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Physics-driven coarse-grained model for biomolecular phase separation with near-quantitative accuracy


Various physics- and data-driven sequence-dependent protein coarse-grained models have been developed to study biomolecular phase separation and elucidate the dominant physicochemical driving forces. Here we present Mpipi, a multiscale coarse-grained model that describes almost quantitatively the change in protein critical temperatures as a function of amino acid sequence. The model is parameterized from both atomistic simulations and bioinformatics data and accounts for the dominant role of ππ and hybrid cation–π/ππ interactions and the much stronger attractive contacts established by arginines than lysines. We provide a comprehensive set of benchmarks for Mpipi and seven other residue-level coarse-grained models against experimental radii of gyration and quantitative in vitro phase diagrams, demonstrating that Mpipi predictions agree well with experiments on both fronts. Moreover, Mpipi can account for protein–RNA interactions, correctly predicts the multiphase behavior of a charge-matched poly-arginine/poly-lysine/RNA system, and recapitulates experimental liquid–liquid phase separation trends for sequence mutations on FUS, DDX4 and LAF-1 proteins.

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Fig. 1: Designing a coarse-grained model for LLPS from PMF calculations and bioinformatics data.
Fig. 2: Obtaining the correct balance of ππ and non-π-based interactions in the Mpipi model.
Fig. 3: Relative contributions of ππ, cation–π and non-π-based interactions in different residue-level models.
Fig. 4: Comparison of single-molecule radii of gyration with experiment.
Fig. 5: Recapitulating the phase behavior of A1-LCD variants.
Fig. 6: Predicting the LLPS propensities of other proteins and multiphasic compartmentalization.

Data availability

All relevant supporting data are available in the figshare data repository at The data for this study were generated with the simulation codes and algorithms outlined in Supplementary Table 14, using the supporting code70, alongside standard command-line tools. Source data are provided with this paper.

Code availability

LAMMPS input scripts and parameter files are available in the figshare data repository at


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We thank D. Frenkel for useful comments on the manuscript, J. Mittal and G. L. Dignon for helping us implement the HPS-KR potential in LAMMPS and G. Tesei and K. Lindorff-Larsen for helping us debug our implementation of their potential. This project has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant no. 803326; R.C.-G.). J.A.J. is a Junior Research Fellow at King’s College. R.C.-G. is an Advanced Fellow of the Winton Programme for the Physics of Sustainability. J.R.E. acknowledges funding from the Oppenheimer Fellowship of the University of Cambridge and the Roger Ekins Fellowship from Emmanuel College. A.G. is funded by the EPSRC (Doctoral Training Partnership, grant no. EP/N509620/1) and the Winton Programme for the Physics of Sustainability. P.Y.C. is funded by the University of Cambridge Ernest Oppenheimer Fund and the Winton Programme for the Physics of Sustainability. K.O.R. is funded by the EPSRC (Doctoral Training Partnership, grant no. EP/T517847/1). This work was performed using resources provided by the Cambridge Tier-2 system operated by the University of Cambridge Research Computing Service funded by EPSRC Tier-2 capital grant no. EP/P020259/1 (R.C.-G., J.A.J. and A.R.). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

Author information




J.A.J. and R.C.-G. conceived the project. J.A.J., A.R. and R.C.-G. designed the model and benchmarking framework. J.A.J. and A.R. implemented and optimized the model. J.A.J., A.R., A.A., P.Y.C., K.O.R., J.R.E. and A.G. validated the model and analyzed the data. J.A.J. and A.R. wrote the manuscript with help from R.C.-G. All authors reviewed the manuscript. J.A.J., A.R. and R.C.-G. acquired funding. J.A.J., A.R. and R.C.-G. supervised the research.

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Correspondence to Jerelle A. Joseph, Aleks Reinhardt or Rosana Collepardo-Guevara.

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Peer review information Nature Computational Science thanks Hue Sun Chan and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available. Handling editor: Jie Pan, in collaboration with the Nature Computational Science team.

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Supplementary information

Supplementary Information

Supplementary Discussion, including amino acid listings, Figs. 1–10 and Tables 1–13.

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Joseph, J.A., Reinhardt, A., Aguirre, A. et al. Physics-driven coarse-grained model for biomolecular phase separation with near-quantitative accuracy. Nat Comput Sci 1, 732–743 (2021).

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