Genetic Threading

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Genetic Threading

• By J.Yadgari and A.Amir
• Published special issue on Bioinformatics in
  Journal of Constraints, June 2001

Alexandre Tchourbanov University of Nebraska at
Lincoln CSCE 421-821 December 4, 2001
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Structure of the presentation

• Introduction to protein native structure
• Methods of finding a native structure
• Physical
• Computational
• Common methods and principles
• Protein threading method
• Protein threading using genetic approach

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Problem of protein structure prediction

• Proteins are key molecules in all life processes
• The function of a protein directly related to its
  three dimensional structure
• Knowing and understanding the structure of
  proteins will have a tremendous impact on
  understanding of biological processes, medical
  discoveries, and biotechnological inventions

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Problem of protein structure preduction

• Given a sequence of amino acids, predict the
  unique 3D folding of molecule minimizing its free
  energy

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Lys
Computational Methods of prediction
Practical use of the 3D structural knowledge
Gly
Leu
Physical methods of prediction
Primary structure
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Protein structure

• A protein is built up from a chain of amino acids
  linked by peptide bonds
• There are 20 amino acids that can be divided into
  several classes based on size and other chemical
  and physical properties
• Depending on type of a residue, protein could be
  either hydrophilic (water loving) or hydrophobic
  (water hating)

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General structure of an amino acid

• Each amino acid consists of
• Common main chain part, containing the heavy
  atoms N, C, O, C? forming amide plane
• Chain residue of size 0 10 additional atoms

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Peptide bond

• Peptide bond connects carboxyl group of the first
  amino acid with amino group of the second acid
• Peptide bonds are planar and rigid

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Sequence of amino acids

• Sequence of amino acids, connected by peptide
  bonds, form protein
• There is no flexibility for rotation around
  peptide bond
• There is more flexibility for protein to rotate
  around N-C?-bond (called the ?-angle) and around
  C-C?-bond (?-angle)
• These angles are restricted to small regions in
  natural proteins

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Part of Protein (PheAspAla)
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Protein folding

• Using the freedom of rotations, the protein can
  fold into a specific and unique three dimensional
  structure (called conformation), forming a native
  structure

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Physical methods of determiningprotein native
structure
X-ray crystallography
Physical methods
NMR (Nuclear Magnetic Resonance)

• X-ray crystallography requires significant
  amounts of purified protein molecules (1014) to
  grow a crystal and protein needs to crystallize
• NMR method applicable to proteins of small and
  average size, which do not crystallize
• Both methods are expensive and give coherent
  results on the same protein, proving to be
  correct
• Structure of many important proteins is still
  unknown

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Protein structure in X-ray crystallography

• X-ray diffraction pattern is recorded and
  processed using FFT to form electron density map
• Regions of map with the highest electron density
  reveal the location of atomic nuclei

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Family of structures in NMR method

• Absorption of radio frequency energy is recorded
  as a 2D spectrum
• Possible 3D structures are constructed by
  computer according to NMR signal

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Computational methods to find a protein structure

• The unique 3D arrangement of protein corresponds
  to lowest free energy conformation
• Most computational approaches for solving the
  protein folding problem look for the lowest free
  energy conformation
• Two principal methods are currently in use for
  computing the lowest energy conformation
• Molecular dynamics
• Monte Carlo

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Molecular dynamics

• Forces acting on each atom at a particular state
  of the system are calculated using an empirical
  force field
• Atoms allowed to move with accelerations
  resulting from forces, changing conformation
• Once atom moved significantly, acting forces are
  recalculated (every 10-15 sec)
• Even super computers can simulate only 10-9 sec
  of folding time, which is insufficient

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Monte Carlo method

• Used with simplified model of protein (does not
  consider structure of every amino acid)
• Procedure makes random move from current
  conformation and evaluates resulting energy
  changes
• If new conformation is better, it replaces old
  one with newly generated, and process repeats
• Method is not powerful enough to find an optimal
  conformation even for simple cases

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Protein threading

• Many proteins in nature are homologous, having
  different primary structure, but forming the same
  conformation to carry out the same functionality
  in a living matter and having the same
  evolutionary origin
• Most protein share the secondary structure
  motifs
• Helices
• Extended strands forming sheets
• Specific turns
• Random coils

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Protein threading

• Threading means mapping a given sequence to a
  given structure
• To assign a structure to a sequence one would
  then need to thread the sequence through all
  known conformations, evaluating compatibility,
  and assign the most compatible structure to the
  sequence
• Upon discovery of completely different structure
  from any known, enter it into database of
  structures

