Extension of the thermodynamics of small systems to open metastable states: An example

By using a simplified model of small open liquid-like clusters with surface effects, in the gas phase, it is shown how the statistical thermodynamics of small systems can be extended to include metastable supersaturated gaseous states not too far from the gas–liquid equilibrium transition point. To accomplish this, one has to distinguish between mathematical divergence and physical convergence of the open-system partition function.

Influenza hemagglutinin is spring-loaded by a metastable native conformation

Enveloped viruses enter cells by protein-mediated membrane fusion. For influenza virus, membrane fusion is regulated by the conformational state of the hemagglutinin (HA) protein, which switches from a native (nonfusogenic) structure to a fusion-active (fusogenic) conformation when exposed to the acidic environment of the cellular endosome. Here we demonstrate that destabilization of HA at neutral pH, with either heat or the denaturant urea, triggers a conformational change that is biochemically indistinguishable from the change triggered by low pH. In each case, the conformational change is coincident with induction of membrane-fusion activity, providing strong evidence that the fusogenic structure is formed. These results indicate that the native structure of HA is trapped in a metastable state and that the fusogenic conformation is released by destabilization of native structure. This strategy may be shared by other enveloped viruses, including those that enter the cell at neutral pH, and could have implications for understanding the membrane-fusion step of HIV infection.

Excitation transfer spectroscopy with two metastable 138Ba+ ions in same trap.

In the absence of lasers approaching trapped ion clock transitions in sharpness we propose to replace the 12.49 m laser field exciting the D3/2-D5/2 transition of the single Ba+ ion A in D3/2 with the near-field of a close by identical ion B in the excited D5/2 state. We tune the frequency of the near-field by the differential Stark shift generated when the center of mass of the tuned ions is slightly moved out of the trap center by a small bias voltage. We demonstrate that the resultant resonant energy exchange can be made considerably faster than the natural lifetime of either metastable level and show how it might be detected.

X-ray structure determination of a metastable state of carbonmonoxy myoglobin after photodissociation.

The x-ray structure of carbon monoxide (CO)-ligated myoglobin illuminated during data collection by a laser diode at the wavelength lambda = 690 nm has been determined to a resolution of 1.7 A at T = 36 K. For comparison, we also measured data sets of deoxymyoglobin and CO-ligated myoglobin. In the photon-induced structure the electron density associated with the CO ligand can be described by a tube extending from the iron into the heme pocket over more than 4 A. This density can be interpreted by two discrete positions of the CO molecule. One is close to the heme iron and can be identified to be bound CO. In the second, the CO is dissociated from the heme iron and lies on top of pyrrole ring C. At our experimental conditions the overall structure of myoglobin in the metastable state is close to the structure of a CO-ligated molecule. However, the iron has essentially relaxed into the position of deoxymyoglobin. We compare our results with those of Schlichting el al. [Schlichting, I., Berendzen, J., Phillips, G. N., Jr., & Sweet, R. M. (1994) Nature 317, 808-812], who worked with the myoglobin mutant (D122N) that crystallizes in the space group P6 and Teng et al. [Teng, T. Y., Srajer, V. & Moffat, K. (1994) Nat. Struct. Biol. 1, 701-705], who used native myoglobin crystals of the space group P2(1). Possible reasons for the structural differences are discussed.

One sequence, two folds: a metastable structure of CD2.

When expressed as part of a glutathione S-transferase fusion protein the NH2-terminal domain of the lymphocyte cell adhesion molecule CD2 is shown to adopt two different folds. The immunoglobulin superfamily structure of the major (85%) monomeric component has previously been determined by both x-ray crystallography and NMR spectroscopy. We now describe the structure of a second, dimeric, form present in about 15% of recombinant CD2 molecules. After denaturation and refolding in the absence of the fusion partner, dimeric CD2 is converted to monomer, illustrating that the dimeric form represents a metastable folded state. The crystal structure of this dimeric form, refined to 2.0-A resolution, reveals two domains with overall similarity to the IgSF fold found in the monomer. However, in the dimer each domain is formed by the intercalation of two polypeptide chains. Hence each domain represents a distinct folding unit that can assemble in two different ways. In the dimer the two domains fold around a hydrophilic interface believed to mimic the cell adhesion interaction at the cell surface, and the formation of dimer can be regulated by mutating single residues at this interface. This unusual misfolded form of the protein, which appears to result from inter- rather than intramolecular interactions being favored by an intermediate structure formed during the folding process, illustrates that evolution of protein oligomers is possible from the sequence for a single protein domain.

