Entropy of chains placed on the square lattice

We obtain the entropy of flexible linear chains composed of M monomers placed on the square lattice using a transfer matrix approach. An excluded volume interaction is included by considering the chains to be self-and mutually avoiding, and a fraction rho of the sites are occupied by monomers. We solve the problem exactly on stripes of increasing width m and then extrapolate our results to the two-dimensional limit to infinity using finite-size scaling. The extrapolated results for several finite values of M and in the polymer limit M to infinity for the cases where all lattice sites are occupied (rho=1) and for the partially filled case rho<1 are compared with earlier results. These results are exact for dimers (M=2) and full occupation (\rho=1) and derived from series expansions, mean-field like approximations, and transfer matrix calculations for some other cases. For small values of M, as well as for the polymer limit M to infinity, rather precise estimates of the entropy are obtained.Comment: 6 pages, 7 figure

The absence of ABCA1 decreases soluble ApoE levels but does not diminish amyloid deposition in two murine models of Alzheimer disease.

J Biol Chem. 2005 Dec 30;280(52):43243-56. Epub 2005 Oct 5. The absence of ABCA1 decreases soluble ApoE levels but does not diminish amyloid deposition in two murine models of Alzheimer disease. Hirsch-Reinshagen V, Maia LF, Burgess BL, Blain JF, Naus KE, McIsaac SA, Parkinson PF, Chan JY, Tansley GH, Hayden MR, Poirier J, Van Nostrand W, Wellington CL. Department of Pathology and Laboratory Medicine, University of British Columbia, Vancouver, British Columbia V4Z 5H5, Canada. Abstract ABCA1, a cholesterol transporter expressed in the brain, has been shown recently to be required to maintain normal apoE levels and lipidation in the central nervous system. In addition, ABCA1 has been reported to modulate beta-amyloid (Abeta) production in vitro. These observations raise the possibility that ABCA1 may play a role in the pathogenesis of Alzheimer disease. Here we report that the deficiency of ABCA1 does not affect soluble or guanidine-extractable Abeta levels in Tg-SwDI/B or amyloid precursor protein/presenilin 1 (APP/PS1) mice, but rather is associated with a dramatic reduction in soluble apoE levels in brain. Although this reduction in apoE was expected to reduce the amyloid burden in vivo, we observed that the parenchymal and vascular amyloid load was increased in Tg-SwDI/B animals and was not diminished in APP/PS1 mice. Furthermore, we observed an increase in the proportion of apoE retained in the insoluble fraction, particularly in the APP/PS1 model. These data suggested that ABCA1-mediated effects on apoE levels and lipidation influenced amyloidogenesis in vivo. PMID: 16207707 [PubMed - indexed for MEDLINE