Spring 2001 -- Vol. 18, No. 1

Geometry Determines Preferred Helix Shape of Protein Spirals

Why do proteins coil up into spirals?  A new answer to this question, which could aid the effort to identify the genetically determined shapes and functions of human proteins, was published in the 20 July 2000 issue of the journal Nature.  "We have discovered a simple explanation, based solely on principles of geometry, for the protein's preference for the helix as a major component of its overall structure," said Jayanth Banavar, professor of physics at Penn State and a member of the team of U.S. and Italian research physicists that made the discovery.  The finding is expected to be useful in such wide-ranging research areas as structural genomics, pharmaceuticals, protein engineering, and materials science.

"We applied mathematical ideas about optimal shapes of strings with maximum ėthickness' to proteins, which are string-like in that they have an amino-acid backbone that curls and bends itself into a number of characteristic shapes, including the helix," Banavar said.

Proteins are the product of genes and also the structural stuff of cells and tissues.  Like any tool, each protein's shape plays a large role in determining its function.  Banavar and his colleagues asked in mathematical language what shape would lead to certain known properties of proteins.  This approach is different from the intensive ongoing effort in biochemical research to understand what shape a protein is most likely to take based on each chemical bond that can form within its backbone's distinctive sequence of amino acids.  "Many different amino-acid sequences fold into the same or similar structures, which suggests that the structure may be of more fundamental importance than the amino-acid sequences," Banavar said. "Our work yields a simple and logical way of looking at protein shapes independent of complex biochemical interactions."

"A fascinating question to think about is why proteins take on certain basic shapes in their folded states," said Amos Maritan, professor of physics at the International School for Advanced Studies in Italy (SISSA) and a member of the research team.

As a simple example of this approach, the researchers asked a series of mathematical questions about the optimal working shape of proteins, including the maximum space around each amino acid in the proteins' folded form, or "native state," and their ability to form that compact shape rapidly.  For each calculation, the answer turned out to be a spiraling helix.

A protein's backbone needs to be compact in order to squeeze out water molecules from its central region.  The backbone also needs to have enough room for its atomic components to fit along its winding path with a little extra space for movement.  When the researchers calculated the shape that would result in just the right compromise between absolute compactness and maximum wiggle room, the result was a helix.

"The main result of this calculation is that the natural consequence of these two constraints alone is a helix with an equal amount of room both along the pitch axis of the helix and in the plane perpendicular to it--a pitch-to-diameter ratio very close to the helices we find in natural proteins," said Cristian Micheletti, a postdoctoral researcher at SISSA and a member of the research team.

"Half a century ago Linus Pauling showed with an extremely beautiful theoretical calculation that to get a repeating pattern along the protein's backbone with strong covalent bonds along the sequence and as many weaker hydrogen bonds as possible, that pattern would have to be a helix with a certain pitch-to-radius ratio determined by the chemistry of the bonds," said Antonio Trovato, a graduate student at SISSA and a member of the team.  Experiments have confirmed this particular helix occurs naturally in proteins.

"Now we have shown it is possible to strip away all the chemistry and still get the same result by asking the even more elementary question of what is the shape of a string that allows the maximum breathing room for the protein's amino acids while still being compact," Banavar explained.

The researchers also investigated the protein's ability to compact itself rapidly and reproducibly into its working native-state shape after initially being formed or being temporarily loosened by various forces.  "Our calculations indicate that the dynamics required for the rapid folding of a denatured protein--or other biologically viable polymer--into its native-state structure also favor the formation of helical motifs," said Maritan.  "This is a simple consequence of the local contacts present in a helix and has been observed experimentally as well."  Banavar added, "A simple analogy is the packing of clothes into a suitcase, which entails the bending and curling of the clothes into lower-dimensional units.  The helix and other component shapes in a protein are indeed such lower-dimensional units."

The researchers also showed how a protein's characteristic shape can be used to predict how it might naturally form.  They asked how the chemical bonds could form rapidly to transform a protein's loose unfolded structure into its compact folded structure held together by all of the fully formed chemical bonds.  "This question is of great interest from an experimental and an engineering point of view," Maritan said.

The researchers compared several natural protein structures to decoy structures they created with compactness similar to the natural proteins but with no secondary motifs like helices.  They then calculated mathematically the number of ways each structure could be taken apart halfway; that is, until only about 50 percent of the bonds remained intact.  They found that the naturally occurring structures had many more of these half-formed configurations than did the artificial structures without any secondary motifs.  "It is faster for a large crowd to enter a stadium through lots of doorways than through just a few doorways," Cristian Micheletti explained.

"There seems to be a principle by which nature selects those structures that have as many transitional entryway structures as possible.  In other words, secondary motifs like helices seem to give proteins many more options for snapping themselves together, so the folding process should be able to proceed more rapidly," said Flavio Seno of the University of Padova, Italy, and a member of the research team. He added, "Moreover, we found certain contacts that seem to appear again and again in these entryway structures, and those are precisely the ones that experimenters have found form early and are critical for the successful folding of a protein."

This direct comparison with experimental results indicates the team's approach could provide further insights into the protein-folding process.

The physicists said their approach of looking for fundamental ways to understand universal features of the protein-folding process using simple principles is complementary to the biochemical approach of developing a tightly focused and detailed understanding of the structure of proteins.  "There may be some value to looking at the same thing in different ways," Micheletti commented.

"The development of an easier way to reliably predict what shape a protein  folds into from a knowledge of the sequence of its amino acids would lead to a renaissance in the field of human genomics and our work may help to advance this effort," Banavar said.  "We also would like to understand what the fundamental shapes are in nature and whether there is some really simple principle behind nature's selection of these shapes."

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