Molecular Surface Abstraction Greg Cipriano Advised 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

Visualizing Molecular 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 at important 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 Predicted Ligand Binding Sites

How we can use decals Ligand Shadows

Abstraction in 4 steps Our method: 1. Diffuse surface fields 2. Smooth mesh 3. Identify and remove remaining high-curvature regions 4. Build surface patches and apply a decal for each patch

Abstraction in 4 steps Our method: 1. Diffuse surface fields 2. Smooth mesh 3. Identify and remove remaining high-curvature regions 4. 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 fields onto each vertex:

Diffusing surface fields We sample scalar fields onto each vertex: And apply our filter to smooth out 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 fields 2. Smooth mesh 3. Identify and remove remaining high-curvature regions 4. 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 has high-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 fields 2. Smooth mesh 3. Identify and remove remaining high-curvature regions 4. Build surface patches and apply a decal for each patch

Further abstraction Select a user-defined percentage of vertices with highest curvature. Grow region about each point. Remove, by edge-contraction, all but a few vertices in each region, proceeding from center outward.

Final smooth mesh OriginalCompletely smoothWith Decals

Abstraction in 4 steps Our method: 1. Diffuse surface fields 2. Smooth mesh 3. Identify and remove remaining high-curvature regions 4. 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 ShadowsPredicted Binding Sites

Maps a piece of the surface to a plane Parameterization

Adding decals – what we do We parameterize the surface with Discrete Exponential Maps* Advantages: Local, Fast Starts at center point, progresses outward over 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 smoothing

BeforeAfter

Examples (1AI5)‏

Examples (1BMA)‏

Examples (1ANK)‏

Functional surface analysis using 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?