Homology Modeling via Protein Threading

1
Homology Modeling via Protein Threading

• Kristen Huber
• ECE 697S
• Topics in Computational Biology
• April 19, 2006

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Fundamentals of Protein Threading

• Protein Modeling
• Homology Modeling
• Protein Threading
• Generalized Overview of a Threading Score
• Score Methodology based on Multiple Protein
  Structure Alignment

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Protein Modeling

• 20,000 entries of proteins in the PDB
• 1000 - 2000 distinct protein folds in nature
• Thought to be only several thousand unique folds
  in all
• Protein Structure Prediction
• aim of determining the three-dimensional
  structure of proteins from their amino acid
  sequences

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Types of Structure Prediction

• De novo protein
• methods seek to build three-dimensional protein
  models "from scratch"
• Example Rosetta
• Comparative protein
• modeling uses previously solved structures as
  starting points, or templates.
• Example protein threading

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Factors that Make Protein Structure Prediction a
Difficult Task

• The number of possible structures that proteins
  may possess is extremely large, as highlighted by
  the Levinthal paradox
• The physical basis of protein structural
  stability is not fully understood.
• The primary sequence may not fully specify the
  tertiary structure.
• chaperones
• Direct simulation of protein folding is not
  generally tractable for both practical and
  theoretical reasons.

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Homology Modeling

• Homolog a protein related to it by divergent
  evolution from a common ancestor
• 40 amino-acid identity with its homolog
• NO large insertions or deletions
• Produces a predicted structure equivalent to that
  of a medium resolution experimentally solved
  structure
• 25 of known protein sequences fall in a safe
  area implying they can be modeled reliably

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Homology Modeling Defined

• Homology modeling
• Based on the reasonable assumption that two
  homologous proteins will share very similar
  structures.
• Given the amino acid sequence of an unknown
  structure and the solved structure of a
  homologous protein, each amino acid in the solved
  structure is mutated computationally, into the
  corresponding amino acid from the unknown
  structure.

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Homology Modeling Limitations

• Cannot study conformational changes
• Cannot find new catalytic/binding sites
• Brainstorm lack of activity vs activity
• Chymotrypsionogen, trypsinogen and plasminogen
• 40 homologous
• 2 active, 1 no activity, cannot explain why
• Large Bias towards structure of template
• Models cannot be docked together

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Why Homology Modeling?

• Value in structure based drug design
• Find common catalytic sites/molecular recognition
  sites
• Use as a guide to planning and interpreting
  experiments
• 70-80 chance a protein has a similar fold to
  the target protein due to X-ray crystallography
  or NMR spectroscopy
• Sometimes its the only option or best guess

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Protein Threading

• A target sequence is threaded through the
  backbone structure of a collection of template
  proteins (fold library)
• Quantitative measure of how well the sequence
  fits the fold
• Based on assumptions
• 3-D structures of proteins have characteristics
  that are semi-quantitatively predictable
• reflect the physical-chemical properties of amino
  acids
• Limited types of interactions allowed within
  folding

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Fold Recognition Methods

• Bowie, Lüthy and Eisenberg (1991)
• 2 approaches to recognition methods
• Derive a 1-D profile for each structure in the
  fold library and align the target sequence to
  these profiles
• Identify amino acids based on core or external
  positions
• Part of secondary structure
• Consider the full 3-D structure of the protein
  template
• Modeled as a set of inter-atomic distances
• NP-Hard (if include interactions of multiple
  residues)

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Protein Threading

• The word threading implies that one drags the
  sequence (ACDEFG...) step by step through each
  location on each template

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Protein Threading
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Generalized Threading Score

• Want to correctly recognize arrangements of
  residues
• Building a score function
• potentials of mean force
• from an optimization calculation.
• G(rAB) kTln (?AB/ ?AB)
• G, free energy
• k and T Boltzmanns constant and temperature
  respectively
• ? is the observed frequency of AB pairs at
  distance r.
• ? the frequency of AB pairs at distance r you
  would expect to see by chance.
• Z-score (ENat - ltEaltgt)/s Ealt
• Natural energies and mean energies of all the
  wrong structures/ standard deviation

