Assessing the Reproducibility of Clustering of Molecular Dynamics Conformations on Self-Organizing Maps

The goal of most clustering algorithms is to find the optimal number of clusters (i.e. fewest number of clusters). However, analysis of molecular conformations of biological macromolecules obtained from computer simulations may benefit from a larger array of clusters. The Self-Organizing Map (SOM) clustering method has the advantage of generating large numbers of clusters, but often gives ambiguous results. In this work, SOMs have been shown to be reproducible when the same conformational dataset is independently clustered multiple times (~100), with the help of the Cramérs V-index (C_v). The ability of C_v to determine which SOMs are reproduced is generalizable across different SOM source codes. The conformational ensembles produced from MD (molecular dynamics) and REMD (replica exchange molecular dynamics) simulations of the penta peptide Met-enkephalin (MET) and the 34 amino acid protein human Parathyroid Hormone (hPTH) were used to evaluate SOM reproducibility. The training length for the SOM has a huge impact on the reproducibility. Analysis of MET conformational data definitively determined that toroidal SOMs cluster data better than bordered maps due to the fact that toroidal maps do not have an edge effect. For the source code from MATLAB, it was determined that the learning rate function should be LINEAR with an initial learning rate factor of 0.05 and the SOM should be trained by a sequential algorithm. The trained SOMs can be used as a supervised classification for another dataset. The toroidal 10×10 hexagonal SOMs produced from the MATLAB program for hPTH conformational data produced three sets of reproducible clusters (27%, 15%, and 13% of 100 independent runs) which find similar partitionings to those of smaller 6×6 SOMs. The χ^2 values produced as part of the C_v calculation were used to locate clusters with identical conformational memberships on independently trained SOMs, even those with different dimensions. The χ^2 values could relate the different SOM partitionings to each other.

Indenture between The Corporation of the Township of Grantham of the County of Lincoln and Samuel DeVeaux Woodruff

Indenture of bargain and sale between The Corporation of the Township of Grantham of the County of Lincoln and Samuel DeVeaux Woodruff of St. Catharines regarding part of the road allowance between Lots no. 12 and 13 of the 8th Concession of the Township of Grantham. This was registered January 8, 1874 in the County of Lincoln - instrument no. 1650, October 24, 1873.

Certificate for One Share of Capital Stock in the Lincoln County Greater Production Company

Certificate for 1 share of capital stock in the Lincoln County Greater Production Company to Hamilton K. Woodruff, Jan. 20, 1919.

Printed blank of Statement of Security Form naming the bond as Jones County Texas Bonds for the purpose of building a courthouse

Printed blank of Statement of Security Form naming the bond as Jones County Texas Bonds for the purpose of building a courthouse. It is made out to S.D. Woodruff and dated June 12, 1885. An envelope addressed to Mr. S.D. Woodruff is also included. The postmarks are Kansas, 1885 and St. Catharines, June 13, 1885.

Article of agreement between Alexander Cook, contractor of Humberstone and the Provisional Municipal Council of the county of Welland

Article of agreement between Alexander Cook, contractor of Humberstone and the Provisional Municipal Council of the county of Welland to construct and build the main drain through the marsh lands tract commencing in lot no. 27 in the 4th concession in the township of Humberstone in a southerly direction (6 pages, handwritten). This is signed by John Frazer, Provisional Warden, Dexter Deverardo and Alexander Cook. (2 copies), Dec. 30, 1854.

Extract from the minutes of a session of the Provisional Municipal Council of the County of Welland

Extract from the minutes of a session of the Provisional Municipal Council of the County of Welland held on Nov. 3rd, 1855. It was decided that the petition of Andrew Drew and others be laid over until the engineer could make a survey of the premises and report to the council. This was signed by Dexter Deverardo, 1855

Memo to the warden and councilors for the County of Welland in council assembled regarding the contract of Edward Henderson

Memo to the warden and councilors for the County of Welland in council assembled regarding the contract of Edward Henderson. The terms of the contract have not been exceeded. This note is not signed, n.d.

Letter to the warden and councilors for the County of Welland in council assembled regarding George Stanford

Letter to the warden and councilors for the County of Welland in council assembled regarding George Stanford. The extra work was authorized by “me”. This is signed, S.D. Woodruff, Dec. 30, 1856.

Notice from Dexter Deverardo regarding minutes of the meeting of the Municipal Council of the County of Welland

Notice from Dexter Deverardo regarding minutes of the meeting of the Municipal Council of the County of Welland that was held May 21, 1857. It was moved that the warden and clerk be requested to procure a plan of the marsh lands tract, May, 1857.

Clipping about county rates paid in the village of Thorold

Clipping about county rates paid in the village of Thorold, June 18, 1867

County of Welland estimate (copy) of work done on the main drain of the marsh lands by Andrew Mains

County of Welland estimate (copy) of work done on the main drain of the marsh lands by Andrew Mains, signed by S.D. Woodruff. Estimate no.6, Jan. and Feb., 1856.

County of Welland estimate of work done on the main drain of the marsh lands by Alexander Cook

County of Welland estimate of work done on the main drain of the marsh lands by Alexander Cook, signed by S.D. Woodruff. Estimate no.7, Jan. and Feb. and Mar., 1856.

County of Welland estimate (copy) of work done on the main drain of the marsh lands by Andrew Mains

County of Welland estimate (copy) of work done on the main drain of the marsh lands by Andrew Mains, signed by S.D. Woodruff. Estimate no.7, Mar., 1856.

County of Welland estimate of work done on the main drain of the marsh lands by Alexander Cook

County of Welland estimate of work done on the main drain of the marsh lands by Alexander Cook, signed by S.D. Woodruff. Estimate no.8, April, 1856.

County of Welland estimate of work done on the main drain of the marsh lands by Alexander Cook

County of Welland estimate of work done on the main drain of the marsh lands by Alexander Cook, signed by S.D. Woodruff. Estimate no.9, May, 1856.