Entropy Tug-of-War Determines Solvent Effects in the Liquid-Liquid Phase Separation of a Globular Protein

Abstract

Liquid-liquid phase separation (LLPS) plays a key role in the compartmentalization of cells via the formation of biomolecular condensates. Here, we combined atomistic molecular dynamics (MD) simulations and terahertz (THz) spectroscopy to determine the solvent entropy contribution to the formation of condensates of the human eye lens protein γD-Crystallin. The MD simulations reveal an entropy tug-of-war between water molecules that are released from the protein droplets and those that are retained within the condensates, two categories of water molecules that were also assigned spectroscopically. A recently developed THz-calorimetry method enables quantitative comparison of the experimental and computational entropy changes of the released water molecules. The strong correlation mutually validates the two approaches and opens the way to a detailed atomic-level understanding of the different driving forces underlying the LLPS.

Figure 1

Schematic illustration of liquid–liquid phase separation (LLPS) in a temperature–concentration phase diagram (top). Upon cooling the homogeneous protein solution (green arrow), the yellow region resembling a dome enters and the system phase-separates into two phases, a condensed and a dilute phase. This process involves the release of a portion of hydration water (red) into the dilute phase, while another portion is retained within the protein condensates (blue). The plot at the bottom displays a THz difference spectrum acquired during LLPS. Two distinct spectroscopic signatures emerge, HB-wrap water (depicted in red) at lower frequencies and bound water (shown in blue) at higher frequencies, which are assigned to the released (HB-wrap) and retained (bound) waters, respectively. The amplitude of the signal is employed to quantify the HB-wrap water, while the slope of the curve between 450 and 650 cm^–1 is utilized to quantify the bound water.

Figure 2

Snapshots from MD simulations of γD-Crystallin systems with different concentrations. The systems at 25 mg mL^–1 and 420 mg mL^–1 are the dilute and condensate phases, respectively.

Figure 3

(A) The number of water molecules in the protein hydration layer (PHL) per protein molecule is plotted as a function of protein concentration, ρ. The PHL is defined as the region within 4 Å of the protein surface. (B) Molar entropy of water in the protein solutions as a function of protein concentration. In A and B, the dilute (ρ_dil = 25 mg mL^–1) and the condensate (ρ_cond = 420 mg mL^–1) phases are indicated by arrows. (C) Number of water molecules released (red squares) and retained (blue circles) per protein molecule in the process of LLPS starting from different initial protein concentrations. (D) Free energy differences, −TΔS (at 273 K), due to water entropy changes associated with γD-Crystallin condensate formation as a function of protein concentration. The red circles and blue hexagons represent contributions from released and retained waters, respectively. The total entropy change is plotted as gray squares (zoom-in shown in the inset). In all panels, the error bars indicate the standard deviations of the three independent trajectories (in some cases, the error bars are smaller than the size of the dots).

Figure 4

THz difference spectra generated by the subtraction of the absorption coefficient (α) of the first γD-Crystallin spectrum acquired from that of the final γD-Crystallin spectrum acquired, Δα = α_final(ν) – α_initial(ν), at each experimental temperature. Evolution of the cavity-wrap water band at 150 cm^–1 and in the bound water (slope between 450 and 650 cm^–1) is observed with changes in temperature. The spectra shown are averages of at least three independent experiments; the error shown is the standard deviation. The raw absorption spectra for 283 K are shown in Figure S3.

Figure 5

Entropy change associated with the wrap waters in THz experiments plotted against the same for the released water in MD simulations (Pearson correlation coefficient R_P = 0.97). The dashed line is a linear fit to the data. The experimental temperatures and corresponding condensate concentrations are given next to each data point. To map the data from the MD simulations of the different protein concentrations (Table S1 and Figure 2), which were carried out at 273 K, to the different experimental temperatures, the concentrations corresponding to the temperatures were determined from the phase diagram in Figure S1. The entropy contribution due to the released water molecules was then obtained from the set of simulated concentrations by cubic spline interpolation between the data points plotted in Figure 3D. Error bars on the abscissa indicate the standard deviation from the three MD trajectories; error bars on the ordinate are the statistical errors from at least three independent THz experiments.