Protein Structure Prediction

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Protein Structure Prediction
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Protein structure

• Most proteins will fold spontaneously in water,
  so amino acid sequence alone should be enough to
  determine protein structure
• However, the physics are daunting
• 20,000 protein atoms, plus equal amounts of
  water
• Many non-local interactions
• Can takes seconds (most chemical reactions take
  place 1012 --1,000,000,000,000x faster)
• Empirical determinations of protein structure are
  advancing rapidly.

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Protein review

• Proteins are polymers of amino acids linked by
  peptide bonds.
• Properties of proteins are determined by both the
  particular sequence of amino acids and by the
  conformation (fold) of the protein.
• Flexibility in thebonds around C?
• ? (phi)
• ? (psi)
• sidechain

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Protein Structure Levels

• Protein structure is described in four levels
• Primary structure amino acid sequence
• Secondary structure local (in sequence) ordering
  into
• (?)Helices compressed, corkscrew structures
• (?)Strands extended, nearly straight structures
• (?)Sheets paired strands, reinforced by hydrogen
  bonds
• parallel (same direction) or antiparallel sheets
• Coils, Turns Loops changes in direction
• Tertiary structure global ordering (all
  angles/atoms)
• Quaternary structures multiple, disconnected
  amino acid chains interacting to form a larger
  structure

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Protein structure cartoons
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Protein Structure Representations

• Differentvisualizationsshow variousaspects
  ofstructure

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Protein Folding

• Proteins are created linearly and then assume
  their tertiary structure by folding.
• Exact mechanism is still unknown
• Mechanistic simulations can be illuminating
• Proteins assume the lowest energy structure
• Or sometimes an ensemble of low energy
  structures.
• Hydrophobic collapse drives process
• Local (secondary) structure proclivities
• Internal stabilizers
• Hydrogen bonds, disulphide bonds, salt bridges.

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Empirical structure determination

• Two major experimental methods for determining
  protein structure
• X-ray Crystallography
• Requires growing a crystal of the protein
  (impossible for some, never easy)
• Diffraction pattern can be inverse-Fourier
  transformed to characterize electron densities
  (Phase problem)
• Nuclear Magnetic Resonance (NMR) imaging
• Provides distance constraints, but can be hard to
  find a corresponding structure
• Works only for relatively small proteins (so far)

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X-ray crystallography

• X-rays, since wavelength is near the distance
  between bonded carbon atoms
• Maps electron density, not atoms directly
• Crystal to get a lot of spatially aligned atoms
• Have to invert Fourier transform to get
  structure, but only have amplitudes, not phases
• Guess! orperturb...

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NMR structure determination

• NMR can detect certain features of hydrogen
  atoms
• NOESY measures distances between non-bonded H's
  within about 5A
• COSY and TOCSY described relations through bonds
• Combination of distance and angle constraints,
  plus knowledge of covalent bonds (amino acid
  sequence) determines a unique (sometimes)
  structure.
• Overlapping measurement limits size 120AA

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Why predict protein structure?

• Neither crystallography nor NMR can keep pace
  with genome sequencing efforts
• Only 10566 (3641 with lt90 identity) human
  proteins in PDB, although growing fast
• Computer scientists love this problem
• Understandable with minimal biology
• Seems like a good discrimination task
• Understand the mechanisms of folding (?)
• First computational Nobel prize?

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Kinds of Structure Prediction

• Comparative modelling
• Homolog has known structure, which is adjusted
  for sequence differences
• Energy minimization and molecular dynamics
• Fold recognition
• Proteins fall into broad fold classes. Models of
  folds that recognize compatible sequences.
  Inverse problem
• Predict more than fold class?
• Ab initio or new fold prediction
• No homologs, not recognized by any fold model

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Ab Initio predictions

• Three broad approaches
• Molecular dynamics, energy minimization
  approaches
• Empirical black box (induce discriminators)
• Mechanistic (follow the actual folding path)
  approaches. Hybrid between energy and empirical
  methods.
• Secondary structure predictions
• Not tremendously useful nor accurate, but
  simplest.
• Can play a role in tertiary predictors
• Tertiary structure predictions
• Best involve a complex mixture of approaches

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Energy Minimization

• Many forces act on a protein
• Hydrophobic inside of protein wants to avoid
  water
• Packing atoms can't be too close, nor too far
  away
• Bond angle/length constraints
• Long distance, e.g.
• Electrostatics Hydrogen bonds
• Disulphide bonds
• Salt bridges
• Can calculate all of these forces, and minimize
• Intractable in general case, but can be useful

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Empirical models

• Pose structure prediction as induction task.
• What are the inputs and outputs?
• Where do we get enough training data?
• Which induction methods work best?
• Long history in bioinformatics

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Initial approaches to secondary structure
prediction

• Input is a "sliding window" of immediately
  surrounding sequence assumed to determine
  structure (no long distance interactions)
  ...mnnstnssnsgla...
  H
• Output is one of three possible secondary
  structure states helix, strand, other

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Why might this work?

