Computational Molecular Biology

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Computational Molecular Biology

• Protein Structure Introduction and Prediction

2
Protein Folding

• One of the most important problem in molecular
  biology
• Given the one-dimensional amino-acid sequence
  that specifies the protein, what is the proteins
  fold in three dimensions?

3
Overview

• Understand protein structures
• Primary, secondary, tertiary
• Why study protein folding
• Structure can reveal functional information
  which we cannot find from the sequence
• Misfolding proteins can cause diseases mad cow
  disease
• Use in drug designs

4
Overview of Protein Structure

• Proteins make up about 50 of the mass of the
  average human
• Play a vital role in keeping our bodies
  functioning properly
• Biopolymers made up of amino acids
• The order of the amino acids in a protein and the
  properties of their side chains determine the
  three dimensional structure and function of the
  protein

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Amino Acid

• Building blocks of proteins
• Consist of
• An amino group (-NH2)
• Carboxyl group (-COOH)
• Hydrogen (-H)
• A side chain group (-R) attached to the central
  a-carbon
• There are 20 amino acids
• Primary protein structure is a sequence of a
  chain of amino acids

Side chain
Aminogroup
Carboxylgroup
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Side chains (Amino Acids)

• 20 amino acids have side chains that vary in
  structure, size, hydrogen bonding ability, and
  charge.
• R gives the amino acid its identity
• R can be simple as hydrogen (glycine) or more
  complex such as an aromatic ring (tryptophan)

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Chemical Structure of Amino Acids
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How Amino Acids Become Proteins
Peptide bonds
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Polypeptide

• More than fifty amino acids in a chain are called
  a polypeptide.
• A protein is usually composed of 50 to 400 amino
  acids.
• We call the units of a protein amino acid
  residues.

amidenitrogen
carbonylcarbon
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Side chain properties

• Carbon does not make hydrogen bonds with water
  easily hydrophobic.
• These water fearing side chains tend to
  sequester themselves in the interior of the
  protein
• O and N are generally more likely than C to
  h-bond to water hydrophilic
• Ten to turn outward to the exterior of the
  protein

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Primary Structure
Primary structure Linear String of Amino Acids
Side-chain
Backbone
... ALA PHE LEU ILE LEU ARG ...
Each amino acid within a protein is referred to
as residues Each different protein has a unique
sequence of amino acid residues, this is its
primary structure
13
Secondary Structure

• Refers to the spatial arrangement of contiguous
  amino acid residues
• Regularly repeating local structures stabilized
  by hydrogen bonds
• A hydrogen atom attached to a relatively
  electronegative atom
• Examples of secondary structure are the ahelix
  and ßpleated-sheet

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Alpha-Helix

• Amino acids adopt the form of a right handed
  spiral
• The polypeptide backbone forms the inner part of
  the spiral
• The side chains project outward
• every backbone N-H group donates a hydrogen bond
  to the backbone C  O group

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Beta-Pleated-Sheet

• Consists of long polypeptide chains called
  beta-strands, aligned adjacent to each other in
  parallel or anti-parallel orientation
• Hydrogen bonding between the strands keeps them
  together, forming the sheet
• Hydrogen bonding occurs between amino and
  carboxyl groups of different strands

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Parallel Beta Sheets
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Anti-Parallel Beta Sheets
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Mixed Beta Sheets
19
Tertiary Structure

• The full dimensional structure, describing the
  overall shape of a protein
• Also known as its fold

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Quaternary Structure

• Proteins are made up of multiple polypeptide
  chains, each called a subunit
• The spatial arrangement of these subunits is
  referred to as the quaternary structure
• Sometimes distinct proteins must combine together
  in order to form the correct 3-dimensional
  structure for a particular protein to function
  properly.
• Example the protein hemoglobin, which carries
  oxygen in blood. Hemoglobin is made of four
  similar proteins that combine to form its
  quaternary structure.

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Other Units of Structure

• Motifs (super-secondary structure)
• Frequently occurring combinations of secondary
  structure units
• A pattern of alpha-helices and beta-strands
• Domains A protein chain often consists of
  different regions, or domains
• Domains within a protein often perform different
  functions
• Can have completely different structures and
  folds
• Typically a 100 to 400 residues long

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What Determines Structure

• What causes a protein to fold in a particular
  way?
• At a fundamental level, chemical interactions
  between all the amino acids in the sequence
  contribute to a proteins final conformation
• There are four fundamental chemical forces
• Hydrogen bonds
• Hydrophobic effect
• Van der Waal Forces
• Electrostatic forces

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Hydrogen Bonds

• Occurs when a pair of nucliophilic atoms such as
  oxygen and nitrogen share a hydrogen between them
• Pattern of hydrogen bounding is essential in
  stabilizing basic secondary structures

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Van der Waal Forces

• Interactions between immediately adjacent atoms
• Result from the attraction between an atoms
  nucleus and it neighbors electrons

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Electrostatic Forces

• Oppositely charged side chains con form
  salt-bridges, which pulls chains together

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Experimental Determination

• Centralized database (to deposit protein
  structures) called the protein Databank (PDB),
  accessible at http//www.rcsb.org/pdb/index.html
• Two main techniques are used to determine/verify
  the structure of a given protein
• X-ray crystallography
• Nuclear Magnetic Resonance (NMR)
• Both are slow, labor intensive, expensive
  (sometimes longer than a year!)

