Untying Knots in Proteins

A shoelace can be readily untied by pulling its ends rather than its loops. Attempting to untie a native knot in a protein can also succeed or fail depending on where one pulls. However, thermal fluctuations induced by the surrounding water affect conformations stochastically and may add to the uncertainty of the outcome. When the protein is pulled by the termini, the knot can only get tightened, and any attempt at untying results in failure. We show that, by pulling specific amino acids, one may easily retract a terminal segment of the backbone from the knotting loop and untangle the knot. At still other amino acids, the outcome of pulling can go either way. We study the dependence of the untying probability on the way the protein is grasped, the pulling speed, and the temperature. Elucidation of the mechanisms underlying this dependence is critical for a successful experimental realization of protein knot untying

The initial stages of cave formation: Beyond the one-dimensional paradigm

The solutional origin of limestone caves was recognized over a century ago, but the short penetration length of an undersaturated solution made it seem impossible for long conduits to develop. This is contradicted by field observations, where extended conduits, sometimes several kilometers long, are found in karst environments. However, a sharp drop in the dissolution rate of CaCO_3 near saturation provides a mechanism for much deeper penetration of reactant. The notion of a "kinetic trigger" - a sudden change in rate constant over a narrow concentration range - has become a widely accepted paradigm in speleogenesis modeling. However, it is based on one-dimensional models for the fluid and solute transport inside the fracture, assuming that the dissolution front is planar in the direction perpendicular to the flow. Here we show that this assumption is incorrect; a planar dissolution front in an entirely uniform fracture is unstable to infinitesimal perturbations and inevitably breaks up into highly localized regions of dissolution. This provides an alternative mechanism for cave formation, even in the absence of a kinetic trigger. Our results suggest that there is an inherent wavelength to the erosion pattern in dissolving fractures, which depends on the reaction rate and flow rate, but is independent of the initial roughness. In contrast to one-dimensional models, two-dimensional simulations indicate that there is only a weak dependence of the breakthrough time on kinetic order; localization of the flow tends to keep the undersaturation in the dissolution front above the threshold for non-linear kinetics.Comment: to be published in Earth and Planetary Science Letter

Reactive-infiltration instabilities in rocks. Fracture dissolution

A reactive fluid dissolving the surface of a uniform fracture will trigger an instability in the dissolution front, leading to spontaneous formation of pronounced well-spaced channels in the surrounding rock matrix. Although the underlying mechanism is similar to the wormhole instability in porous rocks there are significant differences in the physics, due to the absence of a steadily propagating reaction front. In previous work we have described the geophysical implications of this instability in regard to the formation of long conduits in soluble rocks. Here we describe a more general linear stability analysis, including axial diffusion, transport limited dissolution, non-linear kinetics, and a finite length system.Comment: to be published in J. Fluid. Mec