An early morning walk may yield the beautiful sight of the delicate, dewy web of an orb-weaver (Araneus), stretching from one bush to another. The fragility of the web is deceptive. An Araneus spider's silk has a tensile strength higher than steel, yet it is so elastic it can stretch to 30-50 percent of its length or contract by 50 percent before breaking. The tensile strength matches that of Kevlar, a synthetic material used in bulletproof vests, but Kevlar is not so elastic as spider silk.

Scientists take pride in designing new materials like Kevlar that are lighter, stronger, and better for many purposes than materials found in nature. But Professor Dmitrii E. Makarov, of the Institute for Theoretical Chemistry at The University of Texas at Austin, cautions that many natural materials can outperform anything yet designed by humans. His simulations of proteins, running on TACC's Longhorn and Lonestar computers, explore the molecular origins of the marvelous mechanical properties of everything from spider silk to muscle fiber.

Mechanical processes play a role for all proteins, Makarov notes. Recently scientists learned that the unfolding of proteins pulled mechanically through a narrow constriction is a key step in the process through which unneeded or harmful proteins are destroyed by the cell. "Understanding the mechanical properties of proteins will give us two new avenues of research, one into the character of the cellular defensive mechanisms against diseases or impairments, and one into the design of new materials that can function as well as the natural models," Makarov says.

Makarov and his students, Pai-Chi Li, Lei Huang, and Serdal Kirmizialtin, work closely with a number of experimental collaborators, including biophysicists Andres Oberhauser of the UT Medical Branch at Galveston, Helen Hansma of the University of California at Santa Barbara physics department, and Liviu Movileanu of the Syracuse University physics department.

Mechanical Unfolding Studies

The experimentalists use atomic force microscopy (AFM) and molecular force probes to study load-bearing protein molecules. Hansma and colleagues studied spider silk. Others studied kinesin, a molecule whose rearrangements drive the use of our muscles, and titin, which is responsible for muscle elasticity. Many of the AFM experiments involve pinning down one end of a molecule and then pulling on it to determine its tensile strength and the speed with which it unfolds.

Makarov points out that direct comparisons of AFM experiments with simulations are often impossible. "Brute-force, fully atomistic simulations of single-molecule mechanical unfolding experiments are not feasible," he says, because current simulation time scales are about six orders of magnitude shorter (picoseconds to nanoseconds) than the time scales explored by experiments (hundreds of nanoseconds to milliseconds). Moreover, he notes, "at the much faster loading rates typical of molecular dynamics simulations, proteins may unfold via mechanisms different from those explored in experimental studies."

To bridge the time-scale gap, Makarov and his students use atomistic simulations to construct more phenomenological models of the load-bearing proteins. Alternatively, they replace atomistic models with simplified string-of-beads representations of short domains within the protein. Then they look at the energetics of mechanical processes.

How their approach works may be understood from the following analogy. "Imagine a mountain ridge separating two mountain valleys," Makarov says. "These valleys represent the folded and unfolded states of a protein. To accomplish unfolding, one has to overcome the barrier presented by the ridge, and the easiest way to go is to aim for the lowest point on the ridge, i.e., a mountain pass. The higher the barrier, the less likely one is to cross over to the other valley."

The probability of crossing over (unfolding) is therefore determined by how high the ridge is relative to the valley bottom. The effect of a mechanical force is to lower the mountain pass, making unfolding more likely. "All we need to do is to compute this barrier--the free-energy barrier in the case of proteins. This task is still quite challenging because it involves exploration of a very rugged mountain landscape," says Makarov.

Furthermore, while mountain climbers live in a 3D world, the configurational space of proteins involves many dimensions. To navigate in such space, one needs a "guide," or what chemists call a reaction coordinate, which measures progress in moving from one valley to the other. In the mechanical unfolding studies, the protein extension (stretching) provides a natural choice for the reaction coordinate. "We use a number of computational tricks, including replica exchange and umbrella sampling, to extract the free-energy landscapes of proteins from a series of equilibrium molecular dynamics trajectories. This allows us to predict the forces at which proteins will unfold," Makarov says.

For example, for the protein titin, the group began with molecular dynamics simulations of the stretching of a domain of the protein known as I27, using a molecular dynamics code called Tinker, developed at Washington University in St. Louis. A separate simulation was run for each 1-Angstrom (0.1-nanometer) increment in the protein extension. This allowed them to map out the free-energy barrier between the folded and unfolded states and examine its force dependence.

Ultimately, the group found that the distribution of the unfolding forces along the molecule and the dependence of that distribution on the pulling rate were in agreement with AFM experiments. The work was published in the Journal of Chemical Physics in November 2003. The many hundreds of simulations required were carried out on TACC resources.

Protein Resistance to Unfolding

Because titin is a load-bearing protein found in muscle fibers, it is reasonable that it has evolved to sustain large forces and dissipate large amounts of energy under mechanical stresses. The dissipated energy can in fact be much larger than the minimum work required to unfold the protein under equilibrium conditions. "Load-bearing proteins operate far from equilibrium and this property accounts for the toughness of many natural materials," Makarov says.

Makarov and his students also explored ways in which mechanical strength relates to the configuration or topology of important subdomains of load-bearing and similarly configured proteins. In a study published in the Journal of Physical Chemistry B in 2004, Makarov and Pai-Chi Li compared relationships between topology and mechanical unfolding of domains found in titin, ubiquitin, and protein G. Each of these domains contains a clamp-like structure formed by parallel beta-strands (see figure).

"In that study, which also used TACC's high-end computing power, we used our approach to predict the outcome of single-molecule AFM pulling experiments," Makarov says. "We found that replacing the titin domain by either of the other, similar domains yielded very similar time histories and unfolding forces. Remarkably, in a recent study in Biophysical Journal, our colleagues at the University of Leeds measured the mechanical stability of protein L, whose structure is nearly identical to that of protein G, and their measurements were in very good agreement with our predictions."

The high mechanical resistance of such domains to unfolding clearly serves a purpose in the case of titin; but ubiquitin's strength "appears to be accidental," Makarov says, rather than necessitated by its function. When similarly structured domains, even with different evolutionary histories, exhibit similar mechanical properties, the properties may well be very broadly applicable. They could be particularly important in fields like tissue engineering.

Protein Degradation

In addition to stretching and contracting, of course, human and animal load-bearing proteins, as well as other proteins, are also continually built, used, and recycled as are all other contents of the cell (and as are cells themselves).