Advantages :Advantages :

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 conventional methods, that the results obtained can be considered as independent.

Page 51: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Advantages :Advantages :

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

Page 52: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Advantages :Advantages :

The method’s only requirement is that the global minimum of the target function (for the given model 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, more robust in the case of closely-packed structures, or when the molecule deviates significantly from being approximately spherical.

Page 53: Multidimensional Molecular Replacement. Nicholas M. Glykos & Michael Kokkinidis IMBB, FORTH, Heraklion, Crete, GREECE

Conclusion :Conclusion :

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