1. Protein Function Analysis using Computational Mutagenesis
CASB workshop, 9/23/10
Protein Function Analysis using Computational Mutagenesis
Iosif Vaisman
Laboratory for Structural Bioinformatics
proteins.gmu.edu
Department of Bioinformatics and
Computational Biology

2. Dealunay simplices classification

3. Protein representation (Crambin)

4. Neighbor identification in proteins: Voronoi/Delaunay Tessellation in 2D
Delaunay simplex is
defined by points,
whose Voronoi
polyhedra have
common vertex
always a triangle in
a 2D space and a
tetrahedron in a 3D
space
Delaunay Tessellation
Voronoi Tessellation

5. Neighbor identification in proteins: Voronoi/Delaunay Tessellation in 2D6 7 6
Voronoi Tessellation
Delaunay Tessellation

6. Delaunay tessellation of Crambin

7. Delaunay Tessellation of Protein Structure
D (Asp)
Cα or center of mass
Abstract each amino acid to a point
Atomic coordinates – Protein Data Bank (PDB) D3
A22
S64 L6 F7
G62
C63 K4 R5
Delaunay tessellation: 3D “tiling” of space into non-overlapping, irregular tetrahedral simplices. Each simplex objectively defines a quadruplet of nearest-neighbor amino acids at its vertices.

8. Compositional propensities of Delaunay simplicesk j q
ijkl 
log f p
f- observed quadruplet frequency,
pijkl = Caiajakal, a - residue frequency C  4 ! i n  ( t )
AAAA: C = 4! / 4! = 1
AAAV: C = 4! / (3! x 1!) = 4
AAVV: C = 4! / (2! x 2!) = 6
AAVR: C = 4! / (2! x 1! x 1!) = 12
AVRS: C = 4! / (1! x 1! x 1! x 1!) ) = 24 10

9. Counting Quadruplets
assuming order independence among residues comprising Delaunay simplices, the maximum number of all possible combinations of quadruplets forming such simplices is 8855
4845
3420
190
380 20
8855

10. Log-likelihood of amino acid quadruplets with different compositions

11. Log-likelihood of amino acid quadruplets

12. Log-likelihood of amino acid quadruplets

13. Computational Mutagenesis Methodology
Observations:
Relatively few mutant and wt structures of same protein have been solved
Tessellations of mutant and wt protein structures are very similar or identical
Approach:
Obtain topological score (TSmut) and 3D-1D potential profile vector (Qmut) for any mutant protein by using the wt structure tessellation as a template
Simply change the residue label at a given point(s) and re-compute
s(R,D,A,L)
A22
s(I,D,A,L)
A22
s(R,G,F,L)
s(I,G,F,L) L6 L6 D3
Mutation D3 F7 F7
(R5  I5)
s(R,D,K,S)
s(I,D,K,S)
G62
G62 K4 K4
S64
S64
s(R,S,C,G)
s(I,S,C,G) R5 I5
C63
C63
(TSwt, Qwt)
(TSmut, Qmut)

14. Computational Mutagenesis Methodology
Scalar “Residual Score” of a mutant:
(mutant – wt) topological score difference = TSmut – TSwt (empirical measure of relative structural change due to mutation)
Vector “Residual Profile” of a mutant:
R = Qmut – Qwt = (mutant – wt) 3D-1D potential profile difference (environmental perturbation score at every position in structure)
Denote R = < EC1, EC2, EC3,…, ECN >
ECi = qi,mut – qi,wt = relative Environmental Change at position i
Geometric property: If mutant is due to a single substitution at position j, then ECj ≡ mutant residual score (“epicenter” of impact)
The only other nonzero EC components correspond to neighboring positions that participate in simplices with j

15. Approach 1: Protein Topological Score (TS)
Obtained by summing the log-likelihood scores of all simplicial quadruplets defined by the protein tessellation
Global measure of protein sequence-structure compatibility
Total (empirical or statistical) potential of the protein
TS = ∑î s(î), sum taken over all simplex quadruplets î in the entire tessellation.
s(R,D,A,L)
A22
s(R,G,F,L) L6 D3 F7
s(R,D,K,S)
G62 K4
S64
s(R,S,C,G) R5
C63
Close-up view of only the four simplices that use R at position 5 as a vertex (hypothetical)

