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?