Protein Structure Prediction

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Protein Structure Prediction
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What is PSP ?
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Primary sequence (1D)
Tertiary Structure (3D)

• ACLLYYTTCAT

all bonds angles, dihedral angles and bond
lengths between each amino acid residue in
protein
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Solving PSP
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View PSP as a search

• Given any primary sequence of an unknown protein
  (in the sense of its 3D structure)
• Consider PSP as performing a search through the
  configuration space of the given protein

The space of different configurations
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Steps in solving PSP

• Given primary sequence predict the final 3D
  structure
• (1D 3D).
• 2 Step process (1D 2D, 2D 3D)
• 1st find configuration for the secondary
  structure (SS Prediction)
• 2nd find configuration for the side-chains
  (side-chain conformation)

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Required components in solving PSP

• All methods require the definition of a protein
  model
• A simplified protein structure model
• A potential energy function

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Simplified structure model of Protein

• By the above we mean that the protein in
  question has simpler physical properties then an
  actual protein
• This is needed as trying to solve PSP is too
  complex for real proteins
• Good simplified models give a good approximation
  for the actual shape of the protein
• Determining a good model is a research area by
  itself

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Example of Simplified Model of Protein
Simplified model of the protein backbone
Actual model of the protein backbone
3 dihedral angles
is the only dihedral angle
Bond angles
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Potential Energy Function

• How do we know when a predicted structure is the
  native shape of the protein ?

In thermodynamics, A molecule is most
stable when its free energy is at a minimum
native shape is at a free energy minimum

• The potential energy function is a
  simplification of actual forces acting on a real
  protein molecule and its formulation is based on
  the given simplified structural model

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Example of Potential Energy Function
Purpose Minimize

• Etotal EHH Evdw

Hydrophobic Interaction
Van der Waals Interaction
Evdw Cv fvdw
Van der Waals Potential
rij distance between atom i and j Ri van der
waals radii of atom i
Summation over all atoms with rij lt 8A A
Angstrom 1 ten-billionth of meter
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Different approaches to PSP

• Ab Initio Methods
• Knowledge Based Methods

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Ab Initio Methods
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What is Ab Initio ?

• Ab Initio means from 1st principles
• Use thermodynamic laws to figure out the
  configuration of the fold of the given protein
  protein folding problem
• Global/semi-global minimization of the function
• 1D 2D secondary structure problem
• 2D 3D side-chain conformation

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Some Ab Initio Methods

• Molecular Dynamic Simulation
• Using complex energy functions simulate folding
  of the primary sequence until it reaches its
  native state (1D-gt3D)
• Genetic Algorithm
• Used in refining a given potential function so
  that it can best predict the native state of a
  protein
• Simulated Annealing
• Branch and Bound Methods (usually used in
  side-chain conformation)
• Approximation algorithms
• Comparative/Homologue Modeling
• Threading
• Docking

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Knowledge Based Methods
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Knowledge Based Methods

• Using knowledge of currently known protein
  folds, predict the shape of the target protein
• Assumption is the native fold of the target
  protein is similar to a currently known one i.e
  in the same family
• Unable to predict any novel folds, i.e new fold
  family

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Some Knowledge-Based Methods

• Comparative/Homologue Modeling
• Threading
• Docking

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Methodological Framework for solving PSP
Primary Protein Sequence
Knowledge-base, e.g PDB
Ab Initio Methods
Homologue Modeling
Threading
Predicted 3D Structure of Protein
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Side-Chain Prediction

• Find a conformation of the all the side chains
  along the given main chain of a protein
• Usually done as the 2nd step in predicting the
  3D structure of protein
• Also useful in drug design, where drug
  structures have to be designed to be easily
  docked by enzymes for breaking down

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Side-Chain Prediction

• The main chain fold has been computed and given
  as input
• choose positions of all side chains so as to
  minimize some potential energy function
• Problem if solved Ab Initio is proven to be
  NP-Complete (reduce Clique to it)

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Central Dogma

• The more tightly packed Side-chains are, the
  more stable they will be.
• Ponder Richards have shown that there are a
  fixed set of rotations (rotamers) side-chains can
  take.
• Most methods now make use of this library of
  rotamers (abt 67 different rotations)
• Main concern is the search strategy to find the
  best conformation

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Methods in Side-chain prediction

• Simulated Annealing
• A algorithm
• Monte Carlo Minimization
• Molecular Dynamics Simulation
• Dead End Elimination
• Genetic Algorithm

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Dead End Elimination

• Deterministic method to determine the global
  minimum energy conformation (GMEC) of set of
  side-chains.
• Continuously eliminate rotamers from
  consideration in the GMEC, until only 1 rotamer
  is left in each side-chain position (thus giving
  final conformation).
• DEE can be viewed as a mathematical criteria
  that a rotamer must fulfill in order not to be
  eliminated

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Dead End Elimination

• Potential function is described in terms of
  pair-wise interactions of all rotamers at all
  positions.
• Therefore energy function to minimized can be
  formulated as

Sum of pairwise interaction energy
between rotamer r at position j and rotamer u at
positions j
energy of the given backbone fold
Sum of energy of rotamer r at side chain i
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Dead End Elimination

• Assuming p side-chains and n rotamers for each
  side-chain
• Time complexity of finding the configuration
  that minimizes the energy function takes O(pnp)
• Not feasible to use the original formulation

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Original DEE

• A rotamer ir can be eliminated from
  consideration if there is an alternative rotamer
  it at the same position that satisifies

Maximum pairwise interaction energy between it
and every other side-chain j
Energy resulting from using rotamer r at position
i
Minimum pairwise interaction energy between ir
and every other side-chain j
Energy resulting from using rotamer t at position
i
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Original DEE

• Given some relevant energy landscape, the
  previous inequality in fact says the following

Rotamer r at side-chain i can only be eliminated
only if maximum energy conformation using rotamer
t at side-chain i is smaller than the minimum
energy conformation of using rotamer r
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Original DEE

• A simplistic implementation of Original DEE by
  simply translating the inequality to code result
  in a time complexity of O(n2p2)
• There is however still a problem if the
  following happens

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Simple Goldstein DEE

• A rotamer ir can be eliminated from
  consideration if there is an alternative rotamer
  it at the same position that satisifies

Energy resulting from using rotamer r at position
i
Energy resulting from using rotamer t at position
i
Difference in energy of conformation using ir and
conformation using it which are at the point of
closest contact
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Simple Goldstein DEE

• Given some relevant energy landscape, the
  previous inequality in fact says the following

Rotamer r at side-chain i can only be eliminated
by both totamer t1 and rotamer t2 since the
difference is ve at the points of closest
contact. Meaning for any given conformation
using t1 or t2 will result in a smaller overall
energy than using r
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Simple Goldstein DEE

• A simplistic implementation of Simple Goldstein
  DEE by simply translating the inequality to code
  result in a time complexity of O(n3p2)
• There is however still a problem if energy
  profiles of rotamer r and every other rotamer
  intersect.
• More powerful criteria will have to be used
• General GoldStein DEE, Simple Split DEE and
  general Split DEE
• The more powerful the criterion the higher its
  time complexity

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Conclusion

• Myriad of methods to attempt to solve the
  protein prediction problem
• Knowledge-based methods have gained a edge over
  Ab initio methods
• However not much improvement in the prediction
  power of modern heuristics, since the 1st
  experiment by Anfisen 3 decades ago
• Either problem is too hard / More discovery
  awaits the adventurous researcher