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Scoring Different Folds

• Goodness of fit score
• Based on empirical energy function
• Modify to take into account pairwise interactions
  and solvation terms
• High score means good fit
• Low score means nothing learned

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Some Threading Programs

• 3D-pssm (ICNET). Based on sequence profiles,
  solvatation potentials and secondary structure.
• TOPITS (PredictProtein server) (EMBL). Based on
  coincidence of secondary structure and
  accesibility.
• UCLA-DOE Structure Prediction Server (UCLA).
  Executes various threading programs and report a
  consensus.
• 123D Combines substitution matrix, secondary
  structure prediction, and contact capacity
  potentials.
• SAM/HMM (UCSC). Basen on Markov models of
  alignments of crystalized proteins.
• FAS (Burnham Institute). Based on profile-profile
  matching algorithms of the query sequence with
  sequences from clustered PDB database.
• PSIPRED-GenThreader (Brunel)
• THREADER2 (Warwick). Based on solvatation
  potentials and contacts obtained from crystalized
  proteins.
• ProFIT CAME (Salzburg)

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Process of 3D Structure Prediction by Threading

• Has this protein sequence similarity to other
  with a known structure?
• Structure related information in the databases
• Results from threading programs
• Predicted folding comparison
• Threading on the structure and mapping of the
  known data
• A comparison between the threading predicted
  structure and the actual one

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Protein Threading Based on Multiple Protein
Structure AlignmentTatsuya Akutsu and Kim Lan
SimHuman Genome Center, Institute of Medical
Science, University of Tokyo

• NP-Hard if include interactions between 2 or more
  AA
• Determine multiple structural alignments based on
  pair wise structure alignments
• Center Star Method

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Center Star Method

• Let I0 be the maximum number of gap symbols
  placed before the first residue of S0 in any of
  the alignments A(S0 S1) A(S0 SN). Let
  IS0j be the maximum number of gaps placed after
  the last character of S0 in any of the
  alignments, and let Ii be the maximum number of
  gaps placed between character S0i and S0i1,
  where Sji denotes the i-th letter of string Si
• Create a string S0 by inserting I0 gaps before
  S0, IjSo gaps after S0, and Ij gaps between S0I
  and S0i1.
• For each Sj (j gt 0), create a pairwise alignment
  A(S0 Sj) between S0 and Sj by inserting gaps
  into Sj so that deletion of the columns
  consisting of gaps from A(S0 Sj) results in the
  same alignment as A(S0 Sj).
• Simply arrange A(S0 Sj )'s into a single matrix
  A (note that all A(S0 Sj )'s have the same
  length).

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Simple Threading Algorithm

• Apply simple score function based on structure
  alignment algorithm
• Let X x1xN (input amino acid sequence)
• Ci ( i-th column in A)
• Test and analyze results and/or apply constraints

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Protein Threading with Constraints

• Assume part of the input sequence xixik must
  correspond to part of the structure alignment
  cjcjk
• Apply constraints

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Prediction Power

• Entered in CASP3 competition
• 17 predictions made
• 3 targets evaluated as similar to correct folds
• Only team to create a nearly correct model for
  structure T0043
• Best in competition
• 8 evaluated as similar to correct

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Next time.

• In depth detail of
• Multiple structural alignment program
• Multiprospector
• Global Optimum Protein Threading with Gapped
  Alignment
• Quality measures for protein threading models
• Improvements on threading-based models

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Gapped Alignment
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Review

• Homology Modeling
• Based on the reasonable assumption that two
  homologous proteins will share very similar
  structures.
• Threading
• Modeled as a set of inter-atomic distances
• NP-Hard (if include interactions of multiple
  residues)
• Build a score function based on energies in order
  to correctly recognize arrangements of residues
• Threading via multiple structural alignment
• Score function based upon alignment matrix

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Specifics of Protein Threading

• Different Threading Types
• Multiprospector Predictions of Protein-Protein
  Interaction by Multimeric Threading
• Global Optimum Protein Threading with Gapped
  Alignment
• Quality measures for protein threading models
• Improvements on threading-based models

