Descriptive Statistics and Linear Regression

This morning Dr. Battle will introduce descriptive statistics and linear regression and how to apply these concepts in mathematical modeling. You will also learn how to use a spreadsheet to help with statistical analysis and to create graphs.

Correlation between Accurate Electron Density and Linear Optical Properties in Amino Acid Derivatives: L-Histidinium Hydrogen Oxalate

The accurate electron density and linear optical properties of L-histidinium hydrogen oxalate are discussed. Two high-resolution single crystal X-ray diffraction experiments were performed and compared with density functional calculations in the solid state as well as in the gas phase. The crystal packing and the hydrogen bond network are accurately investigated using topological analysis based on quantum theory of atoms in molecules, Hirshfeld surface analysis, and electrostatic potential mapping. The refractive indices are computed from couple perturbed Kohn-Sham calculations and measured experimentally. Moreover, distributed atomic polarizabilities are used to analyze the origin of the linear susceptibility in the crystal, in order to separate molecular and intermolecular causes. The optical properties are also correlated with the electron density distribution. This compound also offers the possibility to test the electron density building block approach for material science and different refinement schemes for accurate positions and displacement parameters of hydrogen atoms, in the absence of neutron diffraction data.

Materials properties from electron density distributions: Molecular magnetism and linear optical properties

The general goal of this thesis is correlating observable properties of organic and metal-organic materials with their ground-state electron density distribution. In a long-term view, we expect to develop empirical or semi-empirical approaches to predict materials properties from the electron density of their building blocks, thus allowing to rationally engineering molecular materials from their constituent subunits, such as their functional groups. In particular, we have focused on linear optical properties of naturally occurring amino acids and their organic and metal-organic derivatives, and on magnetic properties of metal-organic frameworks. For analysing the optical properties and the magnetic behaviour of the molecular or sub-molecular building blocks in materials, we mostly used the more traditional QTAIM partitioning scheme of the molecular or crystalline electron densities, however, we have also investigated a new approach, namely, X-ray Constrained Extremely Localized Molecular Orbitals (XC-ELMO), that can be used in future to extracted the electron densities of crystal subunits. With the purpose of rationally engineering linear optical materials, we have calculated atomic and functional group polarizabilities of amino acid molecules, their hydrogen-bonded aggregates and their metal-organic frameworks. This has enabled the identification of the most efficient functional groups, able to build-up larger electric susceptibilities in crystals, as well as the quantification of the role played by intermolecular interactions and coordinative bonds on modifying the polarizability of the isolated building blocks. Furthermore, we analysed the dependence of the polarizabilities on the one-electron basis set and the many-electron Hamiltonian. This is useful for selecting the most efficient level of theory to estimate susceptibilities of molecular-based materials. With the purpose of rationally design molecular magnetic materials, we have investigated the electron density distributions and the magnetism of two copper(II) pyrazine nitrate metal-organic polymers. High-resolution X-ray diffraction and DFT calculations were used to characterize the magnetic exchange pathways and to establish relationships between the electron densities and the exchange-coupling constants. Moreover, molecular orbital and spin-density analyses were employed to understand the role of different magnetic exchange mechanisms in determining the bulk magnetic behaviour of these materials. As anticipated, we have finally investigated a modified version of the X-ray constrained wavefunction technique, XC-ELMOs, that is not only a useful tool for determination and analysis of experimental electron densities, but also enables one to derive transferable molecular orbitals strictly localized on atoms, bonds or functional groups. In future, we expect to use XC-ELMOs to predict materials properties of large systems, currently challenging to calculate from first-principles, such as macromolecules or polymers. Here, we point out advantages, needs and pitfalls of the technique. This work fulfils, at least partially, the prerequisites to understand materials properties of organic and metal-organic materials from the perspective of the electron density distribution of their building blocks. Empirical or semi-empirical evaluation of optical or magnetic properties from a preconceived assembling of building blocks could be extremely important for rationally design new materials, a field where accurate but expensive first-principles calculations are generally not used. This research could impact the community in the fields of crystal engineering, supramolecular chemistry and, of course, electron density analysis.

NRAS and BRAF mutations in primary cutaneous melanoma: A comparison of mutation rates between radial and vertical growth phases in individual tumors

Primary cutaneous melanoma is a cancer arising from melanocytes in the skin. In recent decades the incidence of this malignancy has increased significantly. Mortality rates are high for patients with tumors measuring over a few millimeters in thickness. Response rates to conventional radiation and chemotherapy are very low in patients with metastatic melanoma. New therapies targeting melanoma’s aberrant cell signaling pathways such as the MAP Kinase pathway are being developed. Mutations of NRAS and BRAF genes are quite common in cutaneous melanoma and lead to constitutive activation of the MAP Kinase pathway. This study tests the hypothesis that NRAS and BRAF mutations increase as a tumor progresses from the noninvasive radial growth phase (RGP) to the invasive vertical growth phase (VGP). Laser capture microdissection was used to obtain separate, pure tumor DNA samples from the RGP and VGP of thirty primary cutaneous melanomas. PCR was used to amplify NRAS exon 2 and BRAF exon 15 tumor DNA. The amplified DNA was sequenced and analyzed for mutations. An overall mutation rate of 74% was obtained for the twenty-three melanomas in which there were complete sequence results. With the exception of one melanoma NRAS and BRAF mutations were mutually exclusive. All seven NRAS exon 2 mutations involved codon 61. Three of these melanomas had mutations in both the RGP and VGP. The remaining four tumors were wild type for NRAS exon 2 in the RGP but mutated in the VGP. Of the fifteen BRAF exon 15 mutated melanomas all but one involved codon 600. Twelve of the fifteen BRAF exon 15 mutations were the T1799A type. Nine of the fifteen BRAF mutated tumors had the same mutation in both the RGP and VGP. Five of fifteen melanomas had wild type RGP DNA and BRAF exon 15 mutated VGP DNA. A single melanoma had BRAF exon 15 mutated DNA in the RGP and wild type DNA in the VGP. Overall, these results suggest a trend toward the acquisition of NRAS and BRAF mutations as cutaneous melanomas change from a noninvasive to an invasive, potentially deadly cancer.^