Rational design of solution additives for the prevention of protein aggregation

Abstract

We have developed a statistical-mechanical model of the effect of solution additives on protein association reactions. This model incorporates solvent radial distribution functions obtained from all-atom molecular dynamics simulations of particular proteins into simple models of protein interactions. In this way, the effects of additives can be computed along the entire association/dissociation reaction coordinate. We used the model to test our hypothesis that a class of large solution additives, which we term "neutral crowders," can slow protein association and dissociation by being preferentially excluded from protein-protein encounter complexes, in a manner analogous to osmotic stress. The magnitude of this proposed "gap effect" was probed for two simple model systems: the association of two spheres and the association of two planes. Our results suggest that for a protein of 20 A radius, an 8 A additive can increase the free energy barrier for association and dissociation by as much as 3-6 kcal/mol. Because the proposed gap effect is present only for reactions involving multiple molecules, it can be exploited to develop novel additives that affect protein association reactions although having little or no effect on unimolecular reactions such as protein folding. This idea has many potential applications in areas such as the stabilization of proteins against aggregation during folding and in pharmaceutical formulations.

FIGURE 1

A free energy diagram along the folding/aggregation reaction coordinate for a globular protein is shown. The first small aggregate (A₂) is formed from an unfolded or partially unfolded state, U, where a hydrophobic patch is exposed to the solvent. After formation of the first small aggregate (A₂), further association reactions may take place to form higher-order aggregates (not shown).

FIGURE 2

In refolding of carbonic anhydrase, interferon-γ, and DNase from the unfolded state (U), Cleland (1991) showed that polyethylene glycol (PEG) binds selectively to the unfolded protein and folding intermediates. This slows aggregation and increases the yield of native protein. The free energy in the absence of additive is shown as a solid line and, in the presence of PEG, as a dotted line.

FIGURE 3

In studies of interferon-γ aggregation from the native state, Kendrick et al. (1998) showed that sucrose decreases the concentration of the aggregation-competent intermediate (I) and therefore slows aggregation. The free energy in the absence of additive is shown as a solid line and, in the presence of sucrose, as a dotted line.

FIGURE 4

If a protein molecule (P) contains narrow channels too small for a large additive (solid circles) to enter as in a, the cosolvent exerts an osmotic stress effect that favors the collapse of these channels and the release of the water (shaded circles) they contain. An analogous effect can occur in any protein state which contains gaps, such as the protein-protein encounter complex shown in b. In this case, the “gap effect” caused by the large additive selectively increases the free energy of encounter complexes that contain such gaps. The gap effect therefore slows isomerization between the associated and dissociated protein states.

FIGURE 5

The hypothesized effect of a neutral crowder on the free energy of protein states along the refolding/aggregation reaction coordinate is shown. The free energy in the absence of additive is shown as a solid line and, in the presence of a neutral crowder, as a dotted line. The neutral crowder is preferentially excluded from the gap between the protein molecules in the association transition state (), increasing the free energy of this state.

FIGURE 6

The definition of each reaction coordinate and the free energy diagrams (Eqs. 5 and 6) are shown for the two model protein systems used in this work. For the spheres, the association/dissociation reaction coordinate, x, is the distance between the sphere centers. For the planes, it is the shortest distance between the planes (which are always parallel). The value x is 0 when the two proteins overlap each other completely.

FIGURE 7

Fits of the protein-water and protein-additive radial distribution functions from molecular dynamics simulations for various additives with the protein RNase T1 using the exponential-6 intermolecular potential. Note that r = 0 is at the surface of the protein. The observed data are shown as crosses, the fits as lines. The corresponding parameters are shown in Table 1.

FIGURE 8

Transfer free energies for pairs of protein molecules transferred into 1 M additive solution as a function of position along the association reaction coordinate, x, are shown. The sizes of the additives are varied although keeping the second virial coefficients constant. The curves are labeled with the additive sizes (r_m in Å) to which they correspond. The left-hand figure is for the association of two spherical proteins 20 Å in radius, and the right-hand figure is for the association of two pseudo-infinite planar proteins with an area of 400 πŲ on each face.

FIGURE 9

The protein free energies along the reaction coordinate for association/dissociation in the presence of neutral crowders at 1 M concentration are shown. This combines μ_{P, 0} (Eqs. 5 and 6) with the transfer free energies shown in Fig. 8. The curves are labeled with the additive sizes (r_m in Å) to which they correspond.

FIGURE 10

The change in association and dissociation rates for 20 Å spherical proteins caused by a 1 M additive is shown as a function of the additive size (x axis) and additive-protein preferential binding coefficient, Γ_XP (labels).

FIGURE 11

The change in association and dissociation rates for planar proteins (with 400 πŲ area on a face) caused by a 1 M additive is shown as a function of the additive size (x axis) and additive-protein preferential binding coefficient, Γ_XP (labels). For the dissociation rate, the Γ_XP dependence is negligible.