Decomposition of Forces in Protein: Methodology and General Properties

In contrast to the central role played by the structure of biomolecules, the complementary force-based view has received little attention in past studies. Here, we proposed a simple method for the force decomposition of multibody interactions and provided some techniques to analyze and visualize the general behavior of forces in proteins. It was shown that atomic forces fluctuate at a magnitude of about 3000 pN, which is huge in the context of cell biology. Remarkably, the average scalar product between atomic force and displacement universally approximates -3kBT. This is smaller by an order of magnitude than the simple product of their fluctuation magnitudes due to the unexpectedly weak correlation between the directions of force and displacement. The pairwise forces are highly anisotropic, with elongated fluctuation ellipsoids. Residue-residue forces can be attractive or repulsive (despite being more likely to be attractive), forming some kind of tensegrity structure stabilized by a complicated network of forces. Being able to understand and predict the interaction network provides a basis for rational drug design and uncovering molecular recognition mechanisms.

Rotation of a helical coordination polymer by mechanical grinding

Anisotropic cell volume expansion by mechanical grinding of the solid facilitates the concerted rotation of the photo-inert helical coordination polymer, which causes the misaligned arms containing olefin functional groups in the neighbouring strands to align to undergo [2+2] cycloaddition reaction in 83% yield.

Rate turnover in mechano-catalytic coupling: A model and its microscopic origin

A novel aspect in the area of mechano-chemistry concerns the effect of external forces on enzyme activity, i.e., the existence of mechano-catalytic coupling. Recent experiments on enzyme-catalyzed disulphide bond reduction in proteins under the effect of a force applied on the termini of the protein substrate reveal an unexpected biphasic force dependence for the bond cleavage rate. Here, using atomistic molecular dynamics simulations combined with Smoluchowski theory, we propose a model for this behavior. For a broad range of forces and systems, the model reproduces the experimentally observed rates by solving a reaction-diffusion equation for a "protein coordinate" diffusing in a force-dependent effective potential. The atomistic simulations are used to compute, from first principles, the parameters of the model via a quasiharmonic analysis. Additionally, the simulations are also used to provide details about the microscopic degrees of freedom that are important for the underlying mechano-catalysis.

Calculation and visualization of atomistic mechanical stresses in nanomaterials and biomolecules

Many biomolecules have machine-like functions, and accordingly are discussed in terms of mechanical properties like force and motion. However, the concept of stress, a mechanical property that is of fundamental importance in the study of macroscopic mechanics, is not commonly applied in the biomolecular context. We anticipate that microscopical stress analyses of biomolecules and nanomaterials will provide useful mechanistic insights and help guide molecular design. To enable such applications, we have developed Calculator of Atomistic Mechanical Stress (CAMS), an open-source software package for computing atomic resolution stresses from molecular dynamics (MD) simulations. The software also enables decomposition of stress into contributions from bonded, nonbonded and Generalized Born potential terms. CAMS reads GROMACS topology and trajectory files, which are easily generated from AMBER files as well; and time-varying stresses may be animated and visualized in the VMD viewer. Here, we review relevant theory and present illustrative applications.

Mechanochemistry and sonochemistry: concluding remarks

This paper offers a perspective on mechanochemistry and offers summarizing commentary on the Faraday Discussion170, “Mechanochemistry: From Functional Solids to Single Molecules”. The connection between the mechanical and the chemical worlds dates back to our earliest written records and beyond, but its renaissance over the past decade or so has had an impact on a huge swathe of modern science and engineering: from metallurgists to polymer scientists to synthetic organic and inorganic chemists to cellular biologists. Connections among the different subfields of mechanochemistry (tribochemistry, trituration, macromolecular, and sonochemistry) are drawn out and the common themes and open questions are considered.

F1-ATPase of Escherichia coli: the ε- inhibited state forms after ATP hydrolysis, is distinct from the ADP-inhibited state, and responds dynamically to catalytic site ligands

F1-ATPase is the catalytic complex of rotary nanomotor ATP synthases. Bacterial ATP synthases can be autoinhibited by the C-terminal domain of subunit ε, which partially inserts into the enzyme's central rotor cavity to block functional subunit rotation. Using a kinetic, optical assay of F1·ε binding and dissociation, we show that formation of the extended, inhibitory conformation of ε (εX) initiates after ATP hydrolysis at the catalytic dwell step. Prehydrolysis conditions prevent formation of the εX state, and post-hydrolysis conditions stabilize it. We also show that ε inhibition and ADP inhibition are distinct, competing processes that can follow the catalytic dwell. We show that the N-terminal domain of ε is responsible for initial binding to F1 and provides most of the binding energy. Without the C-terminal domain, partial inhibition by the ε N-terminal domain is due to enhanced ADP inhibition. The rapid effects of catalytic site ligands on conformational changes of F1-bound ε suggest dynamic conformational and rotational mobility in F1 that is paused near the catalytic dwell position.

