Diffusion-limited contact formation in unfolded cytochrome c: estimating the maximum rate of protein folding.

How fast can a protein fold? The rate of polypeptide collapse to a compact state sets an upper limit to the rate of folding. Collapse may in turn be limited by the rate of intrachain diffusion. To address this question, we have determined the rate at which two regions of an unfolded protein are brought into contact by diffusion. Our nanosecond-resolved spectroscopy shows that under strongly denaturing conditions, regions of unfolded cytochrome separated by approximately 50 residues diffuse together in 35-40 microseconds. This result leads to an estimate of approximately (1 microsecond)-1 as the upper limit for the rate of protein folding.

Symmetries in geology and geophysics

Symmetries have played an important role in a variety of problems in geology and geophysics. A large fraction of studies in mineralogy are devoted to the symmetry properties of crystals. In this paper, however, the emphasis will be on scale-invariant (fractal) symmetries. The earth’s topography is an example of both statistically self-similar and self-affine fractals. Landforms are also associated with drainage networks, which are statistical fractal trees. A universal feature of drainage networks and other growth networks is side branching. Deterministic space-filling networks with side-branching symmetries are illustrated. It is shown that naturally occurring drainage networks have symmetries similar to diffusion-limited aggregation clusters.

Scaling in geology: landforms and earthquakes.

Landforms and earthquakes appear to be extremely complex; yet, there is order in the complexity. Both satisfy fractal statistics in a variety of ways. A basic question is whether the fractal behavior is due to scale invariance or is the signature of a broadly applicable class of physical processes. Both landscape evolution and regional seismicity appear to be examples of self-organized critical phenomena. A variety of statistical models have been proposed to model landforms, including diffusion-limited aggregation, self-avoiding percolation, and cellular automata. Many authors have studied the behavior of multiple slider-block models, both in terms of the rupture of a fault to generate an earthquake and in terms of the interactions between faults associated with regional seismicity. The slider-block models exhibit a remarkably rich spectrum of behavior; two slider blocks can exhibit low-order chaotic behavior. Large numbers of slider blocks clearly exhibit self-organized critical behavior.

Novel dimeric interface and electrostatic recognition in bacterial Cu,Zn superoxide dismutase

Eukaryotic Cu,Zn superoxide dismutases (CuZnSODs) are antioxidant enzymes remarkable for their unusually stable β-barrel fold and dimer assembly, diffusion-limited catalysis, and electrostatic guidance of their free radical substrate. Point mutations of CuZnSOD cause the fatal human neurodegenerative disease amyotrophic lateral sclerosis. We determined and analyzed the first crystallographic structure (to our knowledge) for CuZnSOD from a prokaryote, Photobacterium leiognathi, a luminescent symbiont of Leiognathid fish. This structure, exemplifying prokaryotic CuZnSODs, shares the active-site ligand geometry and the topology of the Greek key β-barrel common to the eukaryotic CuZnSODs. However, the β-barrel elements recruited to form the dimer interface, the strategy used to forge the channel for electrostatic recognition of superoxide radical, and the connectivity of the intrasubunit disulfide bond in P. leiognathi CuZnSOD are discrete and strikingly dissimilar from those highly conserved in eukaryotic CuZnSODs. This new CuZnSOD structure broadens our understanding of structural features necessary and sufficient for CuZnSOD activity, highlights a hitherto unrecognized adaptability of the Greek key β-barrel building block in evolution, and reveals that prokaryotic and eukaryotic enzymes diverged from one primordial CuZnSOD and then converged to distinct dimeric enzymes with electrostatic substrate guidance.

