  A wide variety of biological phenomena can be modeled by the collective
activity of a population of individual units. A common strategy for simulating
such a system, the population density approach, is to take the macroscopic
limit and update its population density function. However, in many cases, the
coupling between the units and noise gives rise to complex behaviors
challenging to existing population density approach methods. To address these
challenges, we develop the asymmetric particle population density (APPD) method
that efficiently and accurately simulates such populations consist of coupled
elements. The APPD is well-suited for a parallel implementation. We compare the
performance of the method against direct Monte-Carlo simulation and verify its
accuracy by applying it to the well-studied Hodgkin-Huxley model, with a range
of challenging scenarios. We find that our method can accurately reproduce
complex macroscopic behaviors such as inhibitory coupling-induced clustering
and noise-induced firing while being faster than the direct simulation.
