Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices

We present the number of dimers $N_d(n)$ on the Sierpinski gasket $SG_d(n)$ at stage $n$ with dimension $d$ equal to two, three, four or five, where one of the outmost vertices is not covered when the number of vertices $v(n)$ is an odd number. The entropy of absorption of diatomic molecules per site, defined as $S_{SG_d}=\lim_{n \to \infty} \ln N_d(n)/v(n)$, is calculated to be $\ln(2)/3$ exactly for $SG_2(n)$. The numbers of dimers on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4,5$ are also obtained exactly. Their entropies are equal to $\ln(6)/7$, $\ln(28)/12$, $\ln(200)/18$, respectively. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for $SG_d(n)$ with $d=3,4,5$. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of $S_{SG_d}$ with $d=3,4,5$ can be evaluated with more than a hundred significant figures accurate.Comment: 35 pages, 20 figures and 1 tabl

Mutation of a single residue, β-glutamate-20, alters protein–lipid interactions of light harvesting complex II

It is well established that assembly of the peripheral antenna complex, LH2, is required for proper photosynthetic membrane biogenesis in the purple bacterium Rhodobacter sphaeroides. The underlying interactions are, as yet, not understood. Here we examined the relationship between the morphology of the photosynthetic membrane and the lipid–protein interactions at the LH2–lipid interface. The non-bilayer lipid, phosphatidylethanolamine, is shown to be highly enriched in the boundary lipid phase of LH2. Sequence alignments indicate a putative lipid binding site, which includes β-glutamate-20 and the adjacent carotenoid end group. Replacement of β-glutamate-20 with alanine results in significant reduction of phosphatidylethanolamine and concomitant raise in phosphatidylcholine in the boundary lipid phase of LH2 without altering the lipid composition of the bulk phase. The morphology of the LH2 housing membrane is, however, unaffected by the amino acid replacement. In contrast, simultaneous modification of glutamate-20 and exchange of the carotenoid sphaeroidenone with neurosporene results in significant enlargement of the vesicular membrane invaginations. These findings suggest that the LH2 complex, specifically β-glutamate-20 and the carotenoids' polar head group, contribute to the shaping of the photosynthetic membrane by specific interactions with surrounding lipid molecules

Psychology and aggression

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68264/2/10.1177_002200275900300301.pd