Introduction to Protein Folding

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Introduction to Protein Folding
Yaohang Li Department of Computer Science North
Carolina AT State University
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Introduction to Protein Folding

• Protein are biologys workhorses
• Nanomachines
• Carry out biochemical function
• Enzyme
• Structural elements
• Antibodies
• Genome
• Blueprint of Protein
• Specify the sequence of amino acids
• Protein Folding
• Protein self-assembles to a particular shape
• The shape determines the function of the
  protein
• Connection between Genome (sequence) and Protein
  Function

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Protein Folding Grand Challenges of
Computational Biology

• Protein Folding
• Predicting the 3-D Structure of protein
• Problems related to folding
• Dynamic structure prediction
• Protein docking
• Protein-protein interaction
• Issues
• Models
• Force fields (e.g. Charmm, Amber)
• Lots of parameters, constrained by experiment
  good enough?
• Sampling
• Can simulate 1ns 10-9 sec in a day
• Need to sample 104 to 106 ns!

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Why simulation?

• Physics ? chemistry ? biology
• Start from the laws of physics and chemistry
• explain the properties of biomolecules
• Experiments
• less detailed
• Spectroscopies, FRET, NMR, etc.
• Crystals are static
• Constrained by the experimental environment
• Costly
• Time Consuming
• Simulations
• very detailed
• Femtosecond time resolution
• Angstrom spatial resolution
• Much like having thousands of completely detailed
  single molecule experiments
• Relatively Cheap

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Goals

• Can we characterize folding computationally?
• Accurate rates
• Detailed mechanisms
• Can we design proteins?
• Specific stable structure
• Retention of function

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Levels of structures in Proteins

• Primary Structure
• amino acid sequence
• Secondary Structure
• Common motifs
• alpha helix
• beta sheet
• coil (turn)
• Tertiary Structure
• 3D conformation
• Quaternary Structure
• Multiple polypeptide chains

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Tertiary Structure Prediction

• Three variants
• Ab initio prediction
• Protein Threading
• Homology-based prediction(Comparative
  modelling)

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Ab initio

• From Merriam-Webster's Dictionary
• Etymology Latin
• Meaning From the beginning
• In the field of Bioinformatics
• Predicting tertiary structure in the absence of
  homology to a known structureAPKFFRGGNWKMNGKRSL
  GELIHTLGDAKLSADTEVVCGI APSITEKVVFQETKAIAD
  NKD WSKVEVHESRIYGGSVTNCK
  ELASQHDVDGFLVGGASLKPVDGFLHALAEGLGVDINAKH.......
  ....

Ab Initio
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Anfinsens thermodynamic hypothesis
The 3D structure of a protein in its native
environment is the one in which the Gibbs free
energy of the whole system is the lowest.
sequence determines structure
Anfinsen, C.B. Principles that govern the folding
of protein chains. Science 181, 223-30 (1973).
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Folding Energy Landscape
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Levinthal paradox
If a protein has 100 amino acids, and each amino
acid has 3 conformational states, then the
protein has 3100 conformational states, of
which 1 is the Native state. Protein High Degree
of Freedom -gt Huge Search Space
Mathematician Curse of Dimensionality
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Ab Initio methods

• Assumption The structure that a protein folds
  into inside cells is the structure with the
  lowest global free energy (or a structure very
  similar to it)
• Finding native-like protein conformations
  requires developing
• an accurate potential function that permits
  calculation of the free energy given a structure
• an efficient method for searching for energy
  minima

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Models

• Models are used to reduce the search space
  (simplify the computation)
• Three kinds of models
• Lattice models
• Discrete state off-lattice models
• Narrowing the search with Local Structure
  Prediction

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Lattice models

• How to reduce complexity
• Represent peptide chains as lattices
• Advantage
• Analytical and computational simplicity
• Disadvantage
• Restricted ability to represent subtle geometric
  considerations (e.g. strand twist)
• Backbone reproduced has accuracies no greater
  than approximately half the lattice spacing

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Discrete State Off-Lattice Models