Structural characteristics of yeast F1-ATPase before and after 16-degree rotation of the γ subunit: theoretical analysis focused on the water-entropy effect

We have recently proposed a novel picture of the rotation mechanism for F(1)-ATPase [T. Yoshidome, Y. Ito, M. Ikeguchi, and M. Kinoshita, J. Am. Chem. Soc. 133, 4030 (2011)]. In the picture, the asymmetric packing in F(1)-ATPase, originating from the water-entropy effect, plays the key role in the rotation. Here, we analyze the differences between the experimentally determined structures of yeast F(1)-ATPase before and after 16° rotation of the γ subunit with the emphasis on the water-entropy effect. For each of these structures, we calculate the hydration entropies of three sub-complexes comprising the γ subunit, one of the β subunits, and two α subunits adjacent to them. The β(E), β(TP), and β(DP) subunits are involved in sub-complexes I, II, and III, respectively. The calculation is performed using a hybrid of the angle-dependent integral equation theory combined with the molecular model for water and the morphometric approach. The absolute value of the hydration entropy is in the following order: sub-complex I > sub-complex II > sub-complex III. The packing efficiency of the sub-complex follows the opposite order. The rotation gives rise to less efficient packing in sub-complex III and a corresponding water-entropy loss. However, the other two sub-complexes, accompanying water-entropy gains, become more efficiently packed. These results are consistent with our picture of the rotation mechanism, supporting its validity. The water-entropy analysis shows that the interfaces of α(DP)-β(DP) and α(E)-β(E) become more open after the rotation, which is in accord with the experimental observation.

Improved crystallization of Escherichia coli ATP synthase catalytic complex (F1) by introducing a phosphomimetic mutation in subunit ε

The bacterial ATP synthase (F(O)F(1)) of Escherichia coli has been the prominent model system for genetics, biochemical and more recently single-molecule studies on F-type ATP synthases. With 22 total polypeptide chains (total mass of ∼529 kDa), E. coli F(O)F(1) represents nature's smallest rotary motor, composed of a membrane-embedded proton transporter (F(O)) and a peripheral catalytic complex (F(1)). The ATPase activity of isolated F(1) is fully expressed by the α(3)β(3)γ 'core', whereas single δ and ε subunits are required for structural and functional coupling of E. coli F(1) to F(O). In contrast to mitochondrial F(1)-ATPases that have been determined to atomic resolution, the bacterial homologues have proven very difficult to crystallize. In this paper, we describe a biochemical strategy that led us to improve the crystallogenesis of the E. coli F(1)-ATPase catalytic core. Destabilizing the compact conformation of ε's C-terminal domain with a phosphomimetic mutation (εS65D) dramatically increased crystallization success and reproducibility, yielding crystals of E. coli F(1) that diffract to ∼3.15 Å resolution.

Rotary catalysis of the stator ring of F(1)-ATPase

F(1)-ATPase is a rotary motor protein in which 3 catalytic β-subunits in a stator α(3)β(3) ring undergo unidirectional and cooperative conformational changes to rotate the rotor γ-subunit upon adenosine triphosphate hydrolysis. The prevailing view of the mechanism behind this rotary catalysis elevated the γ-subunit as a "dictator" completely controlling the chemical and conformational states of the 3 catalytic β-subunits. However, our recent observations using high-speed atomic force microscopy clearly revealed that the 3 β-subunits undergo cyclic conformational changes even in the absence of the rotor γ-subunit, thus dethroning it from its dictatorial position. Here, we introduce our results in detail and discuss the possible operating principle behind the F(1)-ATPase, along with structurally related hexameric ATPases, also mentioning the possibility of generating hybrid nanomotors. This article is part of a Special Issue entitled: 17th European Bioenergetics Conference (EBEC 2012).