General Framework of Pressure Effects on Structures Formed by Entropically Driven Self-Assembly

Entropy of Charge Inversion in DNA including One-Loop Fluctuations

The entropy and charge distributions have been calculated for a simple model of polyelectrolytes attached to the surface of DNA using a field-theoretic method that includes fluctuations to the lowest one-loop order beyond mean-field theory. Experiments have revealed correlation-driven behavior of DNA in charged solutions, including charge inversion and condensation. In our model, the condensed polyelectrolytes are taken to be doubly charged dimers of length comparable to the distance between sites along the phosphate chains. Within this lattice gas model, each adsorption site is assumed to have either a vacancy or a positively charged dimer attached with the dimer oriented either parallel or perpendicular to the double-helix DNA chain. We find that the inclusion of the fluctuation terms decreases the entropy by ∼50% in the weak-binding regime. There, the bound dimer concentration is low because the dimers are repelled from the DNA molecule, which competes with the chemical potential driving them from the solution to the DNA surface. Surprisingly, this decrease in entropy due to correlations is so significant that it overcompensates for the entropy increase at the mean-field level, so that the total entropy is even lower than in the absence of interactions between lattice sites. As a bonus, we present a transparent exposition of the methods used that could be useful to students and others wishing to use this formulation to extend this calculation to more realistic models.

Single-molecule analysis of the rotation of F₁-ATPase under high hydrostatic pressure

F1-ATPase is the water-soluble part of ATP synthase and is an ATP-driven rotary molecular motor that rotates the rotary shaft against the surrounding stator ring, hydrolyzing ATP. Although the mechanochemical coupling mechanism of F1-ATPase has been well studied, the molecular details of individual reaction steps remain unclear. In this study, we conducted a single-molecule rotation assay of F1 from thermophilic bacteria under various pressures from 0.1 to 140 MPa. Even at 140 MPa, F1 actively rotated with regular 120° steps in a counterclockwise direction, showing high conformational stability and retention of native properties. Rotational torque was also not affected. However, high hydrostatic pressure induced a distinct intervening pause at the ATP-binding angles during continuous rotation. The pause was observed under both ATP-limiting and ATP-saturating conditions, suggesting that F1 has two pressure-sensitive reactions, one of which is evidently ATP binding. The rotation assay using a mutant F1(βE190D) suggested that the other pressure-sensitive reaction occurs at the same angle at which ATP binding occurs. The activation volumes were determined from the pressure dependence of the rate constants to be +100 Å(3) and +88 Å(3) for ATP binding and the other pressure-sensitive reaction, respectively. These results are discussed in relation to recent single-molecule studies of F1 and pressure-induced protein unfolding.