pubmed.ncbi.nlm.nih.gov

Small ion effects on self-coacervation phenomena in block polyampholytes - PubMed

  • ️Tue Jan 01 2019

Small ion effects on self-coacervation phenomena in block polyampholytes

Scott P O Danielsen et al. J Chem Phys. 2019.

Abstract

Self-coacervation is a phenomenon in which a solution of polyampholytes spontaneously phase separates into a dense liquid coacervate phase, rich in the polyampholyte, coexisting with a dilute supernatant phase. Such coacervation results in the formation of membraneless organelles in vivo and has further been applied industrially as synthetic encapsulants and coatings. It has been suggested that coacervation is primarily driven by the entropy gain from releasing counter-ions upon complexation. Using fully fluctuating field-theoretic simulations employing complex Langevin sampling and complementary molecular dynamics simulations, we have determined that the small ions contribute only weakly to the self-coacervation behavior of charge-symmetric block polyampholytes in solution. Salt partitioning between the supernatant and coacervate is also found to be negligible in the weak-binding regime at low electrostatic strengths. Asymmetries in charge distribution along the polyampholytes can cause net-charges that lead to "tadpole" configurations in dilute solution and the suppression of phase separation at low salt content. The field and particle-based simulation results are compared with analytical predictions from the random phase approximation (RPA) and postulated scaling relationships. The qualitative trends are mostly captured by the RPA, but the approximation fails at low concentration.

PubMed Disclaimer

Figures

FIG. 1.
FIG. 1.

Schematic of the Gibbs ensemble. The volume is partitioned into two simulation cells corresponding to a dense and a dilute phase. Particle concentrations are exchanged to achieve chemical equilibrium and phase volumes are exchanged to achieve mechanical equilibrium.

FIG. 2.
FIG. 2.

Convergence of Gibbs ensemble calculations for the phase coexistence binodal curves (lB/b = 0.13, v/b3 = 0.0068, a/b = 0.8) to prior results (red dashed lines) for the diblock polyampholyte at different numbers of FTS-CL time steps per Gibbs step (symbols and connecting solid lines). Inset: expansion of the high density region to show the narrowing of error bars at different block averaging conditions.

FIG. 3.
FIG. 3.

Phase diagram showing the relatively weak effects of including explicit counter-ions on the phase diagram of a diblock polyampholyte (A50C50). Symbols are binodal points obtained from FTS-CL and lines are RPA predictions. The Gaussian smearing width is set at a/b = 0.8 and the excluded-volume parameter at v/b3 = 0.0068.

FIG. 4.
FIG. 4.

Total-density structure factor, Sn(k), and charge-weighted structure factor, Se(k), of the diblock polyampholyte (A50C50) in the dilute supernatant and coacervate as a function of the electrostatic strength, lB/b, with and without explicit counter-ions. The supernatant is at a polymer number density of ρpb3 = 7.35 × 10−7, and the coacervate is at ρpb3 = 0.0735. Symbols are obtained from FTS-CL, and lines are RPA predictions. The Gaussian smearing width is set at a/b = 0.8 and the excluded-volume parameter is set at v/b3 = 0.0068.

FIG. 5.
FIG. 5.

Phase diagram showing the modulation of critical electrostatic strength with inclusion of excess salt on the phase diagram of a diblock polyampholyte (A50C50). Symbols are binodal points obtained from FTS-CL, and lines are RPA predictions. The Gaussian smearing width is set at a/b = 0.8 and the excluded-volume parameter is set at v/b3 = 0.0068. The different salt conditions are presented as number fractions ϕsalt,±; the concentration (number density) of both polymer and salt increases along the horizontal axis.

FIG. 6.
FIG. 6.

Total-density structure factor, Sn(k), and charge-weighted structure factor, Se(k), of the diblock polyampholyte (A50C50) in the dilute supernatant and coacervate as a function of the number fraction of excess salt, ϕsalt,±. Symbols are obtained from FTS-CL, and lines are RPA predictions. The supernatant is at a polymer number density of ρpb3 = 7.35 × 10−7, and the coacervate is at ρpb3 = 0.0735. The Gaussian smearing width is set at a/b = 0.8, the excluded-volume parameter is set at v/b3 = 0.0068, and the electrostatic strength is set at lB/b = 0.065.

FIG. 7.
FIG. 7.

Phase diagram showing excess salt shifting the location of the two-phase region for the diblock polyampholyte (A50C50). The shaded region is the region between the binodal curves. Representative tie lines are shown as horizontal solid lines. Dotted (ϕsalt,± = 0.0) and dashed (ϕsalt,± = 0.3) diagonal lines show stoichiometry constraints (i.e., concentration of small ions corresponding to the polymer concentration for each salt condition.) The Gaussian smearing width is set at a/b = 0.8, the excluded-volume parameter is set at v/b3 = 0.0068, and the electrostatic strength is set at lB/b = 0.065.

