ESI 2004 OPTIMIZATION AND DATA MINING

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ESI 2004 OPTIMIZATION AND DATA
MINING

• CLASSIFICATION OF FOLDING TYPES
• IN PROTEINS USING MILP
• FADIME ÜNEY
• (funey_at_ku.edu.tr)
• Supervised by METIN TÜRKAY
• (mturkay_at_ku.edu.tr)
• KOÇ UNIVERSITY, ISTANBUL

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AGENDA

• Proteins
• Structures of proteins
• Classification of folding types
• Folding type prediction
• Propositional Logic
• Model (MILP Formulation)
• Parameters
• Variables
• Objective function
• Constraints
• Illustrative Examples
• Training Set Results
• Future Research

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PROTEINS

• Bones, muscles, skin and hair of organisms
• Used in structure of cells
• Required for proper functioning and regulation of
  organisms such as enzymes, hormones, antibodies
• Amino acids ? PROTEINS
• Molecules of life

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CHEMICAL STRUCTURE OF AMINO ACIDS

• Distinguishing feature
• Different R groups

Carboxyl group
Side Chain
Amino group
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CLASSIFICATION OF AMINO ACID
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PEPTIDE BOND
Repeating units NC? C NC? C
O
O
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PROTEINS

• Since part of the amino acid is lost during
  dehydration synthesis
• units of a protein ? amino acid residues
• Typicall protein 200 -300 residues
• may increase up to 27 000
• Residue content and order is unique for each
  protein
• Sequence and types of side chains determine
• 3D shape, chemical and biological functions

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STRUCTURES OF PROTEINS
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PRIMARY STRUCTURE

• Sequence of amino acids
• A C M V I I C E V
• No arrangement of peptide bonds
• No angles between chemical bonds
• No interactions between any parts of residues
• Amino acid content and order dictates
• Shape of protein molecule
• Its spatial and biochemical properties

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SECONDARY STRUCTURE

• Local spatial arrangement of its main chain atoms
• Without regard to conformation of its side chains
• Without relationship with other segments
• Types of secondary structures
• a-helices
• ß-sheets
• Loops, turns and coils

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CLASSIFICATION OF FOLDING TYPES IN PROTEINS
ALL-ALPHA ? a-helices 40 and ß-sheets 5
(a) ALL-BETA ? a-helices 5 and ß-sheets 40
(ß) ALPHABETA ? a-helices 15 and ß-sheets
15 (aß) (60 antiparallel) ALPHA/BETA ?
a-helices 15 and ß-sheets 15 (a/ß) (60
parallel)
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FOLDING TYPE PREDICTION

• Functions of proteins ? study of fundamental
  biological processes
• Genetic engineering
• In case of human ? DESIGN OF DRUGS
• Experimental methods ? slow, require large
  amounts of resources
• Focal research subject in computational biology
  and bioinformatics

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FOLDING TYPE PREDICTION

• Folding type of a protein depends on amino acid
  composition, Nakashima et. al., 1986
• Several methods studied
• Chou, 1995 (Component coupled, 95.3)
• Bahar et. al., 1997 (Singular Value
  Decomposition, 81)
• Cai Zhou, 200 (Neural Network, 89.2)
• Cai et. al., 2001 (Support Vector Machines,
  93.2)
• Properties of training and test set

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FOLDING TYPE PREDICTION
SVM
MIP
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PROPOSITIONAL LOGIC

• Express relationships among Boolean variables
• Boolean variables (True or False)
• Operators
• OR
• AND
• IMPLICATION

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MIXED-INTEGER LINEAR PROGRAMMING (MILP)
FORMULATION

• Indices
• i protein
• j chain of the protein (A, B, C,...)
• k folding type of the protein (a, ß, aß, a/ß)
• l box that encloses a number of data points
  belonging to a type (1, 2, .., L)
• m amino acid (1, 2, .., 20)
• n bound (lower, upper)

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MILP FORMULATION (cont.)

• Parameters
• compijm composition of amino acid m in the
  subunit j of protein i
• foldtypeijk folding type k of the subunit j of
  protein i
• compU a sufficiently large parameter

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MILP FORMULATION (cont.)

• Variables (binary)
• YBl existence of box l
• YBClk assignment of folding type k to box l
• YPBijl assignment of subunit j of protein i to
  box l
• YPCijk assignment of subunit j of protein i to
  class k
• YLlsm lower bound of box s is between the bounds
  of box l for amino
• acid m
• YUlsm upper bound of box s is between the bounds
  of box l for amino
• acid m
• YCls intersection of box l and box s

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MILP FORMULATION (cont.)

• Variables (continuous)
• Xlmn define bounds n for amino acid m in box l
• XDlkmn define bounds n for amino acid m in box l
  for class k
• XP1ijk model misallocation of subunit j of
  protein i to class k
• XP2ijk model misallocation of subunit j of
  protein i to class k

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MILP FORMULATION (cont.)

OBJECTIVE FUNCTION Minimize
Intersection
Misallocation
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MILP FORMULATION (cont.)
CONSTRAINTS Bounds for boxes

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MILP FORMULATION (cont.)

Relationship between protein-box and protein-class
Relationship between box-class
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MILP FORMULATION (cont.)
Relationship between protein-box-class
Misallocation
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MILP FORMULATION (cont.)
Intersection
l
s
l
s
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MILP FORMULATION (cont.)
Intersection
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MODELING ENVIRONMENT
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ILLUSTRATIVE EXAMPLES
ALP BET APB ASB
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ILLUSTRATIVE EXAMPLES
ALP BET APB ASB
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TRAINING SET

• Better training database
• A good quality of structure
• As many nonhomologous structures as possible
• A typical or distinguishable feature for each
  class
• PDB (Protein Data Bank)
• http//www.rcsb.org/pdb/
• SCOP (Structural Classification of Proteins)
• www.scop.mrc-lmb.cam.ac.uk/scop/
• 30 from each class

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PDB code(Brookhaven National Labrotary)1ABA,
8ATC, etc.5th letter indicates the chain of
the protein
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RESULTS

• Very big problem ?
• Dual Simplex Method
• Iterative solution procedure ?
• Objective Function 0
• 14 Boxes
• 4 ALL ALPHA, 4 ALPHABETA
• 3 ALL BETA, 3 ALPHA/BETA
• Training accuracy 100

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FUTURE RESEARCH

• Test set
• 1600 proteins
• Jack-knife Test
• Prediction accuracy
• Model
• Distance-based classification

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