Redox Potentials of Protein Disulfide Bonds from Free-Energy Calculations

Thiol/disulfide exchange in proteins is a vital process in all organisms. To ensure specificity, the involved thermodynamics and kinetics are believed to be tailored by the structure and dynamics of the protein hosting the thiol/disulfide pair. We here aim at predicting the thermodynamics of thiol/disulfide pairs in proteins. We devise a free-energy calculation scheme, which makes use of the Crooks Gaussian intersection method to estimate the redox potential of thiol/disulfide pairs in 12 proteins belonging to the thioredoxin superfamily, namely, thioredoxins, glutaredoxins, and thiol–disulfide oxidoreductases in disulfide bond formation systems. We obtained a satisfying correlation of computed with experimental redox potentials (varying by 160 mV), with a residual error of ∼40 mV (8 kJ/mol), which drastically reduces when considering a less diverse set of only thioredoxins. Our simple and transferrable approach provides a route toward estimating redox potentials of any disulfide-containing protein given that its (reduced or oxidized) structure is known and thereby represents a step toward a rational design of redox proteins

Macromolecular Entropy Can Be Accurately Computed from Force

A method is presented to evaluate a molecule’s entropy from the atomic forces calculated in a molecular dynamics simulation. Specifically, diagonalization of the mass-weighted force covariance matrix produces eigenvalues which in the harmonic approximation can be related to vibrational frequencies. The harmonic oscillator entropies of each vibrational mode may be summed to give the total entropy. The results for a series of hydrocarbons, dialanine and a β hairpin are found to agree much better with values derived from thermodynamic integration than results calculated using quasiharmonic analysis. Forces are found to follow a harmonic distribution more closely than coordinate displacements and better capture the underlying potential energy surface. The method’s accuracy, simplicity, and computational similarity to quasiharmonic analysis, requiring as input force trajectories instead of coordinate trajectories, makes it readily applicable to a wide range of problems

Stress Propagation through Biological Lipid Bilayers in Silico

Membrane tension plays various critical roles in the cell. We here asked how fast and how far localized pulses of mechanical stress dynamically propagate through biological lipid bilayers. In both coarse-grained and all-atom molecular dynamics simulations of a dipalmitoylphosphatidylcholine lipid bilayer, we observed nanometer-wide stress pulses, propagating very efficiently longitudinally at a velocity of approximately 1.4 ± 0.5 nm/ps (km/s), in close agreement with the expected speed of sound from experiments. Remarkably, the predicted characteristic attenuation time of the pulses was in the order of tens of picoseconds, implying longitudinal stress propagation over length scales up to several tens of nanometers before damping. Furthermore, the computed dispersion relation leading to such damping was consistent with proposed continuum viscoelastic models of propagation. We suggest this mode of stress propagation as a potential ultrafast mechanism of signaling that may quickly couple mechanosensitive elements in crowded biological membranes

On the Cis to Trans Isomerization of Prolyl–Peptide Bonds under Tension

The cis peptide bond is a characteristic feature of turns in protein structures and can play the role of a hinge in protein folding. Such cis conformations are most commonly found at peptide bonds immediately preceding proline residues, as the cis and trans states for such bonds are close in energy. However, isomerization over the high rotational barrier is slow. In this study, we investigate how mechanical force accelerates the cis to trans isomerization of the prolyl–peptide bond in a stretched backbone. We employ hybrid quantum mechanical/molecular mechanical force-clamp molecular dynamics simulations in order to describe the electronic effects involved. Under tension, the bond order of the prolyl–peptide bond decreases from a partially double toward a single bond, involving a reduction in the electronic conjugation around the peptide bond. The conformational change from cis to extended trans takes place within a few femtoseconds through a nonplanar state of the nitrogen of the peptide moiety in the transition state region, whereupon the partial double-bond character and planarity of the peptide bond in the final trans state is restored. Our findings give insight into how prolyl–peptide bonds might act as force-modulated mechanical timers or switches in the refolding of proteins

On the Cis to Trans Isomerization of Prolyl–Peptide Bonds under Tension

The cis peptide bond is a characteristic feature of turns in protein structures and can play the role of a hinge in protein folding. Such cis conformations are most commonly found at peptide bonds immediately preceding proline residues, as the cis and trans states for such bonds are close in energy. However, isomerization over the high rotational barrier is slow. In this study, we investigate how mechanical force accelerates the cis to trans isomerization of the prolyl–peptide bond in a stretched backbone. We employ hybrid quantum mechanical/molecular mechanical force-clamp molecular dynamics simulations in order to describe the electronic effects involved. Under tension, the bond order of the prolyl–peptide bond decreases from a partially double toward a single bond, involving a reduction in the electronic conjugation around the peptide bond. The conformational change from cis to extended trans takes place within a few femtoseconds through a nonplanar state of the nitrogen of the peptide moiety in the transition state region, whereupon the partial double-bond character and planarity of the peptide bond in the final trans state is restored. Our findings give insight into how prolyl–peptide bonds might act as force-modulated mechanical timers or switches in the refolding of proteins

Exploring the Multidimensional Free Energy Surface of Phosphoester Hydrolysis with Constrained QM/MM Dynamics

