Molecular simulations of enzymatic phosphorylation of disordered proteins and their condensates

Understanding the condensation and aggregation of intrinsically disordered proteins in a non-equilibrium environment is crucial for unraveling many biological processes. Active enzymes catalyse many processes by consuming chemical fuels such as ATP. Enzymes called kinases phosphorylate disordered regions of proteins and thus profoundly affect their properties and interactions. Protein phosphorylation is implicated in neurodegenerative diseases and may modulate pathogenesis. However, how protein sequence and molecular recognition of a disordered protein by kinases determine phosphorylation patterns is not understood. In principle, molecular dynamics simulations hold the promise to resolve how phosphorylation affects disordered proteins and their assemblies. In practice, chemically-detailed simulations of enzymatic reactions and the dynamics of enzymes are highly challenging, in particular it is difficult to verify whether implementations of driven simulations are thermodynamically consistent. We can now address this problem with residue-level coarse-grained molecular dynamics simulations, integrating Metropolis Monte Carlo steps to model chemical reactions. Importantly, we show how to verify by Markov-state modeling that the realisation of a non-equilibrium steady state satisfies local-detailed balance. We investigate TDP-43 phosphorylation by the kinase CK1δ in simulations, examining patterns of phosphorylation and assessing its preventive role in chain aggregation, which may be a cytoprotective mechanism in neurodegenerative diseases. We find that the degree of residue phosphorylation is determined by sequence preference and charges, rather than by the position in the chain. The phosphorylation frequency is also affected by the phosphorylation patterns, since the interactions between CK1δ and TDP-43 actively change after each reaction. For TDP-43, our simulations show condensates dissolution through phosphorylation with kinases binding to the condensates and phosphorylating TDP-43 in the condensates.