Molecular dynamics-derived rotamer libraries for d-amino acids within homochiral and heterochiral polypeptides

Abstract

Computational resources have contributed to the design and engineering of novel proteins by integrating genomic, structural and dynamic aspects of proteins. Non-canonical amino acids, such as d-amino acids, expand the available sequence space for designing and engineering proteins; however, the rotamer libraries for d-amino acids are usually constructed as the mirror images of l-amino acid rotamer libraries, an assumption that has not been tested. To this end, we have performed molecular dynamics (MD) simulations of model host–guest peptide systems containing d-amino acids. Our simulations systematically address the applicability of the mirror image convention as well as the effects of neighboring residue chirality. Rotamer libraries derived from these systems provide realistic rotamer distributions suitable for use in both rational and computational design workflows. Our simulations also address the impact of chirality on the intrinsic conformational preferences of amino acids, providing fundamental insights into the relationship between chirality and biomolecular dynamics. While d-amino acids are rare in naturally occurring proteins, they are used in designed proteins to stabilize a desired conformation, increase bioavailability or confer favorable biochemical and physical attributes. Here, we present d-amino acid rotamer libraries derived from MD simulations of alanine-based host–guest pentapeptides and show how certain residues can deviate from mirror image symmetry. Our simulations directly model d-amino acids as guest residues within the chiral l-Ala and d-Ala pentapeptide series to explicitly incorporate any contributions resulting from the chiralities of neighboring residues.

Introduction

Of the 20 standard proteinogenic amino acids, all except Gly have a chiral center at the Cα backbone atom and thus are present as pairs of stereoisomers. Although their occurrence in natural proteins is rare, d-amino acids can be incorporated into natural proteins via non-ribosomal peptide synthetases (Caboche et al., 2008), post-translational conversion of l-amino acids by isomerases (Bai et al., 2009; Ollivaux et al., 2014) or racemization (Fujii et al., 2011). d-amino acids have been observed in antibacterial and antifungal peptides produced by bacteria (Radkov and Moe, 2014); peptide toxins in the venoms of spiders (Agelenopsis aperta) (Shikata et al., 1995), platypuses (Ornithorynchus anatinus) (Torres et al., 2005) and snails (Achatina fulica) (Kamatani et al., 1989) and opiate-like peptides in frogs (Phyllomedusa sauvagei) (Montecucchi et al., 1981). The potent biological functions demonstrated by these peptides has inspired the incorporation of d-amino acids into designed proteins.

There are two primary objectives for the incorporation of d-amino acids into designed and engineered proteins. First, d-amino acids can stabilize specific conformational states via their ability to adopt backbone φ and ψ angles that are unfavorable for l-amino acids. d-amino acids have been incorporated into designed proteins to stabilize α-helices (Rodriguez-Granillo et al., 2011), turns (Imperiali et al., 1992), antiamyloid peptides (Hopping et al., 2014; Kellock et al., 2016), β-hairpins (Makwana and Mahalakshmi, 2016), novel peptide topologies (Rana et al., 2004, 2005), metal-binding sites (Peacock et al., 2009) and large topologies (Valiyaveetil et al., 2004). Second, incorporation of d-amino acids can confer favorable biological and chemical properties to designed proteins. For example, the incorporation of d-amino acids into therapeutic peptides has been shown to increase their resistance to proteolysis, prolonging their biological half-lives (Zhou et al., 2002). Although several successful designs have been reported, random incorporation of a d-amino acid into a protein does not guarantee that design goals will be met (Rodriguez-Granillo et al., 2011). For example, in a systematic study of helix-stabilizing mutations to the Trp-Cage mini protein, Rodriguez-Granillo et al. found that increases in stability were modulated by the identity of the d-amino acid. Also key is the interplay between the backbone and side chain dihedral angles, which are coupled for some residues. Thus, consideration of the accessible conformations and intrinsic flexibilities of both the backbones and side chains of d-amino acids is necessary to make wise design choices.

Sterically allowed combinations of the backbone (φ and ψ) and side chain (χ₁…χ_n) dihedral angles define the accessible conformational space for a given amino acid. However, this conformational landscape is not evenly populated; instead, amino acid side chains preferentially adopt well-defined conformational states, known as rotamers (Chandrasekaran and Ramachandran, 1970; Bahar and Jernigan, 1996). These intrinsic conformational preferences can be summarized as probability distributions in rotamer libraries. These rotamer libraries provide quick access to the most probable rotamer conformations and have widespread applications in molecular modeling (Krivov et al., 2009), protein design (Ota et al., 2001; Renfrew et al., 2014) and protein structure prediction (Gordon et al., 2003; Ryu et al., 2016). In rational protein design applications, rotamer libraries list favorable conformations (ranked by probability) and allow users to identify potential mutations. In automated design applications, algorithms sort through the favorable conformations in rotamer libraries to search for minimum energy sequences that may adopt a desired structure. To this end, many l-amino acid rotamer libraries have been derived from high-resolution static structures deposited in the Protein Data Bank (PDB, www.rcsb.org) (Berman et al., 2000) as well as from solvated atomistic molecular dynamics (MD) simulations of representatives of essentially all protein folds in the Dynameomics database (Dunbrack and Karplus, 1993, 1994; Dunbrack, 2002; Scouras and Daggett, 2011; Hintze et al., 2016; Towse et al., 2016a).

In contrast to the abundance of side chain rotamer information available for l-amino acids, there are limited data available for d-amino acids due to their much rarer occurrence in natural proteins. In a survey of the PDB, Mitchell and Smith found 492 instances of d-amino acid residues distributed among 148 unique PDB entries, which corresponds to 0.6–0.7% (http://www.rcsb.org/pdb/statistics/contentGrowthChart.do?content=total) of the structures available in the PDB at that time (Mitchell and Smith, 2003). Due to the lack of high-quality experimental data for d-amino acids, their conformations and dynamics have been assumed to adhere to the mirror image convention, as evidenced by many organic molecules (Ota et al., 2001; Makwana and Mahalakshmi, 2016). The mirror image convention assumes that mirrored configurational symmetry extends to mirrored dynamic symmetry. That is, the backbone-dependent probability distribution of the side chain dihedral angles for a d-amino acid (P_D) is the mirror image of the same distribution for its enantiomer (P_L) (Equation 1).

$$P_D\left({\chi }_1\dots {\chi }_N|\phi ,\psi \right)=P_L\left(-{\chi }_1\dots -{\chi }_N|-\phi ,-\psi \right)$$ (1)

For a residue with one side chain dihedral angle, this corresponds to a reflection across χ₁ = 0°. For a residue with two dihedral angles, this corresponds to a 180° rotation of the χ₁ vs χ₂ landscape. Previously, it has been stated that the mirror image convention does not apply to Ile and Thr (Gfeller et al., 2013). We wish to clarify that for residues with multiple chiral centers, the mirror image convention can only be applied when the chirality is inverted at all centers. However, if the chirality is inverted at only one site, the mirror image convention cannot be applied. For example, l-Thr (absolute stereochemistry: 2S, 3R) and d-Thr (2R, 3S) have mirrored configurations but l-Thr and d-allo-Thr (2R, 3R) do not. This mirrored behavior has served as the theoretical foundation for the structural refinement and engineering of d-amino acid containing proteins. However, the assumption that amino acid enantiomers within peptide side chains mirror one another ignores the possibility that deviations from symmetry could result from the backbone dipole or the chirality of neighboring residues.

