protein folding - carnegie mellon school of computer scienceckingsf/bioinfo-lectures/... ·...
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Protein FoldingCMSC 423
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Proteins
VC
R
Rresidue
AGG GUC UGU CGA
R V C R
mRNA ∑ = {A,C,G,U}
protein |∑| = 20 amino acids
Amino acids with flexible side chains strung
together on a backbone
Function depends on 3D shape
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Examples of Proteins
Alcohol dehydrogenase
Trypsin: breaks down other proteins
Antibodies
Collagen: forms tendons, bones, etc.
Examples of “Molecules of the Month” from the Protein Data Bank http://www.rcsb.org/pdb/
TATA DNA binding protein
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Backbone
Protein Structure
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Backbone
Protein Structure
Side-chains
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http://www.jalview.org/help/html/misc/properties.gif
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1tim
Alpha helix Beta sheet
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Alpha Helix
Suggested from theoretical considerationby Linus Pauling in 1951.
C’=O of residue n bonds to NH of residue n + 4
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antiparallel parallel
Beta Sheets
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Structure Prediction
Given: KETAAAKFERQHMDSSTSAASSSN…
Determine:
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http://boinc.bakerlab.org/rah_about.php
Folding Ubiquitin with Rosetta@Home
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CASP8
Ben-David et al, 2009 Critical Assessment of protein Structure Prediction
Target BestPrediction
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Structural Genomics
Space of all protein structures
Determinedstructure
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Structure Prediction & Design Successes
Top7: start with unnatural, novel fold at left, designed a sequence of amino acids that will fold into it. (Khulman et al, Science, 2003)
FoldIt players determination the structure of the retroviral protease of Mason-Pfizer monkey virus (causes AIDS-like disease in monkeys). [Khatib et al, 2011]
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Determining the Energy
• Energy of a protein conformation is the sum of several energy terms.
•“Force Fields” such as CHARMM and AMBER give explicit approximations to each of these terms.
van der Waals
electrostatics
bond lengthsbond angles
dihedral angleshydrogen bonds
0+ -
A
B
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Energy Function (AMBER) Details
Hook’s law, spring of ideal length l0 or θ0and tension kb, ka
electrostatic between particles of charge qi and qj: derived from Coulumb’s law
van der Waals potential
Sum over all pairs of atoms
calculate the potential energy of a protein structure
equations typeset courtesy Wikipedia
function dependent on how much a bond is twisted
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Rosetta@Home Algorithm (High-level)
S = linear, unfolded chain
While some part of chain hasn’t been moved a lot:
! Move part of S to get structure S’
! If energy(S’) < energy(Best):
! ! Best = S’
! If energy(S’) < energy(S):
! ! S = S’
! Else with probability related to energy(S) - energy(S’):
! ! S = S’
Stage 1: uses big moves and a simple energy function
State 2: uses small moves and a complex energy function
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Rosetta@Home Algorithm (High-level)
S = linear, unfolded chain
While some part of chain hasn’t been moved a lot:
! Move part of S to get structure S’
! If energy(S’) < energy(Best):
! ! Best = S’
! If energy(S’) < energy(S):
! ! S = S’
! Else with probability related to energy(S) - energy(S’):
! ! S = S’
Stage 1: uses big moves and a simple energy function
State 2: uses small moves and a complex energy function
exp((energy(S) - energy(S’))/T)
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-96
-88
-80
-72
-64
-56
-48
-40
-32
-24
-16 -8 0
0.25
0.5
0.75
1
T = 100
T = 10
exp(Δenergy)/T)
When T is large, more likely to accept a “bad” move.
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Avoiding Local MinimaB
ett
er
Energy landscapes
At low values of T, you will walk down towards a local minima.At high values of T, you may jump out of a valley.Simulated annealing idea: start with a high value of T and decrease over time (cooling schedule).
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Summary
Protein structure vital in understanding protein function.
Prediction of protein structure is a very hard computational problem
Some notable successes over the last ≈10 years
Based on carefully constructed energy functions
Main algorithmic tool: simulated annealing-like randomized algorithms that efficiently explore the space of conformations