FIG. 8.
FIG. 8.

Phase diagram showing charge asymmetry shrinking phase coexistence and shifting binodal boundaries to lower polyampholyte and higher salt concentrations. The shaded region is the region between the binodal curves. Representative tie lines are shown as solid lines. The Gaussian smearing width is set at a/b = 0.8, the excluded-volume parameter is set at v/b3 = 0.0068, and the electrostatic strength is set at lB/b = 0.065.

FIG. 9.
FIG. 9.

Total-density structure factor, Sn(k), and charge-weighted structure factor, Se(k), of the diblock polyampholyte in the dilute supernatant and coacervate as a function of charge asymmetry. Symbols are obtained from FTS-CL, and lines are RPA predictions. The supernatant is at a polymer number density of ρpb3 = 7.35 × 10−7, and the coacervate is at ρpb3 = 0.0735. The Gaussian smearing width is set at a/b = 0.8, the excluded-volume parameter is set at v/b3 = 0.0068, and the electrostatic strength is set at lB/b = 0.065.

FIG. 10.
FIG. 10.

Single chain structure factor, P(k), in the dilute supernatant (ρpb3 = 7.35 × 10−7) as a function of charge asymmetry. The Gaussian smearing width is set at a/b = 0.8, the excluded-volume parameter is set at v/b3 = 0.0068, and the electrostatic strength is set at lB/b = 0.065. Insets: Snapshots from the MD simulations showing globular chain conformations at zero net-charge and the emergence of “tadpole” conformations with increasing charge asymmetry.

FIG. 11.
FIG. 11.

Phase diagram showing multivalent counter-ions shrinking the region for phase coexistence. The shaded region is the region between the binodal curves. Representative tie lines are shown as solid lines. The Gaussian smearing width is set at a/b = 0.8, the excluded-volume parameter is set at v/b3 = 0.0068, and the electrostatic strength is set at lB/b = 0.065.

FIG. 12.
FIG. 12.

Total-density structure factor, Sn(k), and charge-weighted structure factor, Se(k), of the diblock polyampholyte (A50C50) in the dilute supernatant and coacervate as a function of counter-cation valency. Symbols are obtained from FTS-CL, and lines are RPA predictions. The supernatant is at a polymer number density of ρpb3 = 7.35 × 10−7, and the coacervate is at ρpb3 = 0.0735. The Gaussian smearing width is set at a/b = 0.8, the excluded-volume parameter is set at v/b3 = 0.0068, and the electrostatic strength is set at lB/b = 0.065.

FIG. 13.
FIG. 13.

Phase diagram showing the importance of charge neutrality in dictating partitioning and phase coexistence of a charge asymmetric diblock polyampholyte (A48C52) with multivalent counter-ions. The shaded region is the region between the binodal curves. Representative tie lines are shown as solid lines. The Gaussian smearing width is set at a/b = 0.8, the excluded-volume parameter is set at v/b3 = 0.0068, and the electrostatic strength is set at lB/b = 0.065.

Similar articles

Cited by

References

    1. Brangwynne C. P., Eckmann C. R., Courson D. S., Rybarska A., Hoege C., Gharakhani J., Julicher F., and Hyman A. A., Science 324, 1729 (2009).10.1126/science.1172046 - DOI - PubMed
    1. Li P., Banjade S., Cheng H. C., Kim S., Chen B., Guo L., Llaguno M., Hollingsworth J. V., King D. S., Banani S. F., Russo P. S., Jiang Q. X., Nixon B. T., and Rosen M. K., Nature 483, 336 (2012).10.1038/nature10879 - DOI - PMC - PubMed
    1. Kato M., Han T. N. W., Xie S. H., Shi K., Du X. L., Wu L. C., Mirzaei H., Goldsmith E. J., Longgood J., Pei J. M., Grishin N. V., Frantz D. E., Schneider J. W., Chen S., Li L., Sawaya M. R., Eisenberg D., Tycko R., and McKnight S. L., Cell 149, 753 (2012).10.1016/j.cell.2012.04.017 - DOI - PMC - PubMed
    1. Lee C. F., Brangwynne C. P., Gharakhani J., Hyman A. A., and Julicher F., Phys. Rev. Lett. 111, 088101 (2013).10.1103/PhysRevLett.111.088101 - DOI - PubMed
    1. Nott T. J., Petsalaki E., Farber P., Jervis D., Fussner E., Plochowietz A., Craggs T. D., Bazett-Jones D. P., Pawson T., Forman-Kay J. D., and Baldwin A. J., Mol. Cell 57, 936 (2015).10.1016/j.molcel.2015.01.013 - DOI - PMC - PubMed