To our knowledge, there are two rotamer libraries for the d-enantiomer counterparts of the standard amino acids, one available through the SwissSidechain database (Gfeller et al., 2013) and another via the Rosetta molecular Modeling Suite (Renfrew et al., 2012). Gfeller et al. constructed the Swiss side chain rotamer library using complementary physics- and knowledge-based approaches (Gfeller et al., 2013, 2012). In this library, they performed four 50 ns MD simulations of l-Ala host–guest tripeptides (Ac-AXA-Nme, where X = the 20 amino acids) with implicit solvation, mapped propensities between structurally homologous residues and normalized the resulting probability distributions. For residues with achiral side chains, l-amino acid probability distributions were used to derive d-amino acid distributions via the mirror image convention. The second rotamer library for d-amino acids was constructed by Renfrew et al. (2012, 2014) and is available in the Rosetta Molecular Modeling Suite Das and Baker (2008). For this library, Renfrew et al. designed an algorithm that generates rotamer probability distributions for amino acids by iteratively seeding potential conformations followed by energy minimization. This approach used multiple structures of a dipeptide model of the amino acid that were seeded by making periodic rotations about the backbone and side chain dihedral angles. The methods used to generate these rotamer libraries exclude any effects from the chirality of neighboring residues. This is a key point that needs to be addressed given that designed proteins incorporating d-amino acids are almost always heterochiral polypeptide chains.

Although the mirror image convention is expected to apply for molecules that are exact enantiomers, it is not necessarily expected to apply in other cases, notably heterochiral molecules. In these instances, context-specific data are required. Here, we expand on prior work in computationally deriving rotamer libraries for d-amino acids by performing MD simulations of d-amino acid guest residues within two host pentapeptides series: AAxAA and aaxaa, where upper case characters refer to l-amino acids and lower case to d-amino acids. In addition, we perform a comparative analysis with rotamer libraries obtained for l-amino acid guest residues (AAXAA (Childers et al., 2016; Towse et al., 2016b) and aaXaa) and the backbone-independent (BBIND) rotamer library derived from protein simulations in the Dynameomics database. These new MD-derived rotamer libraries complement existing ones by directly simulating the dynamics of d-amino acids and by considering the effects that the chirality of neighboring residues has on guest residue rotamer distributions. Our results provide empirical predictions of the impact of neighboring residue chirality on intrinsic rotamer distributions. In addition, our analysis confirmed that the mirror image convention describes the dynamics of most residues, but several residues demonstrated deviation from mirror image symmetry.

Methods

MD simulations

To comprehensively examine the effects of chirality on side chain rotamers, four host–guest peptide systems (AAXAA, AAxAA, aaXaa and aaxaa) were simulated as end-capped (N-acetylated, C-amidated) pentapeptides with extended starting conformations (φ and ψ angles set to 180° and −180°, respectively). The initial backbone conformations (φ and ψ) for Pro residues were −80° and −180°, respectively. Of the 20 naturally occurring amino acids, two—Ala and Gly—do not have rotameric side chain dihedral angles and these systems are not discussed here. In addition, we have simulated peptides corresponding to the neutral and acidic pH protonation states of Asp (Ash) and Glu (Glh) as well as the three protonation states of His: Hid (δH), Hie (εH) and Hip (both δH and εH). Cysteine was modeled in the reduced state (–CH₂–SH, denoted Cyh). This yields 22 guest residues (Supplementary data available at PEDS online, Table S2) placed into four host peptides for a net total of 88 simulations (Supplementary data available at PEDS online, Table S1). Simulations were performed using the in lucem molecular mechanics (ilmm) package (Beck et al., 2000–2018) with Levitt et al.'s force field (1995), the microcanonical NVE (constant number of particles, volume and energy) ensemble, and the flexible three-center (F3C) water model (Levitt et al., 1997). Non-bonded interactions were treated with an 8 Å force-shifted cutoff (Beck et al., 2005). Simulations were performed at 298 K with explicit water molecules using a box size that reproduced the experimental density at that temperature (0.9970 g/ml). The initial starting conformations were prepared for simulation by performing 1000 rounds of steepest descent energy minimization, followed by solvation in a periodic box extending 10 Å beyond any protein atom. The solvated systems were then subjected to iterative rounds of minimization. Next, production runs were performed for 600 ns each, corresponding to the lengths of our other prior Ala host simulations (Childers et al., 2016; Towse et al., 2016b), and the final 580 ns of each simulation was used to calculate rotamer distributions. The initial 20 ns of each simulation was excluded from rotamer library calculations to allow for movement away from the initial fully extended starting structure, which was used to avoid biasing the conformational sampling. In total, the results from 88 simulations are presented here with an aggregate simulation time >51 μs (Supplementary data are available at PEDS online, Tables S1 and S2).

Mining the Dynameomics database

The Dynameomics database (Beck et al., 2008a; van der Kamp et al., 2010) contains systematic MD simulations of representatives of essentially all known protein folds (97%) as determined by our Consensus Domain Dictionary (Schaeffer et al., 2011). By analyzing all entries in this database, it is possible to construct distributions of structural and dynamical properties that serve as benchmark distributions (Jonsson et al., 2009). One such reference distribution is the BBIND rotamer library constructed using all Dynameomics entires, which we compare to the rotamer distributions observed in our AAXAA simulations to determine whether rotamer distributions are similar in folded proteins and unstructured pentapeptides. In addition, it is possible to extract conformations for individual proteins in the native and temperature-unfolded states. For example, ubiquitin (PDB ID: 1UBQ) was chosen as the representative for the β-grasp, ubiquitin-like fold. Conformations of thermally unfolded ubiquitin (PDB ID: 1UBQ, Vijay-Kumar et al., 1987) were obtained from the Dynameomics database to compare the side chain χ₁ dihedral angles observed in simulation and experiment. Per the Dynameomics protocol (van der Kamp et al., 2010), two 50-ns high-temperature NVE simulations were performed at 498 K using the ilmm (Beck et al., 2000–2018) package and Levitt et al. force field (1995).

