Solution NMR Structure Calculation and Automated NOESY Spectral Analysis using RADAR

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Solution NMR Structure Calculation and Automated
NOESY Spectral Analysis using RADAR

• Torsten Herrmann
• Eidgenössische Technische Hochschule Zürich,
  Switzerland
• The Scripps Research Institute, CA, USA

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Content

• Protein structure determination by NMR
• Conformational constraints
• Hybrid energy function
• Algorithms for 3D structure calculation
• Structure calculation using DYANA
• Molecular dynamics simulation
• Torsion angle dynamics (TAD)
• Distance information from NOEs
• Automated structure determination using RADAR
• NOE assignment problem
• NOE assignment with CANDID
• NOE identification with ATNOS
• Criteria to judge correctness of resulting 3D
  structure

3
Protein Structure Determination by NMR
Protein Sample
NMR spectroscopy
Processing of NMR data
Resonance assignment
Conformational constraints
3D protein structure
Structure analysis refinement
4
Conformational constraints

• NMR provides indirect information about 3D
  structure
• chemical shifts ? torsion
  angles
• coupling constants ? torsion angles
• NOEs ? ? interproton
  distances
• residual dipolar couplings ? bond orientation
• NMR data describes local conformation of the
  protein. The dense network of constraints yields
  the protein 3D structure.

5
Hybrid energy function

• Structure calculation minimization of hybrid
  energy function (target function) which
  incorporates
• experimental NMR data
• a priori information (force field)

Ehybrid ? wi Ei wbondEbond
wangleEangle wdihedral Edihedral
wimproperEimproper wvdWEvdW
wNOEENOE wtorsionEtorsion ...
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Algorithms for 3D structure calculation

• Metrix matrix distance geometry
• DISGEO
• Variable target function approach
• DISMAN, DIANA
• Simulated annealing using cartesian coordinates
• XPLOR
• Simulated annealing using torsion angles
• XPLOR, CNS, DYANA

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Solution NMR structure calculation

• DYANA torsion angle dynamics algorithm

8
Molecular dynamics simulation

• MD numerically solves Newtons equation of motion
  in order to obtain a trajectroy for the molecular
  system.
• Standard MD tries to simulate the behaviour of
  a real physical system as close as possible.
• MD used for NMR structure calculation searches
  the conformational space of the protein for the
  3D structure that fulfills all the restraints
• ? simulated annealing using hybrid energy
  function
• Important difference of MD compared to gradient
  minimization of a target function is the presence
  of kinetic energy.

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Minimization by molecular dynamics

• MD solves Newtons equation of motion A
  trajectory is obtained by numerical calculation
  of the coordinates and velocities using small
  time steps ?t.
• MD can overcome local energy barriers using Ekin
• Temperature control and variation defines
  protocol for minimization of the hybrid energy
  function by simulated annealing.

E
E
E
x
x
x
High temperature
Low temperature
Energy landscape of protein
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Torsion angle dynamics (TAD)

• Newtons equation in generalized coordinates, ?1,
  ..., ?n

Cartesian coordinates
Quantity
Torsion angle space
Degrees of freedom
n torsion angles ?1, ..., ?n
3N coordinates x1, ..., xN
?
?
Lagrange equations dt(?? k L) ?? k L 0 L
Ekin Epot
Newtons equations mi i -?Epot
Equation of motion
.

?
x
? n3 (linear equations) ? n (tree structure)
Proportional to N
Computational complexity
Exploiting the tree structure of proteins, the
computational cost for TAD is proportional to the
system size.
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Simulated annealing protocol

• Structure calculation is started from a
  conformation with all torsion angle
• treated as independent, uniformly distributed
  random variables
• Short minimization 100 conjugated gradient steps
  at target level 3 100 conjugated minimization
  steps at target level ?
• TAD at constant high temperature 1/5 of all
  steps
• TAD with slow cooling close to zero temperature
  4/5 of all steps
• Incorporation of all hydrogen atoms in check for
  steric repulsion. 100 conjugated gradient
  steps, followed by 100 TAD at T 0.
• Final minimization consisting of 1000 conjugated
  gradient steps.

