Protein mechanics probed using simple molecular models.

BACKGROUND: Single-molecule experimental techniques such as optical tweezers or atomic force microscopy are a direct probe of the mechanical unfolding/folding of individual proteins. They are also a means to investigate free energy landscapes. Protein force spectroscopy alone provides limited information; theoretical models relate measurements to thermodynamic and kinetic properties of the protein, but do not reveal atomic level information. By building a molecular model of the protein and probing its properties through numerical simulation, one can gauge the response to an external force for individual interatomic interactions and determine structures along the unfolding pathway. In combination, single-molecule force probes and molecular simulations contribute to uncover the rich behavior of proteins when subjected to mechanical force. SCOPE OF REVIEW: We focus on how simplified protein models have been instrumental in showing how general properties of the free energy landscape of a protein relate to its response to mechanical perturbations. We discuss the role of simple protein models to explore the complexity of free energy landscapes and highlight important conceptual issues that more chemically accurate models with all-atom representations of proteins and solvent cannot easily address. MAJOR CONCLUSIONS: Native-centric, coarse-grained models, despite simplifications in chemical detail compared to all-atom models, can reproduce and interpret experimental results. They also highlight instances where the theoretical framework used to interpret single-molecule data is too simple. However, these simple models are not able to reproduce experimental findings where non-native contacts are involved. GENERAL SIGNIFICANCE: Mechanical forces are ubiquitous in the cell and it is increasingly clear that the way a protein responds to mechanical perturbation is important.

Characterization of the flexibility of the peripheral stalk of prokaryotic rotary A-ATPases by atomistic simulations.

Rotary ATPases are involved in numerous physiological processes, with the three distinct types (F/A/V-ATPases) sharing functional properties and structural features. The basic mechanism involves the counter rotation of two motors, a soluble ATP hydrolyzing/synthesizing domain and a membrane-embedded ion pump connected through a central rotor axle and a stator complex. Within the A/V-ATPase family conformational flexibility of the EG stators has been shown to accommodate catalytic cycling and is considered to be important to function. For the A-ATPase three EG structures have been reported, thought to represent conformational states of the stator during different stages of rotary catalysis. Here we use long, detailed atomistic simulations to show that those structures are conformers explored through thermal fluctuations, but do not represent highly populated states of the EG stator in solution. We show that the coiled coil tail domain has a high persistence length (∼100 nm), but retains the ability to adapt to different conformational states through the presence of two hinge regions. Moreover, the stator network of the related V-ATPase has been suggested to adapt to subunit interactions in the collar region in addition to the nucleotide occupancy of the catalytic domain. The MD simulations reported here, reinforce this observation showing that the EG stators have enough flexibility to adapt to significantly different structural re-arrangements and accommodate structural changes in the catalytic domain whilst resisting the large torque generated by catalytic cycling. These results are important to understand the role the stators play in the rotary-ATPase mechanism. Proteins 2016; 84:1203-1212. © 2016 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

Flexibility within the rotor and stators of the vacuolar H+-ATPase.

The V-ATPase is a membrane-bound protein complex which pumps protons across the membrane to generate a large proton motive force through the coupling of an ATP-driven 3-stroke rotary motor (V1) to a multistroke proton pump (Vo). This is done with near 100% efficiency, which is achieved in part by flexibility within the central rotor axle and stator connections, allowing the system to flex to minimise the free energy loss of conformational changes during catalysis. We have used electron microscopy to reveal distinctive bending along the V-ATPase complex, leading to angular displacement of the V1 domain relative to the Vo domain to a maximum of ~30°. This has been complemented by elastic network normal mode analysis that shows both flexing and twisting with the compliance being located in the rotor axle, stator filaments, or both. This study provides direct evidence of flexibility within the V-ATPase and by implication in related rotary ATPases, a feature predicted to be important for regulation and their high energetic efficiencies.

Fundamental equation of the dual flow rate-solvent gradient elution in liquid chromatography.

An alternative expression of the fundamental equation of multi-mode gradient elution involving simultaneous changes in mobile phase composition and flow rate is derived using simple kinetic arguments and graphic interpretation. The new expression consists of a system of two integral equations and provides an easy and direct way of predicting retention times under dual-mode gradient conditions.

Combined effect of temperature and organic modifier concentration on the retention under single mode gradient conditions in reversed-phase HPLC.

The combined effect of temperature, T, and organic modifier concentration, phi, on the retention under gradient conditions in RPLC is studied by considering, both theoretically and experimentally gradients, of phi at constant T and gradients of T at constant phi. Two approaches are examined: in the first approach the prediction of the elution time of a sample solute is based on the isocratic/isothermal properties of this solute. The second approach is based on a direct fitting procedure of a proper retention model to 2-D isocratic/T-gradient or isothermal/phi-gradient retention data. These approaches were tested using alkylbenzes in eluting systems modified by ACN. We found that both approaches can give excellent predictions under certain prerequisites. However, the first approach exhibits the notable advantage that it can be used effectively to predict retention times under any kind of phi-gradients at constant T or T-gradients at constant phi. The second approach has the advantage that it is relatively simple but its applicability is very restricted since its predictions are satisfactory only if the gradients are of the same kind with those used in the fitting procedure and the conditions lie within those used for fitting.