Definitions of specific conformational regions

The intrinsic backbone sampling preferences were calculated by binning Ramachandran space into six specific conformational regions. For l-amino acids, these regions were defined as follows: α_R: −100°≤ ϕ ≤ −30°, −80°≤ ψ ≤ −5°; near-α_R: −175°≤ ϕ ≤ −100°, −55°≤ ψ ≤ −5°; α_L: 5°≤ ϕ ≤ 75°, 25°≤ ψ ≤ 120°; β: −180°≤ ϕ ≤ −50°, 80°≤ ψ ≤ −170°; P_IIL: −110°≤ ϕ ≤ −50°, 120°≤ ψ ≤ 180°; P_IR: −180°≤ ϕ ≤ −115°, 50°≤ ψ ≤ 100°. An additional region, termed npβ, describes a subset of the β region that does not overlap with either of the polyproline regions (i.e. the non-polyproline β region). For d-amino acids, the corresponding regions were defined according to mirror image symmetry: Dα_R: 30°≤ ϕ ≤ 100°, 5°≤ ψ ≤ 80°; near-Dα_R: 100°≤ ϕ ≤ 175°, 5°≤ ψ ≤ 55°; Dα_L: −75°≤ ϕ ≤ −5°, −120°≤ ψ ≤ −25°; Dβ: 50°≤ ϕ ≤ 180°, −80°≤ ψ ≤ 170°; DP_IIL: 50°≤ ϕ ≤ 110°, −180°≤ ψ ≤ −120°; DP_IR: 115°≤ ϕ ≤ 180°, −100°≤ ψ ≤ −50°(Fig. 1A). Note that the naming convention conveys the mirror image symmetry of the enantiomers, i.e. the Dα_R region corresponds geometrically to a left-handed α-helix. Side chain dihedral angles were classified into rotamers using the canonical bin definitions with the gauche+ (g+), trans (t) and gauche− (g−) nomenclature (Fig. 1B, Supplementary data available at PEDS online, Table S3).

Fig. 1.

Definitions of specific conformational regions (backbone dihedrals) and rotameric states (side chain dihedrals). Intrinsic conformational propensities are determined by measuring the population of specific conformational regions that are defined as basins in dihedral angle space. (A) For intrinsic backbone propensities, the regions corresponding to the six specific conformational regions are outlined on Ramachandran plots for l-amino acids (left) and d-amino acids (right). Adapted from Towse et al. (2014). (B) For intrinsic side chain propensities, the bins corresponding to the gauche+ (g+), trans (t) and gauche− (g−) rotameric states are defined for the tetrameric carbons (left), which applies to most side chain dihedral angles. For the remaining dihedral angles, residue-specific bin definitions are supplied (right). Adapted from Scouras and Daggett (2011), Fig. 2.

Assessment of convergence

To assess convergence, the rotamer populations were compared over different portions of the trajectories (0–6, 0–60 and 0–600 ns). In the case of short production runs, e.g. 6-ns, convergence as not reached in that the rotamer populations for the two halves of the trajectory were distinct (0–3 ns vs 3–6 ns). The simulations are deemed to be converged when the difference between the two halves of the trajectory is minimal.

Calculation of correlation coefficients

The Pearson corrlation coefficient was calculated for each guest residue’s rotamer distribution as follows. First, the production portion of a trajectory was randomly divided into two halves. An n-dimensional histogram (n = number of rotameric side chain dihedral angles) was constructed for each half of the trajectory by splitting each dihedral angle into 36 10° bins. The correlation coefficient was calculated between the bin counts of the resulting histograms. The reported correlation coeffiecents are the average of 50 iterations of this procedure.

Calculation of NMR scalar coupling constants

We checked our simulations against experiment by comparing calculated nuclear magnetic resonance (NMR) scalar couplings for the pentapeptides and thermally unfolded ubiquitin to experimental values obtained for chemically unfolded lysozyme, ubiquitin and protein G. We calculated ³J_Hα,Hβ, ³J_N,Hβ, ³J_C,Hβ, ³J_C,Cγ and ³J_N,Cγ scalar coupling constants from MD simulations using the Karplus (1963):

$${}_{}{}^{3}J\left(\theta \right)=C_0+C_1\cos \theta +C_2\cos 2\theta$$ (2)

where θ = χ₁ by taking the average of the coupling constants calculated for each frame in the simulation. Residue-specific Karplus coefficients (C₀, C₁, and C₂) were obtained from Pérez et al. (2001) and are reproduced in Supplementary data available at PEDS online, Table S4. Experimental data for urea-unfolded ubiquitin and protein G were obtained from the Biological Magnetic Resonance Bank (BMRB, Ulrich et al., 2008) entries 16626 and 16627, respectively (Vajpai et al., 2010). Experimental data for urea-unfolded hen egg white lysozyme (HEWL) were obtained from the supplementary materials accompanying Hennig et al. (1999).

Comparison of rotamer distributions

Rotamer populations were calculated as the fraction of the MD ensemble that lies within the defined rotamer bins. The rotamer distribution for each residue corresponds to an n-dimensional (n = the number of rotameric states) vector and each element in the vector is the fraction of the ensemble that populates that bin. We employed a population displacement metric (Scouras and Daggett, 2011) to quantify the similarity between matched rotamer distribution vectors $\stackrel{⃑}{X}$ and $\stackrel{⃑}{Y}$. To address the extent to which the mirror image convention applies, comparisons between l- and d- enantiomers were done after matching the mirror image conformational states as in Supplementary data available at PEDS online, Table S5. The similarity was calculated as the sum of the fraction of the population that does not change between matched rotamer bins x_i and y_i (Equation 3).

$$\mathrm{Similarity}=\sum _i^n\min (x_i,y_i)$$ (3)

Rotamer library construction and availability

After establishing convergence of the simulations and their agreement with experiment, the simulations were analyzed and rotamer distributions were systematically cataloged. Four separate rotamer libraries were constructed, each corresponding to the guest residues in the four systems: AAXAA, aaxaa, AAxAA and aaXaa. Rotamer populations were calculated as the fraction of the MD ensemble that lies within the defined rotamer bins (Fig. 1B, Supplementary data available at PEDS online, Table S3). For each rotameric state, the modal angles for each side chain dihedral were also recorded. Comparisons between enantiomers were done after the mirror image rotamer conformations were matched (as in Supplementary data available at PEDS online, Table S5). Full rotamer libraries are provided both in tabular form in the Supplementary data available at PEDS online (Table S5) and as a plain text file available on our website (www.dynameomics.org) (upon publication). In addition, we have created a UCSF Chimera (Pettersen et al., 2004) extension that enables in silico mutations using d-amino acids that is also available on our website (www.dynameomics.org).

