A constant radius of curvature model for the organization of DNA in toroidal condensates.

Toroidal DNA condensates have received considerable attention for their possible relationship to the packaging of DNA in viruses and in general as a model of ordered DNA condensation. A spool-like model has primarily been supported for DNA organization within toroids. However, our observations suggest that the actual organization may be considerably different. We present an alternate model in which DNA for a given toroid is organized within a series of equally sized contiguous loops that precess about the toroid axis. A related model for the toroid formation process is also presented. This kinetic model predicts a distribution of toroid sizes for DNA condensed from solution that is in good agreement with experimental data.

A single point mutation in the pore region of the epithelial Na+ channel changes ion selectivity by modifying molecular sieving

The epithelial Na+ channel (ENaC) belongs to a new class of channel proteins called the ENaC/DEG superfamily involved in epithelial Na+ transport, mechanotransduction, and neurotransmission. The role of ENaC in Na+ homeostasis and in the control of blood pressure has been demonstrated recently by the identification of mutations in ENaC β and γ subunits causing hypertension. The function of ENaC in Na+ reabsorption depends critically on its ability to discriminate between Na+ and other ions like K+ or Ca2+. ENaC is virtually impermeant to K+ ions, and the molecular basis for its high ionic selectivity is largely unknown. We have identified a conserved Ser residue in the second transmembrane domain of the ENaC α subunit (αS589), which when mutated allows larger ions such as K+, Rb+, Cs+, and divalent cations to pass through the channel. The relative ion permeability of each of the αS589 mutants is related inversely to the ionic radius of the permeant ion, indicating that αS589 mutations increase the molecular cutoff of the channel by modifying the pore geometry at the selectivity filter. Proper geometry of the pore is required to tightly accommodate Na+ and Li+ ions and to exclude larger cations. We provide evidence that ENaC discriminates between cations mainly on the basis of their size and the energy of dehydration.

The reversible condensation and expansion of the rotavirus genome

Understanding the structural organization of the genome is particularly relevant in segmented double-stranded RNA viruses, which exhibit endogenous transcription activity. These viruses are molecular machines capable of repeated cycles of transcription within the intact capsid. Rotavirus, a major cause of infantile gastroenteritis, is a prototypical segmented double-stranded RNA virus. From our three-dimensional structural analyses of rotavirus examined under various chemical conditions using electron cryomicroscopy, we show here that the viral genome exhibits a remarkable conformational flexibility by reversibly changing its packaging density. In the presence of ammonium ions at high pH, the genome condenses to a radius of ≈180 Å from ≈220 Å. Upon returning to physiological conditions, the genome re-expands and fully maintains its transcriptional properties. These studies provide further insights into the genome organization and suggest that the observed isometric and concentric nature of the condensation is due to strong interactions between the genome core and the transcription enzymes anchored to the capsid inner surface. The ability of the genome to condense beyond what is normally observed in the native virus indicates that the negative charges on the RNA in the native state may be only partially neutralized. Partial neutralization may be required to maintain appropriate interstrand spacing for templates to move around the enzyme complexes during transcription. Genome condensation was not observed either with increased cation concentrations at normal pH or at high pH without ammonium ions. This finding indicates that the observed genome condensation is a synergistic effect of hydroxyl and ammonium ions involving disruption of protein–RNA interactions that perhaps facilitate further charge neutralization and consequent reduction in the interstrand spacing.

Quantification of the hydrophobic interaction by simulations of the aggregation of small hydrophobic solutes in water

The hydrophobic interaction, the tendency for nonpolar molecules to aggregate in solution, is a major driving force in biology. In a direct approach to the physical basis of the hydrophobic effect, nanosecond molecular dynamics simulations were performed on increasing numbers of hydrocarbon solute molecules in water-filled boxes of different sizes. The intermittent formation of solute clusters gives a free energy that is proportional to the loss in exposed molecular surface area with a constant of proportionality of 45 ± 6 cal/mol⋅Å2. The molecular surface area is the envelope of the solute cluster that is impenetrable by solvent and is somewhat smaller than the more traditional solvent-accessible surface area, which is the area transcribed by the radius of a solvent molecule rolled over the surface of the cluster. When we apply a factor relating molecular surface area to solvent-accessible surface area, we obtain 24 cal/mol⋅Å2. Ours is the first direct calculation, to our knowledge, of the hydrophobic interaction from molecular dynamics simulations; the excellent qualitative and quantitative agreement with experiment proves that simple van der Waals interactions and atomic point-charge electrostatics account for the most important driving force in biology.

