Browsing by Subject "Correlation"

Cell division is a biological process fundamental to all life. One aspect of the process that is still under investigation is whether or not cells in a lineage are correlated in their cell-cycle progression. Data on cell-cycle progression is typically acquired either in lineages of single cells or in synchronized cell populations, and each source of data offers complementary information on cell division. To formally assess dependence in cell-cycle progression, I develop a hierarchical statistical model of single-cell measurements and extend a previously proposed model of population cell division in the budding yeast, Saccharomyces cerevisiae. Both models capture correlation and cell-to-cell heterogeneity in cell-cycle progression, and parameter inference is carried out in a fully Bayesian manner. The single-cell model is fit to three published time-lapse microscopy datasets and the population-based model is fit to simulated data for which the true model is known. Based on posterior inferences and formal model comparisons, the single-cell analysis demonstrates that budding yeast mother and daughter cells do not appear to correlate in their cell-cycle progression in two of the three experimental settings. In contrast, mother cells grown in a less preferred sugar source, glycerol/ethanol, did correlate in their rate of cell division in two successive cell cycles. Population model fitting to simulated data suggested that, under typical synchrony experimental conditions, population-based measurements of the cell-cycle were not informative for correlation in cell-cycle progression or heterogeneity in daughter-specific G1 phase progression.

A quantum point contact (QPC) is a quasi-one dimensional electron system, for which the conductance is quantized in unit of $2e^2/h$. This conductance quantization can be explained in a simple single particle picture, where the electron density of states cancels the electron velocity to a constant. However, two significant features in QPCs were discovered in the past two decades, which have drawn much attention: the 0.7 effect in the linear conductance and zero-bias-anomaly (ZBA) in the differential conductance. Neither of them can be explained by single particle pictures.

In this thesis, I will present several electron correlation effects discovered in asymmetric QPCs, as shown below:

The linear conductance of our asymmetric QPCs shows conductance resonances. The number of these resonances increases as the QPC channel length increases. The quantized conductance plateau is also modulated by tuning the gate voltage of the QPCs. These two features, observed in the linear conductance, are ascribed to the formation of quasi-bound states in the QPCs, which is further ascribed to the electron-correlation-induced barriers.

The differential conductance for long channel QPCs shows the zero-bias-anomaly for every other linear conductance resonance valley, suggesting a near even-odd behavior. This even-odd law can be interpreted within the electron-correlation-induced barrier picture, where the quasi-localized non-zero spin in the quasi-bound state (Kondo-like) couples to the Fermi sea in the lead. For a specific case, triple-peak structure is observed in the differential conductance curves, while the electron filling number is still even, suggesting a spin triplet formation at zero magnetic field.

Small differential conductance oscillations as a function of bias voltage were discovered and systematically studied in an asymmetric QPC sample. These oscillations are significantly suppressed in a low in-plane magnetic field, which is completely unexpected. The oscillations are washed out when the temperature is increased to 0.8K. Numerical simulation, based on the thermal smearing of the Fermi distribution, was performed to simulate the oscillation behavior at high temperatures, using the low temperature data as an input. This simulation agrees with the oscillations off zero-bias region, but does not agree with the temperature evolution of the structure near zero-bias. Based on the above oscillation characteristics, all simple single particle pictures were carefully considered, and then ruled out. After exhausting all these pictures, we think these small oscillations are related to novel electronic and spin correlations.

Variations in gene expression are potential risk factors for atherosclerosis, which is one of the most common forms of cardiovascular disease. We performed a localized Pearson correlation test in 372 individuals from seven datasets relevant to cardiovascular disease studies. The genomes of samples were separated into 20Mb windows and correlation tests were performed locally in these windows. The localized Pearson correlation test found chr3:115Mb–135Mb was tightly connected by significantly high proportion of highly correlated pairs (P value = 0.0266 with Z-test). LSAMP, GATA2, MBD4, and other genes in the region were considered associated with cardiovascular disease because they were involved in highly correlated pairs. Furthermore, these genes were also associated with cardiovascular disease by having significantly high SNP odds ratios (P value < 0.1) between patients and controls in an independent Duke University Medical Center database. In addition, a permutation test was performed to demonstrate that chr3:115Mb–135Mb might underlie the regulation of cardiovascular disease. Finally, the localized Pearson correlation test also found some other regions that could be associated with cardiovascular disease.