Temperature T
Time steps ?t
Torsion angle changes ??
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Distance information from NOEs

• Conversion of NOE into distance information
• Isolated spin approximation
• NOEAB ? Ccal
  dAB-6
• Calibration constant Ccal can be derived from
  reference distances
• Ccal
  NOEref / dref6
• Reference distance can either be
  a covalently fixed distance or
• an average distance dref ?
  ?1/N?dk-6 ?1/6
• Treatment of NOE information during simulated
  annealing
• Use of upper distance bound, b, instead of fixed
  distance
• ENOE ?(dABstruct
  b) (dABstruct b)2
• Lower bound is given by vdW repulsion

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Automated NMR structure determination

• Automated NOESY spectral analysis using RADAR

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Content

• Overview and motivation
• CANDID algorithm
• ATNOS algorithm
• Criteria to judge correctness of result
• Proof of principle

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Automated NOESY spectral analysis
Protein sequence Chemical shift list NOESY spectra

• Automated methods
• more efficient
• more exhaustive data evaluation
• more objective
• Iterative process
• all but the first cycle use the intermediate
  structures from the preceding cycle
• Correctness of cycle 1 is crucial for reliablity
  of automated approach

NOE identification
NOE assignment
Structure calculation
Assigned NOESY spectra 3D protein structure
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RADAR incorporates the analysis of the raw NMR
data into the process of automated NMR structure
determination.
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RADARRaw data analysis in NMR
RADAR incorporates and tightly merges the
functionalities of the original algorithms ATNOS
and CANDID. So far, ATNOS and CANDID are
implemented as subroutines of the DYANA torsion
angle dynamics algorithm. An autonomous version,
named RADAR, is in preparation.

• ATNOS for automated NOESY peak picking and NOE
  signal identification
• CANDID for automated NOE assignment

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CANDID Combined Automated NOESY Assignment and
Structure Determination Module

• NOE assignment problem
• Ambiguous distance constraints
• Network-anchored assignment
• Constraint combination

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NOE assignment problem

• Experimental incertainties in the determination
  of chemical shifts and peak positions requires
  the use of chemical shift tolerance windows
  ??tol.
• ? multiple initial assignment possibilities
  based on chemical shift agreement
• ? only minority of peaks can be unambiguously
  assigned sonely based on chemical shift agreement

• Primary selection criteria for NOE assignments
  are chemical shift agreement and spatial
  proximity in 3D structure.

?1 ?A ? ??tol ?2 ?B1 ? ??tol ?2 ?B2
? ??tol
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Chemical shift-based assignment

• 2D NOESY spectrum
• Peaks with 1 assignment N(1) N (1 - p)2n-2
  ? Nexp(-2np)
• Peaks with 2 assignments N(2)
  N2p(n-1)(1-p)2n-3 ? 2npN(1)
• 
  N number of cross peaks
• 
  n number of protons
• 
  p 2? tol/?? probability of finding a 1H
  chemical shift within
• 
  ?-? tol, ??tol, under
  the assumption that shift are
• 
  equally distributed over
  spectral width ??.

N(1)
N(2)
N
N
0.01
0.02
ppm
0.01
0.02
ppm
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3D structure-based assignment

• Assignment ambiguity can be resolved if all but
  one initial assignment possibility correspond to
  proton-proton distances larger than the maximal
  distance dmax for which NOE may be observed.
• Assuming that the protons are evenly distributed
  in a spherical-shaped protein with radius R, the
  probability that two randomly selected protons
  are closer than dmax to each other is given by
• 
  p (dmax/R)3
• Example dmax 5Å, R 15Å ? p 4
• 96 of peaks with 2 assignments can be
  resolved by 3D structure
• Unique assignments Nunique N(1) (1-p)N(2)
  (1-p)2N(3) ...
• ? Nunique
  lt N

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Ambiguous distance constraints

• A NOESY cross peak with a single initial
  assignment (n1) gives rise to a conventional
  upper distance constraint.
• A NOESY cross peak with initial assignments (ngt1)
  gives rise to an ambiguous distance constraint.

deff ? ??dk6?1/6 ? b
b upper distance bound dk distance for
assignment possibility k Sums run over all
assignment possibilities
Nilges et al., 1997, J. Mol. Biol. 269, 408-422
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Motivation for ambiguous distance constraints
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Characteristics of ambiguous distance constraints