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X-ray Crystallography

• A technique that can reveal the precise three
  dimensional positions of most of the atoms in a
  protein molecule
• The protein is first isolated to yield a high
  concentration solution of the protein
• This solution is then used to grow crystals
• The resulting crystal is then exposed to an X-ray
  beam

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Disadvantages

• Not all proteins can be crystallized
• Crystalline structure of a protein may be
  different from its structure
• Multiple maps may be needed to get a consensus

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NMR

• The spinning of certain atomic nuclei generates a
  magnetic moment
• NMR measures the energy levels of such magnetic
  nuclei (radio frequency)
• These levels are sensitive to the environment of
  the atom
• What they are bonded to, which atoms they are
  close to spatially, what distances are between
  different atoms
• Thus by carefully measurement, the structure of
  the protein can be constructed

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Disadvantages

• Constraint of the size of the protein an upper
  bound is 200 residues
• Protein structure is very sensitive to pH.

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Computational Methods

• Given a long and painful experimental methods,
  need computational approaches to predict the
  structure from its sequence.

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Functional Region Prediction
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Protein Secondary Structure
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Tertiary Structure Prediction
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More Details on X-ray Crystallography
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Overview
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Overview
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Crystal

• A crystal can be defined as an arrangement of
  building blocks which is periodic in three
  dimensions

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Crystallize a Protein

• Have to find the right combination of all the
  different influences to get the protein to
  crystallize
• This can take a couple hundred or even thousand
  experiments
• Most popular way to conduct these experiments
• Hanging-drop method

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Hanging drop method

• The reservoir contains a precipitant
  concentration twice as high as the protein
  solution
• The protein solutions is made up of 50 of stock
  protein solution and 50 of reservoir solution
• Overtime, water will diffuse from the protein
  drop into the reservoir
• Both the protein concentration and precipitant
  concentration will increase
• Crystals will appear after days, weeks, months

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Properties of protein crystal

• Very soft
• Mechanically fragile
• Large solvent areas (30-70)

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A Schematic Diffraction Experiment
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Why do we need Crystals

• A single molecule could never be oriented and
  handled properly for a diffraction experiment
• In a crystal, we have about 1015 molecules in the
  same orientation so that we get a tremendous
  amplification of the diffraction
• Crystals produce much simpler diffraction
  patterns than single molecules

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Why do we need X-rays

• X-rays are electromagnetic waves with a
  wavelength close to the distance of atoms in the
  protein molecules
• To get information about where the atoms are, we
  need to resolve them -gt thus we need radiation

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A Diffraction Pattern
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Resolution

• The primary measure of crystal order/quality of
  the model
• Ranges of resolution
• Low resolution (gt3-5 Ao) is difficult to see the
  side chains only the overall structural fold
• Medium resolution (2.5-3 Ao)
• High resolution (2.0 Ao)

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Some Crystallographic Terms

• h,k,l Miller indices (like a name of the
  reflection)
• I(h,k,l) intensity
• 2? angle between the x-ray incident beam and
  reflect beam

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Diffraction by a Molecule in a Crystal

• The electric vector of the X-ray wave forces the
  electrons in our sample to oscillate with the
  same wavelength as the incoming wave

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Description of Waves
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Structure Factor Equation

• fj proportional to the number of electrons this
  atom j has
• One of the fundamental equations in X-ray
  Crystallography

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The Phase

• From the measurement, we can only obtain the
  intensity I(hkl) of any given reflection (hkl)
• The phase a(hkl) cannot be measured

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How to Determine the Phase

• Small changes are introduced into the crystal of
  the protein of interest
• Eg soaking the crystal in a solution containing
  a heavy atom compound

• Second diffraction data set needs to be
  collected
• Comparing two data sets to determine the phases
  (also able to localize the heavy atoms)

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Other Phase Determination Methods
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Electron Density Map

• Once we know the complete diffraction pattern
  (amplitudes and phases), need to calculate an
  image of the structure
• The above equation returns the electron density
  (so we get a map of where the electrons are their
  concentration)

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Interpretation of Electron Density

• Now, the electron density has to be interpreted
  in terms of atom identities and positions.
• (1) packing of the whole molecules is shown in
  the crystal
• (2) a chain of seven amino acids in shown with
  the resulting structure superimposed
• (3) the electron density of a trypophan side
  chain is shown

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Refinement and the R-Factor
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Nuclear Magnetic Resonance

• Concentrated protein solution (very purified)
• Magnetic field
• Effect of radio frequencies on the resonance of
  different atoms is measured.

