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Time-resolved small-angle x-ray scattering was used to measure the radius of gyration of cytochrome c after initiation of folding by a pH jump. Submillisecond time resolution was obtained with a microfabricated diffusional mixer and synchrotron radiation. The results show that the protein first collapses to compact denatured structures before folding very fast to the native state.The stability and folding speed of a protein depend on the structures of the denatured as well as the native state, raising the question: do proteins fold more rapidly from a denatured state of expanded structures or from one of compact structures? Lattice simulations of simplified representations of proteins suggest that slow folding amino acid sequences collapse to compact structures with non-native topologies before folding, while fast folders collapse and fold simultaneously (1-4). We have begun to address this question experimentally with submillisecond small-angle x-ray scattering (SAXS) using synchrotron radiation and a microfabricated diffusional mixer to rapidly initiate folding. SAXS yields the radius of gyration, the most unambiguous measure of compactness. Here we show that, in contrast to the simulations, one of the fastest-folding proteins (cytochrome c: folding ϭ 400 s) first collapses to compact structures before forming the final native state. X-ray scattering by proteins in solution is sensitive to spatial variations in electron density. Scattering at the smallest angles yields the radius of gyration, R g , which in conjunction with the protein molecular weight provides a measure of the compactness of globular proteins. Additional structural information can be obtained from scattering at larger angles, which reflects electron density correlations on length scales shorter than R g . For a compact polymer, such as the native protein or compact denatured structures, I(q)q 2 increases at low q, goes through a maximum, and decreases at large q where I(q)␣q Ϫ4 [I(q) is the scattered intensity; q ϭ 4sin ͞, is the momentum transfer;is the x-ray wavelength, 1.54 Å; and 2 is the scattering angle] (5). In contrast, for a polymer chain undergoing a random walk in space, as can occur for an unfolded protein under strongly denaturing conditions, I(q)q 2 first increases, then plateaus (6), and, at large q, where I(q)␣q

Vibrations in a granular material can spontaneously produce convection rolls reminiscent of those seen in fluids. Magnetic resonance imaging provides a sensitive and noninvasive probe for the detection of these convection currents, which have otherwise been difficult to observe. A magnetic resonance imaging study of convection in a column of poppy seeds yielded data about the detailed shape of the convection rolls and the depth dependence of the convection velocity. The velocity was found to decrease exponentially with depth; a simple model for this behavior is presented here.

Dry granular material confined to a cylindrical vessel convects when subjected to either continuous or discrete vertical oscillations of sufficient intensity. Particles flow upward in the center of the container and fall in a thin stream along the wall. We have studied this motion experimentally in three-dimensional cylinders for a variety of material, container, and vibration parameters using tracer particle techniques and magnetic resonance imaging. By combining these methods, we have characterized both the depth and radial dependence of the vertical flow velocity. We find that the upward flow velocity along the cylinder axis decays exponentially from the top free surface into the bulk of the material. This flow decreases and changes direction as the inner container walls are approached, displaying a radial dependence closely approximated by either a hyperbolic cosine or a modified Bessel function of order zero. We propose a simple model of granular convection consistent with these findings.