Amyloid fibril formation by an SH3 domain

The SH3 domain is a well characterized small protein module with a simple fold found in many proteins. At acid pH, the SH3 domain (PI3-SH3) of the p85α subunit of bovine phosphatidylinositol 3-kinase slowly forms a gel that consists of typical amyloid fibrils as assessed by electron microscopy, a Congo red binding assay, and x-ray fiber diffraction. The soluble form of PI3-SH3 at acid pH (the A state by a variety of techniques) from which fibrils are generated has been characterized. Circular dichroism in the far- and near-UV regions and 1H NMR indicate that the A state is substantially unfolded relative to the native protein at neutral pH. NMR diffusion measurements indicate, however, that the effective hydrodynamic radius of the A state is only 23% higher than that of the native protein and is 20% lower than that of the protein denatured in 3.5 M guanidinium chloride. In addition, the A state binds the hydrophobic dye 1-anilinonaphthalene-8-sulfonic acid, which suggests that SH3 in this state has a partially formed hydrophobic core. These results indicate that the A state is partially folded and support the hypothesis that partially folded states formed in solution are precursors of amyloid deposition. Moreover, that this domain aggregates into amyloid fibrils suggests that the potential for amyloid deposition may be a common property of proteins, and not only of a few proteins associated with disease.

Cross-validated maximum likelihood enhances crystallographic simulated annealing refinement

Recently, the target function for crystallographic refinement has been improved through a maximum likelihood analysis, which makes proper allowance for the effects of data quality, model errors, and incompleteness. The maximum likelihood target reduces the significance of false local minima during the refinement process, but it does not completely eliminate them, necessitating the use of stochastic optimization methods such as simulated annealing for poor initial models. It is shown that the combination of maximum likelihood with cross-validation, which reduces overfitting, and simulated annealing by torsion angle molecular dynamics, which simplifies the conformational search problem, results in a major improvement of the radius of convergence of refinement and the accuracy of the refined structure. Torsion angle molecular dynamics and the maximum likelihood target function interact synergistically, the combination of both methods being significantly more powerful than each method individually. This is demonstrated in realistic test cases at two typical minimum Bragg spacings (dmin = 2.0 and 2.8 Å, respectively), illustrating the broad applicability of the combined method. In an application to the refinement of a new crystal structure, the combined method automatically corrected a mistraced loop in a poor initial model, moving the backbone by 4 Å.

The thermal explosion revisited

The classical problem of the thermal explosion in a long cylindrical vessel is modified so that only a fraction α of its wall is ideally thermally conducting while the remaining fraction 1−α is thermally isolated. Partial isolation of the wall naturally reduces the critical radius of the vessel. Most interesting is the case when the structure of the boundary is a periodic one, so that the alternating conductive α and isolated 1−α parts of the boundary occupy together the segments 2π/N (N is the number of segments) of the boundary. A numerical investigation is performed. It is shown that at small α and large N, the critical radius obeys a scaling law with the coefficients depending on N. For large N, the result is obtained that in the central core of the vessel the temperature distribution is axisymmetric. In the boundary layer near the wall having the thickness ≈2πr0/N (r0 is the radius of the vessel), the temperature distribution varies sharply in the peripheral direction. The temperature distribution in the axisymmetric core at the critical value of the vessel radius is subcritical.

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.

Staphylococcal protein A: Unfolding pathways, unfolded states, and differences between the B and E domains

We present multiple native and denaturation simulations of the B and E domains of the three-helix bundle protein A, totaling 60 ns. The C-terminal helix (H3) consistently denatures later than either of the other two helices and contains residual helical structure in the denatured state. These results are consistent with experiments suggesting that the isolated H3 fragment is more stable than H1 and H2 and that H3 forms early in folding. Interestingly, the denatured state of the B domain is much more compact than that of the E domain. This sequence-dependent effect on the dimensions of the denatured state and the lack of correlation with structure suggest that the radius of gyration can be a misleading reaction coordinate for unfolding/folding. Various unfolding and refolding events are observed in the denaturation simulations. In some cases, the transitions are facilitated through interactions with other portions of the protein—contact-assisted helix formation. In the native simulations, the E domain is very stable: after 6 ns, the Cα root-mean-square deviation from the starting structure is less than 1.4 Å. In contrast, the native state of the B domain deviates more and its inter-helical angles fluctuate. In apparent contrast, we note that the B domain is thermodynamically more stable than the E domain. The simulations suggest that the increased stability of the B domain may be due to heightened mobility, and therefore entropy, in the native state and decreased mobility/entropy in the more compact denatured state.

Probing active galactic nuclei with H2O megamasers.