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NMR

• Behavior of any atom is influenced by neighboring
  atoms
• more closely spaced residues are more perturbed
  than distant residues
• can calculate distances based on perturbation

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NMR spectrum of a protein
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Computational Molecular Biology

• Protein Structure Secondary Prediction

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Primary Structure Symbolic Definition

• A A,C,D,E,F,G,H,I,J,K,L,M,N,P,Q,R,S.T,V,W,Y
  set of symbols denoting all amino acids
• A - set of all finite sequences formed out of
  elements of A, called protein sequences
• Elements of A are denoted by x, y, z ..i.e. we
  write x? A, y? A, z?A, etc
• PROTEIN PRIMARY STRUCTURE any x ? A is also
  called a protein sequence or protein sub-unit

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Protein Secondary Structure (PSS)

• Secondary structure the arrangement of the
  peptide backbone in space. It is produced by
  hydrogen bondings between amino acids
• PROTEIN SECONDARY STRUCTURE consists of protein
  sequence and its hydrogen bonding patterns
  called SS categories

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Protein Secondary Structure

• Databases for protein sequences are expanding
  rapidly
• The number of determined protein structures (PSS
  protein secondary structures) and the number of
  known protein sequences is still limited
• PSSP (Protein Secondary Structure Prediction)
  research is trying to breach this gap.

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Protein Secondary Structure

• The most commonly observed conformations in
  secondary structure are
• Alpha Helix
• Beta Sheets/Strands
• Loops/Turns

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Turns and Loops

• Secondary structure elements are connected by
  regions of turns and loops
• Turns short regions of non-?, non-?
  conformation
• Loops larger stretches with no secondary
  structure.

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Three secondary structure states

• Prediction methods are normally assessed for 3
  states
• H (helix)
• E (strands)
• L (others (loop or turn))

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Secondary Structure

• 8 different categories
• H ? - helix
• G 310 helix
• I ? - helix (extremely rare)
• E ? - strand
• B ? - bridge
• T ?- turn
• S bend
• L the rest

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Three SS states Reduction methods

• Method 1, used by DSSP program
• H(helix) G (310 helix), H (?- helix)
• E (strands) E (?-strand), B (?-bridge) ,
• L all the rest
• Shortly E,B gt E G,H gt H Rest gt C
• Method 2, used by STRIDE program
• H as in Method 1
• E E (?-strand), b (isolated ? -bridge),
• L all the rest

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Three SS states Reduction methods

• Method 3, used by DEFINE program
• H(helix) as in Method 1
• E (strands) E (?-strand),
• L all the rest

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Example of typical PSS Data

• Example
• Sequence
• KELVLALYDYQEKSPREVTHKKGDILTLLNSTNKDWWKYEYNDRQGFVP
• Observed SS
• HHHHHLLLLEEEHHHLLLEEEEEELLLHHHHHHHHLLLEEEEEELLLHHH

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PSS Symbolic Definition

• Given A A,C,D,E,F,G,H,I,J,K,L,M,N,P,Q,R,S.T,V,
  W,Y set of symbols denoting amino acids and a
  protein sequence x ? A
• Let S H, E, L be the set of symbols of 3
  states H (helix), E (strands) and L (loop) and
  S be the set of all finite sequences of elements
  of S.
• We denote elements of S by e, e? S

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PSS Symbolic Definition

• Any one-to-one function
• f A? S i.e. f ? A x S
• is called a protein secondary structure (PSS)
  identification function
• An element (x, e) ? f is a called protein
  secondary structure (of the protein sequence x)
• The element e ? S (of (x, e) ? f ) is called
  secondary structure.

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PSSP

• If a protein sequence shows clear similarity to a
  protein of known three dimensional structure
• then the most accurate method of predicting the
  secondary structure is to align the sequences by
  standard dynamic programming algorithms
• Why?
• homology modelling is much more accurate than
  secondary structure prediction for high levels of
  sequence identity.

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PSSP

• Secondary structure prediction methods are of
  most use when sequence similarity to a protein of
  known structure is undetectable.
• It is important that there is no detectable
  sequence similarity between sequences used to
  train and test secondary structure prediction
  methods.

