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.

Random circular permutation of genes and expressed polypeptide chains: application of the method to the catalytic chains of aspartate transcarbamoylase.

Recent studies on proteins whose N and C termini are in close proximity have demonstrated that folding of polypeptide chains and assembly of oligomers can be accomplished with circularly permuted chains. As yet no methodical study has been conducted to determine how extensively new termini can be introduced and where such termini cannot be tolerated. We have devised a procedure to generate random circular permutations of the catalytic chains of Escherichia coli aspartate transcarbamoylase (ATCase; EC 2.1.3.2) and to select clones that produce active or stable holoenzyme containing permuted chains. A tandem gene construct was made, based on the desired linkage between amino acid residues in the C- and N-terminal regions of the polypeptide chain, and this DNA was treated with a suitable restriction enzyme to yield a fragment containing the rearranged coding sequence for the chain. Circularization achieved with DNA ligase, followed by linearization at random with DNase I, and incorporation of the linearized, repaired, blunt-ended, rearranged genes into a suitable plasmid permitted the expression of randomly permuted polypeptide chains. The plasmid with appropriate stop codons also contained pyrI, the gene encoding the regulatory chain of ATCase. Colonies expressing detectable amounts of ATCase-like molecules containing permuted catalytic chains were identified by an immunoblot technique or by their ability to grow in the absence of pyrimidines in the growth medium. Sequencing of positive clones revealed a variety of novel circular permutations. Some had N and C termini within helices of the wild-type enzyme as well as deletions and insertions. Permutations were concentrated in the C-terminal domain and only few were detected in the N-terminal domain. The technique, which is adaptable generally to proteins whose N and C termini are near each other, can be of value in relating in vivo folding of nascent, growing polypeptide chains to in vitro renaturation of complete chains and determining the role of protein sequence in folding kinetics.

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.

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.

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 modified gambler's ruin model of polyethylene chains in the amorphous region.

Polyethylene chains in the amorphous region between two crystalline lamellae M unit apart are modeled as random walks with one-step memory on a cubic lattice between two absorbing boundaries. These walks avoid the two preceding steps, though they are not true self-avoiding walks. Systems of difference equations are introduced to calculate the statistics of the restricted random walks. They yield that the fraction of loops is (2M - 2)/(2M + 1), the fraction of ties 3/(2M + 1), the average length of loops 2M - 0.5, the average length of ties 2/3M2 + 2/3M - 4/3, the average length of walks equals 3M - 3, the variance of the loop length 16/15M3 + O(M2), the variance of the tie length 28/45M4 + O(M3), and the variance of the walk length 2M3 + O(M2).

A synthetic random basic copolymer with promiscuous binding to class II major histocompatibility complex molecules inhibits T-cell proliferative responses to major and minor histocompatibility antigens in vitro and confers the capacity to prevent murine graft-versus-host disease in vivo.

Graft-versus-host disease (GVHD) is a T-cell-mediated disease of transplanted donor T cells recognizing host alloantigens. Data presented in this report show, to our knowledge, for the first time that a synthetic copolymer of the amino acids L-Glu, L-Lys, L-Ala, and L-Tyr (molecular ratio, 1.9:6.0:4.7:1.0; Mr, 6000-8500) [corrected], termed GLAT, with promiscuous binding to multiple major histocompatibility complex class II alleles is capable of preventing lethal GVHD in the B10.D2 --> BALB/c model (both H-2d) across minor histocompatibility barriers. Administration of GLAT over a limited time after transplant significantly reduced the incidence, onset, and severity of disease. GLAT also improved long-term survival from lethal GVHD: 14/25 (56%) of experimental mice survived > 140 days after transplant compared to 2/26 of saline-treated or to 1/10 of hen egg lysozyme-treated control mice (P < 0.01). Long-term survivors were documented to be fully chimeric by PCR analysis of a polymorphic microsatellite region in the interleukin 1beta gene. In vitro, GLAT inhibited the mixed lymphocyte culture in a dose-dependent fashion across a variety of major barriers tested. Furthermore, GLAT inhibited the response of nylon wool-enriched T cells to syngeneic antigen-presenting cells presenting minor histocompatibility antigens. Prepulsing of the antigen-presenting cells with GLAT reduced the proliferative response, suggesting that GLAT inhibits antigen presentation.

Emergent spindle oscillations and intermittent burst firing in a thalamic model: specific neuronal mechanisms.

The rhythmogenesis of 10-Hz sleep spindles is studied in a large-scale thalamic network model with two cell populations: the excitatory thalamocortical (TC) relay neurons and the inhibitory nucleus reticularis thalami (RE) neurons. Spindle-like bursting oscillations emerge naturally from reciprocal interactions between TC and RE neurons. We find that the network oscillations can be synchronized coherently, even though the RE-TC connections are random and sparse, and even though individual neurons fire rebound bursts intermittently in time. When the fast gamma-aminobutyrate type A synaptic inhibition is blocked, synchronous slow oscillations resembling absence seizures are observed. Near-maximal network synchrony is established with even modest convergence in the RE-to-TC projection (as few as 5-10 RE inputs per TC cell suffice). The hyperpolarization-activated cation current (Ih) is found to provide a cellular basis for the intermittency of rebound bursting that is commonly observed in TC neurons during spindles. Such synchronous oscillations with intermittency can be maintained only with a significant degree of convergence for the TC-to-RE projection.