Protein Mutational Analysis Using Statistical Geometry Methods

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Protein Mutational Analysis Using Statistical
Geometry Methods

• Majid Masso
• mmasso_at_gmu.edu
• http//mason.gmu.edu/mmasso
• Bioinformatics and Computational Biology
• George Mason University

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Protein Basics

• formed by linearly linking amino acid residues
  (aas are the building blocks of proteins)
• 20 distinct aa types
• A,C,D,E,F,G,H,I,K,L,M,N,P,Q,R,S,T,V,W,Y

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Amino Acid Groups

• Brandon/Tooze (affinity for water)
• hydrophobic aas A,V,L,I,M,P,F
• hydrophilic aas
• polar N,Q,W,S,T,G,C,H,Y
• charged D,E,R,K
• Dayhoff (similar wrt structure or function)
• (A,S,T,G,P),(V,L,I,M),(R,K,H),(D,E,N,Q),(F,Y,W),(C
  )
• conservative substitution replacement with an
  amino acid from within the same class
• non-conservative substitution interclass
  replacement

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Protein Basics

• genes code, or blueprint
• proteins product, or building
• protein structure gives rise to function
• why do things go wrong?
• mistakes in blueprint
• incorrectly built, or nonexistent buildings
• Protein Data Bank (PDB) repository of protein
  structural data, including 3D coords. of all
  atoms (www.rcsb.org/pdb/)

PDB ID 1REZ Structure reference Muraki M.,
Harata K., Sugita N., Sato K., Origin of
carbohydrate recognition specificity of human
lysozyme revealed by affinity labeling,
Biochemistry 35 (1996)
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Computational Geometry Approach to Protein
Structure Prediction

• Tessellation
• protein structure represented as a set of points
  in 3D, using Ca coordinates
• Voronoi tessellation convex polyhedra, each
  contains one Ca , all interior points closer to
  this Ca than any other
• Delaunay tessellation connect four Ca whose
  Voronoi polyhedra meet at a common vertex
• vertices of Delaunay simplices objectively define
  a set of four nearest-neighbor residues
  (quadruplets)
• 5 classes of Delaunay simplices
• Quickhull algorithm (qhull program), Barber et
  al., UMN Geometry Center

Voronoi/Delaunay tessellation in 2D space.
Voronoi tessellation-dashed line, Delaunay
tessellation-solid line (Adapted from Singh R.K.,
et al. J. Comput. Biol., 1996, 3, 213-222.)
Five classes of Delaunay simplices. (Adapted from
Singh R.K., et al. J. Comput. Biol., 1996, 3,
213-222.)
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Counting Quadruplets

• assuming order independence among residues
  comprising Delaunay simplices, the maximum number
  of all possible combinations of quadruplets
  forming such simplices is 8855

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Residue Environment Scores

• log-likelihood
• normalized frequency of quadruplets
  containing residues i,j,k,l in a representative
  training set of high-resolution protein
  structures with low primary sequence identity
• i.e., total number of quadruplets in
  dataset containing only residues i,j,k,l divided
  by total number of observed quadruplets
• frequency of random occurrence of the
  quadruplet (multinomial)
• i.e.,
• total number of occurrences of residue i
  divided by total number of residues in the
  dataset
• , where n number of distinct
  residue types in the
• quadruplet, and t i is the
  number of residues of type i.

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Residue Environment Scores

• total statistical potential (topological score)
  of protein sum the log-likelihoods of all
  quadruplets forming the Delaunay simplices
• individual residue potentials sum the
  log-likelihoods of all quadruplets in which the
  residue participates (yields a 3D-1D potential
  profile)

PDB ID 3phvHIV-1 Protease Monomer 99 amino
acids (total potential 27.93)
Structure reference R. Lapatto, T. Blundell, A.
Hemmings, et al., X-ray analysis of HIV-1
proteinase at 2.7 Å resolution confirms
structural homology among retroviral enzymes,
Nature 342 (1989) 299-302.
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Properties of HIV-1 Protease

• functional as a homodimer
• 99 residues per subunit
• monomers form an intermolecular two-fold axis of
  symmetry
• approximate intramolecular two-fold axis of
  symmetry
• dimer interface N and C termini (P1-T4
  C95-F99, respectively) form a four-stranded beta
  sheet
• active site triad D25-T26-G27
• h-phobic flaps (M46-V56) are also G-rich,
  providing flexibility
• accommodate / interact with substrate molecule
• Figure adapted from URL
• http//mcl1.ncifcrf.gov/hivdb/Informative/Facts/fa
  cts.html

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HIV-1 Protease Comprehensive Mutational Profile
(CMP)

• mutate 19 times the residue present at each of
  the 99 positions in the primary sequence
• get total potential and potential profile of each
  artificially created mutant protein
• create 20x99 matrix containing total potentials
  of all the single residue mutants
• columns labeled with residues in the primary
  sequence of wild-type (WT) HIV-1 protease
  monomer, and rows labeled with the 20 naturally
  occurring amino acids
• subtract WT total potential (TP) from each cell,
  then average columns to get CMP
• CMPj (mutant TP)ij-(WT TP)
  (mutant TP)ij-27.93 , j1,,99

