Geometric arrangement algorithms for protein structure determination - - PowerPoint PPT Presentation

Bruce Donald Laboratory

Jeff Martin

Geometric arrangement algorithms for protein structure determination

http://www.cs.duke.edu/donaldlab/

Protein structure determination Protein structure determination

Protein Synthesis

Protein structure determination Protein structure determination

Protein Synthesis

Primary sequence

ANNTTGFTRIIKAAGYSWKGLRAAWINEAAF RQEGVAVLLAVVIACWLDVDAITRVLLISSV MLVMIVEILNSAIEAVVDRIGSEYHELSGRAK DMGSAAVLIAIIVAVITWCILLWSHFG

Protein structure determination Protein structure determination

Protein Synthesis Protein Folding

Primary sequence

ANNTTGFTRIIKAAGYSWKGLRAAWINEAAF RQEGVAVLLAVVIACWLDVDAITRVLLISSV MLVMIVEILNSAIEAVVDRIGSEYHELSGRAK DMGSAAVLIAIIVAVITWCILLWSHFG

Protein structure determination Protein structure determination

Protein Synthesis Protein Folding

Primary sequence

Experimental measurements

ANNTTGFTRIIKAAGYSWKGLRAAWINEAAF RQEGVAVLLAVVIACWLDVDAITRVLLISSV MLVMIVEILNSAIEAVVDRIGSEYHELSGRAK DMGSAAVLIAIIVAVITWCILLWSHFG

d

Why solve protein structures? Why solve protein structures?

Structure determines function! Hence, studying structure helps understand function

How is protein function important? How is protein function important?

Disease mechanisms

MPER: HIV surface protein

P Reardon, et al., (in preparation)

How is protein function important? How is protein function important?

Disease mechanisms

MPER: HIV surface protein

T Zhou, I Georgiev, et al., Science, 2010

VRC01: HIV antibody

P Reardon, et al., (in preparation)

How is protein function important? How is protein function important?

New drugs Disease mechanisms

MPER: HIV surface protein

VRC01: HIV antibody

GrsA PheA: helps manufacture antibiotics

CY Chen, I Georgiev, et al., PNAS, 2009 T Zhou, I Georgiev, et al., Science, 2010 P Reardon, et al., (in preparation)

One protein function: a molecular assembly line One protein function: a molecular assembly line

The domains have specific tasks, but how do they work?

Protein Antibiotic

One protein function: a molecular assembly line One protein function: a molecular assembly line

Solving the structure for a domain shows us how it works.

Protein Antibiotic

One protein function: a molecular assembly line One protein function: a molecular assembly line

If we modify a domain, the protein could perform a new function.

Protein Antibiotic

Protein redesign relies on protein structure Protein redesign relies on protein structure

Cheng-Yu Chen, Ivelin Georgiev, Amy C. Anderson, Bruce R. Donald, Computational structure-based redesign of enzyme activity, PNAS 2009

Switched specificity from Phenylalanine to Leucine!

Prehaps we can engineer molecules to make new drugs?

Predicted binding model for Leucine

Redesign!

Experimental methods Experimental methods

Nuclear Magnetic Resonance spectroscopy (NMR)

Duke NMR Center Crystals of Insulin

X-ray Crystallography

For atomic-precision protein structure determination

d

NMR is often preferred because measurements are in solution state.

How are structures traditionally solved by NMR? How are structures traditionally solved by NMR?