• An ADC corresponds to the sum of individual
  contributions
• NOE ?NOEi
• An ADC will not distort the structure as long as
  the correct assignment is present among the
  initial assignments
• deff ?
  (?dk-6)-1/6 ? b
• BUT
• An ADC has reduced informational content compared
  to conventional DC
• ? reduce initial assignment possibilities
• An ADC can not reduce the effect of an artifact
  DC
• ? detect or at least reduce impact of
  retained wrong ADC

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Ranking of assignment possibilities

• A volume contribution, Ci, is attributed to each
  initial assignment of a peak
• NOE ? CiNOE, 0 ?
  Ci ? 1

• An initial assignment is retained only if Ci gt
  Cmin.

Ci c Pics Ficov Fitrans Finetwork
Pi3D

• Pcs Chemical shift agreement
• Fcov Compatibility with covalent
  polypeptide structure
• Ftrans Presence of symmetry-related cross
  peaks in 3D NOESY
• Fnetwork Network-anchored assignment
• P3D Compatibility with intermediate 3D
  structure (cycle gt 1)
• c normalization constant, chosen such
  that ?Ci 1

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Network-anchored assignment

• Network-anchoring exploits the fact that any
  network of correct NOE peak assignments forms a
  self-consistent set.
• Each initial assignment is weighted by the extent
  to which it can be embedded into the network
  formed by all other NOE peak assignments.
• Network-anchoring evaluates the self-consistency
  of NOE assignments independent of knowledge on
  the 3D structure, thus compensates for the
  absence of 3D structural knowledge at the outset
  of a de novo structure calculation (cycle 1).

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Network-anchored assignment

• Calculation of weighting factor, Finetwork, for
  an initial assignment i that connects atoms A and
  B

Triangular connections ABX Find NOE peaks with
an initial assignment AX or BX, where atom X is
maximally one residue apart from A or B.
FABnetwork ? CAX CBX where CAX and CBX are
the volume contributions for the assignment AX
and BX.
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Filtering of assignment possibilities

• Elimination of initial assignments by retaining
  only assignment possibilities with a certain
  volume contribution Ci gt Cmin. Minimal required
  volume contribution, Cmin, is a function of the
  cycles 1, ..,7.
• Network-anchored assignment dramatically reduces
  the assignment ambiguity at the outset of a
  structure calculation (cycle 1).
• Loss of conformational information, as intrinsic
  feature of ADC, is reduced by network-anchoring.
  Majority of peaks have at most 2-3 retained
  initial assignments.

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Elimination of erroneous peaks

• Network-anchoring (cycle 1, 2, ..., 7)
• If none of the initial assignments can be
  reliably embedded into the network of NOEs formed
  by all other NOE peaks, then this peak is
  considered as artifact and discarded from further
  considerations.
• ? Noise analysis can be started prior to any
  structure calculation.
• Compatibility with 3D structure (cycle 2, ... ,
  7)
• If an ambiguous distance constraints is
  violated by more than a user-defined threshold,
  dcut, in more than a user-defined percentage of
  the conformers, then this peak is considered as
  artifact.

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Constraint combination

• CC reduces the impact of artifact NOE upper
  distance constraints by combining the assignments
  for two or several peaks into a single upper
  distance constraint.

NMR structure using 2 single constraints
NMR structure using CC
Native protein
D
D
C
D
C
C
A
B
B
A
B
A
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Constraint Combination
1 peak with assignment
1 ambiguous distance constraint
A1B1
A1B1
A2B2
A2B2
2 (unrelated) peaks
1 combined ambiguous distance constraint
A1B1
C1D1
A1B1
A2B2
A2B2
C2D2
C1D1
C2D2
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Effect of network-anchoring and constraint
combination
Constraint Combination

-
-

Network-anchoring

-

-
cycle 1
cycle 7
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De novo structure determinations using CANDID

• Proof of principle for the CANDID approach was
  established by comparing the resulting protein
  structures with those obtained by interactive
  procedures.
• The potential of CANDID is further supported by
  in the meantime de novo structure determination
  of about 20 proteins.

