For some combinations of parameters we found that the trajectories were unstable: integration errors due to the finite time step would accrue and compound catastrophically, as is common in molecular dynamics simulations that are performed with a step size that is too high for a particular energy landscape and temperature. The two biggest drivers of instability were the frequency of assignment updates and the strength of the second-order distance restraints. This is intuitive, as the assignment algorithm used here only takes into account the similarity of the atomic environment vectors between the ghost particles and the target atoms. Changes in the assignments could thus introduce discontinuities in the energy and energy gradients that are destabilizing. To minimize the impact of these assignment changes, we recommend that assignment updates are carried out relatively infrequently; we found 5000 steps to be a suitable interval for assignment updates.