Computational and theoretical advances in studies of intrinsically disordered proteins

•Improvements in all-atom simulations and implicit solvent models now allow IDP simulations with realistic dimensions to be performed.•Native-centric coarse-grained simulations are useful for studying coupled folding-binding.•Mesoscale coarse-graining allows IDP phase transitions to be addressed.•Development of new theory will assist in relating the properties and phase behavior of IDPs to their sequences.•Different types of models are needed to cover all the time and length scales relevant to IDPs

Intrinsically disordered proteins (IDPs) are increasingly realized to play diverse biological roles, ranging from molecular signaling to the formation of membraneless organelles. Their high degree of disorder makes them more challenging to study using the techniques of conventional structural biology, because any observable will be averaged over a heterogeneous ensemble of structures. Molecular simulations and theory are therefore a natural complement to experiment for studying the structure, dynamics and function of IDPs. The diverse time and length scales relevant to the roles played by IDPs require flexibility in the techniques applied. Here, I summarize some of the developments in simulation and theory in recent years, which have been driven by the desire to better capture IDP properties at different time- and length-scales. I also provide an outlook for how methods can be improved in the future and emerging problems which may be addressed by theory and simulation.