16. Approach 2: Residue Environment Scores
For each amino acid position, locally sum the log-likelihood scores s(i,j,k,l) of only simplex quadruplets that include it as a vertex
s(R,D,A,L)
A22
s(R,G,F,L) L6 D3
Example: q5 = q(R5) = ∑(i,j,k,l) s(i,j,k,l), sum over all simplex quadruplets (i,j,k,l) that include amino acid R5 F7
s(R,D,K,S)
G62 K4
S64
s(R,S,C,G) R5
C63
The scores of all amino acid positions in the protein structure form a 3D-1D Potential Profile vector Q = < q1, q2, q3,…,qN > (N = length of primary sequence in solved structure)

17. Reversibility Analysis
S1,E1
‘reference’ PDB
S1,E2
Calculated Mutant
Forward Mutation
S2,E2
Mutant PDB
S2,E1
Calculated ‘reference’
Reverse Mutation

18. Reversibility of mutations (T4 lysozyme)
Protein Mutation Score change
1l63 T26E
180l E26T
1l63 A82S
123l S82A
1l63 V87M
1cu3 M87V
1l63 A93C
138l C93A
1l63 T152S
1goj S152T

19. Reversibility Analysis

20. Functional Effects of Amino Acid Substitutions
Change in protein stability:
Effect on melting temperature: ΔTm = Tm (mutant) – Tm (wt)
Effect on thermal denaturation: ΔΔG = ΔG (mutant) – ΔG (wt)
Effect on denaturant denaturation: ΔΔGH2O = ΔGH2O (mutant) – ΔGH2O (wt)
Change in protein activity:
Mutant enzymatic activity relative to wt
Mutant strength of DNA binding relative to wt
Disease potential of human coding nsSNPs
Neutral polymorphism or disease-associated mutation?
For protein targets of inhibitor drugs:
Continued susceptibility or (degree of ) resistance that patients with the mutant protein have to the inhibitor
Inhibitor binding energy to mutant target relative to wt

21. Examples ofExperimental Mutagenesis Data

22. Example: HIV-1 Protease (PR)

23. HIV-1 PR Dataset Example: Residual Profiles of 536 Experimental Mutants… …

24. Experimental Mutants: Residual Scores Elucidate the Structure-Function Relationship
536 HIV-1 protease mutants
4041 lac repressor mutants
630 hIL-3 mutants
371 gene V protein mutants

25. Universal Model Approach: 8635 Experimental Mutants from 7 Proteins

26. Universal Model Approach: 980 Experimental Mutants from 20 Proteins

27. Structure-Function Correlation Based on Residual Scores: nsSNPs
1790 nsSNPs corresponding to single amino acid substitutions in several hundred proteins with tessellatable structures
Function: 1332 nsSNPs associated with disease; 458 neutral
Data obtained from Swiss-Prot and HPI

28. Structure-Function Correlation Based on Residual Scores: Drug Susceptibility

29. Algorithm Performance: 2015 T4 Lysozyme Mutants

30. Learning Curves for HIV-1 protease and T4 lysozyme mutants

31. Real-World Application: T4 Lysozyme Predictions
Experimental data (not part of training set) obtained from ProTherm database
Result: predictions match experiments for 30/35 (~86%) of the mutants

32. T4 Lysozyme Mutational Array
Training set mutants (n = 2015)
Predicted test set mutants (n = 1101)
Active
Inactive
Active
Inactive

33. GVP Mutational Array

34. Support Vector Regression
Capriotti et al. SVM regression (for comparison):
r = 0.71, Standard Error = 1.3 kcal/mol, y = x –

35. Conclusions
Computational mutagenesis derived from a four-body, knowledge-based statistical potential uniquely characterizes each protein mutant using both sequential and structural features
Attributes correlate well with mutant function - valuable for developing accurate machine learning based predictive models

