Stretching single-domain proteins: Phase diagram and kinetics of force-induced unfolding

Single-molecule force spectroscopy reveals unfolding of domains in titin on stretching. We provide a theoretical framework for these experiments by computing the phase diagrams for force-induced unfolding of single-domain proteins using lattice models. The results show that two-state folders (at zero force) unravel cooperatively, whereas stretching of non-two-state folders occurs through intermediates. The stretching rates of individual molecules show great variations reflecting the heterogeneity of force-induced unfolding pathways. The approach to the stretched state occurs in a stepwise “quantized” manner. Unfolding dynamics and forces required to stretch proteins depend sensitively on topology. The unfolding rates increase exponentially with force f till an optimum value, which is determined by the barrier to unfolding when f = 0. A mapping of these results to proteins shows qualitative agreement with force-induced unfolding of Ig-like domains in titin. We show that single-molecule force spectroscopy can be used to map the folding free energy landscape of proteins in the absence of denaturants.

Bond orientational order, molecular motion, and free energy of high-density DNA mesophases.

By equilibrating condensed DNA arrays against reservoirs of known osmotic stress and examining them with several structural probes, it has been possible to achieve a detailed thermodynamic and structural characterization of the change between two distinct regions on the liquid-crystalline phase diagram: (i) a higher density hexagonally packed region with long-range bond orientational order in the plane perpendicular to the average molecular direction and (ii) a lower density cholesteric region with fluid-like positional order. X-ray scattering on highly ordered DNA arrays at high density and with the helical axis oriented parallel to the incoming beam showed a sixfold azimuthal modulation of the first-order diffraction peak that reflects the macroscopic bond-orientational order. Transition to the less-dense cholesteric phase through osmotically controlled swelling shows the loss of this bond orientational order, which had been expected from the change in optical birefringence patterns and which is consistent with a rapid onset of molecular positional disorder. This change in order was previously inferred from intermolecular force measurements and is now confirmed by 31P NMR. Controlled reversible swelling and compaction under osmotic stress, spanning a range of densities between approximately 120 mg/ml to approximately 600 mg/ml, allow measurement of the free-energy changes throughout each phase and at the phase transition, essential information for theories of liquid-crystalline states.

Phase separation in aqueous solutions of lens gamma-crystallins: special role of gamma s.

We have studied liquid-liquid phase separation in aqueous ternary solutions of calf lens gamma-crystallin proteins. Specifically, we have examined two ternary systems containing gamma s--namely, gamma IVa with gamma s in water and gamma II with gamma s in water. For each system, the phase-separation temperatures (Tph (phi)) alpha as a function of the overall protein volume fraction phi at various fixed compositions alpha (the "cloud-point curves") were measured. For the gamma IVa, gamma s, and water ternary solution, a binodal curve composed of pairs of coexisting points, (phi I, alpha 1) and (phi II, alpha II), at a fixed temperature (20 degrees C) was also determined. We observe that on the cloud-point curve the critical point is at a higher volume fraction than the maximum phase-separation temperature point. We also find that typically the difference in composition between the coexisting phases is at least as significant as the difference in volume fraction. We show that the asymmetric shape of the cloud-point curve is a consequence of this significant composition difference. Our observation that the phase-separation temperature of the mixtures in the high volume fraction region is strongly suppressed suggests that gamma s-crystallin may play an important role in maintaining the transparency of the lens.