• 13Cα chemical shifts
• 13Cβ chemical shifts
• 13CO chemical shifts
• 1Hα chemical shifts
• 1HN chemical shifts
• 3JHNHα couplings
• 1H-15N RDCs
• 15N R2
• Nitroxide spin-label PREs
• ATCUN PREs
• NOEs
• O2-induced 13C paramagnetic shifts
• Tryptophan indole solvent accessibility

Experimental Restraints

Geometric restraints on protein structure Geometric restraints on protein structure

• Nuclear Overhauser

Effect (NOE)

• Paramagnetic Relaxation

Enhancement (PRE)

Restraints on distance:

• 13Cα chemical shifts
• 13Cβ chemical shifts
• 13CO chemical shifts
• 1Hα chemical shifts
• 1HN chemical shifts
• 3JHNHα couplings
• 1H-15N RDCs
• 15N R2
• Nitroxide spin-label PREs
• ATCUN PREs
• NOEs
• O2-induced 13C paramagnetic shifts
• Tryptophan indole solvent accessibility

Experimental Restraints

Geometric restraints on protein structure Geometric restraints on protein structure

• Residual Dipolar

Couplings (RDCs) Restraints on orientation:

• 13Cα chemical shifts
• 13Cβ chemical shifts
• 13CO chemical shifts
• 1Hα chemical shifts
• 1HN chemical shifts
• 3JHNHα couplings
• 1H-15N RDCs
• 15N R2
• Nitroxide spin-label PREs
• ATCUN PREs
• NOEs
• O2-induced 13C paramagnetic shifts
• Tryptophan indole solvent accessibility

Experimental Restraints

Geometric restraints on protein structure Geometric restraints on protein structure

• Residual Dipolar

Couplings (RDCs) Restraints on orientation:

• 13Cα chemical shifts
• 13Cβ chemical shifts
• 13CO chemical shifts
• 1Hα chemical shifts
• 1HN chemical shifts
• 3JHNHα couplings
• 1H-15N RDCs
• 15N R2
• Nitroxide spin-label PREs
• ATCUN PREs
• NOEs
• O2-induced 13C paramagnetic shifts
• Tryptophan indole solvent accessibility

Experimental Restraints

How are structures traditionally solved by NMR? How are structures traditionally solved by NMR?

• 13Cα chemical shifts
• 13Cβ chemical shifts
• 13CO chemical shifts
• 1Hα chemical shifts
• 1HN chemical shifts
• 3JHNHα couplings
• 1H-15N RDCs
• 15N R2
• Nitroxide spin-label PREs
• ATCUN PREs
• NOEs
• O2-induced 13C paramagnetic shifts
• Tryptophan indole solvent accessibility

Simulated Annealing: Experimental Restraints

Molecular dynamics simulation and energy minimization

Structure determination of protein complexes Structure determination of protein complexes

traditionally uses simulated annealing as well

Simulated annealing is based on heuristics Simulated annealing is based on heuristics

Stochastic search

Simulated annealing is based on heuristics Simulated annealing is based on heuristics

Stochastic search Simulation & Minimization

Simulation & Minimization

Simulated annealing is based on heuristics Simulated annealing is based on heuristics

Stochastic search Convergence not guaranteed

Protein complexes are composed of subunits Protein complexes are composed of subunits

Homodimers have 2 identical subunits Homo-oligomers have n identical subunits

Structure determination of protein complexes Structure determination of protein complexes

using divide and conquer instead

Divide and conquer Divide and conquer

de novo structure determination

Divide and conquer Divide and conquer

de novo structure determination Oligomeric assembly

Related work in structure determination by solution NMR Related work in structure determination by solution NMR

Chris Bailey-Kellogg, et al., 2000 Wang and Donald, 2004 Wang, Mettu, and Donald, 2006 Zeng, Tripathy, Zhou, and Donald, 2008 Zeng, et al., 2009 Zeng, Zhou, and Donald, 2011 Zeng, Roberts, Zhou, Donald, 2011 Tripathy, Zeng, Zhou and Donald, 2011 Nilges, 1993 Nilges, 1995 Nilges, et al., 1997 Meiler, et al., 2000 Fowler, et al., 2000 Tian, Valafar, and Prestegard, 2001 Herrmann, Güntert, and Wüthrich, 2002 Wedemeyer, Rohl, and Scheraga, 2002 Rieping, et al., 2007 Bardiaux, et al., 2009 Heuristic

de novo determination

Provable Potluri, et al., 2006 Potluri, et al., 2007 Martin, Yan, Bailey-Kellogg, Zhou, and Donald Protein Science, 2011 Martin, Yan, Bailey-Kellogg, Zhou, and Donald J Comp Bio, 2011

