Protein Structure Prediction

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Fold recognition
refine
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Ab initio prediction of protein structure
concept

• Go from sequence to structure by sampling the
  conformational space in a reasonable
• manner and select a native-like conformation
  using a good discrimination function
• Problems conformational space is astronomical,
  and it is hard to design functions that
• are not fooled by non-native conformations (or
  decoys)

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Ab initio prediction of protein structure
sample conformational space such that native-like
conformations are found
hard to design functions that are not fooled by
non-native conformations (decoys)
astronomically large number of conformations 5
states/100 residues 5100 1070
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Sampling conformational space continuous
approaches

• Most work in the field
• Molecular dynamics
• Continuous energy minimisation (follow a valley)
• Monte Carlo simulation
• Genetic Algorithms

• Like real polypeptide folding process
• Cannot be sure if native-like conformations are
  sampled

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Molecular dynamics

• Force -dU/dx (slope of potential U)
  acceleration, m a(t) force
• All atoms are moving so forces between atoms are
  complicated functions of time
• Analytical solution for x(t) and v(t) is
  impossible numerical solution is trivial
• Atoms move for very short times of 10-15 seconds
  or 0.001 picoseconds (ps)
• x(tDt) x(t) v(t)Dt 4a(t) a(t-Dt)
  Dt2/6
• v(tDt) v(t) 2a(tDt)5a(t)-a(t-Dt) Dt/6
• Ukinetic ½ S mivi(t)2 ½ n KBT
• Total energy (Upotential Ukinetic) must not
  change with time

old position
old velocity
acceleration
new position
acceleration
old velocity
new velocity
n is number of coordinates (not atoms)
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Energy minimisation

• For a given protein, the energy depends on
  thousands of x,y,z Cartesian atomic
• coordinates reaching a deep minimum is not
  trivial
• With convergence, we have an accurate
  equilibrium conformation and a well-defined
• energy value

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Monte Carlo simulation

• Discrete moves in torsion or cartesian
  conformational space
• Evaluate energy after every move and compare to
  previous energy (DE)
• Accept conformation based on Boltzmann
  probability
•  
•  
• Many variations, including simulated annealing
  (starting with a high temperature so
• more moves are accepted initially and then
  cooling)
• If run for infinite time, simulation will
  produce a Boltzmman distribution

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Genetic Algorithms

• Generate an initial pool of conformations
• Perform crossover and mutation operations on
  this set to generate a much larger pool of
• conformations
• Select a subset of the fittest conformations
  from this large pool
• Repeat above two steps until convergence

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Sampling conformational space exhaustive
approaches
enumerate all possible conformations view entire
space (perfect partition function)
must use discrete state models to minimise number
of conformations explored
computationally intractable 5 states/100
residues 5100 1070 possible conformations
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Scoring/energy functions

• Need a way to select native-like conformations
  from non-native ones
•  
• Physics-based functions electrostatics, van der
  Waals, solvation, bond/angle terms
• Knowledge-based scoring functions derive
  information about atomic properties from a
• database of experimentally determined
  conformations common parametres include
• pairwise atomic distances and amino acid
  burial/exposure.

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Requirements for sampling methods and scoring
functions

• Sampling methods must produce good decoy sets
  that are comprehensive and include
• several native-like structures
• Scoring function scores must correlate well with
  RMSD of conformations (the better
• the score/energy, the lower the RMSD)

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Overview of CASP experiment

• Three categories comparative/homology
  modelling, fold recognition/threading, and
• ab initio prediction
• Goal is to assess structure prediction methods
  in a blind and rigourous manner blind
• prediction is necessary for accurate assessment
  of methods
• Ask modellers to build models of structures as
  they are in the process of being solved
• experimentally
• After prediction season is over, compare
  predicted models to the experimental
• structures
• Discuss what went right, what went wrong, and
  why
• Compare progress from CASP1 to CASP4
• Results published in special issues of Proteins
  Structure, Function, Genetics 1995,
• 1997, 1999, 2002

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Comparative modelling at CASP - methods

• Alignment PSI-BLAST, FASTA, CLUSTALW - multiple
  sequence alignments
• carefully hand-edited using secondary
  structure information
•  
• More successful side chain prediction methods
  include
• backbone-dependent rotamer libraries (Bower
  Dunbrack)
• segment matching followed by energy minimisation
  (Levitt)
• self-consistent mean field optimisation (Bates
  et al)
• graph-theory knowledge-based functions
  (Samudrala et al)
• More successful loop building methods include
• satisfaction of spatial restraints (Sali)
• internal coordinate mechanics energy
  optimisation (Abagyan et al)
• graph-theory knowledge-based functions
  (Samudrala et al)
• Overall model building there is no substitute
  for careful hand-constructed models
• (Sternberg et al, Venclovas)

