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Title: Presentazione Oratore


1
Presentazione Oratore
  • Romeo.Rizzi_at_dimi.uniud.it
  • cel phone 329.1780915
  • appassionato di Ottimizzazione Combinatorica,
    algoritmi,
  • operante in Biologia Computazionale
  • Ricercatore Operativo ed Informatico

2
More reliable protein NMR peak assignment via
improved 2-interval scheduling
Zhi-Zhong Chen Department of Mathematical
Sciences Tokyo Denki University Joint work with
T. Jiang, G.-H. Lin, R. Rizzi, J. Wen, D. Xu,
and Y. Xu.
http//rnc.r.dendai.ac.jp/chen/papers/pnmr.pdf
3
Agenda
  • Introduction
  • Problem Definition
  • Problem Formulation
  • Old and new results
  • Algorithms the greedy filtering technique
  • Algorithms an approximation algorithm
  • Open problems
  • Biography

4
Agenda
  • Introduction
  • Problem Definition
  • Problem Formulation
  • Old and new results
  • Algorithms the greedy filtering technique
  • Algorithms an approximation algorithm
  • Open problems
  • Biography

5
Introduction
  • Nuclear Magnetic Resonance (NMR)

6
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.

7
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

8
NMR spectroscopy
  • Study the physical, chemical, and biological
    properties.
  • Problem
  • Identified sequence.
  • Unknown (complete) structure.
  • Known basic structure.
  • Unknown the structure corresponding to AAs.

9
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).

10
Agenda
  • Introduction
  • Problem Definition
  • Problem Formulation
  • Old and new results
  • Algorithms the greedy filtering technique
  • Algorithms an approximation algorithm
  • Open problems
  • Biography

11
A Problem of Data Interpretation
  • 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.

12
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.

13
The NMR spectral peak assignment Problem
FID signal
1-D NMR spectral
14
The NMR spectral peak assignment Problem
2-D spectral
1-D spectral
An isolated spin system
15
The NMR spectral peak assignment Problem
correct assignment
16
The NMR spectral peak assignment Problem
A protein a sequence of amino acids
Given
ACVSANDLLEDAVNFGAWEKLSDNWWOQSWERDDSFDMSDFAQLL
Segments of spin systems generated from the
protein
Output A maximum-likelihood assignment of
the segments to contiguous amino acids.
17
Agenda
  • Introduction
  • Problem Definition
  • Problem formulation
  • Old and new results
  • Algorithms the greedy filtering technique
  • Algorithms an approximation algorithm
  • Open problems
  • Biography

18
The interval scheduling problem
Given
A single machine M,
?job j ?time unit u p( j, u) the profit of
starting
executing Job j at time unit u
Output A scheduling that maximizes the total
profit of executed jobs.
19
The k-interval scheduling problem
The special case of the interval scheduling
problem where each job requires at most k time
units.
The 1-interval scheduling problem is exactly the
maximum weight bipartite matching problem.
Chen et al., 2002 ?k?2 The k-interval
scheduling problem is APX-hard, even if the
processing time of each job is 1 or 2 and the
profit of executing a job is proportional to the
processing time of the job.
20
Relationship between the two types of problems
The interval scheduling problem

The NMR spectral peak assignment problem
?k
21
Agenda
  • Introduction
  • Problem Definition
  • Problem Formulation
  • Old and new results
  • Algorithms the greedy filtering technique
  • Algorithms an approximation algorithm
  • Open problems
  • Biography

22
Best known approximation algorithms
Bar-Noy et al., 2001 The interval scheduling
problem has a poly-time 2-approximation
algorithm.
Open question Is there a poly-time
r-approximation algorithm for the interval
scheduling problem with r lt 2 ?
Chen et al., 2002 There is a 1.7778-approximatio
n algorithm for the special case of the
2-interval scheduling problem where profits are
proportional to length of jobs.
23
New results
  • A poly-time (13 / 7)-approximation algorithm for
  • the 2-interval scheduling problem.
  • A new efficient heuristic (namely,
  • Greedy filtering the above algorithm)
  • for the NMR spectral peak assignment problem
  • that outperforms the previous best.