Oligomeric assembly

Wang, Lozano-Pérez, and Tidor, 1998 Wang, Bansal, Jiang, and Prestegard, 2008

* * *

polynomial time algorithms

*

Full citations for Donald lab work Full citations for Donald lab work

Bailey-Kellogg C, Widge A, Kelley JJ, Berardi MJ, Bushweller JH, Donald BR. The NOESY jigsaw: automated protein secondary structure and main- chain assignment from sparse, unassigned NMR data. J Comput Biol. 2000;7(3-4):537-58. PMID: 11108478 Martin JW, Yan AK, Bailey-Kellogg C, Zhou P, Donald BR. A geometric arrangement algorithm for structure determination of symmetric protein homo-oligomers from NOEs and RDCs. J Comput Biol. 2011 Nov;18(11):1507-23. PMID: 22035328 Martin JW, Yan AK, Bailey-Kellogg C, Zhou P, Donald BR. A graphical method for analyzing distance restraints using residual dipolar couplings for structure determination of symmetric protein homo-oligomers. Protein Sci. 2011 Jun;20(6):970-85. doi: 10.1002/pro.620. PMID: 21413097 Donald BR, Martin J. Automated NMR Assignment and Protein Structure Determination using Sparse Dipolar Coupling Constraints. Prog Nucl Magn Reson Spectrosc. 2009 Aug 1;55(2):101-127. PMID: 20160991 Wang L, Donald BR. Exact solutions for internuclear vectors and backbone dihedral angles from NH residual dipolar couplings in two media, and their application in a systematic search algorithm for determining protein backbone structure. J Biomol NMR. 2004 Jul;29(3):223-42. PMID: 15213422. Wang L, Mettu RR, Donald BR. A polynomial-time algorithm for de novo protein backbone structure determination from nuclear magnetic resonance

• data. J Comput Biol. 2006 Sep;13(7):1267-88. PMID: 17037958.

Zeng J, Tripathy C, Zhou P, Donald BR. A Hausdorff-based NOE assignment algorithm using protein backbone determined from residual dipolar couplings and rotamer patterns. Comput Syst Bioinformatics Conf. 2008;7:169-81. PMID: 19642278. Zeng J, Boyles J, Tripathy C, Wang L, Yan A, Zhou P, Donald BR. High-resolution protein structure determination starting with a global fold calculated from exact solutions to the RDC equations. J Biomol NMR. 2009 Nov;45(3):265-81. Epub 2009 Aug 27. PMID: 19711185 Zeng J, Zhou P, Donald BR. Protein side-chain resonance assignment and NOE assignment using RDC-defined backbones without TOCSY data. J Biomol NMR. 2011 Aug;50(4):371-95. Epub 2011 Jun 25. PMID: 21706248 Zeng J, Roberts KE, Zhou P, Donald BR. A Bayesian approach for determining protein side-chain rotamer conformations using unassigned NOE

• data. J Comput Biol. 2011 Nov;18(11):1661-79. Epub 2011 Oct 4. PMID: 21970619

Tripathy C, Zeng J, Zhou P, Donald BR. Protein loop closure using orientational restraints from NMR data. Proteins. 2011 Sep 26. doi: 10.1002/prot.23207. PMID: 22161780 Potluri S, Yan AK, Chou JJ, Donald BR, Bailey-Kellogg C. Structure determination of symmetric homo-oligomers by a complete search of symmetry configuration space, using NMR restraints and van der Waals packing. Proteins. 2006 Oct 1;65(1):203-19. PMID: 16897780. Potluri S, Yan AK, Donald BR, Bailey-Kellogg C. A complete algorithm to resolve ambiguity for intersubunit NOE assignment in structure determination of symmetric homo-oligomers. Protein Sci. 2007 Jan;16(1):69-81. PMID: 17192589

Protein complexes tend to be symmetric Protein complexes tend to be symmetric

50–70% of known complexes are symmetric homo-oligomers

Levy, et.al. Assembly reflects evolution of protein complexes. Nature, 453(7199):1262–1265, June 2008.