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A graph theoretic representation of protein
structure
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Historical perspective on comparative modelling
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Historical perspective on comparative modelling
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Prediction for CASP4 target T128/sodm Ca RMSD of
1.0 Å for 198 residues (PID 50)
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Prediction for CASP4 target T111/eno Ca RMSD of
1.7 Å for 430 residues (PID 51)
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Prediction for CASP4 target T122/trpa Ca RMSD of
2.9 Å for 241 residues (PID 33)
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Prediction for CASP4 target T125/sp18 Ca RMSD of
4.4 Å for 137 residues (PID 24)
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Prediction for CASP4 target T112/dhso Ca RMSD of
4.9 Å for 348 residues (PID 24)
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Prediction for CASP4 target T92/yeco Ca RMSD of
5.6 Å for 104 residues (PID 12)
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Comparative modelling at CASP - conclusions
T128/sodm 1.0 Å (198 residues 50)
T111/eno 1.7 Å (430 residues 51)
T122/trpa 2.9 Å (241 residues 33)
T112/dhso 4.9 Å (348 residues 24)
T92/yeco 5.6 Å (104 residues 12)
T125/sp18 4.4 Å (137 residues 24)
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Fold recognition at CASP - methods

• Visual inspection with sequence comparison
  (Murzin group)
• Procyon - potential of mean force based on
  pairwise interactions and global dynamic
• programming (Sippl group)
• Threader - potential of mean force and double
  dynamic programming (Jones group)
• Environmental 3D Profiles (Eisenberg group)
• NCBI Threading Program using contact potentials
  and models of sequence-structure
• conservation (Bryant group)
•  
• Hidden Markov Models (Karplus group)
• Combination of threading with ab initio
  approaches (Friesner group)
• Environment-specific substitution tables and
  structure-dependent gap penalties
• (Blundell group)

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Fold recognition at CASP - conclusions

• Fold recognition is one of the more successful
  approaches at predicting structure at all
• four CASPs 
• At CASP2 and CASP4, one of the best methods was
  simple sequence searching with
• careful manual inspection (Murzin group)
• At CASP3 and CASP4, none of the threading
  targets could have been recognised by the
• best standard sequence comparison methods such
  as PSI-BLAST
•  
• For the most difficult targets, the methods were
  able to predict ? 60 residues to 6.0 Å
• Ca RMSD, approaching comparative modelling
  accuracies as the similarity between
• proteins increased.

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Ab initio prediction at CASP methods

• Assembly of fragments with simulated annealing
  (Simons et al)
• Exhaustive sampling and pruning using
  knowledge-based scoring functions
• (Samudrala et al)
•  
• Constraint-based Monte Carlo optimisation
  (Skolnick et al)
• Thermodynamic model for secondary structure
  prediction with manual docking of
• secondary structure elements and minimisation
  (Lomize et al)
• Minimisation of a physical potential energy
  function with a simplified representation
• (Scheraga et al, Osguthorpe et al)
• Neural networks to predict secondary structure
  (Jones, Rost)

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Semi-exhaustive segment-based folding
EFDVILKAAGANKVAVIKAVRGATGLGLKEAKDLVESAPAALKEGVSKDD
AEALKKALEEAGAEVEVK
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Historical perspective on ab initio prediction
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Prediction for CASP4 target T110/rbfa Ca RMSD of
4.0 Å for 80 residues (1-80)
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Prediction for CASP4 target T97/er29 Ca RMSD of
6.2 Å for 80 residues (18-97)
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Prediction for CASP4 target T106/sfrp3 Ca RMSD
of 6.2 Å for 70 residues (6-75)
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Prediction for CASP4 target T98/sp0a Ca RMSD of
6.0 Å for 60 residues (37-105)
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Prediction for CASP4 target T126/omp Ca RMSD of
6.5 Å for 60 residues (87-146)
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Prediction for CASP4 target T114/afp1 Ca RMSD of
6.5 Å for 45 residues (36-80)
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Postdiction for CASP4 target T102/as48 Ca RMSD
of 5.3 Å for 70 residues (1-70)
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Ab initio prediction at CASP - conclusions
T97/er29 6.0 Å (80 residues 18-97)
T98/sp0a 6.0 Å (60 residues 37-105)
T102/as48 5.3 Å (70 residues 1-70)
T110/rbfa 4.0 Å (80 residues 1-80)
T114/afp1 6.5 Å (45 residues 36-80)
T106/sfrp3 6.2 Å (70 residues 6-75)
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Computational aspects of structural genomics
(Figure idea by Steve Brenner.)
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Key points

• DNA/gene is the blueprint - proteins are the
  functional representatives of genes
• Protein structure can be used to understand
  protein function
• Large numbers of genes being sequenced - need
  structures
• Protein folding (from primary sequence to
  tertiary structure) is a fast self-organising
• process where a disordered non-functional chain
  of amino acids becomes a stable,
• compact, and functional molecule 
• The free energy difference between the folded
  and unfolded states is not very high
• Experimental methods to determine protein
  structures include x-ray crystallography
• and NMR spectroscopy
•  
• Theoretical methods to predict protein
  structures include comparative/homology
• modelling, fold recognition/threading, and ab
  initio prediction
• For ab initio prediction, you need a method that
  samples the conformational space

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