Exploring the folding free energy surface of a three-helix bundle protein

The multidimensional free energy surface for a small fast folding helical protein is explored based on first-principle calculations. The model represents the 46-residue segment from fragment B of staphylococcal protein A. The relationship between collapse and tertiary structure formation, and the order of collapse and secondary structure formation, are investigated. We find that the initial collapse process gives rise to a transition state with about 30% of the native tertiary structure and 50–70% of the native helix content. We also observe two distinct distributions of native helix in this collapsed state (Rg ≈ 12 Å), one with about 20% of the native helical hydrogen bonds, the other with near 70%. The former corresponds to a local minimum. The barrier from this metastable state to the native state is about 2 kBT. In the latter case, folding is essentially a downhill process involving topological assembly. In addition, the order of formation of secondary structure among the three helices is examined. We observe cooperative formation of the secondary structure in helix I and helix II. Secondary structure in helix III starts to form following the formation of certain secondary structure in both helix I and helix II. Comparisons of our results with those from theory and experiment are made.

Studies using double mutants of the conformational transitions in influenza hemagglutinin required for its membrane fusion activity

Amino acid substitutions widely distributed throughout the influenza hemagglutinin (HA) influence the pH of its membrane fusion activity. We have combined a number of these substitutions in double mutants and determined the effects on the pH of fusion and on the pH at which the refolding of HA required for fusion occurs. By analyzing combinations of mutations in three regions of the metastable neutral-pH HA that are rearranged at fusion pH we obtain evidence for both additive and nonadditive effects and for an apparent order of dominance in the effects of amino acid substitutions in particular regions on the pH of fusion. We conclude that there are at least three components in the structural transition required for membrane fusion activity and consider possible pathways for the transition in relation to the known differences between neutral and fusion pH HA structures.

Spectral bifurcations in dispersive wave turbulence

Dispersive wave turbulence is studied numerically for a class of one-dimensional nonlinear wave equations. Both deterministic and random (white noise in time) forcings are studied. Four distinct stable spectra are observed—the direct and inverse cascades of weak turbulence (WT) theory, thermal equilibrium, and a fourth spectrum (MMT; Majda, McLaughlin, Tabak). Each spectrum can describe long-time behavior, and each can be only metastable (with quite diverse lifetimes)—depending on details of nonlinearity, forcing, and dissipation. Cases of a long-live MMT transient state dcaying to a state with WT spectra, and vice-versa, are displayed. In the case of freely decaying turbulence, without forcing, both cascades of weak turbulence are observed. These WT states constitute the clearest and most striking numerical observations of WT spectra to date—over four decades of energy, and three decades of spatial, scales. Numerical experiments that study details of the composition, coexistence, and transition between spectra are then discussed, including: (i) for deterministic forcing, sharp distinctions between focusing and defocusing nonlinearities, including the role of long wavelength instabilities, localized coherent structures, and chaotic behavior; (ii) the role of energy growth in time to monitor the selection of MMT or WT spectra; (iii) a second manifestation of the MMT spectrum as it describes a self-similar evolution of the wave, without temporal averaging; (iv) coherent structures and the evolution of the direct and inverse cascades; and (v) nonlocality (in k-space) in the transferral process.

Equilibration rates in lipid monolayers

A theoretical analysis is given for the rate of change of domain sizes in lipid monolayers at the air–water interface. The calculation is applicable to liquid domains formed from binary mixtures of lipids that form two coexisting liquid phases. Under conditions where the two lipid molecules have approximately equal areas, the equilibration rate does not involve macroscopic hydrodynamic flow in the subphase but rather depends on the diffusion coefficient of the lipid molecules. The calculation shows that the equilibration rate in binary mixtures of cholesterol and phosphatidylcholine is remarkably slow, the radius of a typical 20-μm diameter domain changing by as little as a part in a million per second. Under these circumstances, equilibration times of the order of days or weeks are expected. Even with such long times, the final state reached by the monolayer will in general be a state of metastable equilibrium, rather than true equilibrium.

Structural determinants of oxidative folding in proteins

A method for determining the kinetic fate of structured disulfide species (i.e., whether they are preferentially oxidized or reshuffle back to an unstructured disulfide species) is introduced. The method relies on the sensitivity of unstructured disulfide species to low concentrations of reducing agents. Because a structured des species that preferentially reshuffles generally first rearranges to an unstructured species, a small concentration of reduced DTT (e.g., 260 μM) suffices to distinguish on-pathway intermediates from dead-end species. We apply this method to the oxidative folding of bovine pancreatic ribonuclease A (RNase A) and show that des[40–95] and des[65–72] are productive intermediates, whereas des[26–84] and des[58–110] are metastable dead-end species that preferentially reshuffle. The key factor in determining the kinetic fate of these des species is the relative accessibility of both their thiol groups and disulfide bonds. Productive intermediates tend to be disulfide-secure, meaning that their structural fluctuations preferentially expose their thiol groups, while keeping their disulfide bonds buried. By contrast, dead-end species tend to be disulfide-insecure, in that their structural fluctuations expose their disulfide bonds in concert with their thiol groups. This distinction leads to four generic types of oxidative folding pathways. We combine these results with those of earlier studies to suggest a general three-stage model of oxidative folding of RNase A and other single-domain proteins with multiple disulfide bonds.

