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Chap. 8 Molecular Structure Prediction

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

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  1. Chap. 8Molecular Structure Prediction Introduction to Computational Molecular Biology

  2. 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.

  3. 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).

  4. 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.

  5. 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.

  6. 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

  7. 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.

  8. Loop Hairpin loop Bulge on i Interior loop Helical region

  9. Dynamic Programming • The dynamic programming formula

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