NMR Peak Assignment : Better Algorithm

1
NMR Peak Assignment Better Algorithm

• Frederick Vizeacoumar
• Tommy Chu

2
Agenda

• Introduction
• Problem Definition
• Previous Works
• Input Parameters
• Design
• Results
• HSQC and Survey on Dipolar Coupling
• Conclusion

3
Agenda

• Introduction
• Problem Definition
• Previous Works
• Input Parameters
• Design
• Results
• HSQC and Survey on Dipolar Coupling
• Conclusion

4
Introduction

• Nuclear Magnetic Resonance (NMR)

5
Introduction

• Nuclear Magnetic Resonance (NMR)
• Use the strong magnetic wave to align nuclei
  (isotopes).
• When this spin transition occurs, the nuclei are
  said to be in resonance with the applied
  radiation.

6
NMR measurement

• Chemical Shift
• ppm
• Electrons in the molecule have small magnetic
  fields
• When applied string magnetic field, electrons
  tend to oppose the applied field.
• NMR Spectrum

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NMR spectroscopy

• Study the physical, chemical, and biological
  properties.
• Problem
• Identified sequence.
• Unknown (complete) structure.
• Known basic structure.
• Unknown the structure corresponding to AAs.

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Procedure to determine protein structure using NMR

• Three steps
• Data generation
• Involves corresponding resonance peaks to AA and
  forming spin system.
• Data interpretation
• Involves matching spin system to amino acids
  providing inter and intra AA distance and angle.
• NMR Structure calculation
• Involves structure determination using Molecular
  Dynamics (MD) Energy Minimization (EM).

9
Agenda

• Introduction
• Problem Definition
• Previous Works
• Input Parameters
• Design
• Results
• HSQC and Survey on Dipolar Coupling
• Conclusion

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Project -- Data Interpretation

• Primary Goal
• (Better) Automated Peak Assignment.
• Steps for doing this data interpretation
• Map resonance peaks from different NMR spectra to
  same residue.
• Identify adjacency relationship.
• Assign the segments to the protein sequence.
• Problem with existing Algorithms
• Low accuracy.
• High time complexity.

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Peak Assignment

• Assignment procedure need to address two crucial
  information
• Different AA types have different distribution of
  spin system.
• The adjacency info, scalar coupling, between spin
  systems are obtained by identifying their common
  resonance frequencies.
• Enhancement techniques
• HSQC
• Dipolar coupling

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Agenda

• Introduction
• Problem Definition
• Previous Works
• Input Parameters
• Design
• Results
• HSQC and Survey on Dipolar Coupling
• Conclusion

13
Previous Works

• 1 formulated NMR assignment problem to a
  Constraint Bipartite Matching (CBM) problem.
• 1 proposed a naïve (two layer) algorithm.
• 1,6 proved D-string CBM is NM-hard.
• 6 proposed two approximation algorithm.
• 5 applied the branch-and-bound techniques.
• 9 attempted to solve CBM using extensive search
  techniques in artificial intelligence.

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Bipartite Matching

• G(U ? V,E)
• U is sequence of AA
• V is the set of Spins
• U ? V ?
• G(U ? V, M) ? G i.e. m ? M cannot share a same
  vertex.

Protein Sequence
Spin Systems
A
3
G
2
C
1
T
4
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Bipartite Matching

• G(U ? V,E)
• U is sequence of AA
• V is the set of Spins
• U ? V ?
• G(U ? V, M) ? G i.e. m ? M cannot share a same
  vertex

Protein Sequence
Spin Systems
A
3
G
2
C
1
T
4
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Bipartite Matching

• Perfect Matching
• All node need to be covered by a match.
• Weighted Bipartite Matching
• Each edge associated with a weight.
• Maximum (Perfect) Weighted Bipartite Matching
• Maximize the total weight for all m ? M .

Protein Sequence
Spin Systems
A
3
G
2
C
1
T
4
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Constraint Bipartite Matching

• For all segment ? V
• If (ui,vj) ? M i.e. ui ? U ? vj ? V
• Then (ui1,vj1) ? M
• D-string CBM
• Specify the problem with maximum segment size is
  D.

Protein Sequence
Spin Systems
A
3
G
2
C
1
T
4
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Two Layered Algorithm 1

• First layer
• Filter out unlikely assignments for long strings.
• Second layer
• Try all possible combinations of assignments for
  long strings to find the maximum one as the
  result.

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Approximation Algorithms 2

• 2D Approximation Algorithm
• Let M be an optimal matching on G.
• Every edges corresponding to a vertex will
  conflict with at most 2 edges in M.
• 3logD Approximation algorithm
• If the length of the longest string in V is at
  most four times the length of shortest string
• Then greedy algorithm will find a solution whose
  weight is at least 1/6 of the optimal.