Results and discussion

Conformational sampling and convergence

Prior to rotamer library construction, we confirmed that all simulations had achieved an equilibrium distribution with stable population frequencies. Convergence of these distributions was assessed by dividing the production trajectories into different ranges of time, e.g. 0–300 and 300–600 ns and comparing the populations of rotameric states between the different portions (Fig. 2). After the point of convergence, the two halves of the production run should have nearly identical populations of rotameric states. Comparison of the rotamer populations over the initial stages of the simulation showed that the two rotamer distributions were not converged, demonstrated by the 0–3 ns vs 3–6 ns data in Fig. 2. However, with longer trajectories, the population in the latter halves of the production runs became more similar, demonstrated by the 0–300 ns vs 300–600 ns data in Fig. 2. Residues with longer side chains took longer to converge due to the increased degrees of freedom; however, these results show that 300 ns of production time is sufficient to achieve convergence even for the most complex residues, Arg and Lys. Our rotamer libraries have been constructed with nearly twice the requisite time to achieve convergence, yielding Boltzmann sampling for better estimates of conformational probability distributions. Extension of the trajectories an additional order of magnitude (i.e. 6 μs) is expected to yield only minimal changes to the population frequencies (Fig. 2).

Fig. 2.

Convergence of the population of rotameric states sampled by Ser, Leu, Met and Arg in the AAXAA system. In each plot, a single point corresponds to a single rotameric state. The population of that state is compared between the first and second halves of the trajectories for the designated times in the simulations. For trajectory halves with identical populations, the points should lie along the diagonal. Plots are shown for three different portions of the trajectories: 0–6 ns (left), 0–60 ns (center) and 0–600 ns (right) for four different residues: serine (A, one side chain dihedral), leucine (B, two side chain dihedrals), methionine (C, three side chain dihedrals) and arginine (D, four side chain dihedrals). Residues with longer side chains converge on slower timescales due to the increased accessible conformational space introduced by additional dihedral angles.

Comparison with NMR coupling constants

Quantitative spectroscopic measurements of intrinsic conformational distributions are challenging to obtain. Furthermore, the values can vary widely when different techniques are employed. For example, experimental studies have placed the polyproline (P_II) content of tri-alanine at various populations ranging between 50% and 92% (Woutersen et al., 2002; Eker et al., 2003; Graf et al., 2007; Schweitzer-Stenner, 2009; Oh et al., 2010; Sharma and Asher, 2010). Despite this, we strive to make quantitative comparisons with experiment whenever possible and have historically obtained good agreement with experiment. In our investigation of the GGXGG system, we showed that MD simulations of the GGAGG peptide reproduced the vicinal spin–spin coupling constant (³J_NHCα) within experimental error (Beck et al., 2008b). In our investigation of the AAXAA system (Towse et al., 2016b), we showed that the average helix content for the AAAAA system (19.4%) was in closer agreement with experimental estimates (10–20%, Firestine et al., 2008; Jiang et al., 2013) than the same system simulated with other force fields (Best et al., 2008): 57.5% (CHARMM27), 62.3% (AMBER03), 94.2% (AMBER99) and 97.6% (AMBER94). In our comparative analysis of the GGXGG and AAXAA systems, we showed that our force field reproduces experimentally derived proton and heavy atom chemical shifts for the GGXGG system obtained in 8 M urea, 298 K, pH 2.5 (Childers et al., 2016). Finally, we showed that our force field also reproduces experimental S² side chain order parameters for side chains with a methyl group (Ala, Ile, Leu, Met, Thr and Val) from a variety of globular proteins (Towse et al., 2016a; Scouras and Daggett, 2011).

While no systematic data exist for the measurement of intrinsic side chain populations, NMR scalar coupling data has been used to gain insight into the χ₁ distributions in the urea-unfolded states of HEWL, ubiquitin and protein G (Hennig et al., 1999; Vajpai et al., 2010). To assess the correspondence between the intrinsic scalar couplings observed in pentapeptide systems to those in unfolded proteins, we calculated ³J_Hα,Hβ, ³J_N,Hβ, ³J_C,Hβ, ³J_C’,Cγ and ³J_N,Cγ scalar coupling constants obtained from our MD simulations using the Karplus relation and the residue-specific Karplus coefficients as determined by Pérez et al. (2001). The resulting comparison shows good agreement between simulation and experiment for most residues (Fig. 3A). We also compared the ³J_Hα,Hβ, ³J_N,Hβ and ³J_C,Hβ scalar coupling constants obtained in our MD simulations of unfolded ubiquitin to its corresponding experimental values (Fig. 3B). More than one point is shown for residues for which stereospecific assignments were made (note that the different rotamers partition above and below 6 Hz in the top panel of Fig. 3B). The resulting comparison shows an improved correspondence relative to the pentapeptide–protein comparison in Fig. 3A. Overall, the best agreement was found for Phe, Pro, Thr, Trp and Tyr, while the worst agreement was found for Asn, Ash and Ile. The disagreement for Asn and Ash may result from the overpopulation of trans conformations in our simulations or the stabilization of gauche conformations within the experimental data relative to the intrinsically dominant conformations. No comparison could be made for Cys or the unprotonated forms of Asp, Glu and His, as these residues were not in the experimental data. The experimental results were obtained for globular proteins in 8 M urea at pH 2.5, hence we can only present a qualitative analysis as solvents (Bennion and Daggett, 2003; Li et al., 2011; Childers et al., 2016; Towse et al., 2016b), potential residual structure (Aznauryan et al., 2016) in the unfolded state and neighboring residue effects (Jung et al., 2014) are known to modulate intrinsic sampling preferences. Finally, experimental data are available for only three proteins and are restricted to the populations of χ₁ dihedrals and for two proteins (ubiquitin and protein G). Nevertheless, although qualitative, the correspondence between the experimental and computational results is encouraging.

Fig. 3.

