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Solution NMR Structure Calculation and Automated NOESY Spectral Analysis using RADAR

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Title: Solution NMR Structure Calculation and Automated NOESY Spectral Analysis using RADAR


1
Solution NMR Structure Calculation and Automated
NOESY Spectral Analysis using RADAR
  • Torsten Herrmann
  • Eidgenössische Technische Hochschule Zürich,
    Switzerland
  • The Scripps Research Institute, CA, USA

2
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 ...
6
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

7
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.

9
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
10
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.
11
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 ??
12
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

13
Automated NMR structure determination
  • Automated NOESY spectral analysis using RADAR

14
Content
  • Overview and motivation
  • CANDID algorithm
  • ATNOS algorithm
  • Criteria to judge correctness of result
  • Proof of principle

15
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
16
RADAR incorporates the analysis of the raw NMR
data into the process of automated NMR structure
determination.
17
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

18
CANDID Combined Automated NOESY Assignment and
Structure Determination Module
  • NOE assignment problem
  • Ambiguous distance constraints
  • Network-anchored assignment
  • Constraint combination

19
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
20
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
21
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

22
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
23
Motivation for ambiguous distance constraints
24
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

25
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

26
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).

27
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.
28
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.

29
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.

30
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
31
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
32
Effect of network-anchoring and constraint
combination
Constraint Combination

-
-

Network-anchoring

-

-
cycle 1
cycle 7
33
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.

34
ATNOSAutomated signal recognition for NOESY
spectra
  • Overview and motivation
  • New concepts for NOESY peak picking
  • Results

35
(No Transcript)
36
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

37
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.

38
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

39
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)
40
ATNOS/CANDID cycles
cycle 1
cycle 2
cycle 7
reference
41
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

42
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

43
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.

44
Output criteria
  • Target function
  • TFcycle1 smaller than 200Å2
  • TFcycle7 smaller than 2Å2
  • RMSD
  • RMSDcycle1 smaller than 3Å
  • RMSDdrift
  • RMSDdrift smaller than RMSD

45
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)

46
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.

47
Acknowledgment
  • Peter Güntert
  • Francesco Fiorito
  • Kurt Wüthrich

48
THE END
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