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MULTIPROSPECTOR

• An algorithm for the prediction of
  protein-protein interactions by multimeric
  threading
• Proteinprotein interactions are fundamental to
  cellular function and are associated with
  processes such as enzymatic activity,
  immunological recognition, DNA repair and
  replication, and cell signaling.
• Function can be inferred from the nature of the
  protein with its interactants
• Use properties related to the topology of the
  interface, solvent-accessible surface area and
  hydrophobicity
• Addressed limitations of existing approaches

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Method Basis

• Thread the sequences through a representative
  structure template library that, in addition to
  monomers, also includes each of the chains in
  representative protein dimer structures.
• Compute the interaction energy between a pair of
  protein chains for those protein structures
  involved in dimeric complexes.
• Stable complex formation determined by the
  magnitude of the interfacial potentials and the
  Z-scores of the complex structures relative to
  that of the monomers.

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Interfacial Statistical Potentials

• Interfacial pair potentials
• P(i, j), (i1, , 20 j 1, ,20),
• Calculated by examining each interface of the
  selected dimers
• Nobs(i, j) is the observed number of interacting
  pairs of i, j between two chains.
• Nexp(i, j) is the expected number of interacting
  pairs of i, j Nexp (i, j) Xi Xj Ntotal
• Apply Boltzman Principal to the ratio to obtain
  potential of mean force between 2 residues

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Multimeric Threading Strategy and Z-Score

• Z-score of the score for each probe-template
  alignment is used to decide if a correct fold is
  found
• is the standard deviation of energies Ei is the
  energy of the i-th sequence of M alternative
  folds (i 1, , M).

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Multimeric Threading
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Results
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Global Optimum Protein Threading with Gapped
Alignment and Empirical Pair Score Functions

• The structural model corresponds to an annotated
  backbone trace of the secondary structure
  segments in the conserved core fold.
• Loops are not considered part of the conserved
  fold, and are modeled by an arbitrary
  sequence-specific loop score function.
• Alignment gaps are confined to the connecting
  non-core loop regions
• Each distinct threading is assigned a score by an
  assumed score function
• Exponentially large search space of possible
  threadings
• NP-hard search spaces as large as 9.6x1031 at
  rates ranging as high as 6.8 x1028 equivalent
  threadings per second

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Gapped Protein Threading Methodology

• Common core of four secondary structure segments
• Spatial interactions. Small circles represent
  amino acid residue positions (core elements), and
  thin lines connect neighbors in the folded core.
• Thread through model by placing successive
  sequence amino acid residues into adjacent core
  elements. Tax indexes the sequence residue placed
  into the first element of segment X. Sequence
  regions between core segments become connecting
  turns or loops.
• Sets used in the branch-and-bound search are
  defined by lower and upper limits (dark arrows,
  labeled bax and dax for segment X)

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General Pairwise Score Function

• For any threading t, let fv(v, t) be the score
  assigned to core element or vertex v
• fe(u, v, t) the score assigned to interaction
  or edge u, v
• f1(?i , t) the score assigned to loop region ?i
• Then the total score of the threading is
• Rewrite function of threading pairs of core
  segments

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Branch-and-Bound Search Algorithm

• branch-and-bound search requires the ability to
• represent the entire search space as a set of
  possibilities
• split any set into subsets
• compute a lower bound on the best score
  achievable within any subset
• After some finite number of steps, the chosen set
  will contain only one threading (equals its lower
  bound)

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Splitting the Search Space

• The set of all legal threadings is represented by
  the hyper-rectangle
• lower bound on the score f(t) attainable by any
  threading t in the set T
• summing lower bounds on each term separately

The enclosing mint?T ensures that the lower bound
will be instantiated on a specific legal
threading tlb?T. This will be used in splitting
T, below. The equation further ensures that the
singleton term, in g1(i, ti ), remains consistent
both with the terms that reflect loop scores, in
g2(i - 1, i, ti-1, ti ), and with the other
(non-loop) pairwise terms, in g2(i, j, ti , uj ).
The inner minu?T allows a different vector u for
each i, but requires u to be a legal threading.
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Search Space Results
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Threading Results
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Quality Measures for Protein Threading Models

