A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Guanidine hydrochloride blocks a critical step in the propagation of the prion-like determinant [PSI+] of Saccharomyces cerevisiae

The cytoplasmic heritable determinant [PSI+] of the yeast Saccharomyces cerevisiae reflects the prion-like properties of the chromosome-encoded protein Sup35p. This protein is known to be an essential eukaryote polypeptide release factor, namely eRF3. In a [PSI+] background, the prion conformer of Sup35p forms large oligomers, which results in the intracellular depletion of functional release factor and hence inefficient translation termination. We have investigated the process by which the [PSI+] determinant can be efficiently eliminated from strains, by growth in the presence of the protein denaturant guanidine hydrochloride (GuHCl). Strains are “cured” of [PSI+] by millimolar concentrations of GuHCl, well below that normally required for protein denaturation. Here we provide evidence indicating that the elimination of the [PSI+] determinant is not derived from the direct dissolution of self-replicating [PSI+] seeds by GuHCl. Although GuHCl does elicit a moderate stress response, the elimination of [PSI+] is not enhanced by stress, and furthermore, exhibits an absolute requirement for continued cell division. We propose that GuHCl inhibits a critical event in the propagation of the prion conformer and demonstrate that the kinetics of curing by GuHCl fit a random segregation model whereby the heritable [PSI+] element is diluted from a culture, after the total inhibition of prion replication by GuHCl.

Evidence in support of a four transmembrane-pore-transmembrane topology model for the Arabidopsis thaliana Na+/K+ translocating AtHKT1 protein, a member of the superfamily of K+ transporters

The Arabidopsis thaliana AtHKT1 protein, a Na+/K+ transporter, is capable of mediating inward Na+ currents in Xenopus laevis oocytes and K+ uptake in Escherichia coli. HKT1 proteins are members of a superfamily of K+ transporters. These proteins have been proposed to contain eight transmembrane segments and four pore-forming regions arranged in a mode similar to that of a K+ channel tetramer. However, computer analysis of the AtHKT1 sequence identified eleven potential transmembrane segments. We have investigated the membrane topology of AtHKT1 with three different techniques. First, a gene fusion alkaline phosphatase study in E. coli clearly defined the topology of the N-terminal and middle region of AtHKT1, but the model for membrane folding of the C-terminal region had to be refined. Second, with a reticulocyte-lysate supplemented with dog-pancreas microsomes, we demonstrated that N-glycosylation occurs at position 429 of AtHKT1. An engineered unglycosylated protein variant, N429Q, mediated Na+ currents in X. laevis oocytes with the same characteristics as the wild-type protein, indicating that N-glycosylation is not essential for the functional expression and membrane targeting of AtHKT1. Five potential glycosylation sites were introduced into the N429Q. Their pattern of glycosylation supported the model based on the E. coli-alkaline phosphatase data. Third, immunocytochemical experiments with FLAG-tagged AtHKT1 in HEK293 cells revealed that the N and C termini of AtHKT1, and the regions containing residues 135–142 and 377–384, face the cytosol, whereas the region of residues 55–62 is exposed to the outside. Taken together, our results show that AtHKT1 contains eight transmembrane-spanning segments.

The structure and organization within the membrane of the helices composing the pore-forming domain of Bacillus thuringiensis δ-endotoxin are consistent with an “umbrella-like” structure of the pore

The aim of this study was to elucidate the mechanism of membrane insertion and the structural organization of pores formed by Bacillus thuringiensis δ-endotoxin. We determined the relative affinities for membranes of peptides corresponding to the seven helices that compose the toxin pore-forming domain, their modes of membrane interaction, their structures within membranes, and their orientations relative to the membrane normal. In addition, we used resonance energy transfer measurements of all possible combinatorial pairs of membrane-bound helices to map the network of interactions between helices in their membrane-bound state. The interaction of the helices with the bilayer membrane was also probed by a Monte Carlo simulation protocol to determine lowest-energy orientations. Our results are consistent with a situation in which helices α4 and α5 insert into the membrane as a helical hairpin in an antiparallel manner, while the other helices lie on the membrane surface like the ribs of an umbrella (the “umbrella model”). Our results also support the suggestion that α7 may serve as a binding sensor to initiate the structural rearrangement of the pore-forming domain.

Broken symmetry and critical transport properties of random metals

Recent experimental data on the conductivity σ+(T), T → 0, on the metallic side of the metal–insulator transition in ideally random (neutron transmutation-doped) 70Ge:Ga have shown that σ+(0) ∝ (N − Nc)μ with μ = ½, confirming earlier ultra-low-temperature results for Si:P. This value is inconsistent with theoretical predictions based on diffusive classical scaling models, but it can be understood by a quantum-directed percolative filamentary amplitude model in which electronic basis states exist which have a well-defined momentum parallel but not normal to the applied electric field. The model, which is based on a new kind of broken symmetry, also explains the anomalous sign reversal of the derivative of the temperature dependence in the critical regime.

