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Biological and biophysical processes of a varying range of complexity occur on timescales ranging from picoseconds to milliseconds. The advent of high-performance computing simulations has greatly aided our understanding of such biological processes at the atomistic level, but these simulations are still limited in the timescales that can be sampled. For this reason, a great deal of work has gone into developing new methodologies, as well as novel approaches applied to pre-existing methods, in order to accelerate timescales and improve the agreement of key biophysical estimates from simulation with experimental data. In this thesis, a range of simulation strategies are used to obtain novel insights into three key biophysical problems whose timescales require careful consideration, ion conduction, drug binding, and gas transport. In doing so, I demonstrate the use of unbiased molecular dynamics in combination with enhanced sampling methods, metadynamics, constant force steered molecular dynamics and adaptive biasing force simulations, together with ab initio QM/MM mechanical calculations, for investigating these problems. The outcomes of this work yielded, for the first time, a quantitative estimate of the potential of mean force of ion conduction in a new family of ion channels, the transient receptor potential (TRP). Using bias-exchange metadynamics, monovalent ion conduction was studied in the vanilloid-1 (TRPV1) ion channel. This channel is shown to be non-selective for monovalent ions (sodium and potassium). This result has ramifications to understanding the gating of this channel, and therefore, the central role of this channel in the human pain sensing mechanism. Secondly, the question of drug-modulated activation and inactivation of membrane proteins was addressed by simulating the binding of volatile general anaesthetics to the TRP ion channel family and psoralen drugs in the potassium channel family. It was found that a multi-site binding model best describes the activation of the TRPV1 ion channel by anaesthetics, while a two-site binding model of the psoralen family onto the voltage-gated potassium ion channels (Kv) was found. The investigation of drug-binding mechanisms was extended to drug-access pathways in the potassium channels, using three sub-families, the voltage-gated, inwardrectifiers and the cardiac two-pore domain potassium ion channels. This revealed atomistic evidence that the cardiac two-pore domain (K2P) ion channels are druggable via lateral fenestrations, which is a novel insight into two-pore domain druggability for heart-related diseases. Finally, the question of gas transport in the family of 2-oxoglutarate-dependent oxygenases, which sense oxygen and are related in the human oxygen sensing cycle is addressed. A novel set of simulations shed light on the gas-access pathways in oxygenases, and a kinetic study is undertaken to estimate the rate of gas turnover in these globular proteins, which is compared to experimental estimates. The output of the work of this thesis is a set of simulations and measurable quantities, including free-energies and transport properties, that can be correlated to experimentally measurable properties, and in doing so provide unique molecular insight into these systems of biophysical and pharmacological importance.