• Evaluation of different prediction methods for
  protein threading
• Purpose
• determine if one method to build a model is
  better than another
• optimize the performance of existing methods.
• Threading Assessment
• ability to predict the correct fold
• the similarity of the model to the correct
  structure

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Methods of Comparison Defined

• Global
• consider all residues in both the model and the
  correct structure in an "alignment dependent
  fashion
• Alignment Dependent
• based on an exact match between the residues in
  the model and the correct structure
• Alignment Independent
• based on a structural superposition between the
  model and the correct structure
• Template Based
• available for models that are created from the
  sequence being aligned onto a single structural
  template.

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Methods of Comparison
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Comparison Results

• Most methods correlate to each other
• 0.51 model-normalized
• 0.41 template-normalized
• High quality homology-models correlate less with
  the rest of the data
• Measures of same type correlate well and tend to
  cluster

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A Need for Improvement

• Resulting models obtained from threading
  approaches are usually of very low quality, with
  gaps and insertions in threading alignments that
  somehow have to be connected or closed
• Various threading methods and their associated
  scoring functions only focus on aspects of
  protein structure and a subset of their possible
  interactions.

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Method of Improvement

• Employs a lattice model
• SICHO (Side Chain Only)
• The model has been refined by incorporating
  evolutionary information into the interaction
  scheme.
• a Monte Carlo annealing procedure attempts to
  find a conformation that maintains some (but not
  all) features of the original template
• optimizes packing and intra-protein interactions

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Lattice Model

• The model chain consists of a string of virtual
  bonds connecting the interaction centers that
  correspond to the center of mass of the side
  chains and the backbone alpha carbons.
• These interaction centers are projected onto an
  underlying cubic lattice with a lattice spacing
  of 1.45 A
• A cluster of excluded volume points is associated
  with each bead of the model chain.
• Each cluster consists of 19 lattice points
• Closest approach distance from another cluster
  labels smallest inter-residue distance

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Interaction Scheme

• Starting Model takes on a tube form
• Energy potentials.
• generic, sequence-independent, biases that
  penalize against non protein-like conformations
• two-body and multibody potentials extracted from
  a statistical analysis of known protein
  structures.
• Evolutionary information extracted from multiple
  sequence alignments.
• The stiffness/secondary structure bias term has
  the following form
• Estiff - ?gen S min0.5, max (0, wi ? wi2)
• - ?gen S min0.5, max (0, wi ? wi4)

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Interaction Scheme

• A weak bias being introduced towards helix-type
  and beta-type expanded states
• Estruct SdH1(i) d H2(i) d E1(i) d E2(i)
• d H1 and d H2 contributions defined as a broad
  range of helical/turn conformations
• d E1 and d E2 as expanded conformations
• Generic packing interactions
• Short range interactions
• Pairwise Interactions
• Multi-body Interactions
• statistical potential for residue type A having
  np parallel and na anti-parallel contacts.
• Emulti SEm(A,np,na)
• Total energy
• Etotal Estiff Emap 0.875EH-bond
  0.75Eshort 1.25Epair 0.5Esurface
  0.5Emulti

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Threading Model Refinement

• a) Generate the threading alignment between the
  unknown sequence and the template structure.
• b) Derive the sequence similarity-based short and
  long range pairwise potentials.
• multiple alignments with homologous sequences of
  unknown structures were used in the potential
  derivation procedures.)
• c) Build the starting continuous model chain onto
  the lattice-projected template structure.
• d) Build the tube around the aligned fragments of
  the template structure. Then, perform the first
  stage of Monte Carlo refinement.
• e) Refinement of the structure
• assume to be the new template
• Narrow restraints
• Select lowest energy structures
• All atom models using MODELLER.24

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RESULTS

• 12 targets/template proteins of low sequence
  similarity
• 3 models used for tuning
• 6 of 9 yield lower rmsd than original
• Effective parameters
• Neglecting part of threading alignment