Conformational influences of glycosylation of a peptide: A possible model for the effect of glycosylation on the rate of protein folding

Improved strategies for synthesis make it possible to expand the range of glycopeptides available for detailed conformational studies. The glycopeptide 1 was synthesized using a new solid phase synthesis of carbohydrates and a convergent coupling to peptide followed by deprotection. Its conformational properties were subjected to NMR analysis and compared with a control peptide 2 prepared by conventional solid phase methods. Whereas peptide 2 fails to manifest any appreciable secondary structure, the glycopeptide 1 does show considerable conformational bias suggestive of an equilibrium between an ordered and a random state. The implications of this ordering effect for the larger issue of protein folding are considered.

A fusion pore phenotype in mast cells of the ruby-eye mouse

Using patch-clamp capacitance and amperometric techniques, we have identified an exocytotic phenotype that affects the function of the fusion pore, the molecular structure that connects the lumen of a secretory vesicle with the extracellular environment during exocytosis. Direct observation of individual exocytotic events in mast cells from the ruby-eye mouse (ru/ru) showed a 3-fold increase in the fraction and duration of transient fusion events with respect to wild-type mice. The fraction of the total fusion events that were transient increased from 0.22 ± 0.02 (wild type) to 0.65 ± 0.02 (ru/ru), and the average duration of these events increased from 418 ± 32 ms (wild type) to 1207 ± 89 ms (ru/ru). We also show that this phenotype can reduce and delay an evoked secretory response by causing the fusion of vesicles that have been previously emptied by repeated cycles of transient fusion. The exocytotic phenotype that we describe here may be a cause of diseases like platelet storage pool deficiency and prolonged bleeding times for which the ruby-eye mouse serves as an animal model. Furthermore, the identification of the gene causing the fusion pore phenotype reported here will illuminate the molecular mechanisms regulating exocytotic fusion.

Identification of fission yeast nuclear markers using random polypeptide fusions with green fluorescent protein

We describe a method for identifying genes encoding proteins with stereospecific intracellular localizations in the fission yeast Schizosaccharomyces pombe. Yeast are transformed with a gene library in which S. pombe genomic sequences are fused to the gene encoding the Aequorea victoria green fluorescent protein (GFP), and intracellular localizations are subsequently identified by rapid fluorescence screening in vivo. In a model application of these methods to the fission yeast nucleus, we have identified several novel genes whose products are found in specific nuclear regions, including chromatin, the nucleolus, and the mitotic spindle, and sequence similarities between some of these genes and previously identified genes encoding nuclear proteins have validated the approach. These methods will be useful in identifying additional components of the S. pombe nucleus, and further extensions of this approach should also be applicable to a more comprehensive identification of the elements of intracellular architecture in fission yeast.

An equilibrium statistical model for the spreading phase of open-ocean convection

A “most probable state” equilibrium statistical theory for random distributions of hetons in a closed basin is developed here in the context of two-layer quasigeostrophic models for the spreading phase of open-ocean convection. The theory depends only on bulk conserved quantities such as energy, circulation, and the range of values of potential vorticity in each layer. The simplest theory is formulated for a uniform cooling event over the entire basin that triggers a homogeneous random distribution of convective towers. For a small Rossby deformation radius typical for open-ocean convection sites, the most probable states that arise from this theory strongly resemble the saturated baroclinic states of the spreading phase of convection, with a stabilizing barotropic rim current and localized temperature anomaly.

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.

A New Model for Nuclear Envelope BreakdownV⃞

Nuclear envelope breakdown was investigated during meiotic maturation of starfish oocytes. Fluorescent 70-kDa dextran entry, as monitored by confocal microscopy, consists of two phases, a slow uniform increase and then a massive wave. From quantitative analysis of the first phase of dextran entry, and from imaging of green fluorescent protein chimeras, we conclude that nuclear pore disassembly begins several minutes before nuclear envelope breakdown. The best fit for the second phase of entry is with a spreading disruption of the membrane permeability barrier determined by three-dimensional computer simulations of diffusion. We propose a new model for the mechanism of nuclear envelope breakdown in which disassembly of the nuclear pores leads to a fenestration of the nuclear envelope double membrane.

