Topological properties of hydrogen bonds

For hydrogen bonds, approximate relations between the density values at BCPs are ρ^IAM(BCP)ρ^IAM−HO(BCP)> ρ^INV(BCP)ρ^MP(BCP)

ρ^MEMIAM (BCP)ρ^MEMIAM−HO(BCP)> ρ^MEMINV (BCP)ρ^MEMMP (BCP)

(5.8)

Figure 5.4: Sections of 6×6 ˚A² of dynamic deformation maps [Eq. (5.4)] of D, L-serine through the plane of the N1–H11· · ·O3 hydrogen bond for (a) IAM prior, (b) IAM-HO prior, (c) INV prior, and (d) MP prior. The numbers on the axes indicate the distance in ˚A with respect to an arbitrarily selected origin. Contours are at 0.05 e/˚A³; solid lines denote positive values, dotted lines denote negative values and dashed lines are the zero contour.

5.4. DISCUSSION 93

Table 5.10: Topological properties of hydrogen bonds of Ala-Tyr-Ala_Etoh: ρBCP (e/˚A³; first line) and ∇²ρBCP (e/˚A⁵; second line) for eight different density maps.

Dynamic model density MEM density

Bond IAM IAM-HO INV MP IAM IAM-HO INV MP

O6. . . H15-O5 0.408 0.408 0.308 0.310 0.435 0.420 0.329 0.338 2.55 2.65 3.54 4.48 1.33 2.28 2.68 3.55 O3. . . H16-O6 0.362 0.362 0.284 0.285 0.310 0.302 0.289 0.291 2.28 2.23 3.66 3.63 2.29 2.94 3.46 2.96 O4. . . H11A-N1 0.335 0.334 0.246 0.251 0.283 0.275 0.258 0.248 2.64 2.66 3.33 3.28 1.97 2.31 3.27 3.17 O2. . . H11C-N1 0.352 0.351 0.250 0.268 0.338 0.339 0.243 0.267 2.33 2.35 3.61 3.59 1.91 2.12 4.15 3.53 O5. . . H11B-N1 0.294 0.292 0.198 0.210 0.294 0.277 0.225 0.237 2.47 2.50 2.98 3.43 0.44 1.17 1.58 2.03 O4. . . H13-N3 0.215 0.214 0.150 0.104 0.184 0.191 0.152 0.145 2.13 2.14 2.19 2.50 1.77 1.56 1.31 1.90 O1. . . H1-C1 0.130 0.128 0.118 0.105 0.125 0.125 0.118 0.098 1.51 1.50 1.70 1.63 0.62 0.45 0.80 1.36 O1. . . H12-N2 0.186 0.185 0.119 0.107 0.118 0.112 0.110 0.101 1.87 1.87 1.84 2.09 2.16 1.78 1.70 1.84

Laplacians are positive for most hydrogen bonds and show the following relations

∇²ρ^IAM(BCP)∇²ρ^IAM−HO(BCP)<∇²ρ^INV(BCP)∇²ρ^MP(BCP)

∇²ρ^MEMIAM (BCP)∇²ρ^MEMIAM−HO(BCP)∇²ρ^MEMINV (BCP)∇²ρ^MEMMP (BCP)

(5.9)

These relations are in agreement with the previous analysis of ρ^IAM(x), ρ^MEMIAM (x) and static MP densities (Netzel and van Smaalen, 2009).

Dynamic deformation densities in hydrogen bonds exhibit similar features for the IAM-HO, INV and MP priors, as shown in Fig. 5.4 for the example of the N–

H11· · ·O3 hydrogen bond of D, L-serine. The qualitatively similar appearances of the dynamic deformation densities with different priors and the numerical analysis at BCPs indicate that a reasonably accurate description of hydrogen bonding can be obtained with both IAM-HO and INV priors.

Table 5.11: Topological properties of covalent bonds of MEM densities of D, L-Serine as obtained by three methods. Method 1: Dynamic IAM model as prior and reflection phases from the INV model. Method 2: Dynamic INV model as prior and reflection phases from the IAM model. INV: prior and reflection phases from the INV model (from Table 5.5).

ρBCP (e/˚A³: first line) and∇²ρBCP (e/˚A⁵; second line).

Bond Method 1 Method 2 INV

C1–O1 2.498 2.589 2.617

Mondal et al. (2012) have demonstrated, forα-glycine andD, L-serine, that at BCPs the dynamic MP density maps at T 20 K provide a good approximation to the static MP density maps. Here we confirm this observation for L-alanine and the tripeptide Ala-Tyr-Ala_Etoh. Furthermore, we show that at both covalent bonds and hydrogen bonds the dynamic INV density maps are good approximations to the dynamic MP density maps.

Four types of dynamic density maps have been employed as prior in MEM calcu-lations on the low-temperature X-ray diffraction data of three different amino acids and one tripeptide. Both the IAM-HO and INV priors lead to reliable MEM den-sities at covalent and hydrogen bonds. The agreement for C–C and C–N bonds is excellent between density values and between Laplacians at BCPs of MEM electron densities obtained with the IAM-HO, INV and MP priors [Eqs. (5.5) and (5.6)].

The agreement is less good for polar C–O bonds, which is commensurate with the large spread of values of topological descriptors of C–O bonds in static MP density

5.5. CONCLUSIONS 95

Table 5.12: Topological properties of hydrogen bonds of MEM densities ofD, L-Serine as obtained by three methods. Method 1: Dynamic IAM model as prior and reflection phases from the INV model. Method 2: Dynamic INV model as prior and reflection phases from the IAM model. INV: prior and reflection phases from the INV model (from Table 5.6).