Protein complexes tend to be symmetric Protein complexes tend to be symmetric

50–70% of known complexes are symmetric homo-oligomers

Levy, et.al. Assembly reflects evolution of protein complexes. Nature, 453(7199):1262–1265, June 2008.

Protein oligomers with cyclic symmetry Protein oligomers with cyclic symmetry

cyclic symmetry (C5) (C3)

Benefits of symmetry Benefits of symmetry

cyclic symmetry (C5) (C3)

If the subunit structure is known, the

• ligomer structure is completely

specified by the symmetry axis

Just need orientation and position relative to subunit

Oligomeric assembly using DISCO Oligomeric assembly using DISCO

Assemble oligomer using the symmetry Compute symmetry axis orientation Compute symmetry axis position

Oligomeric assembly using DISCO Oligomeric assembly using DISCO

Assemble oligomer using the symmetry Compute symmetry axis orientation Compute symmetry axis position

Geometric restraints on protein structure Geometric restraints on protein structure

• Residual Dipolar

Couplings (RDCs) Restraints on orientation:

Principal order frame

Geometric restraints on protein structure Geometric restraints on protein structure

• Residual Dipolar

Couplings (RDCs) Restraints on orientation:

Principal order frame

Geometry of RDC curves Geometry of RDC curves

RDC measurement (scalar) Bond orientation (vector) Alignment tensor (matrix)

Geometry of RDC curves Geometry of RDC curves

RDC measurement (scalar) Bond orientation (vector) Alignment tensor (matrix) Rotation Scaling

Geometry of RDC curves Geometry of RDC curves

RDC measurement (scalar) Bond orientation (vector) Alignment tensor (matrix) Rotation Scaling After rotation:

Geometry of RDC curves Geometry of RDC curves

RDC measurement (scalar) Bond orientation (vector) Alignment tensor (matrix) Rotation Scaling After rotation:

Geometry of RDC curves Geometry of RDC curves

RDC measurement (scalar) Bond orientation (vector) Alignment tensor (matrix) Rotation Scaling After rotation: Quadric surface!

Solving for symmetry axis orientation Solving for symmetry axis orientation

Molecular frame Principal order frame (defined by )

Solving for symmetry axis orientation Solving for symmetry axis orientation

Molecular frame

is unknown

Principal order frame (defined by )

Solving for symmetry axis orientation Solving for symmetry axis orientation

Molecular frame

is unknown

Principal order frame (defined by )

Can solve for (and ) with at least 5 RDCs

Solving for symmetry axis orientation Solving for symmetry axis orientation

Molecular frame Principal order frame z-axis of alignment tensor is parallel to the symmetry axis

is unknown Can solve for (and ) with at least 5 RDCs

Oligomeric assembly using DISCO Oligomeric assembly using DISCO

Assemble oligomer using the symmetry Compute symmetry axis orientation Compute symmetry axis position

Geometric restraints on protein structure Geometric restraints on protein structure

• Nuclear Overhauser

Effect (NOE)

• Paramagnetic Relaxation

Enhancement (PRE)

Restraints on distance:

Solving for the symmetry axis position Solving for the symmetry axis position

Consider the geometry of an inter-subunit distance restraint:

Solving for the symmetry axis position Solving for the symmetry axis position

Consider the geometry of an inter-subunit distance restraint:

Solving for the symmetry axis position Solving for the symmetry axis position

Consider the geometry of an inter-subunit distance restraint:

Analytical solution for the green annulus Analytical solution for the green annulus

