Transfer Free Energies of Test Proteins Into Crowded Protein Solutions Have Simple Dependence on Crowder Concentration

Abstract

The effects of macromolecular crowding on the thermodynamic properties of test proteins are determined by the latter's transfer free energies from a dilute solution to a crowded solution. The transfer free energies in turn are determined by effective protein-crowder interactions. When these interactions are modeled at the all-atom level, the transfer free energies may defy simple predictions. Here we investigated the dependence of the transfer free energy (Δμ) on crowder concentration. We represented both the test protein and the crowder proteins atomistically, and used a general interaction potential consisting of hard-core repulsion, non-polar attraction, and solvent-screened electrostatic terms. The chemical potential was rigorously calculated by FMAP (Qin and Zhou, 2014 ), which entails expressing the protein-crowder interaction terms as correlation functions and evaluating them via fast Fourier transform (FFT). To high accuracy, the transfer free energy can be decomposed into an excluded-volume component (Δμ e−v ), arising from the hard-core repulsion, and a soft-attraction component (Δμ s−a ), arising from non-polar and electrostatic interactions. The decomposition provides physical insight into crowding effects, in particular why such effects are very modest on protein folding stability. Further decomposition of Δμ s−a into non-polar and electrostatic components does not work, because these two types of interactions are highly correlated in contributing to Δμ s−a . We found that Δμ e−v fits well to the generalized fundamental measure theory (Qin and Zhou, 2010 ), which accounts for atomic details of the test protein but approximates the crowder proteins as spherical particles. Most interestingly, Δμ s−a has a nearly linear dependence on crowder concentration. The latter result can be understood within a perturbed virial expansion of Δμ (in powers of crowder concentration), with Δμ e−v as reference. Whereas the second virial coefficient deviates strongly from that of the reference system, higher virial coefficients are close to their reference counterparts, thus leaving the linear term to make the dominant contribution to Δμ s−a .

Calculation of Second Virial Coefficients of Atomistic Proteins Using Fast Fourier Transform

“…Previously, in calculating chemical potentials, a given probe molecule was placed in different regions of the solution box; the need for orientational averaging was modest, since different regions of the solution box effectively sense different relative orientations of the same probe molecule. Thus, at most, a few hundred orientations of the probe molecule, randomly generated, were used . Here the solution box contains a single partner molecule; in each FMAPB2 calculation, it senses only one relative orientation of the probe molecule, so the need for orientational average is greater.…”

“…Here we present a method that breaks this last barrier, based on using FFT. In previous studies, we have already introduced a method called FMAP, or F FT-based m odeling of a tomistic p rotein–protein interactions, and demonstrated its superb speed in calculating the interaction energy of a probe molecule when placed at uniformly distributed positions inside a box of target molecules, enabling fast determination of the chemical potential. − Here we adapt FMAP to calculate B 2 for proteins represented at the atomic level in implicit solvent and test FMAPB2 on five proteins for which extensive experimental data are available: lysozyme, ,,,,,, chymotrypsinogen A, ,, bovine pancreas trypsin inhibitor (BPTI), γD crystallin, and bovine serum albumin (BSA) . After limited tuning of a single parameter in the interaction energy function, the calculated B 2 values, each involving more than 10 11 configurations, agree well with experimental data over wide ranges of solvent conditions (salt concentration, pH, and temperature).…”

Investigating molecular crowding during cell division and hyperosmotic stress in budding yeast with FRET

“…Van Den Berg et al, 1999 ). Several of these studies have described the role of crowding in protein stability ( König et al, 2021 ) and its impact on the free-energy of folding ( Minton, 2006 ; Nguemaha et al, 2019 ) and kinetics of interaction ( Phillip & Schreiber, 2013 ; Stagg et al, 2007 ). In vivo, dynamics of repulsion and attraction forces between macromolecules has been described as one of the effects of crowding ( Garner & Burg, 1994 ), with a role on molecular rearrangement ( Rivas et al, 2004 ), promoting oligomerization and aggregation ( Christiansen et al, 2013 ).…”

Shape-Dependent Macromolecular Crowding on the Thermodynamics and Microsecond Conformational Dynamics of Protein Unfolding Revealed at the Single-Molecule Level

“…About 30% of the cell environment is occupied by macromolecules, and the concentration of macromolecules varies from 40 to 400 g L –1 inside various cell compartments. − There are hundreds of reports describing the modulation of a protein’s structure, dynamics, activity, binding affinity, and aggregation behavior in such a crowded milieu. − There are also an increasing number of reports on the mechanism by which crowders can exert their effect on a protein’s behavior. − For example, the volume excluded by the macromolecules may not be available to the protein, and this hard-core repulsion affects a protein’s behavior significantly. A straightforward conclusion would be that it favors the compact native state compared to the elongated denatured state of the protein. ,,,, This effect is purely entropic because it involves only rearrangement .…”