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Protein threading

• Structure is presented by the black trace
• Sequence (at the top) is threaded through the
  structure, encoding an alignment (at the bottom)
• Zero means structure deletion, values greater
  that one mean sequence deletion, while one is a
  fit

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Protein threading

• The size of the search space to thread sequence
  of length k into structure of size n could be
  found as a selection with repetition
• Search space is huge and problem appears to be
  NP-complete Unger,R., Moult,J. (1993)

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Protein threading

• In order to reduce complexity of search task, (m
  1) core and m non-core regions are introduced
• Usually ?-helices and ?-sheets are core regions,
  connected by loops
• Total number of amino acids in core regions is c

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Protein threading

• Although suffering from some inherent limitations
  (such as prediction of the right structure with
  completely wrong threading), method became a
  significant tool in protein structure prediction
• Any threading procedure must contain two major
  components
• An alignment algorithm to position a sequence on
  a structure
• Score function to evaluate the energy of the
  sequence in given conformation

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Protein threading possible implementations

• Protein threading could be implemented using
• Enumeration for small problems,
• Dynamic programming to find core regions to
  freeze,
• Monte Carlo variants with Gibbs sampling
• Branch and bound search
• Genetic programming with constraints seems to be
  a decent alternative in comparison with other
  methods

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Protein threading using genetic programming

• Genetic Algorithms are parallel computational
  tools that are based on the principle of
  diversity and selection
• Solutions are represented as strings, for example
  11111100111311
• Sum of all terms in the string needs to be equal
  to the number of amino acids in the sequence, as
  well as length of the string equal to the length
  of the structure

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Protein threading using genetic programming

• These strings are maintained as a population that
  undergoes evolutionary process via generic
  operators such as
• Replication (copying of the string to the next
  generation)
• Mutation (changing bits in the string)
• Crossover (concatenating a prefix of one string
  with suffix of another)
• Energy function is a good candidate to evaluate
  fit of an offspring

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Energy function

• Energy functions are subject to minimizations
• Energy functions are calculated by extracting
  from the structural database frequencies of
  interactions between pairs of residues as a
  function of amino acids types and distance
• Tendency of certain hydrophilic residues to be on
  the surface can be approximated by energy term
  related to the position

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Implementing mutation

• An example of mutation could be transformation of
  1111100111311 into 11111100211211, which is also
  a valid encoding
• We need to have validity check every time we do
  mutation and compensate for problems
• Reverting of substrings is especially interesting
  mutation, since it does not violate a valid
  structure of the solution

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Implementing crossovers
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Following issues were addressed

• The linear trade-off between population size and
  the number of generations
• Optimal level of mutation rate
• Locality of mutation operator
• Locality of the crossover operator
• Regular mutations versus reverse mutations
• Magnitude of the mutation operation
• Quality control of the crossover operation

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Results

• For authors examples, the optimal performance is
  achieved with population size of 300 solutions
  and duration of 1000 generations
• The optimal rate of mutations is 0.25 to 0.3 of
  the populations

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The minimal energy of threading runs
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The average energy of the population during
threading
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Structural comparisons
Difference between sequence deletions
and structure deletions plots
Structural alignment
Most similar threading alignment
Least similar threading alignment
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Maximal mutation magnitude
Average score of 5 runs after 600 generations
Average score of 5 runs after 2000 generations
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Summary

• The running time of a GA depends linearly on the
  number of solutions in the population (i.e.
  population size) and also depends linearly on the
  number of generations the process is repeated
• Genetic algorithms method is a feasible and
  efficient approach to threading
• It is especially encouraging that the threading
  alignments are quite similar, quantitatively, to
  the structural alignments

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Summary

• Changing the locality of the mutation and
  crossover operation does not show a consistent
  change in the performance of the algorithm
• Mutations of high magnitude are
  counterproductive, probably because changes
  between the template and the assigned structure
  do not tend to concentrate in single position
• Using crossover under strict quality control was
  shown not to be effective, since genetic
  mechanism has quality control itself

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Summary

• The success of the reverse mutation is quite
  surprising and should be further explored

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Future work

• Threading algorithms should be tested on their
  ability to assign a conformation for new and
  unknown sequence
• Authors plan to implement the genetic algorithm
  in a complete threading package, with all the
  necessary components and to test it in a
  realistic prediction setup.