In part I of this paper, exact expressions were obtained for the partition function and thermodynamic properties of an wX« plane square lattice filled with \mn rigid dimers each occupying two adjacent lattice sites. In this part the correlation properties of the model are studied with the aid of a general perturbation theory for Pfaffians. Closed formulas are derived for the changes in the probability of a dimer occupying a given bond that are induced by the proximity of an edge or a corner of the lattice (singlet correlations) and, in the center of the lattice, by the fixed position of another dimer (pair correlations). We show how to calculate the number of configurations of a dimer lattice containing a pair of monomers (or holes) a fixed distance apart. The explicit result when the separation vector is (p, 0) or (p, 1) involves a Toeplitz determinant |#t_y+i| {i, j=l,2,---p) defined by oo 2 a«e* n * = sgn{cos0} exp[-i cot _1 (r cos0)], where r = x/y and x and y are the activities of x and y dimers. A similar result holds along the diagonals (p, />±1). The relative number of configurations decays to zero with radial separation r as B/r m .

Glycogen synthase kinase-3 (GSK-3) is a serine/threonine kinase regulating diverse cellular functions including metabolism, transcription and cell survival. Numerous intracellular signalling pathways converge on GSK-3 and regulate its activity via inhibitory serine-phosphorylation. Recently, GSK-3 has been involved in learning and memory and in neurodegeneration. Here, we present evidence that implicates GSK-3 in synaptic plasticity. We show that phosphorylation at the inhibitory Ser9 site on GSK-3beta is increased upon induction of long-term potentiation (LTP) in both hippocampal subregions CA1 and the dentate gyrus (DG) in vivo. The increase in inhibitory GSK-3beta phosphorylation is robust and persists for at least one hour postinduction. Furthermore, we find that LTP is impaired in transgenic mice conditionally overexpressing GSK-3beta. The LTP deficits can be attenuated/rescued by chronic treatment with lithium, a GSK-3 inhibitor. These results suggest that the inhibition of GSK-3 facilitates the induction of LTP and this might explain some of the negative effects of GSK-3 on learning and memory. It follows that this role of GSK-3beta in LTP might underlie some of the cognitive dysfunction in diseases where GSK-3 dysfunction has been implicated, including Alzheimer's and other dementias.

Although the mechanism of Aβ action in the pathogenesis of Alzheimer's disease (AD) has remained elusive, it is known to increase the expression of the antagonist of canonical wnt signalling, Dickkopf-1 (Dkk1), whereas the silencing of Dkk1 blocks Aβ neurotoxicity. We asked if clusterin, known to be regulated by wnt, is part of an Aβ/Dkk1 neurotoxic pathway. Knockdown of clusterin in primary neurons reduced Aβ toxicity and DKK1 upregulation and, conversely, Aβ increased intracellular clusterin and decreased clusterin protein secretion, resulting in the p53-dependent induction of DKK1. To further elucidate how the clusterin-dependent induction of Dkk1 by Aβ mediates neurotoxicity, we measured the effects of Aβ and Dkk1 protein on whole-genome expression in primary neurons, finding a common pathway suggestive of activation of wnt–planar cell polarity (PCP)–c-Jun N-terminal kinase (JNK) signalling leading to the induction of genes including EGR1 (early growth response-1), NAB2 (Ngfi-A-binding protein-2) and KLF10 (Krüppel-like factor-10) that, when individually silenced, protected against Aβ neurotoxicity and/or tau phosphorylation. Neuronal overexpression of Dkk1 in transgenic mice mimicked this Aβ-induced pathway and resulted in age-dependent increases in tau phosphorylation in hippocampus and cognitive impairment. Furthermore, we show that this Dkk1/wnt–PCP–JNK pathway is active in an Aβ-based mouse model of AD and in AD brain, but not in a tau-based mouse model or in frontotemporal dementia brain. Thus, we have identified a pathway whereby Aβ induces a clusterin/p53/Dkk1/wnt–PCP–JNK pathway, which drives the upregulation of several genes that mediate the development of AD-like neuropathologies, thereby providing new mechanistic insights into the action of Aβ in neurodegenerative diseases.

No abstract

Alzheimer's disease (AD) is characterized by the presence of neurofibrillary tangles of hyperphosphorylated, aggregated tau protein and extracellular deposits of beta-amyloid peptide. Increased beta-amyloid levels are thought to precede tangle formation, but tau pathology is more closely related to neuronal death. Minocycline, a tetracycline derivative, has potent antiinflammatory, antiapoptotic, and neuroprotective effects in several models of neurodegenerative disease, including models of AD with amyloid pathology. We have used both in vitro and in vivo models of AD to determine whether minocycline may have therapeutic efficacy against tau pathology. In primary cortical neurons, minocycline prevents beta-amyloid-induced neuronal death, reduces caspase-3 activation, and lowers generation of caspase-3-cleaved tau fragments. Treatment of tangle-forming transgenic mice (htau line) with minocycline results in reduced levels of tau phosphorylation and insoluble tau aggregates. The in vivo effects of minocycline are also associated with reduced caspase-3 activation and lowered tau cleavage by caspase-3. In tau mice, we find that conformational changes in tau are susceptible to minocycline treatment, but are not directly associated with the amount of tau fragments produced, highlighting a dissociation between the development of these pathological tau species. These results suggest a possible novel therapeutic role for minocycline in the treatment of AD and related tauopathies.