24
Agenda
  • Introduction
  • Problem Definition
  • Problem Formulation
  • Old and new results
  • Algorithms the greedy filtering technique
  • Algorithms an approximation algorithm
  • Open problems
  • Biography

25
Greedy filtering
ACVSANDLLEDAVNFGAWEKLSDNWWOQSWERDDSFDMSDFAQLLKCVY
TRAKSLDLSKGTE




26
Agenda
  • Introduction
  • Problem Definition
  • Problem Formulation
  • Old and new results
  • Algorithms the greedy filtering technique
  • Algorithms an approximation algorithm
  • Open problems
  • Biography

27
The (13 / 7)approximationalgorithm
  • Very complicated.
  • It consists of four algorithms and
  • outputs the best scheduling returned by them.
  • The main tool in the design
  • maximum weight bipartite matching
  • careful manipulation of the input.

28
The idea behind Algorithm 1
The given time interval
Partition into basic intervals
Partition 1
a basic interval (3 time units)
only the first and the last may have lt3 time
units
29
Algorithm 1constrained scheduling
The given time interval
The given time interval
Partition into basic intervals
Partition 1
The constrained interval scheduling problem for
Partition 1 ? Execute at most one job within
each basic interval. ? Each executed job must
finish within one basic interval. ? Maximize the
total profit of executed jobs.
This constrained problem can be reduced to the
maximum weight bipartite matching problem!
30
Algorithm forconstrained scheduling
The given time interval
The given time interval
Partition into basic intervals
Partition 1
Step 1. Construct an edge-weighted
bipartite graph.
31
Algorithm forconstrained scheduling
The given time interval
The given time interval
Partition into basic intervals
Partition 1
The given set of jobs
Purple profit 1 Blue profit 2 Red
profit 6 Green profit 3
Step 2. Remove invalid edges.
32
Algorithm forconstrained scheduling
The given time interval
The given time interval
Partition into basic intervals
Partition 1
The given set of jobs
Purple profit 1 Blue profit 2 Red
profit 6 Green profit 3
Step 3. Compute a maximum-weight
bipartite matching.
33
The idea behind Algorithm 1
The given time interval
The given time interval
Partition into basic intervals
Partitions 1, 2, 3
Three constrained interval scheduling problems
for them.
Obtain three constrained schedulings in poly-time.
The best among the three constrained schedulings
is good!
34
The idea behind Algorithm 1
The given time interval
The given time interval
Partition into basic intervals
Partitions 1, 2, 3
The best among the three constrained schedulings
achieves a total profit of at least p1(S) / 3
2p2(S) / 3, where S is a maximum-profit
scheduling, p1(S) (resp., p2(S)) is the total
profit of executed 1-jobs (resp., 2-jobs).
35
The idea behind Algorithm 1
Scheduled by S
The given time interval
The given time interval
Job i
Job j
Job k
Partition into basic intervals
Inheriting from S
Partitions 1, 2, 3
Algorithm 1 achieves a better-than-2 ratio if
p2(S) is relatively large compared to p1(S).
36
The main idea behind Algorithms 2 3
The given time interval
Job 4
Job 1
Job 2
Job 3
Job 5
The given set of jobs
? Obtain a maximum-profit preemptive scheduling
(i.e., each 2-job may be split into two
1-jobs) in poly-time.
? Then use the preemptive scheduling to obtain
three nonpreemptive schedulings in a novel way.
37
Computing an optimalpreemptive scheduling
The given time interval
38
Computing an optimalpreemptive scheduling
The given time interval
The given set of jobs
Purple profit 1 Blue profit 2 Red
profit 6 Green profit 3
Step 2. Compute a maximum-weight
matching Mun in the graph.
Blue profit 1 Red profit 3
39
Using Mun to classifythe given time units
The given time interval
The given set of jobs
Purple profit 1 Blue profit 2 Red
profit 6 Green profit 3
Blue profit 1 Red profit 3
40
Sketch ofAlgorithm 2
The given time interval
The given set of jobs
Purple profit 1 Blue profit 2 Red
profit 6 Green profit 3
Blue profit 1 Red profit 3
41
Sketch ofAlgorithm 2
The given time interval
Try to catch those assignments of 1-jobs in S
to isolated or border time units.
The given set of jobs
Purple profit 1 Blue profit 2 Red
profit 6 Green profit 3
For each block , isolate .
Use the idea of Algorithm 1 to compute an
interval scheduling.
Blue profit 1 Red profit 3
42
Sketch ofAlgorithm 3
The given time interval
The given set of jobs
Purple profit 1 Blue profit 2 Red
profit 6 Green profit 3
Blue profit 1 Red profit 3
43
Sketch ofAlgorithm 3
The given time interval
The given set of jobs
Purple profit 1 Blue profit 2 Red
profit 6 Green profit 3
Partition the given time interval by grouping
each block.
Blue profit 1 Red profit 3
Compute a constrained scheduling s.t. each block
hosts only one job.
44
CombiningAlgorithms 2 and 3
The given time interval
Try to catch those assignments of 1-jobs in S
to isolated or border time units.
The given time interval
Try to catch those assignments of 1-jobs in S
to isolated or internal time units.
Algorithm 2 or 3 achieves a better-than-2 ratio,
if the 1-jobs assigned to the isolated time
units by S have a relatively large total profit
compared to p(S).
45
Sketch of Algorithm 4
The given time interval
The given set of jobs
Union of odd sets gives a scheduling of some
jobs, and union of even sets gives a scheduling
of the rest.
46
CombiningAlgorithms 1 and 4
The given time interval
Algorithm 1 or 4 achieves a better-than-2 ratio,
if the 1-jobs assigned to the isolated time
units by S have a relatively small total profit
compared to p(S).
47
Agenda
  • Introduction
  • Problem Definition
  • Problem Formulation
  • Old and new results
  • Algorithms the greedy filtering technique
  • Algorithms an approximation algorithm
  • Open problems
  • Biography