We describe the characteristics of the rapidly rotating molecular disk in the nucleus of the mildly active galaxy NGC4258. The morphology and kinematics of the disk are delineated by the point-like watervapor emission sources at 1.35-cm wavelength. High angular resolution [200 microas where as is arcsec, corresponding to 0.006 parsec (pc) at 6.4 million pc] and high spectral resolution (0.2 km.s-1 or nu/Deltanu = 1.4 x 10(6)) with the Very-Long-Baseline Array allow precise definition of the disk. The disk is very thin, but slightly warped, and is viewed nearly edge-on. The masers show that the disk is in nearly perfect Keplerian rotation within the observable range of radii of 0.13-0.26 pc. The approximately random deviations from the Keplerian rotation curve among the high-velocity masers are approximately 3.5 km.s-1 (rms). These deviations may be due to the masers lying off the midline by about +/-4 degrees or variations in the inclination of the disk by +/-4 degrees. Lack of systematic deviations indicates that the disk has a mass of <4 x 10(6) solar mass (M[symbol: see text]). The gravitational binding mass is 3.5 x 10(7) M[symbol: see text], which must lie within the inner radius of the disk and requires that the mass density be >4 x 10(9) M[symbol: see text].pc-3. If the central mass were in the form of a star cluster with a density distribution such as a Plummer model, then the central mass density would be 4 x 10(12) M[symbol: see text].pc-3. The lifetime of such a cluster would be short with respect to the age of the galaxy [Maoz, E. (1995) Astrophys. J. Lett. 447, L91-L94]. Therefore, the central mass may be a black hole. The disk as traced by the systemic velocity features is unresolved in the vertical direction, indicating that its scale height is <0.0003 pc (hence the ratio of thickness to radius, H/R, is <0.0025). For a disk in hydrostatic equilibrium the quadrature sum of the sound speed and Alfven velocity is <2.5 km.s-1, so that the temperature of the disk must be <1000 K and the toroidal magnetic field component must be <250 mG. If the molecular mass density in the disk is 10(10) cm-3, then the disk mass is approximately 10(4) M[symbol: see text], and the disk is marginally stable as defined by the Toomre stability parameter Q (Q = 6 at the inner edge and 1 at the outer edge). The inward drift velocity is predicted to be <0.007 km.s-1, for a viscosity parameter of 0.1, and the accretion rate is <7 x 10(-5) M[symbol: see text].yr-1. At this value the accretion would be sufficient to power the nuclear x-ray source of 4 x 10(40) ergs-1 (1 erg = 0.1 microJ). The volume of individual maser components may be as large as 10(46) cm3, based on the velocity gradients, which is sufficient to supply the observed luminosity. The pump power undoubtedly comes from the nucleus, perhaps in the form of x-rays. The warp may allow the pump radiation to penetrate the disk obliquely [Neufeld, D. A. & Maloney, P. R. (1995) Astrophys. J. Lett. 447, L17-L19]. A total of 15 H2O megamasers have been identified out of >250 galaxies searched. Galaxy NGC4258 may be the only case where conditions are optimal to reveal a well-defined nuclear disk. Future measurement of proper motions and accelerations for NGC4258 will yield an accurate distance and a more precise definition of the dynamics of the disk

Sticky ions in biological systems.

Aqueous gel sieving chromatography on Sephadex G-10 of the Group IA cations (Li+, Na+, K+, Rb+, Cs+) plus NH4+ as the Cl- salts, in combination with previous results for the halide anions (F-, Cl-, Br-, I-) as the Na+ salts [Washabaugh, M.W. & Collins, K.D. (1986) J. Biol. Chem. 261, 12477-12485], leads to the following conclusions. (i) The small monovalent ions (Li+, Na+, F-) flow through the gel with water molecules attached, whereas the large monovalent ions (K+, Rb+, Cs+, Cl-, Br-, I-) adsorb to the nonpolar surface of the gel, a process requiring partial dehydration of the ion and implying that these ions bind the immediately adjacent water molecules weakly. (ii) The transition from strong to weak hydration occurs at a radius of about 1.78 A for the monovalent anions, compared with a radius of about 1.06 A for the monovalent cations (using ionic radii), indicating that the anions are more strongly hydrated than the cations for a given charge density. (iii) The anions show larger deviations from ideal behavior (an elution position corresponding to the anhydrous molecular weight) than do the cations and dominate the chromatographic behavior of the neutral salts. These results are interpreted to mean that weakly hydrated ions (chaotropes) are "pushed" onto weakly hydrated surfaces by strong water-water interactions and that the transition from strong ionic hydration to weak ionic hydration occurs where the strength of ion-water interactions approximately equals the strength of water-water interactions in bulk solution.