KNOTFIND: A SIMPLE ALGORITHM FOR DETECTING KNOTS IN PROTEINS

Firas Khatib, Carol Rohl Department of Biomolecular Engineering

Can you tell which of these two

protein chains are knotted?

How can we tell if a protein chain is knotted?

This was the highest scoring model using Rosetta’s automated server Robetta for Target 202 in the

CASP6 blind prediction experiment.

Unfortunately this model is knotted. Knotted

Region

Can you tell which of these two

protein chains are knotted?

How can we tell if a protein chain is knotted?

KnotFree

This was the model submitted

by our group using the same alignment as Robetta. It is

devoid of knots.

• Knots in polypeptide chains have been found in very few proteins. [Nureki et al., 2002]

• Only 8 knots have been found in over 2000 known protein structures. [Taylor, 2000, 2002]

• We set out to write a program that checked modeled structures for knots.

Why Knots?

Detecting Knots without Knot Theory

• Joining the ends of a protein chain can create additional knots and cause other problems.

• In daily life we often encounter knots without closed loops: telephone cords, ethernet cables, extension cords, headphones…etc.

• We define such knots as: “pulling both ends results in a tangle that cannot be undone.”

Potential Knot

This is 1Ni5A. How can we find out if it is knotted?

Pulling Both Ends of the Chain

Simplifying

Pulling Both Ends of the Chain

Simplifying

Pulling Both Ends of the Chain

Simplifying

Pulling Both Ends of the Chain

Simplifying

Rotating and moving

Pulling Both Ends of the Chain

Simplifying

Pulling Both Ends of the Chain

Simplifying

Pulling Both Ends of the Chain

Simplifying

Pulling Both Ends of the Chain

Simplifying

Pulling Both Ends of the Chain

Simplifying

Pulling Both Ends of the Chain

Simplifying

Simplifying

Pulling Both Ends of the Chain

N and C termini connected. Therefore 1Ni5A has no knot.

Pulling Both Ends of the Chain

• This concept of “pulling the ends of the chain”

was the basis for the Knotfind Algorithm.

• Knotfind goes through the chain three residues at

a time and simulates the pulling of the ends of the

chain in an attempt to simplify it.

The Knotfind Algorithm

Example of our Algorithm

First iteration through the chain

Example of our Algorithm

Therefore this chain has no knots

This chain cannot be simplified further, so

this is a knot.

In this final stage, all triangles of

three consecutive residues have line segments going through

them.

Example of our Algorithm with a knot

Localizing the Knot

But once we know a knot exists, how

do we find it?

Localizing the Knot

Knotfind specifies the region that

could not be simplified.

Localizing the Knot

Using Knotfind we are able to locate the knotted region of the chain.

Knotfind Results on CASP5 Experiment

After running Knotfind on all of Rosetta’s comparative modeling CASP5 decoy sets from University of Washington’s group:

Total number of chains : 45,366 Total number of knots : 2,163

4.8% of the decoys had knots.

Why do comparative modeling techniques lead to knots in some modeled structures?

We noticed three types of knots

• Two different loop regions linking with one another.

• A loop region threading itself through the template.

• A loop region knotting with itself:

This occurs extremely rarely and is likely the result of a high gap penalty.

• For CASP6 we filtered our loops:

– Libraries of loops were filtered before being placed onto the template.

– They were screened for knots with themselves as well as knots with the template.

How can we prevent knots?

Target 262

The green region is a loop region that conflicted with the template. Because of this, we selected a different alignment for this target.

How did we prevent knots in CASP6?

Robetta’s best model knots itself

with the template

One of our knotted decoys that we

discarded due to two conflicting loop

regions

Both models used the same template,

shown in blue

Knotfind Results after CASP6

After running Knotfind on all of Rosetta’s comparative modeling CASP6 decoy sets from UCSC:

Total number of chains : 117,200 Total number of knots : 1,300

1.1% of the decoys had knots.

For CASP5, 4.8% of the decoys had knots.

Conclusions

• The Knotfind algorithm is simple and fast.

• Knot formation correlates with breaks in the chain.

• Early filtering of loop libraries helps prevent the formation of knots.

• Future work: detecting regions that may not define a knot but are unproteinlike (such as tied shoelaces) .

Acknowledgements

Carol RohlJosue SamayoaDavid Bernick

Craig LoweMatt WeirauchPaul BourkeBrian Raney

Art LyubimovKevin Karplus