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Mean Change in Total Protein Potential
Residue
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Experimental Data

• 536 single point missense mutations
• 336 published mutants Loeb D.D., Swanstrom R.,
  Everitt L., Manchester M., Stamper S.E.,
  Hutchison III C.A. Complete mutagenesis of the
  HIV-1 protease. Nature, 1989, 340, 397-400
• 200 mutants provided by R. Swanstrom (UNC)
• each mutant placed in one of 3 phenotypic
  categories, positive, negative, or intermediate,
  based on activity
• mutant activity to be compared with change in
  sequence-structure compatibility elucidated by
  potential data

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Experimental Data
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Observations

• set of mutants with unaffected protease activity
  exhibit minimal (negative) change in potential
• set of mutants that inactivate protease exhibit
  large negative change in potential, weighted
  heavily by NC
• set of mutants with intermediate phenotypes
  exhibit moderate negative change in potential
  (similar among C and NC) wide range for
  intermediate phenotype in the experiments

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Evolutionarily Conserved Residue Positions
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• Apply chi-square test statistic on tables above,
  with the null hypothesis being no association
  between residue position conservation and level
  of sensitivity to mutation
• LHS table (1 df) ?2 10.44, reject null with p
  lt 0.01
• RHS table (2 df) ?2 75.49, reject null with p
  lt 0.001

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Mutagenesis at the Dimer Interface

• Q2, T4, T96, and N98 are polar and side chains
  directed outward P1, I3, L97, and F99 are
  hydrophobic and side chains directed toward body
• F99 in one subunit makes extensive contacts with
  I3, V11, L24, I66, C67, I93, C95, and H96 in the
  complementary chain

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Mutagenesis at the Dimer Interface

• Alanine scan conducted on interface residues
  individually and in pairs, in one subunit and in
  both chains activity of mutants measured by
  cleavage of ß-galactosidase containing a protease
  cleavage site
• S. Choudhury, L. Everitt, S.C. Pettit, A.H.
  Kaplan, Mutagenesis of the dimer interface
  residues of tethered and untethered HIV-1
  protease result in differential activity and
  suggest multiple mechanisms of compensation,
  Virology 307 (2003) 204-212.
• Results Good correlation between cleavage
  (protease activity) and topological scores
  (protease sequence-structure compatibility)

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Conformational Changes Due to Dimerization and/or
Ligand Binding

• PDB ID 1g35
• HIV-1 Protease Dimer with Inhibitor aha024
• monomer in a dimeric configuration with an
  inhibitor obtain profile for 1g35, plot 3D-1D
  only for g35A
• isolated monomer eliminate all PDB coordinate
  lines in 1g35 except those for 1g35A, obtain
  profile, plot 3D-1D
• plot interface difference between the 1g35A
  3D-1Ds in the dimer and monomer configurations

Structure reference W. Schaal, A. Karlsson, G.
Ahlsen, et al., Synthesis and comparative
molecular field analysis (CoMFA) of symmetric and
nonsymmetric cyclic sulfamide HIV-1 protease
inhibitors, J. Med. Chem. 44 (2001) 155-169
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Observations

• majority of residues forming both dimer interface
  and flap region exhibit increase in stability
  following dimerization Q2, T4, I47-I54, T96,
  L97, and F99
• all h-phobic except Q2
• increase in stability due to inhibitor binding
  evident for the active site residues D25, T26,
  and G27 also true for the surrounding h-phobic
  residues L24 and A28

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Significance of Hydrophobic Residues in HIV-1
Protease

• 35/99 amino acids with scores exceeding 1.0
• 27 of these are hydrophobic
• altogether, 44/99 amino acids in protease are
  hydrophobic
• Assuming h-phobic residues no more likely than
  others (polar/charged) to have scoregt1.0
• expect (35/99)x44, i.e. 15 or 16 h-phobics gt1.0
• P(27 h-phobicsgt1.0)
  lt 0.001, yet this is exactly what we observe!
• What about other cut-off scores, and other
  proteins?
• applied similar test to all 996 proteins in the
  training setwhile varying cut-off between
  0.0-5.0 in 0.25 increments, binomial
  probabilities were calculated for each protein.
  For a given p-value, of proteins with a lower
  significance level at each cut-off score was
  tabulated

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Significance of Hydrophobic Residues

• optimal cut-off score for rejection of the null
  is clearly distinct for each of the individual
  proteins.
• Ex. 827 proteins reject a null with 2.0 cut-off
  score at p 0.05, but 918 proteins reject the
  null at the same significance level if all
  cut-off scores considered.
• alternate approach 92,343 h-phobic amino acids
  and 136,329 others (polar/charged), total of
  228,672 residues in the 996 proteins assuming no
  differ. in the mean of the scores in both groups,
  apply t-test.
• Result t126.48, with 228,670 df gt reject null!

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Acknowledgements

• Iosif Vaisman (Ph.D. advisor, first to apply
  Delaunay to protein structure)
• Zhibin Lu (Java programs for calculating
  statistical potentials from tessellations)
• Ronald Swanstrom (experimental HIV-1 protease
  mutants and activity measure)