Molecularly informed field theory for estimating critical micelle concentrations of intrinsically disordered protein surfactants

Abstract

The critical micelle concentration (CMC) is a crucial parameter in understanding the self-assembly behavior of surfactants. In this study, we combine simulation and experiment to demonstrate the predictive capability of molecularly informed field theories in estimating the CMC of biologically based protein surfactants. Our simulation approach combines the relative entropy coarse-graining of small-scale atomistic simulations with large-scale field-theoretic simulations, allowing us to efficiently compute the free energy of micelle formation necessary for the CMC calculation while preserving chemistry-specific information about the underlying surfactant building blocks. We apply this methodology to a unique intrinsically disordered protein platform capable of a wide variety of tailored sequences that enable tunable micelle self-assembly. The computational predictions of the CMC closely match experimental measurements, demonstrating the potential of molecularly informed field theories as a valuable tool to investigate self-assembly in bio-based macromolecules systematically.

FIG. 1.

Schematic of the multi-scale simulation workflow to construct a molecularly informed field-theoretic model of IDP surfactants. (a) Species involved in the all-atom system, which include the IDP surfactant and water. Instead of simulating the full surfactant sequence, we split the surfactant into the head (blue), composed of n_h repeats of the sequence (SPAEAKSPVEVK), and the tail (red) domains. At the connection point of the two domains in the full sequence, we attach neutral C-terminal amide (NME) and N-terminal acetyl (ACE) capping groups to the head and tail, respectively. (b) A coarse-grained particle-based model parameterized by relative entropy minimization. (c) An exact mapping from the coarse-grained particle-based description of the micelle to a field-theoretic model. This schematic also illustrates the CMC calculation approach, which involves matching the chemical potentials in the micellar, μ_i,mic, and disordered, μ_i,dis, states of compositions ρ_i,mic and ρ_i,dis, respectively.

FIG. 2.

Reference AA systems and CG mapping schemes considered in constructing the IDP surfactant model. Black arrows depict the biasing potential between the centers of mass of any two amino acids (see the main text for a detailed discussion).

FIG. 3.

Example grand free energy difference βΔΩ between a spherical micelle and the homogeneous phase as a function of (a) surfactant concentration in the homogeneous phase ρ_idp,dis (chain and monomer basis) and (b) surfactant chemical potential βμ_idp. (c) To account for finite-size errors, we extrapolate the CMC linearly with respect to the inverse of the box size length.

FIG. 4.

Pyrene I_I/I_III fluorescence emission ratio across concentrations of the IDP surfactant with n_h = 6.5. Solutions containing 0.1–300 μM surfactant in 2 µM pyrene and 10 mM phosphate buffer, pH 6.5, were excited at 330 nm, and the emission was recorded at 373 nm (I_I) and 384 nm (I_III).

FIG. 5.

(a) Binodals calculated from representative parameter sets for four IDP models at varying numbers of hydrophilic repeating units, n_h. The symbol denotes the experimentally determined CMC (EC₅₀ value) at n_h = 6.5. (b) Corresponding χ parameters against n_h. The dotted line denotes χ = 0.5.

FIG. 6.

CMC at n_h = 6.5 calculated from 20 replicates for models Ia and Ib against χ. The higher average χ of model Ia suggests that this model is slightly more hydrophobic than model Ib, resulting in a lower average CMC value.

FIG. 7.

Sensitivity analysis of the CMC with respect to the change in excluded volume parameters v₁₁, v₃₃, and v₁₃. A plot that shows the percentage change in the CMC with respect to the change in the excluded volume parameter from the base value.

FIG. 8.

Density profile of micelles at n_h = 6.5 from representative parameter sets for models (a) Ia and (b) Ib at the corresponding CMCs. The inset is a snapshot of the micelle from CGMD reconstructed based on the equilibrium aggregation number calculated in the field theory.