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Branch and bounded algorithm

• A systematic method for solving optimization
  problems.
• Construct a search tree and apply a carefully
  selected criterion to determine which node to
  expand the search.
• Exponential time in the worst case

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AUTOASSIGN/AUTOPEAK

• 5 Major Searches
• Make strongest matches
• Allow degenerate shifts
• Extend assigned segments
• Match weaker spin systems
• Finish Assignments
• Claims to have 98 accuracy.
• Test only on RNA single strand sequence.
• Infeasible to compute using protein sequences.

22
Agenda

• Introduction
• Problem Definition
• Previous Works
• Input Parameters
• Design
• Results
• HSQC and Survey on Dipolar Coupling
• Conclusion

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Input Parameters

• Protein Sequence
• Sequence of location and AA
• Spin Systems
• Segment of chemical shift separated by comma
• Score Scheme
• A table storing the score between an AA and the
  range of chemical shift

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Example input for protein sequence

• 1 GLY
• 2 SER
• 3 VAL
• 4 GLU
• 5 GLN
• 6 ILE
• 7 SER
• 8 GLY

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Input Parameters

• Protein Sequence
• Sequence of location and AA
• Spin Systems
• Segment of chemical shift separated by comma
• Score Scheme
• A table storing the score between an AA and the
  range of chemical shift

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Example input for spin system (three segments)

• 12.5
• 13.5 ,
• 5.35
• 6.4
• 7.21 ,
• 16.1
• 17.2

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Input Parameters

• Protein Sequence
• Sequence of location and AA
• Spin Systems
• Segment of chemical shift separated by comma
• Score Scheme
• A table storing the score between an AA and the
  range of chemical shift

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Example input for score scheme

• 5
• GLY
• SER
• VAL
• GLU
• GLN
• 4
• 0 5
• 5 10
• 10 15
• 15 20

• 1 5 2 4
• 2 1 4 0
• 1 2 3 4
• 2 4 1 3
• 2 3 3 6

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Agenda

• Introduction
• Problem Definition
• Previous Works
• Input Parameters
• Design
• Results
• HSQC and Survey on Dipolar Coupling
• Conclusion

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Implemented Design

• CBM Two layer approximation algorithm
• As mentioned earlier we use the bipartite graph
  matching problem with some constraints to solve
  the peak assignment problem
• Key idea is the multi-dimensional NMR spectra
  contains inter residual peaks that convey the
  connectivity information between residues
• We match the inter- and intra residual peaks
  using their chemical shift making the
  connectivity information straightforward

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CBM Two layer Approximation

• layerOne( sequence, spin, score, threshold)
• for every segment Ui in spin do
• for every position Vj in the sequence do
• if score (Ui,Vj) threshold then
• mark Vj as possible assignment
  position
• layerTwo( sequence, spin, score)
• smax -8
• for every possible legal combination set from
  layerOne
• do calculate the score and call it si
• if si gt smax then
• smax si and store current position
  as final assignment

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2 Approximation Algorithm

• Key Idea is to form a Weighted Bipartite Graph
  and use it to find the matching.
• We use some restriction and constraints in
  identifying the leading innermost edge as
  explained.
• We find an innermost edge, add that with all its
  conflicting edges and take the minimum weight on
  this set and subtract it and remove the edges
  with weight 0.
• The above process is called on the new set of
  graph formed recursively to obtain feasible
  matching

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3 Log D Approximation

• The idea is if there are m different segments in
  the spin system we group these m small sets into
  overlapping groups based on some formulas
• find the score for each group and maximize the
  final score and assignment to feasible solution
• This also uses weighted bipartite graph
• As explained before this problem includes still
  more constraints in identifying there is no
  overlapping between segments.

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3 Log D Approximation

• 3 log D Approximation(Score U, Spin V)
• r lmax / lmin , where lmax and lmin are max
  and min length of
• string in V
• group V into g max(2, log4r) subsets Vi such
  that
• 4i-1 s / lmin 4i
• for every i ? 1,2, g
• cal the set Ei of edges of G incident to
  strings in Vi
• initialize Mi Ø
• while (Ei ? Ø)
• find an edge e ? Ei of maximum
  weight
• add e to Mi and delete e and
  all edges conflicting with e from Ei
• greedily extend Mi to a maximal feasible
  matching of G
• output the heaviest one among Mi

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Improved Two layer Algorithm

• The threshold value in CBM algorithm is good to
  eliminate but determination of this threshold
  value is trial and error basis.
• 6 considers 3LogD approximation is better than
  2 approximation.
• In 3 Log D approximation, the partitioning the
  subsets of segments in the spin system is based
  on the formula 4i-1 s / lmin 4i . Does this
  always give a better improvement in score ?

