Structure Prediction

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Structure Prediction

• dmitra

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Methods

• Ab initio
• Heuristics
• Machine learning
• Homology modeling
• Threading

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RNA Structure Prediction Ab-initio

• Sequence over A, C, G, U
• Complementary pairs attract, form base-pairs or
  minimizes energy
• We are not interested in overall energy of the
  sequence, just the process of minimization
• Just the linear sequence, zero base pairs,
  energy0
• Physics is embedded within free-energy
  parameter/function
• Minimization of energy is objective

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RNA Structure Prediction Knot-free

• Knot-free assumption
• Knot base pairs (I, j) and (k, l) where Iltjltkltl
• Knot-free causes planar graph, and makes DP
  algorithm feasible
• Base pairs are disjoint or embed in each other

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RNA Structure Prediction Principle of optimality

• Assumption 1 Base-pairing do not affect each
  others energy
• Now one can add energy minimization by all base
  pairs in a string and check which configuration
  produces lowest energy
• Combinatorics is exponential
• Need further assumption

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RNA Structure Prediction DP Algorithm

• Assume energy for each component can be
  calculated independently
• a(r,k) free energy for base pair (r,k), where r,
  k from ACGU
• a is zero for self-pairing (impossible)

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RNA Structure Prediction DP Algorithm

• E(Sij) min
• E(SI1,j-1 ) a(ri,rj), when i,j pairs,
• MinE(SI,k-1) E(Sk1,j ), when j pairs with
  k, Iltkltj
• Compute (n x n) matrix for I and j, bottom up,
  for I-j0, I-j1, I-j2,
• Complexity O(n3)

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RNA Structure Prediction relax assumptions

• Consider some special energy functions, other
  than just the base pairing ones a(r,k)
• This means different types of base pairings
• Some more practical topology

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RNA Structure Prediction Loops

• Say, base pair at (I,j) and Iltultvltwltj
• v is accessible from base pair (I,j) if there is
  no base pair at (u,v)
• Loop is the bases accessible from base pair (I,j)
• Note, still no knot
• Some loops p249

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RNA Structure Prediction Energy over loops

• Say, (I,j) base pair closes a loop
• Si1,j-1 may not have the minimum energy
  configuration
• Because energy of Si1,j-1 plus free energy of
  a(ri,rj) may be less than min-energy
  configuration of string (I1 to j-1) without base
  pairing at (I,j)
• This interactive-ness was ignored at the previous
  assumption level
• Dynamic Programming can still be done, if we
  explicitly specify energy parameters

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RNA Structure Prediction Energy over loops

• E(Sij) min
• E(SI1,j ), I is not paired
• E(SI1,j-1 ), j is not paired
• minE(S,i,k-1) E(Sk1,j ), when i or j pairs
  with k, iltkltj,
• E(LI,j ), when (I,j) base pairs and all special
  structures may appear within embeds first
  formula of previous assumption

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RNA Structure Prediction More assumptions

• Disregard free energies that do not belong to any
  loops
• Added energy of only components is the final
  energy of the string no interaction between
  components
• Only 4 types of loops as in p249 for E(LI,j ),
  (can add more, if you know their energy
  parameterization)

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RNA Structure Prediction free energies for 4
loops

• Hairpin loop of size k Zi(k)
• Additional stabilizing energy for two adjacent
  base pairs(in addition to a(r,k)) eta, constant
• Destabilizing energy for bulge of size k
  beta(k)
• Destabilizing energy for interior loop of size k
  gamma(k)

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RNA Structure Prediction E(LI,j )

• Hairpin a(ri,rj) zi(j-I1)
• Stacked-pair a(ri,rj)etaE(Si1,j-1)
• Bulge on i mina(ri,rj)beta(k) E(Sik1,j-1),
  kgt1
• Bulge on j mina(ri,rj)beta(k) E(Si1,j-k-1),
  kgt1
• Interior loop mina(ri,rj)gamma(k1k2)
  E(Sik11,j-k2-1), k1,k2gt1