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Classification and Classifiers

• Given a database table DB with a special
  atribute C, called a class attribute (or decision
  attribute). The values C1, C2, ...Cn of the
  class atrribute are called class labels.
• Example

A1 A2 A3 A4 C
1 1 m g c1
0 1 v g c2
1 0 m b c1
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Classification and Classifiers

• The attribute C partitions the records in the DB
• divides the records into disjoint subsets
  defined by the attributes C values, CLASSIFIES
  the records.
• It means we use the attributre C and its values
  to divide the set R of records of DB into n
  disjoint classes
• C1 r?DB Cc1 ...... Cnr?DB Ccn
• Example (from our table)
• C1 (1,1,m,g), (1,0,m,b) r1,r3
• C2 (0,1,v,g) r2

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Classification and Classifiers

• An algorithm is called a classification algorithm
  if it uses the data and its classification to
  build a set of patterns.
• Those patterns are structured in such a way that
  we can use them to classify unknown sets of
  objects- unknown records.
• For that reason (because of the goal) the
  classification algorithm is often called shortly
  a classifier.
• The name classifier implies more then just
  classification algorithm. A classifier is final
  product of a data set and a classification
  algorithm.

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Classification and Classifiers

• Building a classifier consists of two phases
• training and testing.
• In both phases we use data (training data set
  and disjoint with it test data set) for which the
  class labels are known for ALL of the records.
• We use the training data set to create patterns
• We evaluate created patterns with the use of of
  test data, which classification is known.
• The measure for a trained classifier accuracy is
  called predictive accuracy.
• The classifier is build i.e. we terminate the
  process if it has been trained and tested and
  predictive accuracy was on an acceptable level.

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Classifiers Predictive Accuracy

• PREDICTIVE ACCURACY of a classifier is a
  percentage of well classified data in the testing
  data set.
• Predictive accuracy depends heavily on a choice
  of the test and training data.
• There are many methods of choosing test and and
  training sets and hence evaluating the predictive
  accuracy. This is a separate field of research.

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Accuracy Evaluation

• Use training data to adjust parameters of method
  until it gives the best agreement between its
  predictions and the known classes
• Use the testing data to evaluate how well the
  method works (without adjusting parameters!)
• How do we report the performance?
• Average accuracy fraction of all test examples
  that were classified correctly

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Accuracy Evaluation

• Multiple cross-validation test has to be
  performed to exclude a potential dependency of
  the evaluated accuracy on the particular test set
  chosen
• Jack-Knife
• Use 129 chains for setting up the tool (training
  set)
• 1 for estimating the performance (testing)
• This has to be repeated 130 times until each
  protein has been used once for testing
• The average over all 130 tests gives an estimate
  of the prediction accuracy

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PSSP Datasets

• Historic RS126 dataset. Contains126 sub-units
  with known secondary structure selected by Rost
  and Sander. Today is not used anymore
• CB513 dataset. Contains 513 sub-units with known
  secondary structure selected by Cuff and Barton
  in 1999. Used quite frencently in PSSP research
• HS17771 dataset. Created by Hobohm and Scharf.
  In March-2002 it contained 1771 sub-units
• Lots of authors has their own and secret
  datasets

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Measures for PSSP accuracy

• http//cubic.bioc.columbia.edu/eva/doc/measure_sec
  .html (for more information)
• Q3 Three-state prediction accuracy (percent of
  succesful classified)
• Qi obs How many of the observed residues were
  correctly predicted?
• Qi prd How many of the predicted residues were
  correctly predicted?

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Measures for PSSP Accuracy

• Aij number of residues predicted to be in
  structure type j and observed to be in type i
• Number of residues predicted to be in structure
  i
• Number of residues observed to be in structure i

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Measures for SSP Accuracy

• The percentage of residues correctly predicted to
  be in class i relative to those observed to be in
  class i
• The percentages of residues correctly predicted
  to be in class i from all residues predicted to
  be in i
• Overall 3-state accuracy

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PSSP Algorithms

• There are three generations in PSSP algorithms
• First Generation based on statistical
  information of single amino acids (1960s and
  1970s)
• Second Generation based on windows (segments) of
  amino acids. Typically a window containes 11-21
  amino acids (dominating the filed until early
  1990s)
• Third Generation based on the use of windows on
  evolutionary information

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PSSP First Generation

• First generation PSSP systems are based on
  statistical information on a single amino acid
• The most relevant algorithms
• Chow-Fasman, 1974
• GOR, 1978
• Both algorithms claimed 74-78 of predictive
  accuracy, but tested with better constructed
  datasets were proved to have the predictive
  accuracy 50 (Nishikawa, 1983)

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Chou-Fasman method

• Uses table of conformational parameters
  determined primarily from measurements of the
  known structure (from experimental methods)
• Table consists of one likelihood for each
  structure for each amino acid
• Based on frequencies of residues in a-helices,
  b-sheets and turns
• Notation P(H) propensity to form alpha helices
• f(i) probability of being in position 1 (of a
  turn)

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Chou-Fasman Pij-values
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Chou-Fasman

• A prediction is made for each type of structure
  for each amino acid
• Can result in ambiguity if a region has high
  propensities for both helix and sheet (higher
  value usually chosen)

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Chou-Fasman

• How it works
• 1. Assign all of the residues the appropriate set
  of parameters
• 2. Identify a-helix and b-sheet regions. Extend
  the regions in both directions.
• 3. If structures overlap compare average values
  for P(H) and P(E) and assign secondary structure
  based on best scores.
• 4. Turns are calculated using 2 different
  probability values.

