A λ-Dynamics Investigation of Insulin Wakayama and Other A3 Variant Binding Affinities to the Insulin Receptor

Abstract

Insulin Wakayama is a clinical insulin variant where a conserved valine at the third residue on insulin's A chain (Val^A3) is replaced with a leucine (Leu^A3), weakening insulin receptor (IR) binding by 140-500-fold. This severe impact on binding from a subtle modification has posed an intriguing problem for decades. Although experimental investigations of natural and unnatural A3 mutations have highlighted the sensitivity of insulin-IR binding at this site, atomistic explanations of these binding trends have remained elusive. We investigate this problem computationally using λ-dynamics free energy calculations to model structural changes in response to perturbations of the Val^A3 side chain and to calculate associated relative changes in binding free energy (ΔΔG_bind). The Wakayama Leu^A3 mutation and seven other A3 substitutions were studied in this work. The calculated ΔΔG_bind results showed high agreement compared to experimental binding potencies with a Pearson correlation of 0.88 and a mean unsigned error of 0.68 kcal/mol. Extensive structural analyses of λ-dynamics trajectories revealed that critical interactions were disrupted between insulin and the insulin receptor as a result of the A3 mutations. This investigation also quantifies the effect that adding an A3 C_δ atom or losing an A3 C_γ atom has on insulin's binding affinity to the IR. Thus, λ-dynamics was able to successfully model the effects of mutations to insulin's A3 side chain on its protein-protein interactions with the IR and shed new light on a decades-old mystery: the exquisite sensitivity of hormone-receptor binding to a subtle modification of an invariant insulin residue.

Figure 1

Fully bound insulin–insulin receptor ectodomain (PDBID: 6PXV). The two IR homodimers are shown in green and cyan. Insulins are bound at IR sites 1 and 2, shown in dark blue and red, respectively.

Figure 2

Thermodynamic cycle used to compute relative binding free energies (ΔΔG_bind) of a protein–protein complex, when one protein (P1) is mutated into a new sequence state (P1′).

Figure 3

Correlation between experimental and λD calculated relative binding free energies for eight insulin A3 variants bound to the IR, relative to native insulin Val^A3. Computed results were obtained over three calculation sets (Set 1 in blue, Set 2 in orange, and Set 3 in green). Ideal y = x agreement between calculated and experimental ΔΔG_bind results is represented by a solid black line; ΔΔG_bind errors within ±0.5 kcal/mol and ±1.0 kcal/mol are represented by darker and lighter gray bands, respectively. Linear regression lines are represented as color coded dashed lines.

Figure 4

One-dimensional χ₁ dihedral angle distribution plots of insulin A3 variants: Val (A), Abu (B), Thr (C), and Tle (D). Each plot is divided into conformational groups of 120° and are labeled as gauche plus (60°, g⁺), trans (180°, t), and gauche minus (300°, g^–). Group populations are labeled if it contains 20% or more frames. Val^A3 frames were combined from Sets 1–3. Each distribution plot is normalized with respect to the maximum density.

Figure 5

Two-dimensional χ₁, χ₂ dihedral angle distribution plots of insulin A3 variants: Leu (A), Ile (B), Ail (C), and Nva (D). Each plot is divided into conformational groups of 120° per χ angle and are labeled as gauche plus (60°, g⁺), trans (180°, t), and gauche minus (300°, g^–), with the χ₁ label listed first. Group populations are labeled if it contains 20% or more frames. Leu^A3 frames were combined from Sets 1–3. Each distribution plot is normalized with respect to the maximum density.

Figure 6

Representative frames for insulin A3 variant primary clusters: Val (A), Leu (B), Ail (C), Ile (D), Tle (E), Ala (F), Abu (G), Nva (H), Thr (I). A3 side chains are shown as stick representations, extending from insulin’s A-chain terminal helix. Side chain heavy atom probability densities are represented on a rainbow color scale from lower probability density (blue) to higher probability density (red).

Figure 7

(A) Insulin bound at IR site 1. The black box shows the section and perspective of these images. In panels B–L, the αCT peptide is hidden to allow full view of all A3 side chains. (B–L) Representative frames of insulin A3 variant primary (1°) and secondary (2°) clusters aligned with Val^A3’s C_γ2 probability density. Probability density is represented on a rainbow color scale from lower (blue) to higher (red) density.

Figure 8

Insulin A^Nter and Asn711 distance and dihedral measurements for insulin A3 variant primary clusters. All violin plots are normalized to have the same area; solid lines represent median values, and dashed lines show the interquartile range. (A) Structural depiction of three distance and two dihedral measurements in the insulin–IR complex. Insulin Glu^A4’s χ₂ is highlighted in cyan. IR Asn711’s χ₁ is highlighted in pink. Distances are shown as colored dashed lines. (B) IR Asn711 C_α–insulin A3 N atom distance (d₁). The red line shows Val^A3’s median value. (C) Insulin Glu^A4 χ₂. The gray bar shows the dihedral window that facilitates hydrogen bonding between Asn711 and Glu^A4 residues. (D) IR Asn711 χ₁. The gray bar shows the dihedral window that facilitates hydrogen bonding to insulin A4 or A3 residues. (E) IR Asn711 N_δ–insulin Glu^A4 O_ε distance (d₂). The gray bar highlights distances below 3.4 Å. (F) IR Asn711 O_δ–insulin A3 N distance (d₃). The gray bar highlights distances below 3.4 Å.