Here, we used the mechanics of rigid bodies to develop an optimization strategy for constraint molecular topologies to achieve quicker constraint convergence with the LINCS algorithm. We did not consider alternative ways of solving the constraint equations or other numerical methods to invert the matrix I -A n in LINCS. In the optimization of the constraint topology, we minimized the largest absolute value of the eigenvalues of the A n matrix, λ max . We also provide a python script to rapidly evaluate the quality of the constraint topology in terms of λ max (available at coupling-analysis). We demonstrate the optimization strategy for the Martini 2 cholesterol model. By fully preserving the force field and the dynamics in the limit of infinitesimal time We further investigated the magnitude of the artifacts and their impact on cholesterolprotein interactions using a membrane embedded β 2 -adrenergic receptor. Whereas the temperature of the original cholesterol model deviated significantly from the target temperature of the thermostat at larger time steps, there were no significant differences observed when using the optimized model. For MD simulations of membrane proteins with the optimized cholesterol model, we recommend the combined use of at least lincs order= 6 with at most a 30 fs time step.