Validation of peptide dynamics via a comparison with experimental ³J coupling constants. (A) Experimental ³J_Hα,Hβ, ³J_N’,Hβ, ³J_C’,Hβ, ³J_C’,Cγ and ³J_N’,Cγ scalar coupling constants for urea-unfolded ubiquitin, protein G and HEWL (blue points) are presented. The experimental data for ubiquitin and protein G contain stereospecific assignments for the scalar coupling constants of prochiral H_β1 and H_β2 atoms. The corresponding values over the MD ensembles for the AAXAA series (orange points) were obtained using the Karplus relation (Equation 2) and coefficients as determined by Pérez et al. (2001). Error bars denote standard deviations. (B) Comparison of experimental (blue) and MD-derived (orange) NMR coupling constants for urea-unfolded (blue) and temperature-unfolded (orange) ubiquitin. In the experimental data, prochiral hydrogen atoms were stereospecifically assigned where possible and both values were plotted along with the two individual values by MD. For example, the values for rotamers are split roughly above and below 6 Hz in the top panel in B.

Rotamer distributions in folded and unfolded states

After establishing that our simulations qualitatively reproduced side chain distributions observed in unfolded states, we next compared the distributions observed in our peptides to the distributions observed in MD simulations of globular proteins in the folded state. We compared the intrinsic rotameric preferences sampled in pentapeptides with rotameric preferences within globular proteins by comparing rotamer distributions for l-amino acids derived from AAXAA simulations to the Dynameomics BBIND rotamer library obtained from the Dynameomics data set as described in the Methods section (Scouras and Daggett, 2011; Towse et al., 2016a). This comparison tests whether rotamer distributions observed in folded, globular proteins are recapitulated in the unfolded state as modeled by simple pentapeptides. We found that the two distributions were qualitatively similar but distinct (Fig. 4, Supplementary data available at PEDS online, Table S5). Residues with short side chains, such as Ser and Pro, had the most similar distributions between the two states. For example, the distribution of Ser rotamers was 23% (gauche+, g+)/ 2% (trans, t)/ 75% (gauche−, g−) in the Dynameomics BBIND Library and 18% (g+)/ 1% (t)/ 81% (g−) in the AASAA peptide. Residues with bulkier side chains and charged residues showed greater deviations between the AAXAA and BBIND libraries. These are the residues likely to form more complex interactions in specific structural environments. The residues with the greatest difference for a rotameric state between the folded and unfolded models were the g+, t rotamers of Ile (BBIND: 43%, AAIAA: 75%) and the t, g+ rotamers of Asp (BBIND: 66%, AADAA: 86%) (Fig. 4, Supplementary data available at PEDS online, Table S5). The largest differences in sampling were restricted to the dominantly populated rotamers in the BBIND library.³³ In other words, the differences between the AAXAA series and BBIND library were not the result of a rotamer switching between a low population in BBIND and high population in the pentapeptides (or vice versa). Instead, the population of dominant rotamers in the BBIND library increased in the AAXAA systems, implying that the dominant rotamers in peptides and proteins are similar and that intrinsically dominant rotamers tend to be preserved in the native state. Moreover, the presence of secondary and tertiary interactions in folded protein structures can increase the population of rotamers that are not intrinsically preferred. No comparison could be made for the protonated states of Asp (Ash), Glu (Glh) or diprotonated His (Hip) as the Dynameomics data set contains simulations at neutral pH.

Fig. 4.

Similarity plots of rotamer distributions derived from the Dynameomics BBIND library and pentapeptide simulations. Each matrix reports the similarity coefficients for the rotamer distributions of a given guest residue across each of the four pentapeptide systems plus the Dynameomics BBIND library. For comparisons between l- and d-amino acids, comparisons were made between the matched rotamer distributions. High-similarity coefficients (blue) indicate that two rotamer distributions are similar, whereas low-similarity coefficients (red) indicate that the two rotamer distributions are distinct. Black squares indicate that no valid comparison is available. Adapted from Scouras and Daggett (2011), Fig. 3.

Symmetry in rotamer dynamics

We previously confirmed through MD simulations of GGXGG and GGxGG that the mirror image convention applies for the backbone dihedral angles ϕ and ψ in an achiral host (Towse et al., 2016b). To investigate to what extent the mirror image convention applies to the side chain dihedral angles of l- and d- guest residue pairs, we calculated the similarity between matched rotamer distributions for enantiomeric pairs (i.e. AAXAA and aaxaa; AAxAA and aaXaa) (Table I). To investigate the impact that the chirality of neighboring residues had on guest residue rotamer distributions, we calculated the similarity between the rotamer distributions for the diastereoisomeric pairs for a given guest residue chirality (i.e. AAXAA and aaXaa; AAxAA and aaxaa) (Table II). A similarity score of 100% indicates that the mirror image convention applies while lower scores can be attributed to deviation from the mirror image convention. The average similarity value calculated between three replicate simulations of the GGWGG peptide was 96.9 ± 1.4%. This calculation estimates that percent similarity differences of up to 4.5% can be attributed to dynamic variability among the simulations. Deviation from mirror image symmetry was predicted for residue pairs with less than 91% similarity. This stringent threshold (twice that predicted by replicate simulations) was chosen to minimize false positives.

Table I.

The similarity percentage between enantiomeric peptide pairs reflects the extent to which the mirror image convention describes the rotamer populations for l- and d-amino acid pairs

Residue	Homochiral similarity (AAXAA vs aaxaa)	Heterochiral similarity (AAxAA vs aaXaa)
Arg	92.9	94.2
Asn	96.7	97.8
Asp	99.6	99.5
Ash	99.7	99.5
Cyh	98.8	99.2
Gln	98.7	98.2
Glu	98.6	99.2
Glh	99.4	99.3
Hid	96.5	97.7
Hie	98.1	96.4
Hip	94.0	95.1
Ile	56.0	54.2
Leu	97.7	97.3
Lys	95.6	95.8
Met	98.2	98.7
Phe	96.4	99.4
Pro	>99.9	99.3
Ser	99.6	99.6
Thr	67.0	78.8
Trp	94.4	96.8
Tyr	98.6	98.6
Val	74.2	96.9

Table II.