Visualization of a water-selective pore by electron crystallography in vitreous ice

The water-selective pathway through the aquaporin-1 membrane channel has been visualized by fitting an atomic model to a 3.7-Å resolution three-dimensional density map. This map was determined by analyzing images and electron diffraction patterns of lipid-reconstituted two-dimensional crystals of aquaporin-1 preserved in vitrified buffer in the absence of any additive. The aqueous pathway is characterized by a size-selective pore that is ≈4.0 ± 0.5Å in diameter, spans a length of ≈18Å, and bends by ≈25° as it traverses the bilayer. This narrow pore is connected by wide, funnel-shaped openings at the extracellular and cytoplasmic faces. The size-selective pore is outlined mostly by hydrophobic residues, resulting in a relatively inert pathway conducive to diffusion-limited water flow. The apex of the curved pore is close to the locations of the in-plane pseudo-2-fold symmetry axis that relates the N- and C-terminal halves and the conserved, functionally important N76 and N192 residues.

Aggregation and disaggregation of senile plaques in Alzheimer disease

We quantitatively analyzed, using laser scanning confocal microscopy, the three-dimensional structure of individual senile plaques in Alzheimer disease. We carried out the quantitative analysis using statistical methods to gain insights about the processes that govern Aβ peptide deposition. Our results show that plaques are complex porous structures with characteristic pore sizes. We interpret plaque morphology in the context of a new dynamical model based on competing aggregation and disaggregation processes in kinetic steady-state equilibrium with an additional diffusion process allowing Aβ deposits to diffuse over the surface of plaques.

Huntingtin aggregation monitored by dynamic light scattering

An initial stage of fibrillogenesis in solutions of glutathione S-transferase-huntingtin (GST-HD) fusion proteins has been studied by using dynamic light scattering. Two GST-HD systems with poly-l-glutamine (polyGln) extensions of different lengths (20 and 51 residues) have been examined. For both systems, kinetics of z-average translation diffusion coefficients (Dapp) and their angular dependence have been obtained. Our data reveal that aggregation does occur in both GST-HD51 and GST-HD20 solutions, but that it is much more pronounced in the former. Thus, our approach provides a powerful tool for the quantitative assay of GST-HD fibrillogenesis in vitro.

Stabilization of tetanus and diphtheria toxoids against moisture-induced aggregation.

The progress toward single-dose vaccines has been limited by the poor solid-state stability of vaccine antigens within controlled-release polymers, such as poly(lactide-co-glycolide). For example, herein we report that lyophilized tetanus toxoid aggregates during incubation at 37 degrees C and elevated humidity--i.e., conditions relevant to its release from such systems. The mechanism and extent of this aggregation are dependent on the moisture level in the solid protein, with maximum aggregation observed at intermediate moisture contents. The main aggregation pathway is consistent with formaldehyde-mediated cross-linking, where reactive electrophiles created and stored in the vaccine upon formalinization (exposure to formaldehyde during vaccine preparation) react with nucleophiles of a second vaccine molecule to form intermolecular cross-links. This process is inhibited by the following: (i) succinylating the vaccine to block reactive amino groups; (ii) treating the vaccine with sodium cyanoborohydride, which presumably reduces Schiff bases and some other electrophiles created upon formalinization; and (iii) addition of low-molecular-weight excipients, particularly sorbitol. The moisture-induced aggregation of another formalinized vaccine, diphtheria toxoid, is also retarded by succinylation, suggesting the generality of this mechanism for formalinized vaccines. Hence, mechanistic stability studies of the type described herein may be important for the development of effective single-dose vaccines.

Diffusion and formation of microtubule asters: physical processes versus biochemical regulation.

Microtubule asters forming the mitotic spindle are assembled around two centrosomes through the process of dynamic instability in which microtubules alternate between growing and shrinking states. By modifying the dynamics of this assembly process, cell cycle enzymes, such as cdc2 cyclin kinases, regulate length distributions in the asters. It is believed that the same enzymes control the number of assembled microtubules by changing the "nucleating activity" of the centrosomes. Here we show that assembly of microtubule asters may be strongly altered by effects connected with diffusion of tubulin monomers. Theoretical analysis of a simple model describing assembly of microtubule asters clearly shows the existence of a region surrounding the centrosome depleted in GTP tubulin. The number of assembled microtubules may in some cases be limited by this depletion effect rather than by the number of available nucleation sites on the centrosome.