Evaluating statistical methods used to estimate the number of postsynaptic receptors.

Calcium levels in spines play a significant role in determining the sign and magnitude of synaptic plasticity. The magnitude of calcium influx into spines is highly dependent on influx through N-methyl D-aspartate (NMDA) receptors, and therefore depends on the number of postsynaptic NMDA receptors in each spine. We have calculated previously how the number of postsynaptic NMDA receptors determines the mean and variance of calcium transients in the postsynaptic density, and how this alters the shape of plasticity curves. However, the number of postsynaptic NMDA receptors in the postsynaptic density is not well known. Anatomical methods for estimating the number of NMDA receptors produce estimates that are very different than those produced by physiological techniques. The physiological techniques are based on the statistics of synaptic transmission and it is difficult to experimentally estimate their precision. In this paper we use stochastic simulations in order to test the validity of a physiological estimation technique based on failure analysis. We find that the method is likely to underestimate the number of postsynaptic NMDA receptors, explain the source of the error, and re-derive a more precise estimation technique. We also show that the original failure analysis as well as our improved formulas are not robust to small estimation errors in key parameters.

Interactions between cyclosporin A, low-density lipoprotein and the low-density lipoprotein receptor

Cyclosporine A (CSA) is a cyclic eleven amino acid, lipophilic molecule used therapeutically as an immunosuppressive agent. Cyclosporine can specifically inhibit the transcription of a number of different genes. It is known that CSA is bound almost exclusively to lipoproteins in plasma, however, the relationship between the low density lipoprotein (LDL), the LDL receptor, and CSA has not been fully elucidated. The exact mechanism of cellular uptake of CSA is unknown, but it is believed to be by simple passive diffusion across the cell membrane. In addition, it has been recently shown that the frequent finding of hypercholesterolemia seen in patients treated with CSA can be explained by a CSA-induced effect. The mechanism by which CSA induces hypercholesterolemia is not known. We have used an LDL receptor-deficient animal model, the Watanabe Heritable Hyperlipidemic (WHHL) rabbit to investigate the role of LDL and the LDL receptor in the cellular uptake of CSA. Using this animal model, we have shown that CSA uptake by lymphocytes is predominantly LDL receptor-mediated. Chemical modification of apoB-100 on LDL particles abolishes their ability to bind to the LDL receptor. When CSA is incubated with modified LDL much less is taken-up than when native LDL is incubated with CSA. Treatment of two human cell lines with CSA results in a dose-dependent decrease in LDL receptor mRNA levels. Using a novel transfection system involving the 5$\sp\prime$-flanking region of the LDL receptor gene, we have found that CSA decreases the number of transcripts, but is dependent on whether or not cholesterol is present and the stage of growth of the cells. ^

The effects of population density on the spread of disease

The objective of this study is to identify the relationship between population density and the initial stages of the spread of disease in a local population. This study proposes to concentrate on the question of how population density affects the distribution of the susceptible individuals in a local population and thus affects the spread of the disease, measles. Population density is measured by the average of the number of contacts with susceptible individuals by each individual in the population during a fixed-length time period. The term “contact with susceptible individuals” means sufficient contact between two people for the disease to pass from an infectious person to a susceptible person. The fixed-length time period is taken to be the average length of time an infected person is infectious without symptoms of the disease. For this study of measles, the time period will be seven days. ^ While much attention has been given to modeling the entire epidemic process of measles, attempts have not been made to study the characteristics of contact rates required to initiate an epidemic. This study explores the relationship between population density, given a specific herd immunity rate in the population, and initial rate of the spread of the disease by considering the underlying distribution of contacts with susceptibles by the individuals in the population. ^ This study does not seek to model an entire measles epidemic, but to model the above stated relationship for the local population within which the first infective person is introduced. This study describes the mathematical relationship between population density parameters and contact distribution parameters. ^ The results are displayed in graphs that show the effects of different population densities on the spread of disease. The results support the idea that the number of new infectives is strongly related to the distribution of susceptible contacts. The results also show large differences in the epidemic measures between populations with densities equal to four versus three. ^