An Atomic Four-Body Potential for the Prediction of Protein-Ligand Binding Affinity

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An Atomic Four-Body Potential for the Prediction
of Protein-Ligand Binding Affinity

• Majid Masso
• School of Systems Biology, George Mason
  University
• Manassas, Virginia 20110, USA
• CSBW BIBM 2012, Philadelphia, Pennsylvania

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Knowledge-Based Potentials of Mean Force

• Generated via statistical analysis of observed
  features in a diverse training set of structures
  selected from the PDB
• Alternative to physics or molecular mechanics
  energy functions
• Assumption observed features follow a Boltzmann
  distribution
• Examples
• Well-documented in the literature
  distance-dependent pairwise interactions at the
  atomic or amino acid level
• This study inclusion of higher-order
  contributions by developing an all-atom four-body
  statistical potential
• Motivation (our prior work)
• Four-body protein potential at the amino acid
  level

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Motivational ExamplePairwise Amino Acid
Potential

• The 20-letter protein alphabet yields 210 residue
  pairs
• Obtain a diverse PDB training set of single
  protein chains represent each protein as a set
  of amino acid points in 3D
• For each residue pair (i, j), calculate the
  relative frequency fij with which they appear
  within a given distance (e.g., 12 angstroms) of
  each other in all the protein structures
• Calculate a rate pij expected by chance alone by
  using a background or reference distribution
  (more later)
• Apply inverted Bolzmann principle sij log(fij
  / pij) quantifies interaction propensity and is
  proportional to the energy of interaction (by a
  factor of RT) for the pair

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All-Atom Four-Body Statistical Potential

• Diverse PDB training set of 1417 single chain and
  multimeric proteins, many complexed to ligands
  (see paper for text file)
• Six-letter atomic alphabet C, N, O, S, M
  (metals), X (other)
• Apply Delaunay tessellation to the atomic point
  coordinates of each PDB file objectively
  identifies all nearest-neighbor quadruplets of
  atoms in the structure (8 angstrom cutoff)

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All-Atom Four-Body Statistical Potential

• The six-letter atomic alphabet yields 126
  distinct quadruplets
• Calculate observed rate fijkl of quad (i, j, k,
  l) occurrence among all tetrahedra from the 1417
  structure tessellations
• Compute rate pijkl expected by chance from a
  multinomial reference distribution
• an proportion of atoms from all structures that
  are of type n
• tn number of occurrences of atom type n in the
  quad

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Summary Data for the 1417 Structure Files and
their Delaunay Tessellations
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All-Atom Four-Body Statistical Potential
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Topological Score (TS)

• Delaunay tessellation of any macromolecular
  structure yields an aggregate of tetrahedral
  simplices
• Each simplex can be scored using the all-atom
  four-body potential based on the quad present at
  the four vertices
• Topological score (or total potential) of the
  structure sum the scores of all constituent
  simplices in tessellation

sijkl
TS Ssijkl
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Topological Score Difference (?TS)
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Application of ?TS Predicting Protein Ligand
Binding Energy

• MOAD repository of exp. dissociation constants
  (kd) for proteinligand complexes whose
  structures are in PDB
• Collected kd values for 300 complexes reflecting
  diverse protein structures
• Obtained exp. binding energy from kd via ?Gexp
  RTln(kd)
• Calculated ?TS for complexes

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Predicting Protein Ligand Binding Energy

• Randomly selected 200 complexes to train a model
• Correlation coefficient r 0.79 between ?TS and
  ?Gexp
• Empirical linear transformation of ?TS to reflect
  energy values
• ?Gcalc L (?TS)
• Linear gt same r 0.79 value between ?Gcalc and
  ?Gexp
• Also, standard error of SE 1.98 kcal/mol and
  fitted regression line of y 1.18x (y ?Gcalc
  and x ?Gexp)

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Predicting Protein Ligand Binding Energy

• For the test set of 100 remaining complexes
• r 0.79 between ?Gcalc and ?Gexp
• SE 1.93 kcal/mol
• Fitted regression line is y 1.11x 0.63
• All training/test data is available online as a
  text file (see paper)

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References and Acknowledgments

• PDB (structure DB) http//www.rcsb.org/pdb
• MOAD (ligand binding DB) http//bindingmoad.org/
• Qhull (Delaunay tessellation) http//www.qhull.or
  g/
• UCSF Chimera (ribbon/ball-stick structure
  visualization) http//www.cgl.ucsf.edu/chimera/
• Matlab (tessellation visualization)
  http//www.mathworks.com/products/matlab/