ρBCP (e/˚A³; first line) and∇²ρBCP (e/˚A⁵; second line).

Bond Method 1 Method 2 INV

O1· · ·H4–O3 0.352 0.316 0.320

maps. Density values and Laplacians at BCPs of hydrogen bonds adopt similar values in MEM electron-density maps obtained with all four kinds of prior. This can be explained by the small values and small spatial variation of the densities in these regions, as expressed by small magnitudes for the Laplacians.

The MEM density map obtained with the IAM prior is clearly different from the other MEM density maps. Despite similar behavior in bonding regions of dynamic IAM and IAM-HO densities, used as prior the latter leads to more reliable MEM density maps than the former does. These observations show interesting parallels to MP refinements (Jelsch et al., 2005; Domagala et al., 2012). One accepted procedure of solving for MP parameters involves the generation of those parameters on the basis of the IAM-HO, while the IAM generally leads to less good MP models (Jelsch et al., 2005; Domagala et al., 2012). In other approaches it has been suggested that the use of an invariom model for providing initial values for the MP parameters in a MP refinement will lead to the most reliable MP model (Dittrich et al., 2005; 2008). We therefore conclude that 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 reliable MP models as well as reliable MEM densities.

The MEM is intended to provide an estimate of the electron density distribution independently from a MP refinement. Both the IAM-HO and INV priors serve this purpose. This feature becomes especially important for the intended applications to large systems (e.g. protein crystals), where the free refinement of the MP model is not possible (Jelsch et al., 2000; Housset et al., 2000; Guillot et al., 2008; Schmidt et al., 2011).

Chapter 6

Dynamic electron density of the protein Crambin using a high

resolution X-ray diffraction data ¹

6.1 Introduction

In recent years there is an increase in the number of protein structures solved at subatomic resolution (Jelsch et al., 2000; Housset et al., 2000; Podjarny et al., 2002;

Ko et al., 2003; Kang et al., 2004; B¨onisch et al., 2005; Hakanp¨a¨a et al., 2006;

Wang et al., 2007; Guillot et al., 2008; Schmidt et al., 2011). Protein structures at subatomic resolution (dmin <1˚A) allow detailed analysis of electron density distribu-tion, which in turn may help to understand the enzymatic action and intermolecular interactions involved in proteins (Dauter et al., 1997; Housset et al., 2000; Schmidt and Lamzin, 2002). Generally, protein structures are described on the basis of the independent atom model (IAM). However to understand the effect of chemical bond-ing, consideration of the aspherical multipole (MP) model is necessary. While the MP method (see Chapter 2) is the established method for studying the electron den-sity distribution of small molecules, only few protein structures were studied by this method (Jelsch et al., 2000; Housset et al., 2000; Guillot et al., 2008; Schmidt et al., 2011). However, due to the large number of atoms in proteins, such MP refinements suffer from correlated parameters. In an alternative approach, MP models can also

1Part of this Chapter has been published as Topological Properties of Chemical Bonds from Static and Dynamic Electron densities. S. J. Prathapa, J. Netzel, S. Van Smaalen. Z. Anorg. Allg.

Chem. in press, (2013)

97

be obtained by using fixed MP parameters from a database and refining only the positional and thermal parameters like in an IAM refinement (Pichon-Pesme et al., 1995; Dittrich et al., 2006).

Information on chemical bonding of proteins can be rationalised by the QTAIM (Bader, 1990) applied on the static densities obtained from an MP model. The static density obtained from an MP model is deconvoluted from the thermal motion. How-ever, the atomic thermal motion plays an important role in proteins (Parthasarathy and Murthy, 2000; Yuan et al., 2003). Generally, atomic thermal vibrations are taken into account by atomic displacement parameters (ADPs) and are included in the B-factors [B = 8π² < Ueq >] which gives insights into protein dynamics and defines the degree of flexibility of protein molecule. The degree of flexibility is of-ten related to their function and chemical properties (Branden and Tooze, 1999).

The consideration of dynamic electron density (time-averaged) can reveal the effect of thermal motion on electron densities, as we have successfully demonstrated in Chapter 4 and 5 by computing the dynamic electron densities of small molecules.

Here we consider the small protein Crambin (PDB ID:3NIR) (Schmidt et al., 2011) for dynamic electron density analysis. The protein Crambin was chosen, be-cause of the availability of high-resolution diffraction data (dmin = 0.48 ˚A). The crystallographic details of Crambin are given in Table 6.1. Crambin is a small hy-drophobic plant protein (VanEtten et al., 1965) formed by 46 amino acids. The bio-logical function of Crambin is not discovered yet and still is an open scientific issue.

The crystal structure of Crambin (Fig. 6.1) was first reported by Teeter and Hen-drickson (1979), it consist of twoα helices and two β strands which are cross-linked by three disulfide bridges giving stability to the structure. It has been proposed that the structure of Crambin is further stabilised by a salt-bridge interaction, formed by an ion pairing through hydrogen bonds between the guanidinium group of the argi-nine residue ARG10 and the carboxyl group of the C-terminal asparagine residue ASN46 (Yamano and Teeter, 1994; Bang et al., 2009) (Fig. 6.1). Here the analysis of static and dynamic densities is mainly focussed on the two residues of Crambin which are involved in the salt-bridge interaction. The dynamic electron density, both from the IAM-HO and ELMAM2 model densities have been constructed and compared together with the corresponding static model densities in order to find out the effect of thermal motion on electron densities. And thereby understanding the properties of chemical bonds in Crambin. The effect of B-factors on electron densities and corresponding topological properties are analyzed and compared with a small molecule D, L-serine presented in Chapter 4.

6.2. COMPUTATIONAL DETAILS 99

6.2 Computational details