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.

Analysis of linear trade models and relation to scale economies

We discuss linear Ricardo models with a range of parameters. We show that the exact boundary of the region of equilibria of these models is obtained by solving a simple integer programming problem. We show that there is also an exact correspondence between many of the equilibria resulting from families of linear models and the multiple equilibria of economies of scale models.

Phylogenetic assessment of length variation at a microsatellite locus

Sixty-six haplotypes at a locus containing a simple dinucleotide (CA)n microsatellite repeat were isolated by PCR–single-strand conformational polymorphism from populations of the horseshoe crab Limulus polyphemus. These haplotypes were sequenced to assess nucleotide variation directly. Thirty-four distinct sequences (alleles) were identified in a region 570 bp long that included the microsatellite motif. In the repeat region itself, CA-number varied in integer values from 5 to 11 across alleles, except that a (CA)8 class was not observed. Differences among alleles were due also to polymorphisms at 22 sites in regions immediately flanking the microsatellite repeats. Nucleotide substitutions in these regions were used to estimate phylogenetic relationships among alleles, and the gene phylogeny was used to trace the evolution of length variation and CA repeat numbers. A low correlation between size variation and genealogical relationships among alleles suggests that absolute fragment size (as normally scored in microsatellite assays) is an unreliable indicator of historical affinities among alleles. This finding on the molecular fine structure of microsatellite variation suggests the need for caution in the use of repeat counts at microsatellite loci as secure indicators of allelic relationships.

The role of Wolbachia bacteria in reproductive incompatibilities and hybrid zones of Diabrotica beetles and Gryllus crickets

A rickettsial bacterium in the genus Wolbachia is the cause of a unidirectional reproductive incompatibility observed between two major beetle pests of maize, the western corn rootworm, Diabrotica virgifera virgifera, and the Mexican corn rootworm, D. v. zeae. These subspecies are allopatric except for two known regions of sympatry in Texas and Mexico. We demonstrate that populations of D. v. virgifera, with the exception of two populations in southern Arizona, are infected with a strain of Wolbachia. Populations of D. v. zeae are not infected. Treatment of D. v. virgifera with tetracycline eliminated the Wolbachia and removed the reproductive incompatibility. Similar patterns of reproductive incompatibility exist among taxa of the cricket genus Gryllus. Gryllus assimilis, G. integer, G. ovisopis, G. pennsylvanicus, and G. rubens are infected with Wolbachia whereas G. firmus is usually not. Populations of G. rubens and G. ovisopis carry the same Wolbachia strain, which is distinct from that of G. integer. G. pennsylvanicus is infected with two Wolbachia strains, that found in G. rubens and one unique to G. pennsylvanicus. Moreover, a proportion of G. pennsylvanicus individuals harbors both strains. Wolbachia may have influenced speciation in some members of the genus Gryllus by affecting the degree of hybridization between species. Given that Wolbachia infections are relatively common in insects, it is likely that other insect hybrid zones may be influenced by infections with Wolbachia.

High pressure fosters protein refolding from aggregates at high concentrations

High hydrostatic pressures (1–2 kbar), combined with low, nondenaturing concentrations of guanidine hydrochloride (GdmHCl) foster disaggregation and refolding of denatured and aggregated human growth hormone and lysozyme, and β-lactamase inclusion bodies. One hundred percent recovery of properly folded protein can be obtained by applying pressures of 2 kbar to suspensions containing aggregates of recombinant human growth hormone (up to 8.7 mg/ml) and 0.75 M GdmHCl. Covalently crosslinked, insoluble aggregates of lysozyme could be refolded to native, functional protein at a 70% yield, independent of protein concentration up to 2 mg/ml. Inclusion bodies containing β-lactamase could be refolded at high yields of active protein, even without added GdmHCl.

Sequential mechanism of solubilization and refolding of stable protein aggregates by a bichaperone network

A major activity of molecular chaperones is to prevent aggregation and refold misfolded proteins. However, when allowed to form, protein aggregates are refolded poorly by most chaperones. We show here that the sequential action of two Escherichia coli chaperone systems, ClpB and DnaK-DnaJ-GrpE, can efficiently solubilize excess amounts of protein aggregates and refold them into active proteins. Measurements of aggregate turbidity, Congo red, and 4,4′-dianilino-1,1′-binaphthyl-5,5′-disulfonic acid binding, and of the disaggregation/refolding kinetics by using a specific ClpB inhibitor, suggest a mechanism where (i) ClpB directly binds protein aggregates, ATP induces structural changes in ClpB, which (ii) increase hydrophobic exposure of the aggregates and (iii) allow DnaK-DnaJ-GrpE to bind and mediate dissociation and refolding of solubilized polypeptides into native proteins. This efficient mechanism, whereby chaperones can catalytically solubilize and refold a wide variety of large and stable protein aggregates, is a major addition to the molecular arsenal of the cell to cope with protein damage induced by stress or pathological states.

