Modeling Fibrillogenesis of Collagen-Mimetic Molecules

Abstract

One of the most robust examples of self-assembly in living organisms is the formation of collagen architectures. Collagen type I molecules are a crucial component of the extracellular matrix, where they self-assemble into fibrils of well-defined axial striped patterns. This striped fibrillar pattern is preserved across the animal kingdom and is important for the determination of cell phenotype, cell adhesion, and tissue regulation and signaling. The understanding of the physical processes that determine such a robust morphology of self-assembled collagen fibrils is currently almost completely missing. Here, we develop a minimal coarse-grained computational model to identify the physical principles of the assembly of collagen-mimetic molecules. We find that screened electrostatic interactions can drive the formation of collagen-like filaments of well-defined striped morphologies. The fibril axial pattern is determined solely by the distribution of charges on the molecule and is robust to the changes in protein concentration, monomer rigidity, and environmental conditions. We show that the striped fibrillar pattern cannot be easily predicted from the interactions between two monomers but is an emergent result of multibody interactions. Our results can help address collagen remodeling in diseases and aging and guide the design of collagen scaffolds for biotechnological applications.

Figure 1

Modeling collagen fibrillogenesis. (A) Collagen type I molecules self-assemble into fibrils of a characteristic pattern with gap and overlap regions, termed D-periodicity. Here, we show just 10 molecules per fibril diameter for illustration. (B) A single collagen-mimetic molecule simulated here consists of 36 beads with a charge distribution as indicated (positive charges are colored in pink and negative charges are colored in purple), resembling the one of D-mimetic synthetic peptide (7). (C) Simulation snapshots are given, showing the dynamic self-assembly of such molecules into periodic fibrils for isotropic attraction ε = 0.05 kT, electrostatic interaction A = 10 kT σ, monomer rigidity k_angle = 50 kT, and molecule concentration c_mol = 0.001 σ⁻³. (D) A phase diagram is given of fibrillogenesis as a function of the strength of electrostatic interactions A and the isotropic attraction ε for monomer rigidity k_angle = 100 kT and molecule concentration c_mol = 0.001 σ⁻³. Periodic fibrils are only formed when the electrostatic interactions dominate, whereas otherwise, isolated clusters are formed. The transition between the two phases is not sharp, and the indicated border and coloring are a guide to the eye. For more details on the aggregate structures in each phase, see Fig. S1. (E) To analyze the periodicity of the fibrils, the local density along the fibril backbone (indicated with a yellow line) is measured. The periodicity is defined as the mean distance between peaks of the density profile. To see this figure in color, go online.

Figure 2

Analyzing fibril periodicity. (A) Distribution of periodicity p is shown, scaled by the molecule length l for fibrils that are formed by isotropic attraction ϵ = 0.05 kT, electrostatic interaction A = 10 kT σ, monomer rigidity κ_angle = 50 kT, and molecule concentration c_mol = 0.001 σ⁻³. (B) Scaled fibril periodicity is shown as a function of time t for ϵ = 0.05 kT, A = 10 kT σ, κ_angle = 50 kT, and c_mol = 0.001 σ⁻³. (C) Scaled fibril periodicity is shown as a function of the isotropic attraction ϵ for A = 10 kT σ, κ_angle = 50 kT, and c_mol = 0.001 σ⁻³. (D) Scaled fibril periodicity is shown as a function of the strength of the electrostatic interaction A for ϵ = 0.05 kT, κ_angle = 50 kT, and c_mol = 0.001 σ⁻³. (E) Scaled fibril periodicity is shown as a function of the monomer rigidity κ_angle for ϵ = 0.05 kT, A = 10 kT σ, and c_mol = 0.001 σ⁻³. (F) Scaled fibril periodicity is shown as a function of the molecule concentration c_mol for ε = 0.05 kT, A = 10 kT σ, and κ_angle = 50 kT. The error bars in all the plots represent the standard deviation. To see this figure in color, go online.

Figure 3

Analytical model for determining fibril formation and fibril morphologies. (A) A schematic figure of the analytical model developed to predict the impact of the single-molecule charge distribution on the fibril periodicity is given. For that purpose, the energy of the focus molecule (in the potential field that is created by its surrounding molecules found in a minimal two-stranded fibril) is measured and minimized as a function of the three geometrical parameters offset, radial gap, and lateral gap. (B) For the charge distribution of the D-mimetic molecule, either D-periodic or non-D-periodic configurations are found. The periodicity is defined as the sum of one gap and one overlap region. (C) Value of radial gap that minimizes the energy of the system as a function of the strength of the electrostatic interactions A and isotropic attraction ε is given. The radial gap determines whether a fibril is D-periodic (radial gap > 1.12 σ) or not (radial gap < 1.12 σ). (D) Value of offset that minimizes the energy of the focus molecule as a function of electrostatic interaction A and isotropic attraction ε is given. (E) Periodicity of D-mimetic fibrils predicted by the analytical model as a function of the electrostatic interactions A and isotropic attraction ε is shown. Remarkably, the periodicity does not substantially change throughout the phase space. To see this figure in color, go online.

Figure 4

Connecting molecular design to the fibril morphologies. (A) Different distributions of charges decorating single molecules for which we analyzed the fibril periodicity are shown. (B) Periodic fibril configurations predicted by the analytical model for the diverse charge distributions shown in (A) are given. (C) Corresponding MD simulations, exemplary shown for the molecules S3 and A1, show D-periodic fibril structures that are remarkably similar to the ones predicted by the analytical model as shown in (B). (D) The periodicity p and molecule length l predicted by the analytical model for the different charge distributions that are shown in (A) are given. The error bars indicate the maximal range of periodicities that are measured. To see this figure in color, go online.