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Improved Two Layer Algo.

• layerOne (sequence U, spin V, score)
• for every subset Vi of the set spin system V
  do
• Ei all edges incident from Vi to U
• Mi Ø
• while (Ei ? Ø)
• find an edge e ? Ei of max weight
• add e to Mi and delete e and all
  conflicting edges with e from Ei
• mark positions in sequence set for
  corresponding Mi set as possible
• assignment

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Improved Two Layer Algo.

• layerTwo (sequence, spin, score, possible
  assignment)
• smax -8
• for every possible assingment position in U do
• calculate the score and call it si
• if si gt smax then
• smax si and store current position
  as final assignment
• If there are m groups of spin segments, then
  total number
• of search would be 2m-1 .

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Agenda

• Introduction
• Problem Definition
• Previous Works
• Input Parameters
• Design
• Results
• HSQC and Survey on Dipolar Coupling
• Conclusion

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Current Results
40
Expected Results
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Agenda

• Introduction
• Problem Definition
• Previous Works
• Input Parameters
• Design
• Results
• HSQC and Survey on Dipolar Coupling
• Conclusion

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Interface with HSQC

• Main work in Hetero-nuclear Single Quantum
  Correlation involves in identifying the NH amide
  side chain.
• Basically it is a biological experiments which
  yields data related to the NHx group directly
  attached to proton
• All AA produces one signal for N-H amide group
  (except proline) based on its pH value and the
  chemical shift exhibited, the NH side chain is
  visible.

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HSQC cont

• Folded proteins or protein domains display a
  broad distribution of NMR frequencies resulting
  good spread-out.
• Unfolded proteins do exhibit same resulting in
  overlapping frequencies.
• HSQC technique adds ligand shifting signals which
  changes the overlapping.
• This process also involves few calculation that
  results in a better spin system values.

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Survey on Dipolar Coupling

• Unlike HSQC enabling to identify the NH amide
  side chain, Dipolar coupling identifies the Ca -
  Cb side chain.
• Provides long range info which is lacking in NMR
  experiments
• This is also an biological experimental process
  to improve the spin system which is the main part
  in identifying the protein structure.
• The results of this experiment enables us to
  determine the side chain rotamer states using
  rotamer prediction algorithm.

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Dipolar Coupling cont

• NMR solutions structures are determined primarily
  using restraints derived from nuclear overhauser
  effects. This derivation yields to the
  proton-proton distance less than 5Å. Hence for
  elongated molecules, NMR is not efficient.
• Elongated molecules are present in the helical
  structure of the protein sequence.
• This local error on elongated molecules tends to
  add over the length resulting in poor protein
  structure determination.

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Dipolar Coupling Cont

• The size of dipolar coupling observed bet 2
  nuclei is given by
• DPQ(q,f)DaPQ(3cos2q 1)1.5 R sin2q cos 2f
• Where R is rhombicity (shape of molecule)
• The value obtained here helps to observe
  elongated molecules as well

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Agenda

• Introduction
• Problem Definition
• Previous Works
• Input Parameters
• Design
• Results
• HSQC and Survey on Dipolar Coupling
• Conclusion

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Conclusion

• Major part of NMR technique involves in peak
  assignment process.
• The main goal of our project in finding the
  better algorithm lead us to think about improving
  the matching and score scheme rather than the
  improvement on the computational process of the
  algorithms.
• From the already existing algorithm, we found
  that if there are m segments, a reduces amount of
  subsets was taken and a better matching was done.
  We thought it would be nice to look if all the
  possible subsets are taken and observed for a
  better match score value.

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Future Directions

• As given in the CBM two layer algorithm, if the
  NMR experiment could someway help in identifying
  the threshold value, then in our improved
  version, the number of checks could be reduced
  with this threshold value.
• Extracting the results from HSQC experiment and
  with some algorithms developed for this data set,
  we can get a better spin system for the NH amide
  side chain and improve our assignment process
• Using the data from the Dipolar coupling to
  identify the Ca - Cb side chain would get us even
  better spin segments. This might yield to a
  better protein structure determination.

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Acknowledgements

• Our Sincere thanks to
• Dr. Guohui Lin, Professor, U of A.
• Mr. Xiang Wan, Ph.D. Student, U of A.
• Mr. Jon McCall, Spectrum Research LLC.
• Dr. Gaetano T. Montelione, Rutgers Univ.

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