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Assign Pij values
1. Assign all of the residues the appropriate
set of parameters
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Scan peptide for a-helix regions
2. Identify regions where 4 out of 6 have a
P(H) gt100 alpha-helix nucleus
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Extend a-helix nucleus
3. Extend helix in both directions until a set of
four consecutive residues with P(H) lt100.
Find sum of P(H) and sum of P(E) in the extended
region If region is long enough ( gt 5 letters)
and sum P(H) gt sum P(E) then declare the extended
region as alpha helix
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Scan peptide for b-sheet regions
4. Identify regions where 3 out of 5 have a
P(E) gt100 b-sheet nucleus 5. Extend b-sheet
until 4 continuous residues with an average P(E)
lt 100 6. If region average gt 100 and the
average P(E) gt average P(H) then b-sheet
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Overlapping

• Resolving overlapping alpha helix beta sheet
• Compute sum of P(H) and sum of P(E) in the
  overlap.
• If sum P(H) gt sum P(E) gt alpha helix
• If sum P(E) gt sum P(H) gt beta sheet

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Turn Prediction

• An amino acid is predicted as turn if all of the
  following holds
• f(i)f(i1)f(i2)f(i3) gt 0.000075
• Avg(P(ik)) gt 100, for k0, 1, 2, 3
• Sum(P(t)) gt Sum(P(H)) and Sum(P(E)) for ik,
  (k0, 1, 2, 3)

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PSSP Second Generation

• Based on the information contained in a window of
  amino acids (11-21 aa.)
• The most systems use algorithms based on
• Statistical information
• Physico-chemical properties
• Sequence patterns
• Graph-theory
• Multivariante statistics
• Expert rules
• Nearest-neighbour algorithms

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PSSP First Second Generation

• Main problems
• Prediction accuracy lt70
• SS assigments differ even between crystals of the
  same protein
• SS formation is partially determined by
  long-range interactions, i.e., by contacts
  between residues that are not visible by any
  method based on windows of 11-21 adjacent residues

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PSSP First Second Generation

• Main problems
• Prediction accuracy for b-strand 28-48, only
  slightly better than random
• beta-sheet formation is determined by more
  nonlocal contacts than in alpha-helix formation
• Predicted helices and strands are usually too
  short
• Overlooked by most developers

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Example of Second Generation

• Example for typical secondary structure
  prediction of the 2nd generation.
• The protein sequence (SEQ ) given was the SH3
  structure.
• The observed secondary structure (OBS ) was
  assigned by DSSP (H helix E strand blank
  non-regular structure the dashes indicate the
  continuation).
• The typical prediction of too short segments (TYP
  ) poses the following problems in practice.
• (i) Are the residues predicted to be strand in
  segments 1, 5, and 6 errors, or should the
  helices be elongated?
• (ii) Should the 2nd and 3rd strand be joined, or
  should one of them be ignored, or does the
  prediction indicate two strands, here? Note the
  three-state per-residue accuracy is 60 for the
  prediction given.

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PSSP Third Generation

• PHD First algorithm in this generation (1994)
• Evolutionary information improves the prediction
  accuracy to 72
• Use of evolutionary information
• 1. Scan a database with known sequences with
  alignment methods for finding similar sequences
• 2. Filter the previous list with a threshold to
  identify the most significant sequences
• 3. Build amino acid exchange profiles based on
  the probable homologs (most significant
  sequences)
• 4. The profiles are used in the prediction,
  i.e. in building the classifier

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PSSP Third Generation

• Many of the second generation algorithms have
  been updated to the third generation

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PSSP Third Generation

• Due to the improvement of protein information in
  databases i.e. better evolutionary information,
  todays predictive accuracy is 80
• It is believed that maximum reachable accuracy is
  88. Why such conjecture?

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Why 88

• SS assignments may vary for two versions of the
  same structure
• Dynamic objects with some regions being more
  mobile than others
• Assignment differ by 5-15 between different
  X-ray (NMR) versions of the same protein
• Assignment diff. by about12 between structural
  homologues
• B. Rost, C. Sander, and R. Schneider, Redefining
  the goals of protein secondary structure
  predictions, J. Mol. Bio.