48
Open problems
Is there a poly-time r-approximation
algorithm for the interval scheduling problem
with r lt 2 ?
Better fast heuristics for NMR spectral peak
assignment ?
49
Agenda
  • Introduction
  • Problem Definition
  • Problem Formulation
  • Old and new results
  • Algorithms the greedy filtering technique
  • Algorithms an approximation algorithm
  • Open problems
  • Biography

50
References
  • 1 Y. Xu, D. Xu, D. Kim, V. Olman, J.
    Razumovskaya, and T. Jiang. "Automated assignment
    of backbone NMR peaks using constrained bipartite
    matching", IEEE Computing Science Engineering,
    450-62,2002.
  • 2 C. Bartels, T. Xia, M. Billeter, P. Gu, and
    K. Wu, "The program XEASY for computer-supported
    NMR spectral analysis of biological
    acromolecules", J. Biol. NMR 6, 1-10, 1995.
  • 3 K. P. Neidig, M. Geyer, A. Go, C. Antz, R.
    Saffrich, W. Beneicke,and H. R. Kalbitzer.
    "AURELIA, a program for computer-aided analysis
    of multidimensional NMR spectra", J. Biomol. NMR
    6, 255-270, 1995.
  • 4 B. R. Brooks, R. E. Bruccoleri, B. D.
    Olafson, D. J. States, S. Swaminathan, and M.
    Karplus. "CHARMM A Program for Macromolecular
    Energy, Minimization, and Dynamics Calculations",
    J. Comp. Chem. 4, 187-217, 1983.
  • 5 G. Lin, D. Xu, Z-Z. Chen, T. Jiang, J. Wen,
    Y. Xu. "An Efficient Branch-and-Bound Algorithm
    for the Assignment of Protein Backbone NMR
    Peaks", in Proceeding of the IEEE Computer
    Society Bioinformatics Conference 2002 (CSB
    2002), P165 - 174.
  • 6 Z-Z. Chen, T. Jiang, G. Lin, J. Wen, D. Xu,
    Ying Xu. "Better Approximation Algorithms for NMR
    Spectral Peak Assignment." The second Workshop on
    Algorithms in Bioinformatics (WABI)", LNCS 2454,
    pp. 82-96, 2002.
  • 7 F.Tian, H.Valafar and J.H. Prestegard. "A
    dipolar coupling based strategy for simultaneous
    resonance assignment and structure determination
    of protein backbones", Journal of the American
    Chemical Society, 12311791-11796, 2001.
  • 9 D E. Zimmerman, C A. Kulikowski, Y Huang, W
    Feng, M Tashiro, S Shimotakahara,C-Y Chien, R
    Powers, and G T. Montelione. "Automated Analysis
    of Protein NMR Assignments Using Methods from
    Artificial Intelligence'', J. Mol Biol 269,
    592-610, (1997).
  • 10 J.J. Warren and P.B. Moore. "Application of
    dipolar coupling data to refinement of the
    solution structure of the Sarcin-Ricin loop
    RNA''. Journal of Bimolecular NMR, 20 311-323,
    2001.
  • 11 Michael Andrec, Yuichi Harano, Mathew P.
    Jacobson, Richard A Friesner and Ronald M Levy,
    "Complete Protein Structure Determination Using
    Backbone Residual Dipolar Couplings and Side
    chain Rotamer Prediction''.
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