(305h) Thermodynamics and Kinetics of Biomolecular Condensation from Simulations and Experiments in Small, Finite Volumes.

The Liquid-liquid phase separation of polymer and protein solutions plays a vital role in various fields, including the synthesis of stimuli-responsive materials, synthetic biology, and the formation of membrane-less organelles in cells.
Across these research fields, it is vital to understand the thermodynamics and the kinetics of phase separation, which is initiated by the nucleation of a dense liquid droplet within a lean liquid solution.

The nucleation of bio(polymer) condensates is a concentration-driven self-assembly process. As such, when condensates form in small, isolated volumes, confinement conditions impose constraints on the process, affecting both the thermodynamics and the dynamics of the nucleation process.
In extreme cases, confinement in isolated small volumes can suppress the nucleation process entirely [1-3]. Nevertheless, when a phase transition can still occur despite confinement limitations, the nucleation process produces a single, stable droplet of the condensate phase with a well defined steady-state size [4].

Here, we take advantage of a general theoretical description of the thermodynamics of liquid droplet condensation in small confined volumes based on classical nucleation theory [1-3] to analyse both nucleation simulations in the canonical ensemble and microfluidic experiments of liquid-liquid phase separation.

In particular, we use the fact that at steady-state, both NVT simulations of phase separation and microfluidic experiments generate a single stable droplet, corresponding to a local minimum in the free energy profile associated with nucleation in a confined environment.

On the simulation side, we use this information to infer information on the nucleation thermodynamics and kinetics of coarse-grained models of phase separating proteins in the macroscopic limit, where direct simulations would be challenging.
We apply our approach to two phase-separating systems with different physicochemical characteristics: NDDX4 and FUS.
From the properties of steady-state condensate droplets obtained in canonical coarse-grained molecular simulations, we estimate the macroscopic equilibrium density of the dilute protein solution of these two peptides and their respective condensate surface tensions.

Obtaining these parameters allows us to estimate nucleation free energy barriers without performing computationally expensive free energy calculations. Furthermore, an analysis of the nucleation free energies reveals that NDDX4 solutions are kinetically unstable over a considerable interval of concentrations, while FUS solutions are associated with activated nucleation events.

Remarkably, we can adapt the theoretical framework used to interpret canonical simulations [1-3] to elucidate the phase behaviour of metastable polymer solutions undergoing phase separation in microfluidic droplets [4].
Confinement effects are generated in these experiments because each droplet is isolated and cannot exchange mass with the surrounding environment.

We apply the theoretical analysis to experiments investigating the behaviour of a phase-separating polymer able to mimic the protein phase separation at different concentrations and temperatures.
We discover that the nucleation process is non-activated for the polymer studied. Therefore, the kinetics of droplet evolution can be interpreted through an overdamped Langevin dynamics in reaction coordinate space, leading to the reconstruction of nucleation kinetics data from the mean thermodynamic force, expressed as a function of the droplet size.

While the sources of confinement effects differ between canonical molecular dynamics simulations and experiments performed in microfluidic devices, the approach proposed here is general. Furthermore, it provides a straightforward and efficient route for obtaining emergent, thermodynamic, and kinetic properties of protein condensate the steady-state nucleus properties.

References

[1] D Reguera, RK Bowles, Y Djikaev, and H Reiss. J Chem Phys, 118(1):340–353, 2003.
[2] J Wedekind, D Reguera, and R Strey. J Chem Phys, 125(21):214505, 2006.
[3] M Salvalaglio, C Perego, F Giberti, M Mazzotti, and M Parrinello. Proc Nat Acad Sci, 112(1):E6–E14, 2015.
[4] R. Grossier, S. Veesler, Cryst. Growth Des. 2009, 9, 1917.

Figure: Free Energy profile associated with a typical nucleation process in a finite sized system. The free energy surface displays two stationary points, corresponding to the critical nucleus size and to the steady state droplet formed in confined conditions. As shown in figure this framework can be used to interpret both simulations performed in the canonical ensemble, or experiments performed in confined droplets.