36. Acknowledgements Structural Bioinformatics Laboratory (GMU):
Tariq Alsheddi (structure alignment)
David Bostick (topological similarity)
Andrew Carr (functional sites, visualization)
Sunita Kumari (structural genomics)
Yong Luo (evolutionary structure analysis)
Majid Masso (mutagenesis, HIV-1 protease, LAC repressor, T4 lysozyme, SNP)
Ewy Mathe (mutagenesis, p53)
Olivia Peters (protein-protein interfaces)
Vadim Ravich (HIV RT mutagenesis)
Greg Reck (hydration potentials, amyloids)
Todd Taylor (statistical potentials, secondary structure, topology, protein stability)
Bill Zhang (mutagenesis, BRCA1)
Collaborators:
John Grefenstette (GMU)
Curt Jamison (GMU)
Dmitri Klimov (GMU)
Dan Carr (GMU)
Estela Blaisten (GMU)
Vladimir Karginov (IB)
Unpublished data:
Clyde Hutchison (UNC)
Ron Swanstrom (UNC)
Funding:
NSF
NIH-Innovative Biologics
GMU-INOVA Research Fund

40. Evaluating Algorithm Performance
Overall goal: Develop model with known examples to accurately predict class (or value) of instances that have not yet been assayed experimentally (potentially great savings of time and money)
Ideal situation: split large original dataset into 3 subsets
Training set (learn model)
Validation set (optimize model by tweaking model parameters)
Test set (evaluate model on new data not used to develop model)
Errors measured at each step (resubstitution, validation, generalization)
Approaches: Tenfold cross-validation (10-fold CV);
leave-one-out CV (i.e., jackknife or N-fold CV, N = dataset size);
% split (e.g., use only 2/3 for training, 1/3 held out for testing)

41. Evaluating Algorithm Performance
10-fold CV
Randomly split the dataset instances into 10 equally-sized subsets
Hold-out subset 1; combine subsets 2-10 into one training set for learning a model; use trained model to predict classes of instances in subset 1
Repeat previous step 9 more times (e.g., hold-out subset 2, combine subsets 1 and 3-10 together to train a model, use model to predict subset 2, etc)
We end up with 10 models, each trained using 90% of the original dataset, and each used to predict the held-out 10% subset.
In the end, each instance has one class prediction – compare to actual class
LOOCV (leave-one-out CV, jackknife, or N-fold CV)
Similar to above, but each subset contains only 1 instance
Deterministic – no randomness to which instances are grouped as subsets
Overall prediction accuracy provides rough idea of how a model trained with the full dataset will perform
% split (self-explanatory)

42. Evaluating Algorithm Performance
Assume instances belong to two generic classes (Pos/Neg)
Results of comparing predictions with actual classes based on the approaches described (10-fold CV, LOOCV, % split) can be summarized in a confusion matrix:
Classification performance measures:
accuracy = (TP+TN) / (TP+FP+TN+FN); sensitivity = TP / (TP+FN);
specificity = TN / (TN+FP); precision = TP / (TP+FP);
BER = 0.5 × [FP / (FP+TN) + FN / (FN+TP)];
MCC = (TP×TN – FP×FN) / (TP+FN)(TP+FP)(TN+FN)(TN+FP);
AUC = area under ROC curve (plot of sensitivity vs. 1 – specificity)
For regression models: correlation coefficient, standard error
Predicted as
Pos Neg TP FN FP TN
Actual
class
Pos
Neg

43. ROC Curve
Plot of true positive rate (sensitivity) versus false positive rate (1 – specificity) in the unit square
AUC = probability that classifier will rank a randomly chosen positive instance higher than a randomly chosen negative one
AUC ~ 0.5 (ROC close to diagonal line joining points (0,0) and (1,1)) suggests no signal in dataset and that trained model is not likely to perform any better than random guessing
AUC = 1 (piecewise linear ROC joining (0,0) to (0,1) and (0,1) to (1,1)) indicates a perfect classifier