Flexibility of the Kir6.2 inward rectifier K+ channel pore

Interactions of sulfhydryl reagents with introduced cysteines in the pore-forming (Kir6.2) subunits of the KATP channel were examined. 2-Aminoethyl methanethiosulfonate (MTSEA+) failed to modify Cd2+-insensitive control-Kir6.2 channels, but rapidly and irreversibly modified Kir6.2[L164C] (L164C) channels. Although a single Cd2+ ion is coordinated by L164C, four MTSEA+ “hits” can occur, each sequentially reducing the single-channel current. A dimeric fusion of control-Kir6.2 and L164C subunits generates Cd2+-insensitive channels, confirming that at least three cysteines are required for coordination, but MTSEA+ modification of the dimer occurs in two hits. L164C channels were not modified by bromotrimethyl ammoniumbimane (qBBr+), even though qBBr+ caused voltage-dependent block (as opposed to modification) that was comparable to that of MTSEA+ or 3-(triethylammonium)propyl methanethiosulfonate (MTSPTrEA+), implying that qBBr+ can also enter the inner cavity but does not modify L164C residues. The Kir channel pore structure was modeled by homology with the KcsA crystal structure. A stable conformation optimally places the four L164C side chains for coordination of a single Cd2+ ion. Modification of these cysteines by up to four MTSEA+ (or three MTSPTrEA+, or two qBBr+) does not require widening of the cavity to accommodate the derivatives within it. However, like the KcsA crystal structure, the energy-minimized model shows a narrowing at the inner entrance, and in the Kir6.2 model this narrowing excludes all ions. To allow entry of ions as large as MTSPTrEA+ or qBBr+, the entrance must widen to >8 Å, but this widening is readily accomplished by minimal M2 helix motion and side-chain rearrangement.

Direct conversion of an oligopeptide from a β-sheet to an α-helix: A model for amyloid formation

A 16-amino acid oligopeptide forms a stable β-sheet structure in water. In physiological solutions it is able to self-assemble to form a macroscopic matrix that stains with Congo red. On raising the temperature of the aqueous solution above 70°C, an abrupt structural transition occurs in the CD spectra from a β-sheet to a stable α-helix without a detectable random-coil intermediate. With cooling, it retained the α-helical form and took several weeks at room temperature to partially return to the β-sheet form. Slow formation of the stable β-sheet structure thus shows kinetic irreversibility. Such a formation of very stable β-sheet structures is found in the amyloid of a number of neurological diseases. This oligopeptide could be a model system for studying the protein conformational changes that occurs in scrapie or Alzheimer disease. The abrupt and direct conversion from a β-sheet to an α-helix may also be found in other processes, such as protein folding and protein–protein interaction. Furthermore, such drastic structure changes may also be exploited in biomaterials designed as sensors to detect environmental changes.

A quantitative model for membrane fusion based on low-energy intermediates

The energetics of a fusion pathway is considered, starting from the contact site where two apposed membranes each locally protrude (as “nipples”) toward each other. The equilibrium distance between the tips of the two nipples is determined by a balance of physical forces: repulsion caused by hydration and attraction generated by fusion proteins. The energy to create the initial stalk, caused by bending of cis monolayer leaflets, is much less when the stalk forms between nipples rather than parallel flat membranes. The stalk cannot, however, expand by bending deformations alone, because this would necessitate the creation of a hydrophobic void of prohibitively high energy. But small movements of the lipids out of the plane of their monolayers allow transformation of the stalk into a modified stalk. This intermediate, not previously considered, is a low-energy structure that can reconfigure into a fusion pore via an additional intermediate, the prepore. The lipids of this latter structure are oriented as in a fusion pore, but the bilayer is locally compressed. All membrane rearrangements occur in a discrete local region without creation of an extended hemifusion diaphragm. Importantly, all steps of the proposed pathway are energetically feasible.

Altered potassium balance and aldosterone secretion in a mouse model of human congenital long QT syndrome

The voltage-dependent K+ channel responsible for the slowly activating delayed K+ current IKs is composed of pore-forming KCNQ1 and regulatory KCNE1 subunits, which are mutated in familial forms of cardiac long QT syndrome. Because KCNQ1 and KCNE1 genes also are expressed in epithelial tissues, such as the kidneys and the intestine, we have investigated the adaptation of KCNE1-deficient mice to different K+ and Na+ intakes. On a normal K+ diet, homozygous kcne1−/− mice exhibit signs of chronic volume depletion associated with fecal Na+ and K+ wasting and have lower plasma K+ concentration and higher levels of aldosterone than wild-type mice. Although plasma aldosterone can be suppressed by low K+ diets or stimulated by low Na+ diets, a high K+ diet provokes a tremendous increase of plasma aldosterone levels in kcne1−/− mice as compared with wild-type mice (7.1-fold vs. 1.8-fold) despite lower plasma K+ in kcne1−/− mice. This exacerbated aldosterone production in kcne1−/− mice is accompanied by an abnormally high plasma renin concentration, which could partly explain the hyperaldosteronism. In addition, we found that KCNE1 and KCNQ1 mRNAs are expressed in the zona glomerulosa of adrenal glands where IKs may directly participate in the control of aldosterone production by plasma K+. These results, which show that KCNE1 and IKs are involved in K+ homeostasis, might have important implications for patients with IKs-related long QT syndrome, because hypokalemia is a well known risk factor for the occurrence of torsades de pointes ventricular arrhythmia.