The mechanism of the hydrolysis of phosphate monoesters, a ubiquitous biological reaction, has remained under debate. We here investigated the hydrolysis of a nonenzymatic model system, the monomethyl phosphate dianion, by hybrid quantum mechanical and molecular mechanical simulations. The solvation effects were taken into account with explicit water. Detailed free energy landscapes in two-dimensional and three-dimensional space were resolved using the multidimensional potential of mean constraint force, a newly developed method that was demonstrated to be powerful for free energy calculations along multiple coordinates. As in previous theoretical studies, the associative and dissociative pathways were indistinguishable. Furthermore, the associative pathway was investigated in great detail. We propose a rotation of an O–H bond in the transition between two pentacoordinated structures, during which an overall transition state was identified with an activation energy of 50 kcal/mol. This is consistent with experimental data. The results support a concerted proton transfer from the nucleophilic water to the phosphate group, and then to the leaving group

Stability of Biological Membranes upon Mechanical Indentation

Mechanical perturbations are ubiquitous in living cells, and many biological functions are dependent on the mechanical response of lipid membranes. Recent force-spectroscopy studies have captured the stepwise fracture of stacks of bilayers, avoiding substrate effects. However, the effect of stacking bilayers, as well as the exact molecular mechanism of the fracture process, is unknown. Here, we use atomistic and coarse-grained force-clamp molecular dynamics simulation to assess the effects of mechanical indentation on stacked and single bilayers. Our simulations show that the rupture process obeys the laws of force-activated barrier crossing, and stacking multiple membranes stabilizes them. The rupture times follow a log-normal distribution which allows the interpretation of membrane rupture as a pore-growth process. Indenter hydrophobicity determines the type of pore formation, the preferred dwelling region, and the resistance of the bilayer against rupture. Our results provide a better understanding of the nanomechanics underlying the plastic rupture of lipid membranes

Stability of Biological Membranes upon Mechanical Indentation

Mechanical perturbations are ubiquitous in living cells, and many biological functions are dependent on the mechanical response of lipid membranes. Recent force-spectroscopy studies have captured the stepwise fracture of stacks of bilayers, avoiding substrate effects. However, the effect of stacking bilayers, as well as the exact molecular mechanism of the fracture process, is unknown. Here, we use atomistic and coarse-grained force-clamp molecular dynamics simulation to assess the effects of mechanical indentation on stacked and single bilayers. Our simulations show that the rupture process obeys the laws of force-activated barrier crossing, and stacking multiple membranes stabilizes them. The rupture times follow a log-normal distribution which allows the interpretation of membrane rupture as a pore-growth process. Indenter hydrophobicity determines the type of pore formation, the preferred dwelling region, and the resistance of the bilayer against rupture. Our results provide a better understanding of the nanomechanics underlying the plastic rupture of lipid membranes

Sampling Long- versus Short-Range Interactions Defines the Ability of Force Fields To Reproduce the Dynamics of Intrinsically Disordered Proteins

Molecular dynamics (MD) simulations have valuably complemented experiments describing the dynamics of intrinsically disordered proteins (IDPs), particularly since the proposal of models to solve the artificial collapse of IDPs <i>in silico</i>. Such models suggest redefining nonbonded interactions, by either increasing water dispersion forces or adopting the Kirkwood-Buff force field. These approaches yield extended conformers that better comply with experiments, but it is unclear if they all sample the same intrachain dynamics of IDPs. We have tested this by employing MD simulations and single-molecule Förster resonance energy transfer spectroscopy to sample the dimensions of systems with different sequence compositions, namely strong and weak polyelectrolytes. For strong polyelectrolytes in which charge effects dominate, all the proposed solutions equally reproduce the expected ensemble’s dimensions. For weak polyelectrolytes, at lower cutoffs, force fields abnormally alter intrachain dynamics, overestimating excluded volume over chain flexibility or reporting no difference between the dynamics of different chains. The TIP4PD water model alone can reproduce experimentally observed changes in extensions (dimensions), but not quantitatively and with only weak statistical significance. Force field limitations are reversed with increased interaction cutoffs, showing that chain dynamics are critically defined by the presence of long-range interactions. Force field analysis aside, our study provides the first insights into how long-range interactions critically define IDP dimensions and raises the question of which length range is crucial to correctly sample the overall dimensions and internal dynamics of the large group of weakly charged yet highly polar IDPs

Kirkwood–Buff Approach Rescues Overcollapse of a Disordered Protein in Canonical Protein Force Fields

Understanding the function of intrinsically disordered proteins is intimately related to our capacity to correctly sample their conformational dynamics. So far, a gap between experimentally and computationally derived ensembles exists, as simulations show overcompacted conformers. Increasing evidence suggests that the solvent plays a crucial role in shaping the ensembles of intrinsically disordered proteins and has led to several attempts to modify water parameters and thereby favor protein–water over protein–protein interactions. This study tackles the problem from a different perspective, which is the use of the Kirkwood–Buff theory of solutions to reproduce the correct conformational ensemble of intrinsically disordered proteins (IDPs). A protein force field recently developed on such a basis was found to be highly effective in reproducing ensembles for a fragment from the FG-rich nucleoporin 153, with dimensions matching experimental values obtained from small-angle X-ray scattering and single molecule FRET experiments. Kirkwood–Buff theory presents a complementary and fundamentally different approach to the recently developed four-site TIP4P-D water model, both of which can rescue the overcollapse observed in IDPs with canonical protein force fields. As such, our study provides a new route for tackling the deficiencies of current protein force fields in describing protein solvation