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ATNOSAutomated signal recognition for NOESY
spectra

• Overview and motivation
• New concepts for NOESY peak picking
• Results

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New concepts for NOESY peak picking

• Covalent polypeptide structure is used to derive
  spectrum-specific threshold parameters, e.g.,
  signal-to-noise ratio
• Multipass-filtering applied to different peak
  classes using chemical shift data and
  intermediate 3D structure

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Definition of covalent peaks

• Fixed bond lengths, bond angles and chiralities
  of the covalent polypeptide structure of the
  protein imposes NOE oberservable upper distance
  limits on certain intraresidual and sequential
  1H-1H distances.
• for example intraresidual H?-HN distance
• dmin ? dH?HN ? dmax lt 5 Å
  for all possible conformations
• Covalent peak ? Local extremum with at least one
  initial assignment to an atom pair AB with a
  covalent structure-imposed maximal distance
  dmaxAB smaller than 5 Å.

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Exploiting chemical shift knowledge

• Grid spanned by the frequency of all assigned
  atoms is overlaid onto the NOESY spectrum.
• Each grid point is considered as origin for local
  search.
• Potential NOEs are assigned and classified
• - covalent peaks and other peaks (cycle 1)
• - structural compatible peaks and all other
  peaks (cycle 2, ..., 7)

Multipass-filtering

• Filtering based on
• Peak separation
• Chemical shift agreement
• Network-anchoring
• Symmetry of NOESY
• Compatibility with 3D structure

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Criteria for NOE validation using chemical shift
data

• Chemical shift agreement

• Network-anchoring

• Compatibility with intermediate structure

wA
Atom A
Atom B
wB
(w1,w2)
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ATNOS/CANDID cycles
cycle 1
cycle 2
cycle 7
reference
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Criteria used to jugde the correctness of the
resulting 3D protein structure
Derived from experience gained during software
development and applications of the algorithms
for de novo structure determinations.

• 2 Input requirements
• 3 Output criteria

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Input requirements for succesful application of
ATNOS/CANDID

• Requirement 1
• Completness of chemical shifts
• gt 90 of non-labile and backbone amide 1H (and
  corresponding 13C/15N, in case of 3D NOESY)

• Requirement 2
• Correctness of Calibration
• Chemical shifts and NOE signal must be
  self-consistent within tolerance window ??tol.
• As reference NOE signals, all atom pairs are
  considered with covalent structure-imposed
  distance lt 5 Å.
• e.g. intraresidual H?-HN contact
• gt 85 of covalent contacts must be found in the
  NOESY

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Output criteria used to jugde the correctness of
resulting 3D protein structure

• Residual DYANA target function value
• ? TFcycle1 lt 200Å2, TFcycle7 lt 2Å2
• Root mean square deviation (RMSD) value
• ? RMSDcycle1 lt 3Å
• Evolution of RMSDdrift value
• ? The RMSD value between the mean coordinates
  of the k-th and the last cycle should be in the
  order of the RMSD value of the k-th cycle.

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Output criteria

• Target function
• TFcycle1 smaller than 200Å2
• TFcycle7 smaller than 2Å2
• RMSD
• RMSDcycle1 smaller than 3Å
• RMSDdrift
• RMSDdrift smaller than RMSD

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De novo structure determinations using
ATNOS/CANDID

• TM1816 (124 aa)
• TM1290 (116 aa)
• TM1492 (66 aa)
• En-2 (60 aa)
• En-1 (52 aa)

• GPYDs (159 aa)
• Mouse PrP (113 aa)
• Horse PrP (113 aa)
• Crotamine (42 aa)

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Conclusions

• ATNOS/CANDID enables direct feedback between the
  protein structure, the NOE assignments and the
  experimental NOESY spectra.
• ATNOS/CANDID achieves the correct fold of the
  protein already after the first cycle.
• ATNOS/CANDID results in greatly enhanced
  efficiency of de novo NMR structure
  determination.
• ATNOS/CANDID provides an objective tool for 3D
  protein NMR structure determination.

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Acknowledgment

• Peter Güntert

• Francesco Fiorito

• Kurt Wüthrich

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THE END