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Chap. 8 Molecular Structure Prediction. Introduction to Computational Molecular Biology. Background. Given a primary 1-D molecular sequence, Determine its 3-D secondary or higher order structure. 3-D structure determine the function of a molecule

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chap 8 molecular structure prediction

Chap. 8Molecular Structure Prediction

Introduction to Computational Molecular Biology

background
Background
  • Given a primary 1-D molecular sequence,

Determine its 3-D secondary or higher order structure.

  • 3-D structure determine the function of a molecule
  • Techniques for molecular structural determination
    • such as X-ray crystallography and NMR
      • costly and not always feasible.
    • Computer-based prediction
      • allows us to do some assessment about the molecular function based on the predicted structure.
background3
Background
  • Focus in this chapter
    • In RNA
      • focus on secondary structure prediction
        • concerning how bases are paired.
    • In proteins
      • we study two problems
        • protein folding and protein threading.
  • A basic assumption
    • the primary sequence uniquely determines how the molecule folds (in both RNA and proteins).
secondary structure prediction
Secondary Structure Prediction
  • Given an RNA molecule
    • R = r1 r2 ... rn
    • the secondary structure S = {... (ri, rj) ...}
      • ri, rj in {A, C, G, U} and ri is a complement to rj.
  • Constraints
    • threshold t : j - i > t
      • the molecule does not bend too much on itself.
    • No knots.
      • (ri, rj) in S, (rk, rl) in S, and i < k < j < l.
      • exclusion of knots simples the problem
      • inferred at a later stage of structure prediction.
    • Minimum free energy.
independent base pairs
Independent Base Pairs
  • The total free energy E of a structure S is given by
  • (ri, rj) is the free energy of base pair (ri, rj)
    • a(ri, rj) < 0 if i ≠ j
    • a(ri, rj) = 0 if i = j.
independent base pairs6
Independent Base Pairs
  • Compute the free energy
    • Using the dynamic programming concept.
    • Consider a substring Ri,j = ri ri+1 ... rj
    • There are two cases:
      • ri pairs to rj.
      • rj pairs to rk (i < k < j)
  • The dynamic programming formula
structures with loops
Structures with Loops
  • In a structure with loops, a base may be unpaired.
  • Consider a substring Ri,j = ri ri+1 ... rj.
    • There are four cases:
      • (1) ri is unpaired.
      • (2) rj is unpaired.
      • (3) rj is paired to rk (i < k < j).
      • (4) ri is paired to rj.
slide8
Loop

Hairpin loop

Bulge on i

Interior loop

Helical region

dynamic programming
Dynamic Programming
  • The dynamic programming formula
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