PHARMACEUTICAL BIOINFORMATICS ALGORITHM
-
Upload
charles-roy -
Category
Documents
-
view
3 -
download
2
description
Transcript of PHARMACEUTICAL BIOINFORMATICS ALGORITHM
![Page 1: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/1.jpg)
QSD – Quadratic Shape Descriptors
Surface Matching and Molecular Docking Using Quadratic Shape
Descriptors
Goldman BB, Wipke WT. Quadratic Shape Descriptors. 1. Rapid Superposition of Dissimilar Molecules Using Geometrically Invariant Surface Descriptors.J.Chem. Inf. Comput. Sci., 40 (3), 644 -658, 2000
![Page 2: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/2.jpg)
QSD idea
Define a geometrical invariant representation of small surface sections (if two molecules have a similar surface region then its small parts are also similar) .
In case a geometrical invariant allows to define a reference frame then the number of all superpositions is n*m. n (m) - number of invariants in the first (second) molecule
Principle curvature and principle directions provide an elegant formalism that captures these notions.
![Page 3: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/3.jpg)
Reminder: curvature properties
|k1| > |k2| > |k3| =0
![Page 4: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/4.jpg)
knormal curvature - curvature of normal section at p
Principal Curvatures: kmax , kmin - normal curvatures with maximal-minimal values
Principal Directions: λ max , λ min - tangent vectors associated with principal curvatures.
kmax ≠ kmin → λ max ┴ λ min
p
(a surface curve)
![Page 5: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/5.jpg)
Molecular Surface Calculation• The preprocessing stage of the
algorithm computes the molecular surface of a molecule by using the original Connolly MS program.
Critical Points Calculation• The critical points of the surface as
defined by Lin et al.40 are calculated.• These critical points are the center of
gravity of each face of the Connolly surface projected back onto the surface.
![Page 6: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/6.jpg)
Critical Points• To reduce the number
of the critical points used to describe a molecule, the critical points associated with the toroidal sections (light purple) of the surface are not used.
![Page 7: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/7.jpg)
S = {p1, ..., pn}, where p = (v, n) is composed of the surface point location v in three-dimensional space and n is the unit vector normal to the surface at p.v
C = {c1, ..., cm} - set of critical points, where ci in S
Surface neighborhood around c:
![Page 8: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/8.jpg)
N is transformed s.t. :c.v = (0,0,0)c.n = (0,0,1)
Hessian matrix (second fundamental form):
Redefine points N:
Local principal curvatures and directions are eigenvalues and eigenvectors, respectively, of the II matrix.
![Page 9: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/9.jpg)
Calculate matrix II by fitting the points of N to the second order part of the Taylor expansion of w:
Notice: w(0,0)=0 and so the first derivatives.
w(u,v) ~
![Page 10: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/10.jpg)
The least-squares estimator of is given by
Finally, two right-handed orthogonal coordinate systems can be constructed from the local principal curvature directions:
![Page 11: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/11.jpg)
Principal curvature directions are in cyan.
![Page 12: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/12.jpg)
Shape Index (κ min, λ min) and (κ max, λ max) represent the local principal curvatures
and directions of the surface patch.The shape index represents the degree of concavity of a local surface section and is defined by :
![Page 13: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/13.jpg)
Shape Index Similarity
• The shape index provides a convenient mechanism for determining the similarity between two section of surface.
• The Similarity measure for two surface patches with shape indexes S1 and S2 is :
1.0 – shapes are identical0.0 – shapes are exactly opposite
![Page 14: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/14.jpg)
Total Shape Similarity Score Y
• The score is simply a summation of the individual similarity scores for each pair of matching descriptors.ML = {ml0,…,mln}, where ml = (ri,lj) indicates that ith QSD on the receptor matchs the jth QSD on the ligand.S(ml.x) represent the value of the shape index S for the match list QSD ml.x.
