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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 l.jpg

Chap. 8Molecular Structure Prediction

Introduction to Computational Molecular Biology


Background l.jpg
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.


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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).


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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.


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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.


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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


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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.


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Loop

Hairpin loop

Bulge on i

Interior loop

Helical region


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Dynamic Programming

  • The dynamic programming formula


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