108
PSSP Data Preparation

• Public Protein Data Sets used in PSSP research
  contain protein secondary structure sequences. In
  order to use classification algorithms we must
  transform secondary structure sequences into
  classification data tables.
• Records in the classification data tables are
  called, in PSSP literature (learning) instances.
• The mechanism used in this transformation process
  is called window.
• A window algorithm has a secondary structure as
  input and returns a classification table set of
  instances for the classification algorithm.

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Window

• Consider a secondary structure (x, e).
• where (x,e) (x1x2 xn, e1e2en)
• Window of the length w chooses a subsequence of
  length w of x1x2 xn, and an element ei from
  e1e2en, corresponding to a special position in
  the window, usually the middle
• Window moves along the sequences
• x x1x2 xn and e e1e2en
• simultaneously, starting at the beginning moving
  to the right one letter at the time at each step
  of the process.

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Window Sequence to Structure

• Such window is called sequence to structure
  window. We will call it for short a window.
• The process terminates when the window or its
  middle position reaches the end of the sequence
  x.
• The pair (subsequence, element of e ) is often
  written in a form
• subsequence ? H, E or L
• is called an instance, or a rule.

111
Example Window

• Consider a secondary structure (x, e) and the
  window of length 5 with the special position in
  the middle (bold letters)
• Fist position of the window is
• x A R N S T V V S T A A .
• e H H H H L L L E E E
• Window returns instance
• A R N S T ? H

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Example Window

• Second position of the window is
• x A R N S T V V S T A A .
• e H H H H L L L E E E
• Windows returns instance
• R N S T V ? H
• Next instances are
• N S T V V ? L
• S T V V S ? L
• T V V S T ? L

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Symbolic Notation

• Let f be a protein secondary structure (PSS)
  identification function
• f A? S i.e. f ? A x S
• Let x x1x2xn, e e1e2en, f(x) e, we define
• f(x1x2xn)xi ei, i.e. f(x)xi ei

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ExampleSemantics of Instances

• Let
• x A R N S T V V S T A A .
• e H H H H L L L E E E
• And assume that the windows returns an instance
  
• A R N S T ? H
• Semantics of the instance is
• f(x)NH,
• where f is the identification function and N is
  preceded by A R and followed by S T and the
  window has the length 5

115
Classification Data Base (Table)

• We build the classification table with attributes
  being the positions p1, p2, p3, p4, p5 .. pw
• in the window, where w is length of the
  window.
• The corresponding values of attributes are
  elements of of the subsequent on the given
  position.
• Classification attribute is S with values in the
  set H, E, L assigned by the window operation
  (instance, rule).
• The classification table for our example (first
  few records) is the following.

116
Classification Table (Example)

• x A R N S T V V S T A A .
• e H H H H L L L E E E

p1 p2 p3 p4 p5 S
A R N S T H
R N S T V H
N S T V V L
S T V V S L
Semantics of record r r(p1, p2, p3,p4,p5, S) is
f(x)Vp3 Vs where Va denotes a value of
the attribute a.
117
Size of classification datasets (tables)

• The window mechanism produces very large datasets
• For example window of size 13 applied to the
  CB513 dataset of 513 protein subunits produces
  about
• 70,000 records (instances)

118
Window

• Window has the following parameters
• PARAMETER 1 i ? N, the starting point of the
  window as it moves along the sequence x x1 x2
  . xn. The value i1 means that window starts
  at x1, i5 means that window starts at x5
• PARAMETER 2 w ? N denotes the size (length)
  of the window.
• For example the PHD system of Rost and Sander
  (1994) uses two window sizes 13 and 17.

119
Window

• PARAMETER 3 p ? 1,2, , w
• where p is a special position of the window
  that returns the classification attribute values
  from S H, E, L and w is the size (length) of
  the window
• PSSP PROBLEM
• find optimal size w, optimal special position
  p for the best prediction accuracy

120
Window Symbolic Definition

• Window Arguments window parameters and secondary
  structure (x,e)
• Window Value (subsequence of x, element of e)
• OPERATION (sequence to structure window)
• W is a partial function
• W N ? N ? 1,, k ?(A ? S ) ? A ? S
• W(i, k, p, (x,e)) (xi x(i1). x(ik-1),
  f(x)x(ip)) where (x,e) (x1x2 ..xn, e1e2en)

121
Neural network models

• machine learning approach
• provide training sets of structures (e.g.
  a-helices, non a -helices)
• are trained to recognize patterns in known
  secondary structures
• provide test set (proteins with known structures)
• accuracy 70 75

122
Reasons for improved accuracy

• Align sequence with other related proteins of the
  same protein family
• Find members that has a known structure
• If significant matches between structure and
  sequence assign secondary structures to
  corresponding residues

