Proteins in Knots? NOT!

Knot-detecting algorithm discovers that proteins are rarely knotted

When you accidentally twist a shoelace, garden hose, or necklace, it can get annoyingly tangled into intractable knots. On the microscopic level, biopolymers—string-like molecules such as DNA—also form knots, with one mysterious exception: knotted proteins are rare. Physicists have now used computational methods to quantify just how rare in the May 2006 issue of PLoS Computational Biology.


“We found that the proportion of proteins with knots is several orders of magnitude smaller than chance would predict,” says author Alexander Grosberg, PhD, professor of physics at the University of Minnesota. “The degree of it is spectacular.”


Chain “A” of the protein Ubiquitin Hydrolase, which contains the most complicated knot that Grosberg and Lua found in a protein. It has a knot with at least five crossings in it when viewed as a flat object. Courtesy of Rhonald Lua.To envision a knot in a protein, imagine grasping the ends of an amino acid chain (the N-terminus and C-terminus), one end in each hand, and then stretching it out. If you can’t stretch it into a straight line, then it contains a knot.


Of course, finding knots in real proteins requires a computer rather than a pair of hands. Grosberg and his co-author, postdoc Rhonald Lua, PhD, developed a knot-detecting algorithm that they used to scan 4716 proteins with known shapes from the Protein Data Bank. They found only 19 proteins (0.4 percent) with knots. Bolstering their findings, two other groups (from MIT and Italy) independently arrived at almost the same list of knotted proteins (they missed two of Grosberg’s).


Grosberg and Lua next set out to quantify how often proteins would be expected to form knots if only chance was at work. They simulated the shapes of random polymers with chains of equal length, density, and flexibility as proteins using a statistical technique—random walk on a lattice. Starting at a single point, this algorithm draws a path in three dimensions by randomly moving one unit at a time in one of six possible directions: up, down, forward, backward, right, or left. The end result is a randomly crinkled chain that may or may not contain knots. The proportion of these random polymers with knots trounced that found in real proteins: Simulated poly- mers at lengths of a typical protein (200-500 amino acids) formed knots 15-60 percent of the time.


Marc Mansfield, PhD, a professor of chemistry and chemical biology at the Stevens Institute of Technology, did pioneering work on knotted proteins in the early 1990s. He says the researchers’ method of generating random polymers produces some bias, but the bias did not significantly affect the result and had no impact on the study’s overall conclusions.


As to the mystery of why proteins avoid knots, Grosberg says “it has to be a product of evolution.” Mansfield agrees: “My money is still on the explanation that a knotted protein just would not fold well, so nature doesn’t use them.”


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