The similarity percentage between heterochiral diastereoisomeric pairs measure the impact of host residue chirality on the rotamer populations on l- and d-guest residues

Residue	l-AA guest (AAXAA vs aaXaa)	d-AA guest (AAxAA vs aaxaa)
Arg	86.4	88.2
Asn	95.4	93.6
Asp	98.1	98.4
Ash	98.9	99.3
Cyh	96.9	96.0
Gln	94.3	93.5
Glu	97.4	98.1
Glh	96.1	96.8
Hid	95.6	93.8
Hie	88.1	88.1
Hip	84.2	86.5
Ile	89.2	86.3
Leu	95.4	98.1
Lys	88.5	89.9
Met	94.3	94.4
Phe	95.0	91.8
Pro	97.3	96.6
Ser	99.9	99.3
Thr	97.2	88.0
Trp	91.5	89.9
Tyr	94.6	96.2
Val	90.4	61.6

Adherence to the mirror image convention was anticipated for enantiomeric pairs (AAXAA and aaxaa; AAxAA and aaXaa). However, in the homochiral enantiomers (AAXAA and aaxaa) the β-branched residues (Ile, Thr and Val) all deviated from mirror image symmetry (Fig. 4, Table I, Supplementary data available at PEDS online, Table S5). The magnitude of the deviation from mirror image symmetry was dependent on the side chain: Ile (44% deviation) > Thr (33%) > Val (26%). For the heterochiral enantiomers (AAxAA and aaXaa) (Fig. 4, Table II, Supplementary data available at PEDS online, Table S5) the results also showed a symmetry deviation for Ile and Thr (Fig. 4). Again, the magnitude of this deviation was dependent on the side chain, with Ile displaying a greater deviation (46%) than Thr (21%). Heterochiral configurations reduced the magnitude of the deviation for Thr and resulted in mirror image symmetry for Val (Fig. 4, Table II). Our results suggest that β-branched configurations can result in deviations from mirror image symmetry.

Intrinsic sampling in heterochiral diasteroisomers

After confirming mirrored behavior in enantiomeric pairs, we examined the extent to which host residue chirality affected the rotamer distributions of the guest residues by calculating the similarity values for heterochiral diastereoisomer pairs (AAXAA vs aaXaa and aaxaa vs AAxAA). Deviations from 100% similarity indicate that guest residue rotamer distributions are affected by the chirality of neighboring residues. This sensitivity to neighboring residue chirality was predicted for pairs with less than 91% similarity. For most of the guest residues, the rotamer distributions were insensitive to the chirality of the neighboring host residues (Table II). However, for l-amino acid guest residues, Arg, Hie, Hip, Ile, Lys and Val exhibited sensitivity to the chirality of neighboring residues (Fig. 4, Table II, Supplementary data available at PEDS online, Table S5). For d-amino acid guest residues, Arg, Hie, Hip, Ile, Lys, Thr, Trp and Val exhibited sensitivity to the chirality of neighboring residues (Fig. 4, Table II, Supplementary data available at PEDS online, Table S5). Modulations in the rotamer populations due to host chirality are exemplified by the t, Ng+ (7% populated in AAHAA, 14% populated in aaHaa) and g−, Cg− (22% in AAHAA, 13% in aaHaa) rotamers of l-Hip. Our rotamer libraries have been developed using the simplest chiral side chain –Ala. Greater deviations in rotamer similarity are anticipated for host residues with more complex side chains.

pH-dependent rotameric preferences

To our knowledge, there are no libraries that compare the rotamer distributions for alternate protonation states of Asp (Ash), Glu (Glh) and His (Hie, Hid and Hip). A common protein design goal is to develop a system with structural and/or functional properties that are linked with changes in pH. In these circumstances, the introduction or removal of ionizable residues is key (Guranda et al., 2004; Leone and Picone, 2016). Therefore, we examined the effect that pronation could have on rotamer populations for the titratable residues and witnessed a focusing of the rotamer populations (Supplementary data available at PEDS online, Fig. S1). The populations in the dominant rotameric states of the neutral forms of Asp, Glu and His increased for the charged forms of these residues; the other minor rotamer populations correspondingly decreased. This finding indicates that the charge on an amino acid affects its intrinsic side chain conformational propensities as well as backbone conformational propensities (Childers et al., 2016). The charged residues also had the greatest difference in sampling between the AAXAA systems and the Dynameomics BBIND rotamer library, suggesting that tertiary interactions within folded proteins affect the side chain sampling of titratable residues. The tertiary structure influence is expected given the specific nature of charged interactions in salt bridges, hydrogen bond networks and functional sites.

Breakdown in valine’s mirror image symmetry

As described above, the β-branched residues had the greatest deviation from mirror image symmetry. This behavior was unanticipated for Ile, Thr and Val. In the SwissSidechain library, deviations from mirrored behavior were anticipated for Ile and Thr as d-allo-Ile and d-allo-Thr were simulated in that library (Gfeller et al., 2013). To investigate the molecular origins of this deviation, we performed an analysis of the dynamics of Val guest residues. We first determined whether deviation from mirror image symmetry was observed in achiral host systems, i.e. the GGVGG and GGvGG peptides. Previously, we showed that in achiral hosts, l- and d- enantiomers have mirrored backbone propensities (Towse et al., 2014). As a control, we extended the GGVGG and GGvGG simulations to 900 ns and our prior results were maintained in longer simulations (Fig. 5B). Furthermore, in the achiral host peptide simulations, l-Val and d-Val rotamer distributions were mirrored (Supplementary data available at PEDS online, Table S5). Thus, deviations in mirror image symmetry for l-Val and d-Val occur only when the host residues enforce backbone chirality and impose steric constraints on the guest residue. When deviations in mirror image symmetry occur, they must be accompanied by a change in the probability of transition between rotameric states and/or changes in interactions that contribute to the stabilization of different rotameric states. Consequently, we calculated the populations of specific conformational regions for the backbone dihedral angles for the Val peptides. In an achiral host, l-Val and d-Val have mirror image backbone propensities. In our chiral hosts, however, Val demonstrated context-dependent sampling of specific conformational regions in the backbone (Fig. 5). In the all-d system, the nPβ and P_IIL regions were sampled (~20 and ~35%, respectively) to a larger extent than in the all-l system (~15 and ~30%, respectively) (Fig. 5A). The increased sampling of conformations in the β quadrant was met with decreased sampling of α_R conformations in the all-d system (~10%) relative to the all-l system (~20%). Although both residues have low sampling of the α_L conformation, d-Val had an order of magnitude lower sampling of this region (0.2%) than l-Val (2.7%) (Fig. 5A). Closer inspection of the dominant helical basins for l-Val and d-Val showed that the energy landscapes spanning the α_R and Dα_R basins were asymmetric (Fig. 5). As a control, we extended the AAVAA and aavaa simulations to 900 ns (Fig. 5). The asymmetric sampling of backbone conformations was maintained in the longer simulations, demonstrating that these deviations cannot be attributed to errors in conformational sampling. Similar results were obtained for the other β-branched residues, Ile and Thr (Fig. 5).

