Note that if there were other non-ghost particles in the system (e.g. water molecules, proteins or other solutes), then additional non-bonded forces would be required that take into account the dynamical attributes ({σ i }, {ε i }, {q i }). While these are not included in the work presented here, examples that implement these interactions are the subject of future work and are already available to the reader in the Flexible Topology repository. The dynamics of both the positions and the attributes are propagated by a custom OpenMM integrator. The source code for the integrator (CustomHybridIntegratorConstCharge) is given in the Flexible Topology code repository (src/flexibletopology/utils/integrators.py).