Multiparticle collision dynamics simulations of the flagellar apparatus in <i>Chlamydomonas reinhardtii</i>

Using multiparticle collision dynamics simulations, we investigate the swimming dynamics, orientational behavior, and hydrodynamic interactions of a model swimmer designed to mimic the isolated flagellar apparatus (FA) of Chlamydomonas reinhardtii. We represent the FA as a chain of monomers connected by elastic springs, with two traveling waves originating at its center and propagating in opposite directions along the chain. Our simulations show that an FA whose beat pattern has non-zero mean curvature sustains ballistic motion for several hundred beats before transitioning to a diffusion-dominated regime via rotational diffusion. In contrast, a flagellar apparatus with zero mean curvature FA0—generates mirror-symmetric deformations and fails to achieve net propulsion. Both the active FA and FA0 exhibit orientational autocorrelation functions that decay exponentially—matching those of their inactive counterparts—indicating that active beating does not influence the FA's rotational diffusion. Driving the two flagellar arms at different frequencies reproduces the epitrochoid-like trajectory observed experimentally. Finally, hydrodynamic interactions between two FAs give rise to co-moving bound pairs in either parallel or antiparallel configurations, with their stability governed by the phase difference of the curvature waves. Together, our results establish a versatile model microswimmer with tunable dynamics—offering a blueprint for the rational design of artificial, flagella-driven microswimmers.