Fig. 5.

Enantiomeric β-branched amino acid sample backbone conformations asymmetrically within chiral host peptides. (A) Ramachandran plots of the three β-branched residues within each of the four host peptides (AAXAA, aaxaa, AAxAA and aaXaa). For each plot, Ramachandran space was divided into 5° by 5° bins and each bin was colored according to the number of conformations observed in that bin over the course of the simulation. Note, plots for d-amino acids have been rotated by 180° to facilitate comparisons with l-amino acids. Sets of plots show that β-branched guest residues in stereoisomer peptides asymmetrically sample regions of Ramachandran space when placed in a chiral host system. In contrast, when the β-branched residues are placed in the achiral Gly–host system, l-Val and d-Val have symmetric sampling of Ramachandran space in agreement with our previous studies. (B) This behavior is quantitatively shown in Hinton plots for each of the β-branched guest residues. Here, each row corresponds to a single guest residue and reflects the distribution of the trajectory among each of the seven specific conformational regions (columns). The size and color of each box are proportional to the fraction of simulation time spent within that region. For the GGXGG, GGxGG, AAXAA and aaxaa plots for Val guest residues, the upper boxes correspond to 600 ns of production time and the lower boxes correspond to 900 ns of production time, marked with an asterisk.

Next, we examined the lifetimes and transition probabilities for Val. If mirror image convention extends to dynamics, then we should observe a mirroring of dynamic properties such as the probability of transition between rotamers and the lifetimes within rotamers. This was not the case, instead, the four peptides displayed system-dependent dynamics. For example, while the lifetimes for the g+ and g− rotamers were mirrored, the average lifetime of the t rotamer was significantly lower in aavaa than in AAVAA (Table III). This suggests a destabilization of the trans conformation in aavaa as the source of the breakdown in mirror image symmetry.

Table III.

The average rotameric state lifetimes for rotameric states of valine in homochiral valine enantiomeric peptides

	AAVAA	aavaa	aaVaa	AAvAA
Rotamer	Lifetime (ps)	Lifetime (ps)	Lifetime (ps)	Lifetime (ps)
g+	118 ± 161	202 ± 283	111 ± 130	181 ± 304
t	145 ± 238	23 ± 56	180 ± 241	187 ± 260
g−	259 ± 413	114 ± 144	214 ± 268	101 ± 136

Prior rotamer libraries have shown that the rotamers of the β-branched residues' rotamers have a strong dependence on the backbone conformation (Dunbrack and Karplus, 1993; Towse et al., 2016a). We analyzed the relationship between the backbone and side chain dihedrals for Val by constructing backbone Ramachandran plots when the side chain was in each of the three rotameric states (Fig. 6). We found that the trans rotamer conformation was the dominant rotamer in the α_L basin as well as in the α_R and Dα_R basins below ψ ≈ −20° and above ψ ≈ 20°, respectively (Fig. 6). Thus, asymmetry in the population of α_R and Dα_R helical structures, as well as a substantial decrease in the sampling of Dα_L conformations for d-Val, contributed to the breakdown in the mirror image symmetry for Val. Similar results were obtained for the other β-branched residues, Ile and Thr (Fig. 6).

Fig. 6.

Side chain dependent Ramachandran plots reflect backbone-dependent sampling of rotameric states for β-branched residues. Sets of three Ramachandran plots are shown for each β-branched guest residue in each of the four host peptides. For each trajectory, separate Ramachandran plots were constructed for each rotameric state of the side chain to illustrate the backbone-dependent sampling of rotameric states. Furthermore, when the β-branched guest residues are placed within a chiral host system, asymmetry in the sampling of backbone conformations (Fig. 5) results in asymmetric sampling of side chain conformations.

The modal angles supplied with rotamer libraries define the default placement of a specific rotamer in modeling applications. In the AAVAA and aavaa peptides, the modal angles were not mirrored, demonstrating further deviation from mirror image symmetry. For example, the most populated angle in the g− rotamer for AAVAA was −71°, while the most populated angle in the g+ rotamer for aavaa was 81°. Collectively, these results predict that while the configurations of the AAVAA and aavaa peptides are mirrored, their dynamics are imperfectly mirrored. Because the side chain conformation for Val is coupled with the backbone conformation, the deviations in the α_R and Dα_R basins translate to deviations in the rotamer populations. The molecular origins of this deviation remain elusive; though two possibilities present themselves. First, deviations in the solvation of the AAVAA and aavaa peptides may modulate the intrinsic conformational propensities. Second, minute steric interactions may be imperfectly mirrored in the two systems. Moreover, this effect may become more pronounced in more complex sequences than have been probed in these simple Ala-based peptides (Table IV).

Table IV.

The correlation coefficients and root-mean-squared difference calculated over randomly sampled trajectories indicates converged rotamer distributions

