molecular surface abstraction
DESCRIPTION
Greg Cipriano Advised by Michael Gleicher and George N. Phillips Jr. Molecular Surface Abstraction. Structural Biology: form influences function. Standard metaphor: Lock and key Proteins and their ligands have complementary Shape Charge Hydrophobicity. - PowerPoint PPT PresentationTRANSCRIPT
Molecular Surface Abstraction
Greg CiprianoAdvised by Michael Gleicher and George N. Phillips Jr.
Structural Biology: form influences function
Standard metaphor: Lock and key
Proteins and their ligands have complementary• Shape• Charge• Hydrophobicity
A functional surface... too much detail
Hard to visualize.Hard to compute with.
(2POR)
What we're up to...
Creating tools for structural biology.
Molecular surface abstraction for:• Visualization• Functional surface analysis
VisualizingMolecular Surface
Abstractions
How scientists currently look at molecular surfaces
Salient features:• Solvent-excluded interface• Charge field• Binding partners (in yellow)
Our surface abstraction
Simplified• Geometry• Surface fields
Decals applied atimportant features
Ligands were here.
The molecular surface
Here's the geometric surface
How is it made?
Molecular surfaces
Confusing surface detail
Catalytic Antibody (1F3D)Rendered with PyMol
How do biologists deal with complicated things?
Clearer ribbon representation.
Confusing stick-and-ball model
How do they do the same things with surfaces?
... they don't.
Prior art: QuteMol
Stylized shading helps convey shape
Our method: abstraction
Simplifies both geometry and surface fields (e.g. charge).
How to convey additional information
We can now show interesting regions as decals applied directly to the surface.
Why? Smooth surfaces are easier to parameterize.
How we can use decals
Peaks and bowls
How we can use decals
PredictedLigand
Binding Sites
How we can use decals
Ligand Shadows
Abstraction in 4 steps
Our method:
1. Diffuse surface fields2. Smooth mesh3. Identify and remove remaining high-curvature regions4. Build surface patches and apply a decal for each patch
Abstraction in 4 steps
Our method:
1. Diffuse surface fields2. Smooth mesh3. Identify and remove remaining high-curvature regions4. Build surface patches and apply a decal for each patch
Diffusing surface fields
Starting with a triangulated surface:• Edges in blue• Vertices at points where
edges meet
Diffusing surface fields
Starting with a triangulated surface:
We sample scalar fieldsonto each vertex:
Diffusing surface fields
We sample scalar fieldsonto each vertex:
And apply our filter to smoothout them, preserving large regions of uniform value.
Starting with a triangulated surface:
Smoothing
Standard Gaussian smoothing tends to destroy region boundaries:
Weights pixel neighbors by distance when averaging.
Bilateral filtering
A bilateral filter* smooths an image by taking into account both distance and value difference when averaging neighboring pixels.
* C. Tomasi and R.Manduchi. Bilateral filtering for gray and color images. In ICCV, pages 839–846, 1998.
Bilateral filtering
A bilateral filter* smooths an image by taking into account both distance and value difference when averaging neighboring pixels.
...producing a smooth result while still retaining sharp edges.
Bilateral filtering
We do the same thing, but on a irregular graph:
Here's one vertex, and its immediate neighbors
Abstraction in 4 steps
Our method:
1. Diffuse surface fields2. Smooth mesh3. Identify and remove remaining high-curvature regions4. Build surface patches and apply a decal for each patch
Smoothing the mesh
Taubin* (lamda/mu) smoothing: simple and fast
* G. Taubin. A signal processing approach to fair surface design. In Proceedings of SIGGRAPH 95, pages 351–358.
The trouble with smoothing...
Resulting mesh still hashigh-curvature regions!
Taubin* (lamda/mu) smoothing: simple and fast
A quick digression: what is curvature?
In 2D, defined by an osculating circle tangent to a given point.
A quick digression: what is curvature?
In 3D, it's now defined by radial planes, going through a point P and its normal, N.
For us, curvature = maximum over all planes
So for us, high curvature = pointy in some direction
High-curvature (pointy) regions
Abstraction in 4 steps
Our method:
1. Diffuse surface fields2. Smooth mesh3. Identify and remove remaining high-curvature regions4. Build surface patches and apply a decal for each patch
Further abstraction
Select a user-defined percentageof vertices with highest curvature.
Grow region about each point.
Remove, by edge-contraction, allbut a few vertices in each region, proceeding from center outward.
Final smooth mesh
Original Completely smooth With Decals
Abstraction in 4 steps
Our method:
1. Diffuse surface fields2. Smooth mesh3. Identify and remove remaining high-curvature regions4. Build surface patches and apply a decal for each patch
Building surface patches
We highlight interesting regions using surface patches.Just a few of them:
Ligand Shadows Predicted Binding Sites
Maps a piece of the surface to a plane
Parameterization
Parameterization
Adding decals – what we do
We parameterize the surface with Discrete Exponential Maps*
Advantages:Local, Fast
Starts at center point,progresses outwardover surface.
* R. Schmidt, C. Grimm, and B.Wyvill. Interactive decal compositing with discrete exponential maps. ACM Transactions on Graphics, 25(3):603–613, 2006.
Decals representing points of interest
'H' stickers represent potential hydrogen-bonding sites
Surface patch construction
Surface patch construction
Surface patch smoothing
Surface patch smoothing
Surface patch smoothing
Before After
Examples
(1AI5)
Examples
(1BMA)
Examples
(1ANK)
Functional surface analysisusing abstractions
Automated analysis
To date, comparative studies of protein action usually consider the functional surface indirectly.
• Sequence comparison• Backbone• 3D atom locations• etc...
Why not use the functional surface?
But molecules interact through the functional surface!
So why not look at it directly?
Functional surface has much more data:• Charge• Hydrophobicity• Van der Waals forces• etc...
Surfaces reveal differences
But sometimes the surface tells you more.
4 different RRM domains and their surfaces
Surfaces reveal differences
Two Ribonuclease proteins with 80% sequence homology but a 100x difference in enzymatic activity
What are we going to do?
Reduce functional surfaces down to a manageable size.
How?
Use abstractions! We already know how to abstract the surface.
How?
And we know how to abstract other functional fields.
Proteins are constantly moving
How can we justify using abstractions?• Atoms in molecules wiggle around
So the detail contained in a single snapshot is an inaccurate picture of what's going on, anyway.
Descriptors
Characterize a point's neighborhood using feature vectors.A classic example: facial recognition.
(1,0,0,1,...,1)(1,0,0,1,...,0)
(0,0,1,1,...,1)
Surface descriptors
Each surface sample gets its own descriptor.
We look for statistical properties over regions...individual descriptors don't matter much.
What to work on?
Surface analysis• Classification• Comparison• Binding/specificity prediction• Automatic searching across a database
Conclusion
Molecular surface abstractions:• Simple, stripped-down representation• Good for visualization• Promising for surface analysis
A quick demonstration
Acknowledgments
Thanks: • Michael Gleicher• George Phillips• Aaron Bryden• Nick Reiter
And to CIBM grant NLM-5T15LM007359
Questions?