• There are local propensities to secondary
  structural classes (largely hydropathy)
• Helices no prolines, sometimes amphipathic (show
  alternating hydropathy with period 3.6 residues)
• Strands either alternating hydropathy or ends
  hydrophillic and center hydrophobic
• Neither small, polar flexible residues.
  Prolines.
• Minimum lengths for secondary structures (helices
  longer than strands)

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Early methods

• Chou-Fasman method looked at frequency of each
  amino acid in window
• GOR defined an information measure I(SR)
  logP(SR)/P(S) where S is secondary structure
  and R is amino acid. Define information gain as
  I(SR) - I(SR) and predict state with
  highest gain.
• How to combine info gain for each element of
  sliding window? Independently (just add) or by
  pairs

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How well did they work?

• Not very Roughly 50-55 accurate on a residue by
  residue basis.
• Random prediction that obeyed the observed
  distribution of helix/strand/other would be 40
• Different ways to calculate "correctness"
• Needs to be unbiased (especially wrt homology)!
• Getting number of helices and strands or order
  right is harder than just counting residue by
  residue (like the difference between nucleotide
  and exon level gene finding).

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Fancier induction techniques

• Same setup as Chou-Fasman or GOR
• Sliding window across amino acid sequence as
  input
• Three class output (helix/sheet/other)
• Various different induction techniques over same
  data, give modest improvements
• LDA/QDA
• Decision trees
• Neural networks
• Best results from neural networks ( 62)

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Add multiple sequence alignment information

• This is helpful in principle
• insertions/deletions more likely to be coil/turn
• conserved hydropathy more important for
  prediction than non-conserved.
• GOR method improves 8-9 points (to about 64
  correct residue by residue).
• Similar improvement for NNs (to 68)
• SVMs gain a bit more, to about 70

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But the information isn't there

• Prediction quality has not improved much even
  with huge growth of training data.
• Secondary structure is not completely determined
  by local forces
• Long distance interactions do not appear in
  sliding window
• Empirical studies show same amino acid sequences
  can assume multiple secondary structures.

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Mechanistic models

• Move from purely empirical to include some
  knowledge of folding mechanisms
• Compact nature of conformations
• Hydrophobic packing
• Sequences of secondary structures
• Secondary structure predispositions
• Heuristic global energy minimization

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Hydrophobic packing models

• Dill's HP model
• Two classes of amino acids, hydrophobic (H) and
  polar (P)
• Lattice model for position of (point) amino
  acids.
• Thread chain of H's and P's through lattice to
  maximize number of H-H contacts

3D
2D
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But...

• Even the 2D HP packing problem (which is easier
  than the 3D one) turns out to be NP complete!
• Good approximation results exist.
• 3/8 of optimal approximation (3D)
• In triangular lattice, algorithm for gt60 of
  optimal packing
• Other interesting results in the model, e.g.
• Which sequences have a single optimal fold?

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CASP changed the landscape

• Critical Assessment of Structure Prediction
  competition. Even numbered years since 1994
• Solved, but unpublished structures are posted in
  May, predictions due in September, evaluations in
  December
• Various categories
• Relation to existing structures, ab initio,
  homology, fold, etc.
• Partial vs. Fully automated approaches
• Produces lots of information about what aspects
  of the problems are hard, and ends arguments
  about test sets.
• Results showing steady improvement, and the value
  of integrative approaches.

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CASP 6 Categories

• Human intervention versus fully automated
  predictions
• Comparative modeling
• A structure exists for a good homolog
• Looking for mutations, bond rotations, etc.
• Fold recognition (Homologs)
• Distant homolog recognition and adaptation
• Looking at loop placement, domain boundaries
• Fold recognition (Analogous)
• No homolog, but similar structures in DB
• Finding the right model structure
• Ab Initio
• No similar structures in DB. Most fundamental
  problem.
• Other issues
• Domain boundaries, disordered regions,
  residue-residue contacts

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CASP Results

• Fully automated methods now nearly as good as
  ones with human intervention
• Consensus methods (looking for agreement among
  servers) do best overall, but not by much and not
  all the time.
• Consistent best approach is Rosetta from David
  Bakers lab

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CASP performance improving
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Baker best strategy so far

• Two step process
• Generate a good sized collection of plausible
  structures and near-miss bad structures
• Requires a good energy function, good
  optimization approach
• Quality of decoy (incorrect, but plausible
  folds) is important
• Build discriminators to separate correct from
  decoy structures.
• Rosetta (Baker lab) and fully automated Robetta.
• Ran away with CASP4, still the best at CASP5 6
• Robetta almost as good as Rosetta
• Outstanding at ab initio, competitive at the
  rest.

