Recent advances in the spectroscopy of biomolecules have highlighted the possibility of quantum coherence playing an active role in biological energy transport. The revelation that quantum coherence can survive in the hot and wet environment of biology has generated a lively debate across both the physics and biology communities. In particular, it remains unclear to what extent non-trivial quantum effects are used in biology and what advantage, if any, they afford. We propose an analogue quantum simulator, based on currently available techniques in ultra-cold atom physics, to study a model of energy and electron transport based on the Holstein Hamiltonian. By simulating the salient aspects of a biological system in a tunable laboratory set-up, we hope to gain insight into the validity of several theoretical models of biological quantum transport in a variety of relevant parameter regimes.