123
3 State Neural Network
124
Neural Network
125
Input Layer

• Most of approach set w 17. Why?
• Based on evidence of statistical correlation with
  secondary structure as far as 8 residues on
  either side of the prediction point
• The input layer consists of
• 17 blocks, each represent a position of window
• Each block has 21 units
• The first 20 units represent the 20 aa
• One to provide a null input used when the moving
  window overlaps the amino- or carboxyl-terminal
  end of the protein

126
Binary Encoding Scheme

• Example
• Let w 5, and let say we have the sequence
• A E G K Q.
• Then the input layer is
• A,C,D,E,F,G,,N,P,Q,R,S.T,V,W,Y
• 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0
• 0 0 1 0 ..
• 0 0 1 0 ..

127
Hidden Layer

• Represent the structure of the central aa
• Encoding scheme
• Can use two units to present
• (1,0) H, (0,1) E, (0,0) L
• Some uses three units
• (1,0,0) H, (0,1,0) E, (0,0,1) L
• For each connection, we can assign some weight
  value.
• This weight value can be adjusted to best fit the
  data (training)

128
Output Level

• Based on the hidden level and some function f,
  calculate the output.
• Helix is assigned to any group of 4 or more
  contiguous residues
• Having helix output values greater than sheet
  outputs and greater than some threshold t
• Strand (E) is assigned to any group of two or
  more contiguous resides, having sheet output
  values greater than helix outputs and greater
  than t
• Otherwise, assigned to L
• Note that t can be adjusted as well (training)

129
How PHD works

• Step 1. BLAST search with input sequence
• Step 2. Perform multiple seq. alignment and
  calculate aa frequencies for each position

130
How PHD works

• Step 3. First Level Sequence to structure net
• Input alignment profile, Output units for H,
  E, L
• Calculate occurrences of any of the residues
  to be present in either an a-helix, b-strand, or
  loop.

1 2 3 4 5 6 7
H 0.05 E 0.18 L 0.67
N0.2, S0.4, A0.4
131
How PHD works

• Step 3. Second Level Structure to structure
  net
• Input First Level values, Output units for H,
  E, L
• Window size 17

H 0.59 E 0.09 L 0.31
E0.18
Step 4. Decision level
132
Prepare Data for PHD Neural Nets

• Starting from a sequence of unknown structure
  (SEQUENCE ) the following steps are required to
  finally feed evolutionary information into the
  PHD neural networks
• a data base search for homologues (method Blast),
  
• a refined profile-based dynamic-programming
  alignment of the most likely homologues (method
  MaxHom)
• a decision for which proteins will be considered
  as homologues (length-depend cut-off for pairwise
  sequence identity)
• a final refinement, and extraction of the
  resulting multiple alignment. Numbers 1-3
  indicate the points where users of the
  PredictProtein service can interfere to improve
  prediction accuracy without changes made to the
  final prediction method PHD .
• http//cubic.bioc.columbia.edu/papers/2000_rev_hum
  ana/paper.html

133
PHD Neural Network
134
Prediction Accuracy
135
Where can I learn more?

• Protein Structure Prediction Center
• Biology and Biotechnology Research
  ProgramLawrence Livermore National Laboratory,
  Livermore, CA
• http//predictioncenter.llnl.gov/Center.html

DSSP Database of Secondary Structure
Prediction http//www.sander.ebi.ac.uk/dssp/
136
Computational Molecular Biology

• Protein Structure Tertiary Prediction via
  Threading

137
Objective

• Study the problem of predicting the tertiary
  structure of a given protein sequence

138
A Few Examples
actual
predicted
predicted
actual
actual
actual
predicted
predicted
139
Two Comparative Modeling

• Homology modeling identification of homologous
  proteins through sequence alignment structure
  prediction through placing residues into
  corresponding positions of homologous structure
  models
• Protein threading make structure prediction
  through identification of good
  sequence-structure fit
• We will focus on the Protein Threading.

140
Why it Works?

• Observations
• Many protein structures in the PDB are very
  similar
• Eg many 4-helical bundles, globins in the set
  of solved structure
• Conjecture
• There are only a limited number of unique
  protein folds in nature

141
Threading Method

• General Idea
• Try to determine the structure of a new sequence
  by finding its best fit to some fold in library
  of structures
• Sequence-Structure Alignment Problem
• Given a solved structure T for a sequence t1t2tn
  and a new sequence S s1s2 sm, we need to find
  the best match between S and T

142
What to Consider

• How to evaluate (score) a given alignment of s
  with a structure T?
• How to efficiently search over all possible
  alignments?