Suppression of protein synthesis in brain during hibernation involves inhibition of protein initiation and elongation

Protein synthesis (PS) has been considered essential to sustain mammalian life, yet was found to be virtually arrested for weeks in brain and other organs of the hibernating ground squirrel, Spermophilus tridecemlineatus. PS, in vivo, was below the limit of autoradiographic detection in brain sections and, in brain extracts, was determined to be 0.04% of the average rate from active squirrels. Further, it was reduced 3-fold in cell-free extracts from hibernating brain at 37°C, eliminating hypothermia as the only cause for protein synthesis inhibition (active, 0.47 ± 0.08 pmol/mg protein per min; hibernator, 0.16 ± 0.05 pmol/mg protein per min, P < 0.001). PS suppression involved blocks of initiation and elongation, and its onset coincided with the early transition phase into hibernation. An increased monosome peak with moderate ribosomal disaggregation in polysome profiles and the greatly increased phosphorylation of eIF2α are both consistent with an initiation block in hibernators. The elongation block was demonstrated by a 3-fold increase in ribosomal mean transit times in cell-free extracts from hibernators (active, 2.4 ± 0.7 min; hibernator, 7.1 ± 1.4 min, P < 0.001). No abnormalities of ribosomal function or mRNA levels were detected. These findings implicate suppression of PS as a component of the regulated shutdown of cellular function that permits hibernating ground squirrels to tolerate “trickle” blood flow and reduced substrate and oxygen availability. Further study of the factors that control these phenomena may lead to identification of the molecular mechanisms that regulate this state.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

Unbinding process of adsorbed proteins under external stress studied by atomic force microscopy spectroscopy

We report the study of the dynamics of the unbinding process under a force load f of adsorbed proteins (fibrinogen) on a solid surface (hydrophilic silica) by means of atomic force microscopy spectroscopy. By varying the loading rate rf, defined by f = rf t, t being the time, we find that, as for specific interactions, the mean rupture force increases with rf. This unbinding process is analyzed in the framework of the widely used Bell model. The typical dissociation rate at zero force entering in the model lies between 0.02 and 0.6 s−1. Each measured rupture is characterized by a force f0, which appears to be quantized in integer multiples of 180–200 pN.

How do owls localize interaurally phase-ambiguous signals?

Owls and other animals, including humans, use the difference in arrival time of sounds between the ears to determine the direction of a sound source in the horizontal plane. When an interaural time difference (ITD) is conveyed by a narrowband signal such as a tone, human beings may fail to derive the direction represented by that ITD. This is because they cannot distinguish the true ITD contained in the signal from its phase equivalents that are ITD ± nT, where T is the period of the stimulus tone and n is an integer. This uncertainty is called phase-ambiguity. All ITD-sensitive neurons in birds and mammals respond to an ITD and its phase equivalents when the ITD is contained in narrowband signals. It is not known, however, if these animals show phase-ambiguity in the localization of narrowband signals. The present work shows that barn owls (Tyto alba) experience phase-ambiguity in the localization of tones delivered by earphones. We used sound-induced head-turning responses to measure the sound-source directions perceived by two owls. In both owls, head-turning angles varied as a sinusoidal function of ITD. One owl always pointed to the direction represented by the smaller of the two ITDs, whereas a second owl always chose the direction represented by the larger ITD (i.e., ITD − T).

A positivity result in the theory of Macdonald polynomials

We outline here a proof that a certain rational function Cn(q, t), which has come to be known as the “q, t-Catalan,” is in fact a polynomial with positive integer coefficients. This has been an open problem since 1994. Because Cn(q, t) evaluates to the Catalan number at t = q = 1, it has also been an open problem to find a pair of statistics a, b on the collection

Origin of Genes

We discuss two tests of the hypothesis that the first genes were assembled from exons. The hypothesis of exon shuffling in the progenote predicts that intron phases will be correlated so that exons will be an integer number of codons and predicts that the exons will be correlated with compact regions of polypeptide chain. These predictions have been tested on ancient conserved proteins (proteins without introns in prokaryotes but with introns in eukaryotes) and hold with high statistical significance. We conclude that introns are correlated with compact features of proteins 15-, 22-, or 30-amino acid residues long, as was predicted by “The Exon Theory of Genes.”

Biological impact on mineral dissolution: Application of the lichen model to understanding mineral weathering in the rhizosphere

Microorganisms modify rates and mechanisms of chemical and physical weathering and clay growth, thus playing fundamental roles in soil and sediment formation. Because processes in soils are inherently complex and difficult to study, we employ a model based on the lichen–mineral system to identify the fundamental interactions. Fixed carbon released by the photosynthetic symbiont stimulates growth of fungi and other microorganisms. These microorganisms directly or indirectly induce mineral disaggregation, hydration, dissolution, and secondary mineral formation. Model polysaccharides were used to investigate direct mediation of mineral surface reactions by extracellular polymers. Polysaccharides can suppress or enhance rates of chemical weathering by up to three orders of magnitude, depending on the pH, mineral surface structure and composition, and organic functional groups. Mg, Mn, Fe, Al, and Si are redistributed into clays that strongly adsorb ions. Microbes contribute to dissolution of insoluble secondary phosphates, possibly via release of organic acids. These reactions significantly impact soil fertility. Below fungi–mineral interfaces, mineral surfaces are exposed to dissolved metabolic byproducts. Through this indirect process, microorganisms can accelerate mineral dissolution, leading to enhanced porosity and permeability and colonization by microbial communities.

Ergodic theorems along sequences and Hardy fields.

Let a(x) be a real function with a regular growth as x --> infinity. [The precise technical assumption is that a(x) belongs to a Hardy field.] We establish sufficient growth conditions on a(x) so that the sequence ([a(n)])(infinity)(n=1) is a good averaging sequence in L2 for the pointwise ergodic theorem. A sequence (an) of positive integers is a good averaging sequence in L2 for the pointwise ergodic theorem if in any dynamical system (Omega, Sigma, m, T) for f [symbol, see text] in L2(Omega) the averages [equation, see text] converge for almost every omicron in. Our result implies that sequences like ([ndelta]), where delta > 1 and not an integer, ([n log n]), and ([n2/log n]) are good averaging sequences for L2. In fact, all the sequences we examine will turn out to be good averaging for Lp, p > 1; and even for L log L. We will also establish necessary and sufficient growth conditions on a(x) so that the sequence ([a(n)]) is good averaging for mean convergence. Note that for some a(x) (e.g., a(x) = log2 x), ([a(n)]) may be good for mean convergence without being good for pointwise convergence.