Formation of a GNRA tetraloop in P5abc can disrupt an interdomain interaction in the Tetrahymena group I ribozyme

The secondary structure of a truncated P5abc subdomain (tP5abc, a 56-nucleotide RNA) of the Tetrahymena thermophila group I intron ribozyme changes when its tertiary structure forms. We have now used heteronuclear NMR spectroscopy to determine its conformation in solution. The tP5abc RNA that contains only secondary structure is extended compared with the tertiary folded form; both forms coexist in slow chemical exchange (the interconversion rate constant is slower than 1 s−1) in the presence of magnesium. Kinetic experiments have shown that tertiary folding of the P5abc subdomain is one of the earliest folding transitions in the group I intron ribozyme, and that it leads to a metastable misfolded intermediate. Previous mutagenesis studies suggest that formation of the extended P5abc structure described here destabilize a misfolded intermediate. This study shows that the P5abc RNA subdomain containing a GNRA tetraloop in P5c (in contrast to the five-nucleotide loop P5c in the tertiary folded ribozyme) can disrupt the base-paired interdomain (P14) interaction between P5c and P2.

Kinetic stability as a mechanism for protease longevity

The folding of the extracellular serine protease, α-lytic protease (αLP; EC 3.4.21.12) reveals a novel mechanism for stability that appears to lead to a longer functional lifetime for the protease. For αLP, stability is based not on thermodynamics, but on kinetics. Whereas this has required the coevolution of a pro region to facilitate folding, the result has been the optimization of native-state properties independent of their consequences on thermodynamic stability. Structural and mutational data lead to a model for catalysis of folding in which the pro region binds to a conserved β-hairpin in the αLP C-terminal domain, stabilizing the folding transition state and the native state. The pro region is then proteolytically degraded, leaving the active αLP trapped in a metastable conformation. This metastability appears to be a consequence of pressure to evolve properties of the native state, including a large, highly cooperative barrier to unfolding, and extreme rigidity, that reduce susceptibility to proteolytic degradation. In a test of survival under highly proteolytic conditions, homologous mammalian proteases that have not evolved kinetic stability are much more rapidly degraded than αLP. Kinetic stability as a means to longevity is likely to be a mechanism conserved among the majority of extracellular bacterial pro-proteases and may emerge as a general strategy for intracellular eukaryotic proteases subject to harsh conditions as well.

Lifetimes of intermediates in the β-sheet to α-helix transition of β-lactoglobulin by using a diffusional IR mixer

The extremely slow α-helix/β-sheet transition of proteins is a crucial step in amylogenic diseases and represents an internal rearrangement of local contacts in an already folded protein. These internal structural rearrangements within an already folded protein are a critical aspect of biological action and are a product of conformational flow along unknown metastable local minima of the energy landscape of the compact protein. We use a diffusional IR mixer with time-resolved Fourier transform IR spectroscopy capable of 400-μs time resolution to show that the trifluoroethanol driven β-sheet to α-helix transition of β-lactoglobulin proceeds via a compact β-sheet intermediate with a lifetime of 7 ms, small compared with the overall folding time of β-lactoglobulin.

Conformational trapping in a membrane environment: a regulatory mechanism for protein activity?

Functional regulation of proteins is central to living organisms. Here it is shown that a nonfunctional conformational state of a polypeptide can be kinetically trapped in a lipid bilayer environment. This state is a metastable structure that is stable for weeks just above the phase transition temperature of the lipid. When the samples are incubated for several days at 68 degrees C, 50% of the trapped conformation converts to the minimum-energy functional state. This result suggests the possibility that another mechanism for functional regulation of protein activity may be available for membrane proteins: that cells may insert proteins into membranes in inactive states pending the biological demand for protein function.

A soluble domain of the membrane-anchoring chain of influenza virus hemagglutinin (HA2) folds in Escherichia coli into the low-pH-induced conformation.

The extensive refolding of the membrane-anchoring chain of hemagglutinin (HA) of influenza virus (termed HA2) in cellular endosomes, which initiates viral entry by membrane fusion, suggests that viral HA is meta-stable. HA2 polypeptide residues 38-175 expressed in Escherichia coli are reported here to fold in vivo into a soluble trimer. The structure appears to be the same as the low-pH-induced conformation of viral HA2 by alpha-helical content, thermodynamic stability, protease dissection, electron microscopy, and antibody binding. These results provide evidence that the structure of the low-pH-induced fold of viral HA2 (TBHA2) observed crystallographically is the lowest-energy-state fold of the HA2 polypeptide. They indicate that the HA2 conformation in viral HA before low pH activation of its fusion potential is metastable and suggest that removal of the receptor-binding chain (HA1) is enough to allow HA2 to adopt the stable state. Further, they provide direct evidence that low pH is not required to form the membrane-fusion conformation but acts to make this state kinetically accessible in viral HA.