143
Three Main Approaches

• Protein Sequence Alignment
• 3D Profile Method
• Contact Potentials

144
Protein Sequence Alignment Method

• Align two sequences S and T
• If in the alignment, si aligns with tj, assign si
  to the position pj in the structure
• Advantages
• Simple
• Disadvantages
• Similar structures have lots of sequence
  variability, thus sequence alignment may not be
  very helpful

145
3D Profile Method

• Actually uses structural information
• Main idea
• Reduce the 3D structure to a 1D string describing
  the environment of each position in the protein.
  (called the 3D profile (of the fold))
• To determine if a new sequence S belongs to a
  given fold T, we align the sequence with the
  folds 3D profile
• First question How to create the 3D profile?

146
Create the 3D Profile

• For a given fold, do
• For each residue, determine
• How buried is it?
• Fraction of surrounding environment that is polar
• What secondary structure is it in (alpha-helix,
  beta-sheet, or neither)

147
Create the 3D profile

• 2. Assign an environment class to each position
• Six classes describe the burial and polarity
  criteria (exposed, partially buried, very buried,
  different fractions of polar environment)

148
Create the 3D Profile

• These environment classes depend on the number of
  surrounding polar residues and how buried the
  position is.
• There are 3 SS for each of these, thus have 18
  environment classes

149
Create the 3D Profile

• 3. Convert the known structure T to a string of
  environment descriptors
• 4. Align the new sequence S with E using dynamic
  programming

150
Scores for Alignment

• Need scores for aligning individual residues with
  environments.
• Key Different aa prefer diff. environment. Thus
  determine scores by looking at the statistical
  data

151
Scores for Alignment

1. Choose a database of known structures
2. Tabulate the number of times we see a particular
   residue in a particular environment class -gt
   compute the score for each env class and each aa
   pair
3. Choose gap penalties, eg. may charge more for
   gaps in alpha and beta environments

152
Alignment

• This gives us a table of scores for aligning an
  aa sequence with an environment string
• Using this scoring and Dynamic Programming, we
  can find an optimal alignment and score for each
  fold in our library
• The fold with the highest score is the best fold
  for the new sequence

153
Contact Potentials Method

• Take 3D structure into account more carefully
• Include information about how residues interact
  with each other
• Consider pairwise interactions between the
  position pi, pj in the fold
• For a given alignment, produce a score which is
  the sum over these interactions

154
Problem

• Have a sequence from the database T t1tn with
  known positions p1pn, and a new sequence S
  s1sm.
• Find 1 lt r1 lt r2 lt lt rn lt m which maximize
• where ri is the index of the aa in S which
  occupies position pi
• This problem is NP-complete for pairwise
  interactions

155
How to Define that Score?

• Use so-called knowledge-based potentials, which
  comes from databases of observed interactions.
• The general form

156
How to Define the Score

• General Idea
• Define cutoff parameter for contact (e.g. up to
  6 Angstroms)
• Use the PDB to count up the number of times aa i
  and j are in contact
• Several method for normalization. Eg.
  Normalization is by hypothetical random
  frequencies

157
Other Variations

• Many other variations in defining the potentials
• In addition to pairwise potentials, consider
  single residue potentials
• Distance-dependent intervals
• Counting up pairwise contacts separately for
  intervals within 1 Angstrom, between 1 and 2
  Angstroms

158
Threading via Tree-Decomposition
159
Contact Graph

1. Each residue as a vertex
2. One edge between two residues if their spatial
   distance is within given cutoff.
3. Cores are the most conserved segments in the
   template

template
160
Simplified Contact Graph
161
Alignment Example
162
Alignment Example
163
Calculation of Alignment Score

164
Graph Labeling Problem

• Each core as a vertex
• Two cores interact if there is an interaction
  between any two residues, each in one core
• Add one edge between two cores that interact.

h
f
b
d
s
m
c
a
e
i
j
k
l
Each possible sequence alignment position for a
single core can be treated as a possible label
assignment to a vertex in G Di be a set of
all possible label assignments to vertex i. Then
for each label assignment A(i) in Di, we have
165
Tree Decomposition
166
Tree DecompositionRobertson Seymour, 1986
Greedy minimum degree heuristic
h

1. Choose the vertex with minimum degree
2. The chosen vertex and its neighbors form a
   component
3. Add one edge to any two neighbors of the chosen
   vertex
4. Remove the chosen vertex
5. Repeat the above steps until the graph is empty

167
Tree Decomposition (Contd)
Tree Decomposition
168
Tree Decomposition-Based Algorithms

• Bottom-to-Top Calculate the minimal F function
• 2. Top-to-Bottom Extract the optimal assignment

A tree decomposition rooted at Xr
The score of component Xi
The scores of subtree rooted at Xl
The score of subtree rooted at Xi
The scores of subtree rooted at Xj