Fractal-like Self-Assembly in Citrate Synthase: Delineating Growth Patterns with Coarse-Grained Simulations

Fractals are complex, repeating, and infinitely self-similar patterns. While natural fractals such as snowflakes, coastlines, and other shapes have been reported, emergent work shows that fractal growth may underlie biomolecular self-assembly. However, biomolecular fractals have been observed to be of limited range and, owing to physical realities, prone to exhibiting imperfections. We herein explore Sierpiski fractal-like self-assembly of citrate synthase, a fractal captured recently with cryo-electron microscopy experiments. We first atomistically remodel the basic unit of growth, the initial dimer, and further investigate the geometric, energetic, and dynamical principles underlying the hierarchical self-assembly of citrate synthase oligomers. Using coarse-grained molecular dynamics and subsequent analyses, we quantify deviations from ideal fractality and fluctuations with an increasing fractal level. We analyze solvent-accessible regions lacking amino acid occupancy to characterize the hallmark void of the Sierpiski fractal architecture using a custom algorithm. Since fractals exhibit scaling, we uncover the underlying power law exponents of the structural and thermodynamic signatures of growth. This work provides a framework to understand how hierarchical assembly, structural fluctuations, and scaling behavior contribute to the stability of protein fractal architectures and lend insights into plausible factors that limit higher ordered fractal growth in biomolecular systems.