Protein structure prediction

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Protein structure prediction
Alexander Churbanov University of Nebraska at
Omaha CSCI 8980 February 14, 2002
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Structure of the presentation

• Introduction
• Protein native structure
• Computational methods of finding a native
  structure
• Common methods and principles
• Specific methods
• Homology finding
• Threading
• Modeling on lattice

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Introduction

• In Greek mythology, Sisyphus is condemned to an
  eternity of hard labor his labor is a
  frustrating and fruitless, for just as he is
  about to achieve his goal, his work is undone and
  he must start again from the beginning
• Those who work in protein structure prediction
  seem to share the same fate

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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 prediction

• For over 30 years, there has been an ardent
  search for methods to the predict
  three-dimensional (3D) structure from the
  sequence
• Many methods were found which looked initially
  very promising - but always the hope has been
  dashed

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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

1
2
3
Lys
Computational Methods of prediction
Practical use of the 3D structural knowledge
Gly
Leu
Physical methods of prediction
Primary structure
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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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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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Knowledge based structure prediction methods

• The most successful structure prediction tools
  are knowledge-based, using a combination of
  statistical theory and empirical rules
• The most successful theoretical approach is
  homology modelling

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Homology modeling

• Given a sequence of unknown fold (denote U), if U
  has significant sequence similarity to a protein
  of known structure (T) (i.e., if the pairwise
  sequence identity is gt25), it is possible to
  construct an approximate 3D model which has a
  correct fold but inaccurate loop regions

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Homology modeling

• The basic assumption of homology modelling is
  that U and the homologous template protein of
  known structure (T) have nearly identical
  backbone structure in the aligned regions
• A new generation of alignment methods are based
  on Hidden Markov Models and another on Genetic
  algorithms

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Homology modeling

• For sequence identities down to about 30
  sequence identity, U and T will still have the
  same fold, but the number of loops inserted grows
  and the divergence between U and T becomes
  considerable
• Modelling of loop regions is still a difficult
  problem even the best methods only rarely
  achieve atomic accuracy and are often completely
  different to the correct structure

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Homology modeling

• A pessimistic view is that the accuracy of
  resulting 3D predictions is typically at the
  level of ribbon plots, i.e. the mutual
  orientation of elements such as helices and
  sheets can be identified
• The optimistic version is that even down to
  levels of 30 sequence identity homology
  modelling occasionally yields correct predictions
  at atomic resolution

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Three difficult problems of homology modeling

• Remote homology modelling (lt25) has three
  obstacles to overcome
• the remote homology between U and T has to be
  detected
• U and T have to be aligned correctly
• the homology modelling procedure has to be
  tailored to the harder problem of extremely low
  sequence identity

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Solution to the first problem

• In the early 1990s, there was a great deal of
  optimism that the first obstacle, the detection
  of similar folds, would be solved by threading
  methods
• The basic idea is to thread the sequence of U
  into the backbone 3D structure of T, at each step
  evaluating the 'fitness of sequence for
  structure' using environment-based or
  knowledge-based mean-force-potentials

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Protein threading

• Many proteins in nature are homologous
• They have different primary structure
• They form similar conformation to carry out the
  same functionality in a living matter
• There are groups of proteins having the same
  evolutionary origin

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Protein threading

• 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 structure prediction on lattice

• Another way to model protein folding in 3D space
  is to assume certain simplifications
• Modeling on Lattice is a way to fight the
  complexity of the prediction problem
• Though the problem solution on Lattice is still
  NP-complete, we can expand size of the protein
  modeled significantly

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Protein simplification for lattice model

• Monomers (or residues) are represented using a
  unified size
• Bond length is unified
• The positions of the monomers are restricted to
  positions in a lattice
• Simplified energy function

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HP - model

• 20 letter alphabet of amino acids is reduced to a
  two letter alphabet, namely H and P
• H represents non-polar or hydrophobic amino acid
• P represents polar or hydrophilic amino acid

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The energy function

• The energy function for HP-model is given by the
  matrix

• Energy contribution of a contact between two
  monomers is 1 if both are H-monomers, and 0
  otherwise

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Contact energy

• Two monomers form a contact in some specific
  conformation if they are not connected via a
  bond, but occupy neighboring positions in the
  conformation
• A conformation with minimal energy is just a
  conformation with the maximal number of contacts
  between H-monomers

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Sample conformation

• A sample conformation for the sequence PHPPHHPH
  in the two-dimentional lattice with energy 2 is

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Cubic lattice

• Lattice 3D space

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Native conformation
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Vertical and horizontal contribution to the
surface of a conformation in
Vertical contribution to the surface
Horizontal contribution to the surface
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Conclusions

• Native 3D structures of proteins are encoded by a
  linear sequence of amino acid residues
• To predict 3D structure from sequence is a task
  challenging enough to have occupied a generation
  of researchers
• Have they finally succeeded in their goal? The
  bad news is no, we still cannot predict
  structure for any sequence
• The good news are we have come closer, and
  growing databases facilitate the task.