Interfacial Dynamics and Growth Modes of β2-Microglobulin Dimers

Abstract

Protein aggregation is a complex process, strongly dependent on environmental conditions and highly structurally heterogeneous, both at the final level of fibril structure and intermediate level of oligomerization. Since the first step in aggregation is the formation of a dimer, it is important to clarify how certain properties of the latter (e.g., stability or interface geometry) may play a role in self-association. Here, we report a simple model that represents the dimer's interfacial region by two angles and combine it with a simple computational method to investigate how modulations of the interfacial region occurring on the ns-μs time scale change the dimer's growth mode. To illustrate the proposed methodology, we consider 15 different dimer configurations of the β₂m D76N mutant protein equilibrated with long Molecular Dynamics simulations and identify which interfaces lead to limited and unlimited growth modes, having, therefore, different aggregation profiles. We found that despite the highly dynamic nature of the starting configurations, most polymeric growth modes tend to be conserved within the studied time scale. The proposed methodology performs remarkably well taking into consideration the nonspherical morphology of the β₂m dimers, which exhibit unstructured termini detached from the protein's core, and the relatively weak binding affinities of their interfaces, which are stabilized by nonspecific apolar interactions. The proposed methodology is general and can be applied to any protein for which a dimer structure has been experimentally determined or computationally predicted.

Figure 1

Three-dimensional cartoon representation of the native structure of D76N (pdb id: 2YXF) (A) and the I₂ intermediate state populated by D76N, which features a well-preserved core and two unstructured and decoupled termini (B). The I₂ structure still retains a conserved structural core that corresponds to residues 23–27 (in strand B), 36–39 (in strand C), 51–55 (in strand D), 62–66 (in strand E), and 78–82 (in strand F). Data are from refs (30) and (33).

Figure 2

A simple protocol for dimer duplication and polymeric growth. To generate a polymerized chain of dimers, we consider a starting dimer conformation formed by monomers A and B. We subsequently create a duplicate dimer conformation where monomers A and B are respectively renamed A′ and B′. Finally, we use PyMOL to structurally align monomer A′ from the duplicate dimer with monomer B of the preceding dimer and repeat this operation a desired number of times.

Figure 3

Schematics of points and vectors (A) used in the calculation of the polymerization angle, θ_pol (B), and dihedral, ϕ_pol (C). Monomer A and its geometric center are respectively represented by a large yellow sphere and a small yellow sphere each with a red contour, while monomer B and its geometric center are respectively represented by a large cyan sphere and a small cyan sphere each with a blue contour. The geometric center of the contact interfaces of monomers A and B is represented by small spheres with orange and green contours, respectively, while the projection of their interfaces on the opposing monomer is represented as small spheres with a dotted contour colored orange and green, respectively. On the polymerization dihedral, red arrows represent the vectors used to calculate the normal vector P⃗_A, and the blue arrows represent the vectors used to calculate the normal vector P⃗_B.

Figure 4

(A) Sphere model for a polymerized chain corresponding to an interface with θ_pol = 81° and ϕ_pol = 160°. The original monomer A and monomer B are represented in white and black, respectively, and the consecutively added monomers follow the colors light-blue, blue, light-green, green, light-orange, orange, red, and pink. (B) Three dimensional representation of a polymerized chain of a β₂m dimer with the same interfacial angles (BM-3, replicate 2). A representation of the side and top views of the monomer is given side by side.

Figure 5

Growth landscape as a function of the θ_pol angle and ϕ_pol dihedral angle. The black dots represent the upper limit of angle/dihedral combinations that yield a limited growth polymer as predicted by the simple model. The orange region represents the region where polymer growth is limited, the yellow color represents the uncertain region (one that requires visual inspection), and the region in white represents the unlimited growth.

Figure 6

Pearson correlation coefficient between the average binding energy values of the long MD simulations and the short relaxation MD. The data of the 15 dimer set was used. The binding energies of the long MD equilibration replicates were averaged in intervals of 10 ns to show the correlation time evolution.

Figure 7

Examples of the different β₂m dimer growth modes identified in our study. Each represented growth mode consists of 32 monomers. The BMs selected to illustrate the helical (U_hel), linear (U_lin), head-to-head (L_h2h), and doughnut (L_don) growth modes were BM-4 (R1), BM-3 (R1), BM-6 (R2), and H-1 (R2), respectively.

Figure 8

Growth landscape of BM-3 (A), 2 (B), and 9 (C). The black, blue, and red dots represent the ensemble of 250 dimer conformations extracted from the equilibrated part of replicates 1, 2, and 3, respectively. The structure closer to the average θ_pol and ϕ_pol values of each replicate is shown in the corresponding color tone (gray, cyan, and dark red). These are the structures used to generate the polymerization modes represented on the right-hand side of each growth landscape. The green triangle represents the starting structure obtained from the initial MD relaxation step.