Extracting Ramachandran torsional angle distributions from 2D NMR data using Tikhonov regularization /

Solid state nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for studying structural and dynamical properties of disordered and partially ordered materials, such as glasses, polymers, liquid crystals, and biological materials. In particular, twodimensional( 2D) NMR methods such as ^^C-^^C correlation spectroscopy under the magicangle- spinning (MAS) conditions have been used to measure structural constraints on the secondary structure of proteins and polypeptides. Amyloid fibrils implicated in a broad class of diseases such as Alzheimer's are known to contain a particular repeating structural motif, called a /5-sheet. However, the details of such structures are poorly understood, primarily because the structural constraints extracted from the 2D NMR data in the form of the so-called Ramachandran (backbone torsion) angle distributions, g{^,'4)), are strongly model-dependent. Inverse theory methods are used to extract Ramachandran angle distributions from a set of 2D MAS and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) data. This is a vastly underdetermined problem, and the stability of the inverse mapping is problematic. Tikhonov regularization is a well-known method of improving the stability of the inverse; in this work it is extended to use a new regularization functional based on the Laplacian rather than on the norm of the function itself. In this way, one makes use of the inherently two-dimensional nature of the underlying Ramachandran maps. In addition, a modification of the existing numerical procedure is performed, as appropriate for an underdetermined inverse problem. Stability of the algorithm with respect to the signal-to-noise (S/N) ratio is examined using a simulated data set. The results show excellent convergence to the true angle distribution function g{(j),ii) for the S/N ratio above 100.

Proposal for Construction of Brock’s Monument, Queenston, newspaper fragment, 1824

Brock’s Monument is owned by Parks Canada and maintained by the Niagara Parks Commission in collaboration with the Friends of Fort George and Niagara National Historic Sites. It is located in Queenston Heights Park atop the Niagara Escarpment. On March 14, 1815, Parliament passed an act to erect a monument to the memory of General Isaac Brock. A design by engineer Francis Hall was selected. He envisioned a 135 ft. tall Tuscan column, made out of stone with a winding staircase inside. By the spring of 1824, work had begun on the monument. In June of that year, the cornerstone was laid and William Lyon Mackenzie was in attendance at the ceremony. It was on October 13th, 1824 (the anniversary of Brock’s death) that 6000 people traveled to Queenston to inter the remains of Brock and Lieutenant-Colonel Macdonell. This was the second burial for both. After 3 years the tower had reached 135 feet, but there was no inscription at the base, the fence around the observation deck had not been installed and there was no statue of Brock. Hall submitted a plan to finish the statue, but he was turned down and a simple ornament was placed where the Brock statue should have been. A massive blast of gunpowder destroyed the monument in 1840. It is alleged that an American sympathizer with the Upper Canada Rebellion set off the blast. Brock and Macdonell’s bodies were reburied in the Hamilton Family Cemetery in Queenston. The present monument was rebuilt in 1853. William Thomas (designer of St. Michael’s Cathedral in Toronto) was the architect. Brock and Macdonell were once again laid to rest in separate vaults at the statue. In 1968, Brock’s Monument was declared a national historical site. In 2005, it was closed to the public due to safety concerns, but it reopened in 2010. Source: http://www.thecanadianencyclopedia.com/articles/brocks-monument-queenston-heights

Letter (unsigned) to George H. Gillespie regarding Col. Clark’s proposal regarding timber in Long Point

Letter (unsigned) to George H. Gillespie regarding Col. Clark’s proposal regarding timber in Long Point. The writer [S.D. Woodruff] makes the argument that the point was purchased as a sporting preserve so it is desirable not to take the timber off the land, Aug. 5, 1868.

Letter to S.D. Woodruff from George H. Gillespie stating that Col. Clark has withdrawn his proposal about timber on the point

Letter to S.D. Woodruff from George H. Gillespie stating that Col. Clark has withdrawn his proposal about timber on the point. “Please send your views”, Aug. 10, 1868.