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Investigations on microorganism locomotion in complex fluids are important in understanding a variety of biological phenomena. It is observed in experiments recently that as the fluid rheology is changed, Chlamydomonas reinhardtii exhibits changes in both flagellar kinematics and the swimming speed. In order to understand the effects of rheology on both gait and swimming performance, we develop a computational model of the swimmer. We use flagellar strokes fit from experimental data to set up a constrained system, determining the forces on the swimmer and its swimming velocity. We discover that stroke patterns are the dominant factor for changing swimming speeds, and stroke patterns observed in viscoelastic fluids generate much lower stress at the cost of lower swimming speed. Joint work with Bob Guy and Becca Thomases.