Computer Simulation of a Possible Magic Number Effect in the Phase Transition of the Eukaryotic Photosynthetic Organelle, the Pyrenoid

In most eukaryotic algae, an organelle called the pyrenoid helps concentrate CO₂ to enhance carbon fixation. We recently found that in Chlamydomonas reinhardtii, pyrenoid has liquid-like behavior including rapid condensation and dissolution during cell division. Our data suggests that the matrix is primarily composed of Rubisco and a linker protein, EPYC1. Rubisco and EPYC1 each have multiple binding sites for the other, allowing the two proteins to form a highly interconnected matrix. We now seek to understand the biophysical principles that allow the system to undergo phase transition to a state where the Rubisco and EPYC1 dissolve into the surrounding chloroplast. Here, we apply the Monte Carlo method to simulate the binding of EPYC1 and Rubisco on a 2D lattice. We find that specific numbers of Rubisco binding sites on EPYC1 promote dissolution, which we call a “magic number” effect. We explore different parameter regimes and find that the magic number effect is robust to Rubisco shape and valency. Our theoretical results provide guidance for the reconstitution of phase-separated liquid droplets from purified EPYC1 and Rubisco proteins in vitro. More broadly, our work reveals fundamental principles that may have widespread relevance to multivalent polymer systems in biology.