Symmetry causes uncertainty Symmetry causes uncertainty

For homo-trimers and higher, subunit assignments for distance restraints are not known Subunit ambiguity

Symmetry causes uncertainty Symmetry causes uncertainty

For homo-trimers and higher, subunit assignments for distance restraints are not known Subunit ambiguity

Encoding subunit ambiguity Encoding subunit ambiguity

Each assignment generates a constraint annulus Annuli are combined using set union

Analysis of multiple distance restraints Analysis of multiple distance restraints

DISCO computes the Maximally Satisfying Regions by analyzing the arrangement of the unions of annuli

Efficient computation of the MSRs Efficient computation of the MSRs

Compute the arrangement from the circular curves bounding the annuli in CGAL

Efficient computation of the MSRs Efficient computation of the MSRs

Compute face depths using BFS Search dual graph

Efficient computation of the MSRs Efficient computation of the MSRs

Efficient computation of the MSRs Efficient computation of the MSRs

Efficient computation of the MSRs Efficient computation of the MSRs

Efficient computation of the MSRs Efficient computation of the MSRs

Efficient computation of the MSRs Efficient computation of the MSRs

Polynomial time computation of the MSRs Polynomial time computation of the MSRs

Let n be the number of distance restraints Let a be the max number of assignments per distance restraint There are O(an) curves in the arrangement

Search dual graph

Polynomial time computation of the MSRs Polynomial time computation of the MSRs

O(a2n2) faces O(a2n2) edges Let n be the number of distance restraints Let a be the max number of assignments per distance restraint There are O(an) curves in the arrangement

Search dual graph

Expected O(a2n2) time

Polynomial time computation of the MSRs Polynomial time computation of the MSRs

O(a2n2) nodes O(a2n2) edges O(a2n2) faces O(a2n2) edges Let n be the number of distance restraints Let a be the max number of assignments per distance restraint There are O(an) curves in the arrangement

Search dual graph

Expected O(a2n2) time

Polynomial time computation of the MSRs Polynomial time computation of the MSRs

Compute face depths using BFS in expected O(a2n2) time O(a2n2) nodes O(a2n2) edges O(a2n2) faces O(a2n2) edges Let n be the number of distance restraints Let a be the max number of assignments per distance restraint There are O(an) curves in the arrangement

Search dual graph

Expected O(a2n2) time

Polynomial time computation of the MSRs Polynomial time computation of the MSRs

Compute face depths using BFS in expected O(n2) time O(n2) nodes O(n2) edges O(n2) faces O(n2) edges Let n be the number of distance restraints Let a be bounded by a small constant There are O(n) curves in the arrangement

Search dual graph

Expected O(n2) time

Oligomeric assembly using DISCO Oligomeric assembly using DISCO

Assemble oligomer using the symmetry Compute symmetry axis orientation Compute symmetry axis position

Oligomeric assembly using DISCO Oligomeric assembly using DISCO

Compute symmetry axis position

DISCO guarantees:

• Compute all satisfying symmetry axis positions
• Runs in polynomial time

Validation using experimental data Validation using experimental data

• Diacylglycerol Kinase

– DAGK – Membrane protein Homotrimer 121x3 residues 67 orientational restraints 23 distance restraints

Van Horn et al., 2009

Ground Truth aka Reference Structure

PDB: 2KDC Model 1

Symmetry axis orientations computed by DISCO Symmetry axis orientations computed by DISCO

Using 67 restraints on orientation Using 67 restraints on orientation

Symmetry axis positions computed by DISCO Symmetry axis positions computed by DISCO

Using 23 uncertain distance restraints Using 23 uncertain distance restraints

Individual structure evaluation Individual structure evaluation

Ensemble of structures computed by DISCO Ensemble of structures computed by DISCO

Reference DISCO

All structures within 1.5 Å backbone RMSD

Acknowledgements Acknowledgements

We are very grateful for funding from:

The National Institutes of Health

DISCO is open source software