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Rosetta approach

• Integrated method
• I-Sites much finer grained substructures than
  secondary structures. A library of all
  consistent structures of short polypeptides is
  defined (taken from PDB)
• Build initial models by assigning I-sites to new
  amino acid sequence (many possibilities)
• Monte Carlo search through assignments of I-Sites
  to minimize energy function.
• Use of sophisticated global energy function
• Take good scoring structures, and test them on a
  decoy detector, which looks for high scoring
  but non-native structure patterns.

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I-Sites

• I-sites are a set of sequence patterns that
  strongly correlate with protein structure at the
  local level.
• Ungapped amino acid sequence motifs
• Length 3-9 (now longer)
• Originally 82 classes (now more)
• Defined by amino acid log odds matrix and phi/psi
  angles
• Far more detailed than the 3 state
  helix/sheet/other local structure models

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Example I-Site

• Proline containing alpha helix C-cap

f/j
cartoon
AA log odds
member structures
Motif position
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How I-sites are defined

• Starting from all sequences in PDB at the time
• Remove sequences with 25 or greater sequence
  identity to compensate for oversampling of
  certain families
• Cluster all possible subsequences of these
  structures of length 3-15.
• For each cluster, define paradigm structure.
• Remove members that are too far away structurally
• Add new members that are structurally similar
• If can't distinguish well (bimodal scores)
  between members and non-members, drop the cluster

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I-sites are not unique

• One amino acid subsequence may be compatible with
  several I-sites
• I-sites are not defined to be mutually exclusive
  over sequence.
• Slightly different starting positions or lengths
  may yield quite different (even incompatible)
  I-sites for the same sequence region.
• This has biological relevance
• Local predispositions are not determinative or
  unique
• Multiple predispositions are more informative
  than none.

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I-sites pro and con

• Lots of ad hoc fiddling to get I-site library
• Distance measure on sequence has two free
  parameters
• Many different structure distance measures tried
• K-means clustering (K is free parameter)
• Test for bimodal scoring (two more parameters)
• Occasional subdivision of an I-Site that seemed
  to have two good structures associated with it
• Corresponds reasonably well to existing
  crystallographic concepts (e.g. Type II b turns)
• They are more predictable than H/S/C

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HMMSTR

• I-sites often overlap (sequences of sites
  corresponds to traditional local structures)
• Basic idea Hidden Markov Model for sequences of
  I-sites
• No in/dels. States specifydistributions of
• Amino acids
• secondary structures
• f/j angles (discretized)
• structural context

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Simple HMMSTR

• Simple example for well knownstructural motif
• Combination of twoI-sites which overlap
• States defined bypositions in an I-site
• Alternative pathsfor different I-sites

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• Whole HMMSTRmodel
• Each node hasstart probability
• Specifies transitionsbetween typesof local
  structureas well as within them

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Training of HMMSTR

• Many ad hoc approaches based on biological
  intuitions
• When to merge overlapping states?
• Dynamic programming to find likely transitions
  between I-sites
• Null transition state to connect otherwise
  disconnected subtrees.
• Model surgery adding, splitting and deleting
  states.
• Structure predictions by voting rather than
  most probable parse.

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Beating HMMSTR

• OK, but not great results in predictive accuracy.
  
• Too many alternative paths through the model, and
  difficulty choosing between them on the basis of
  sequence alone.
• Only local information no global measures used.
• Rosetta add global information to I-site
  assignments and get a big improvement

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Rosetta prediction method

• Define global scoring function that estimates
  probability of a structure given a sequence
• Generate version of I-sites with fixed length
  subsequences (9 amino acids)
• Calculate P(I-Sitesequence) for all sequences
  and I-sites
• Generate structures by Monte Carlo sampling of
  assignments of fixed size I-sites to subsequences
• End up with ensemble of plausible structures

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Rosetta Scoring Function

• Global scoring function issues
• Distinguish native-like structures from not.
  Generation methods unlikely to produce exact
  native structure.
• Decoy testing. Create many structures that are
  plausible and not too far from native fold, and
  try to distinguish these
• Bayesian approach
• Sequence dependent and sequence independent
  evaluation of predicted structure.

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Score Decomposition
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Good Performance

• An ab initio target
• Red correct, Grey incorrect
• Missed a sheet
• Good overalltopology

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And bad

• Hardest structure forall prediction methods
• Central sheet regioncontains loops andtwo small
  helices
• Single hydrogen bondextends and alterstwo
  substructures