![Page 15: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/15.jpg)
QSD Preprocessing Algorithm.Input: M Coordinates of Molecule ρ Distance parameter
Variables: A Alignment Matrix S Shape Index
Algorithm: Create molecular surface for molecule M the Connolly algorithm. Calculate critical points C = {c1,…,cm } of surface using Lin’s method. for each c C (c,S,A) Create QSD at point c with distance range ρ store (c,S,A) end
![Page 16: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/16.jpg)
Surface matching phase
• This phase of the algorithm commences with the input of the ligand and proteins atomic coordinates along with the set of quadratic shape descriptors approximating threir molecular surface.
• The surface of the active site has been inverted, and shape complementary between the ligand and receptor surfaces is referred to as shape similarity.
• An additional input parameter, the shape filter ΔS, is used as a filter to determine the extant of similarity between two surface sections.
![Page 17: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/17.jpg)
Surface matching phaseInput:
ML,MR Coordinates of Ligand and receptorQL,QR QSD set describing Ligand and receptorΔS Shape Filter
Algorithm:for each ql QL
for each qr QR
if (|ql.S – qr.S|) ΔS) Dock QL to QR as dictated by alignment of ql to qr
if (sufficient QSDs from QR superimpose on QSD from QL) Dock ML onto MR as dictated by alignment of ql onto qr
if (acceptable steric clash* between MR and transformed ML) store docking end if end if end if end forend for
*Steric collisions are quickly evaluated usinga three-dimensional grid-based procedure.
![Page 18: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/18.jpg)
Scoring
The scoring module uses three types of scoring routines to prioritize the computed dockings:• Empirical estimate of Δgbinding (using Bohm’s algorithm).• Measure of shape similarity Υ.• Clustering algorithm.
![Page 19: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/19.jpg)
Matching & Scoring Phase Complexity
• Let n,m represent the number of QSDs used to describe the shape of the target molecule and the moving molecule.
• The total number of the dockings calculated O(mn).• For each docking calculated, all of the QSDs in the
moving set are transformed, matched with QSDs in the target set and then the surface similarity score assessed.
• The total complexity of the matching phase is thus O(nm2).
![Page 20: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/20.jpg)
Create Molecular Surface for Ligand and Receptor
High level flow chart for QSD docking algorithm
![Page 21: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/21.jpg)
Create Molecular Surface for Ligand and Receptor
High level flow chart for QSD docking algorithm
Calculate Molecular Surface Critical Points
![Page 22: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/22.jpg)
Create Molecular Surface for Ligand and Receptor
High level flow chart for QSD docking algorithm
Calculate Molecular Surface Critical Points
Calculate Quadratic Shape Descriptors
Preprocessing
![Page 23: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/23.jpg)
Create Molecular Surface for Ligand and Receptor
High level flow chart for QSD docking algorithm
Calculate Molecular Surface Critical Points
Calculate Quadratic Shape Descriptors
Dock Ligands To Receptor Using QSD
Preprocessing
![Page 24: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/24.jpg)
Create Molecular Surface for Ligand and Receptor
High level flow chart for QSD docking algorithm
Calculate Molecular Surface Critical Points
Calculate Quadratic Shape Descriptors
Dock Ligands To Receptor Using QSD
Score Successful Dockings
Preprocessing
Object Recognition
![Page 25: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/25.jpg)
Preprocessing Times
![Page 26: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/26.jpg)
Crystallographic Scores
![Page 27: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/27.jpg)
QSD Matching Results
![Page 28: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/28.jpg)
QSD Docking Results on Ligand Into Protein and Comparison With Cocrystalized
Structure Position
![Page 29: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/29.jpg)
Comparison of QSDock a Times to DOCK2 and Geometric
Hashing (GH)
![Page 30: PHARMACEUTICAL BIOINFORMATICS ALGORITHM](https://reader030.fdocuments.us/reader030/viewer/2022020520/577cc7821a28aba711a12b67/html5/thumbnails/30.jpg)
Conclusion
• QSDock is capable of reproducing the crystallographically determined orientations using only shape.
• QSD for shape-based docking dretically reduces the computational complexity of the docking problem.