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RNA Structure Prediction complexity

• O(n2) table entries
• On each entry
• First 2 formulae O(1) leading to O(n2)
• Third formula O(n) O(n3)
• 4.1 (E(L) hairpin) O(1) O(n2)
• 4.2 O(1) O(n2)
• 4.3 O(n), run on k O(n3)
• 4.4 O(n), run on k O(n3)
• 4.5 O(n2), run on k1, k2 O(n4)
• Final complexity from 4.4 O(n4)

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Protein Threading

• Interactions in proteins are between 20x20
  residues, as opposed to 4x4 NAa at most in RNAs
• Residue interactions are quite non-local, causing
  much more structural complexity
• Proteins have frequent loops (helices are loops)
• So, prediction by Ab initio is extremely difficult

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Protein Threading

• Number of protein folds are few (1,000 for
  20,000 proteins)
• Threading map the target sequence over a
  template fold
• Threading is an alignment problem, Torda, Fig1
• Find the fold to which target aligns optimally
  (minimum energy function)
• Needs basic scoring functions as in sequence
  alignment

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Protein Threading number of folds

• More the number of folds in database more time
  to find correct template
• Scoring function for threading is quite
  imperfect need more available templates
  (contradictory requirements)

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Protein Threading Scoring functions

• Full force field is not necessarily ideal
• it involves dynamics between molecules, stretch,
  torsion, etc.
• Unimportant for a static alignment

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Protein Threading Scoring functions

• Scoring function could be between residues from
  the same sequence for coming close to each other
  on the alignment
• Torda, Fig 5
• Example scoring function (free energy)
• For pair of residues A and B to be at distance r
  (Torda, p7)
• G(AB) kT ln(rho-rAB / rho-0-rAB),
• rho-rAB is probability of AB to be at distance
  r,
• rho-0 is probability of random occurrence of
  that (k,T usual)

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Protein Threading Scoring functions

• Probabilities are collected from PDB proteins
  with known structure
• Different threading scheme uses different scoring
  functions, but mostly they are derived from PDB

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Protein Threading Scoring functions

• Example (Setubal-Meidanis, p257)
• G1(I, ti) for placing i-th residue in sequence to
  the ti position in the fold
• G2(I, j, ti, tj) simultaneous placements of i, j,
  for Iltj
• Constrained to be within a range, say bilttiltei

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Protein Threading

• Optimization is not only on placement, but also
  on multiple folds in database
• Accuracy is very sensitive to alignment errors

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Protein Threading Dynamic programming

• Advantage/disadvantage of DP is that it is
  deterministic
• Problem adjacency is hard to define in 3D

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Protein Threading Dynamic programming

• DP try out different combination of adjacent
  residues on different parts of a template (Torda,
  Fig 5c adjacent comes from template sequence)
• Start with smaller number of elements and build
  up to the full sequence
• Alternative approach start with placing each
  residue to one of its possible positions and
  see where next residue should go continue
  residue by residue

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Protein Threading Probabilistic algorithm

• Monte Carlo simulation randomly throw residues
  at positions on fold and check aggregate scoring
  function
• Simulated annealing gradually move residues to
  optimize, stochastically making random shifts to
  avoid local optimum
• Time consuming, the result is non-deterministic

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Protein Threading Branch and bound

• In the worst case try all possible alignments,
  but prune the search space for non-useful
  branches using some bounding function

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Protein Threading Search on folds

• Divide and conquer over the space of folds
• Assumption folds can be ordered for their
  goodness for the target protein
• Example Setubal-Meidanis, p258

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Protein Threading Future

• Slow
• Subsumed by Ab intio of IBM Blue Gene type
  projects
• De Novo technique using linear programming (Xu
  and Li, 2003)
• Threading techniques are not only useful for
  structure prediction but for fold recognition
  problem also no alignment, just find the
  template (fold suggests function)