• How to reduce complexity
• Only allow certain side chain structures and
  limited peptide-bond rotations, e.g.
• limit side chain to a single rotamer
• limit the backbone to specific Phi/Psi pairs
• The Omega angle tends to be planar (0 or 180o)

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Narrowing the search withLocal Structure
Prediction

• How to reduce complexity
• Use Local Structure Biases Local Structures
  excised from proteins can fold independent of the
  full protein
• But, Strength and Multiplicity of Local Structure
  Biases are highly sequence dependent
• Use sequence motifs (Bystroff et al)
• Have strong tendencies to adopt a single local
  conformation (in different sequences)
• Made good predictions in CASP2

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Scoring Functions

• Scoring function
• Appropriate for the reduced space and
• can be calculated rapidly
• Three examples
• Solvation-based scores Classify sites in known
  proteins by degree of solvent exposure and
  determine frequencies of each amino acid in each
  site
• Pair interactions How likely two residues are
  to be near each other
• Secondary Structure Arrangement Score how well
  secondary structure elements match with each other

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Who is ROSETTA

• ROSETTA Stone(From http//www.ba.dlr.de/ne/pe/vi
  rtis/stone1.htm)
• ROSETTAThe "Translation" of silent symbols into
  a living languageSilent symbols ?
  Living language hieroglyphs ?
  Greekanalogically polypeptide
  ? Tertiary Structure

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What is ROSETTA Method

• Kim T. Simons, Rich Bonneau, David Baker, et al
• Model Narrow the search with Local Structure
  Prediction
• Scoring function Solvation-based Pair
  interactions
• Method outline (two steps)
• "Get tiny pieces" sequence profile alignment
• "Put them together" Monte-Carlo
  method Bayesian scoring function
  
  N near-native structures

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"Get tiny pieces"

• AssumptionDistribution of conformations sampled
  for a given nine residue segment of the chain is
  reasonably well approximated by the distribution
  of structures adopted the sequence(and closely
  related sequences) in known protein structures.
• MethodFragment libraries for each three and nine
  residue segment of the chain are extracted from
  PDB using sequence profile alignment

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"Put them together"
?
?
?

• Which is better ?You need
• Energy function and
• Space searching method

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"Put them together"(cont.)

• Sample the resulting conformational space with
  Monte-Carlo method
• Bayesian scoring function
• Chose the most likely structure given the
  sequence

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ROSETTA -- Scoring Function (cont.)
Bayesian Theorem
In ab initio folding, we assume P(structure)
Comparing different structures of the same
sequence, it is a constant
In threading wih pairs of positions
independent rij distance between residues i
and j
Using Bayesian theorem for each i and j
Independent of structure in same sequence
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ROSETTA -- Scoring Function (cont.)

• Thus we get

The Scoring Function favours Compact
structure Buried hydrophobic residues (Paired
beta-strands)
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Metropolis-Hastings Method

• Simulating a Markov Chain
• Generate a new state y from the current state x
• Change the configuration of a random selected
  3-residues
• Metropolis-Hastings Ratio
• rgt1, accept y
• rlt1, accept y with probability r
• Reject y

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Simulated Annealing

• Physically motivated approachhigh temperature
  --gt move around low temperature --gt no
  free energy to movecool quickly --gt
  defective crystal cool slowly --gt
  perfect crystal
• Analogue Natural annealing process lt----gt
  Monte Carlo methodThe best crystal structure
  lt----gt Native conformation

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My Contribution Accelerated Simulated Tempering
Scheme
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Our Simulation Results
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The CASP contest

• CASP(Critical Assessment of Structure
  Prediction)
• Experimentalists announce some protein sequences
  that they are going to resolve structurally
• CASP put these sequence on web for prediction
  with deadline
• Computational biologists submit their predictions
• CASP evaluates the predictions according to the
  results resolved by experimentalists

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ROSETTA results

• FactsLeft Native structuresRight
  Predictions

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Protein Folding Application Research in the Mad
Cow Disease
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Summary

• Before you ask me questions
• Is Rosetta really ab initio?