	AAXAA		aaxaa		aaXaa		AAxAA
Res	Ra	RMSDb	Ra	RMSDb	Ra	RMSDb	Ra	RMSDb
Arg	0.986	1.25 × 10−4	0.970	1.54 × 10−4	0.952	1.82 × 10−4	0.972	1.42 × 10−4
Asn	>0.999	3.49 × 10−3	>0.999	3.48 × 10−3	>0.999	4.63 × 10−3	>0.999	3.73 × 10−3
Asp	>0.999	3.68 × 10−3	>0.999	3.87 × 10−3	>0.999	3.85 × 10−3	>0.999	3.34 × 10−3
Ash	>0.999	3.38 × 10−3	>0.999	3.78 × 10−3	>0.999	3.55 × 10−3	>0.999	3.01 × 10−3
Cyh	>0.999	2.52 × 10−2	>0.999	2.20 × 10−2	>0.999	1.42 × 10−2	>0.999	1.84 × 10−2
Gln	0.997	6.71 × 10−4	0.996	7.41 × 10−4	0.996	7.4 × 10−4	0.996	6.83 × 10−4
Glu	0.997	7.4 × 10−4	0.996	9.81 × 10−4	0.996	8.46 × 10−4	0.997	8.09 × 10−4
Glh	0.997	6.56 × 10−4	0.996	7.07 × 10−4	0.997	6.27 × 10−4	0.997	6.26 × 10−4
Hid	0.999	3.69 × 10−3	>0.999	3.34 × 10−3	0.999	3.93 × 10−3	>0.999	3.18 × 10−3
Hie	0.999	3.57 × 10−3	0.999	3.56 × 10−3	0.999	3.67 × 10−3	>0.999	3.37 × 10−3
Hip	>0.999	4.35 × 10−3	>0.999	3.14 × 10−3	>0.999	3.54 × 10−3	>0.999	3.68 × 10−3
Ile	>0.999	3.74 × 10−3	>0.999	3.41 × 10−3	>0.999	3.55 × 10−3	>0.999	3.74 × 10−3
Leu	>0.999	3.79 × 10−3	>0.999	3.46 × 10−3	>0.999	3.03 × 10−3	>0.999	3.85 × 10−3
Lys	0.987	1.26 × 10−4	0.988	1.23 × 10−4	0.985	1.57 × 10−4	0.979	2.33 × 10−4
Met	0.996	7.95 × 10−4	0.997	6.51 × 10−4	0.997	7.34 × 10−4	0.997	7.12 × 10−4
Phe	>0.999	3.85 × 10−3	>0.999	3.72 × 10−3	0.999	3.92 × 10−3	>0.999	3.41 × 10−3
Pro	0.995	1.88 × 10−1	>0.999	6.31 × 10−2	0.945	5.5 × 10−1	0.987	2.74 × 10−1
Ser	>0.999	2.72 × 10−2	>0.999	1.43 × 10−2	>0.999	1.89 × 10−2	>0.999	2.20 × 10−2
Thr	>0.999	1.56 × 10−2	>0.999	2.34 × 10−2	>0.999	2.07 × 10−2	>0.999	1.14 × 10−2
Trp	0.979	2.27 × 10−2	0.988	1.79 × 10−2	0.979	2.27 × 10−2	0.996	1.02 × 10−2
Tyr	>0.999	3.79 × 10−3	>0.999	3.59 × 10−3	>0.999	3.51 × 10−3	>0.999	3.75 × 10−3
Val	>0.999	1.66 × 10−2	>0.999	2.33 × 10−2	>0.999	1.81 × 10−2	>0.999	1.20 × 10−2

^aPearson’s correlation coefficient, averaged over 50 iterations, comparing each 10° × 10° bins.

^bRMS difference between two sets, averaged over 50 iterations, this is average RMSD per bin (%).

Our simulations predict that at convergence (Table IV) the dynamics of several residues are incompletely described by the mirror image convention. Interestingly, the set of residues identified here include those that are known to induce the neighboring residue effect, by which a residue modulates the φ/ψ distribution of its nearest neighbors (Avbelj and Baldwin, 2004). This set also includes residues that have a strong coupling between the side chain and backbone dihedral angles (Dunbrack and Karplus; 1994; Towse et al., 2016a). Our results contribute to mounting evidence that the unique rotamer dynamics for these residues may play important roles in determining protein folding pathways, the population of heterogeneous structures by IDPs and in protein–protein interaction sites.

While many assume that mirror image symmetry must be obeyed, deviation from mirror image symmetry for the amino acids is not unheard of; indeed, several studies have reported deviations from mirror image symmetry at various levels of structural organization. The Shinitzky group showed that the l- and d-enantiomers of 24-residue polyglutamate and polylysine peptides have energetic differences in the helix–coil transition, which they attributed to solvation differences between d- and l-amino acids (Scolnik et al., 2005). X-ray crystal structures of l- and d-monellin (PDB ID: 1KRL) show several significant differences at the dimer interface, which results in a 0.91–1.02 Å main chain root-mean-square deviation (RMSD) (Hung et al., 1999). In that study the authors also found that asymmetry in the crystal structures was accompanied by asymmetric primary solvation layers around the l- and d-monellin monomers. Thus, minute deviations from mirror image symmetry present at the level of a single residue can be propagated to quaternary structure.

Expanding protein design space

Natural proteins are not restricted to the 20 proteinogenic amino acids coded for by DNA. Both prokaryotes and eukaryotes can incorporate non-canonical amino acids, including selenocysteine via a SECIS (selenocysteine insertion sequence) element (Su et al., 2005) and some methanogenic prokaryotes can incorporate pyrrolysine (Borrel et al., 2014). In total, over 140 amino acids have been observed in natural proteins (Ambrogelly et al., 2007) and over 50 non-natural amino acids have been engineered into proteins (Young and Schultz, 2010). Thus, d-amino acids represent only one class of non-standard amino acids that can be used in protein design. A thorough description of the structural and dynamical features of these amino acids is necessary before their routine incorporation into designs. Our approach shows that MD simulations of simple systems can yield predictions for conformational propensities as well as insights into the dynamics that contribute to the stabilization of specific conformations. We have shown that intrinsic conformational propensities are sensitive to structural context and that it is not always possible to simply map conformational propensities from one amino acid to a homologous residue. Our group is committed to an exploration of intrinsic structural propensities and we regularly update our Structural Library of Intrinsic Residue Preferences (SLIRP) (publically available at www.dynameomics.org), which is comprised of intrinsic backbone and side chain propensities as well as conformational behaviors of short fragments of protein structure (Beck et al., 2008b; Scouras and Daggett, 2011; Rysavy et al., 2014; Towse et al., 2014, 2016a,b; Childers et al., 2016).

Conclusions

The relatively few instances of non-standard amino acids in high-resolution protein structures precludes the generation of empirical data sets to define heuristic rules for protein design with these residues. However, computational methods can be employed to obtain conformational propensities for non-standard amino acids. Here, we have systematically studied the impact of backbone chirality on intrinsic rotamer distributions for l- and d-amino acids. In the studies presented here, the rotamer propensities of d-amino acids did not always mirror those of l-amino acids, although the mirror image convention was upheld for most residues. Deviation from symmetry in the propensities was most prominent for the β-branched residues. In some cases, the preferred d-amino acid side chain conformations exhibited sensitivity to the chirality of neighboring residues, highlighting that chain configuration is one of the many cumulative factors contributing to the observed conformational preferences. We anticipate that future protein design efforts in which both d- and l-amino acids are used will benefit from our libraries, which consider the impact of chain and residue chirality on rotamer distributions.

Funding

This work was supported by the National Institutes of Health (GMS R01 95808 to V.D. and the Bioengineering Cardiovascular Training Grant, NIH/NIBIB T32EB1650 to M.C.C.), and the Amyloidosis Foundation (to C-L.T). We thank the National Energy Research Scientific Computing Center, supported by the DOE Office of Biological Research, which is supported by the U.S. Department of Energy under contract number DE-AC02-05CH11231, for providing computing time. This work also used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562.