Electron densities by the maximum entropy method (MEM) for various types of prior densities: a case study on three amino acids and a tripeptide

Abstract

Dynamic model densities according to Mondal et al. [(2012), Acta Cryst. A68, 568-581] are presented for independent atom models (IAM), IAMs after high-order refinements (IAM-HO), invariom (INV) models and multipole (MP) models of -glycine, dl-serine, l-alanine and Ala-Tyr-Ala at T ' 20 K. Each dynamic model density is used as prior in the calculation of electron density according to the maximum entropy method (MEM). We show that at the bond-critical points (BCPs) of covalent C-C and C-N bonds the IAM-HO and INV priors produce reliable MEM density maps, including reliable values for the density and its Laplacian. The agreement between these MEM density maps and dynamic MP density maps is less good for polar C-O bonds, which is explained by the large spread of values of topological descriptors of C-O bonds in static MP densities. The density and Laplacian at BCPs of hydrogen bonds have similar values in MEM density maps obtained with all four kinds of prior densities. This feature is related to the smaller spatial variation of the densities in these regions, as expressed by small magnitudes of the Laplacians and the densities. It is concluded that the use of the IAM-HO prior instead of the IAM prior leads to improved MEM density maps. This observation shows interesting parallels to MP refinements, where the use of the IAM-HO as an initial model is the accepted procedure for solving MP parameters. A deconvolution of thermal motion and static density that is better than the deconvolution of the IAM appears to be necessary in order to arrive at the best MP models as well as at the best MEM densities.

Topological Properties of Chemical Bonds from Static and Dynamic Electron Densities

“…The topological analyses of the small molecule densities 19 , 21 show good agreement between positions of local maxima of non-hydrogen atoms found in dynamic electron densities and corresponding static densities. For dynamic densities, hydrogen atoms may be included in atomic basins of their parent atoms due to atomic displacements, 37 which is true for most of the hydrogen atoms of the small molecules discussed in the present contribution.…”

“…20 K of α-glycine, 34 l -alanine, 35 d , l -serine 22 and the tripeptide alanyl-tyrosyl-alanine (Ala-Tyr-Ala) 36 have been reconstructed and analyzed in the literature. 19 , 21 These studies comprised the analysis of electron densities based on IAM, IAM-HO, Invariom model (transferable multipole parameters from the Invariom-database 13 ), and the multipole (MP) model. We summarize the major findings of references 19 , 21 herein.…”

“… 19 , 21 These studies comprised the analysis of electron densities based on IAM, IAM-HO, Invariom model (transferable multipole parameters from the Invariom-database 13 ), and the multipole (MP) model. We summarize the major findings of references 19 , 21 herein.…”

“…For dynamic densities, hydrogen atoms may be included in atomic basins of their parent atoms due to atomic displacements, 37 which is true for most of the hydrogen atoms of the small molecules discussed in the present contribution. 19 , 21 The comparison of density values at local maxima from dynamic and static densities indicates that the dynamic density is smeared near the nuclei, which is apparent as lower density values. In dynamic densities at ca.…”

“…An overview is given of the features of dynamic electron densities at very low temperatures in comparison to static electron densities for several amino acids and a tripeptide, especially concentrating on topological properties. 19 , 21 The previously published multi-temperature study of dynamic electron densities of d , l -serine is reviewed. 19 , 22 These results are then used for a discussion of chemical bonding in the protein crambin [Protein Data Bank 23 (PDB) reference: 3nir] on the basis of static and dynamic densities derived from X-ray diffraction data at 100 K published by Schmidt et al 6 In accordance with a parallel study on hen egg-white lysozyme HEWL, 20 we find that atomic displacement parameters (ADPs) assume values in crambin at 100 K that are comparable to or larger than values of ADPs of small molecules at room temperature.…”