Oxford Molecular Motors

Abstract:

The rotary motor F(1)-ATPase from the thermophilic Bacillus PS3 (TF(1)) is one of the best-studied of all molecular machines. F(1)-ATPase is the part of the enzyme F(1)F(O)-ATP synthase that is responsible for generating most of the ATP in living cells. Single-molecule experiments have provided a detailed understanding of how ATP hydrolysis and synthesis are coupled to internal rotation within the motor. In this work, we present evidence that mesophilic F(1)-ATPase from Escherichia coli (EF(1)) is governed by the same mechanism as TF(1) under laboratory conditions. Using optical microscopy to measure rotation of a variety of marker particles attached to the γ-subunit of single surface-bound EF(1) molecules, we characterized the ATP-binding, catalytic and inhibited states of EF(1). We also show that the ATP-binding and catalytic states are separated by 35±3°. At room temperature, chemical processes occur faster in EF(1) than in TF(1), and we present a methodology to compensate for artefacts that occur when the enzymatic rates are comparable to the experimental temporal resolution. Furthermore, we show that the molecule-to-molecule variation observed at high ATP concentration in our single-molecule assays can be accounted for by variation in the orientation of the rotating markers.

Abstract:

Objective

While the importance of cortical structure quantification is increasingly underscored by recent literature, conventional analysis techniques obscure potentially important regional variations in cortical structure. The objective of this study was to characterize the spatial variability in cortical geometry and microstructure at the distal radius and tibia using high resolution peripheral quantitative computed tomography (HR-pQCT). We show that spatially-resolved analysis is able to identify cortical sub-regions with increased sensitivity to the effects of gender and aging.

Methods

HR-pQCT scans of 146 volunteers (92 female/54 male) spanning a wide range of ages (20-78years) were analyzed. For each subject, radius and tibia scans were obtained using a clinical HR-pQCT system. Measures describing geometry (cortical bone thickness (Ct.Th)), microstructure (porosity (Ct.Po), pore diameter (Ct.Po.Dm), and pore size heterogeneity (Ct.Po.Dm SD)), and cortical bone density were calculated from the image data. Biomechanical parameters describing load and stress distribution were calculated using linear finite element analysis. Cortical quadrants were defined based on anatomic axes to quantify regional parameter variation. Subjects were categorized by gender, and age, and menopausal status for analysis.

Results

Significant regional variation was found in all geometric and microstructural parameters in both the radius and tibia. In general, the radius showed more pronounced and significant variations in all parameters as compared with the tibia. At both sites, Ct.Po displayed the greatest regional variations. Correlation coefficients for Ct.Po and Ct.Th with respect to load and stress distribution provided evidence of an association between regional cortical structure and biomechanics in the tibia. Comparing women to men, differences in Ct.Po were most pronounced in the anterior quadrant of the radius (36% lower in women (p<0.01)) and the posterior quadrant of the tibia (27% lower in women (p<0.01)). Comparing elderly to young women, differences in Ct.Po were most pronounced in the lateral quadrant of the radius (328% higher in elderly women (p<0.001)) and the anterior quadrant of the tibia (433% higher in elderly women (p<0.001)). Comparing elderly to young men, the most pronounced age differences were found in the anterior radius (205% higher in elderly men, (p<0.001)) and the anterior tibia (190% higher in elderly men (p<0.01)). All subregional Ct.Po differences provided greater sensitivity to gender and age effects than those based on the global means.

Conclusion

These results show significant regional variation in all geometric and microarchitectural parameters studied in both the radius and tibia. Quantification of region-specific parameters provided increased sensitivity in the analysis of age- and gender-related differences, in many cases providing statistically significant differentiation of groups where conventional global analysis failed to detect differences. These results suggest that regional analysis may be important in studies of disease and therapeutic effects, particularly where microstructural parameters based on global analyses have thus far failed to identify a response in bone quality.

Abstract:

We consider an age-structured model that describes the regulation of erythropoiesis through the negative feedback loop between erythropoietin and hemoglobin. This model is reduced to a system of two ordinary differential equations with two constant delays for which we show existence of a unique steady state. We determine all instances at which this steady state loses stability via a Hopf bifurcation through a theoretical bifurcation analysis establishing analytical expressions for the scenarios in which they arise. We show examples of supercritical Hopf bifurcations for parameter values estimated according to physiological values for humans found in the literature and present numerical simulations in agreement with the theoretical analysis. We provide a strategy for parameter estimation to match empirical measurements and predict dynamics in experimental settings, and compare existing data on hemoglobin oscillation in rabbits with predictions of our model.

Abstract:

The bacterial flagellar motor, one of the few rotary motors in nature, produces torque to drive the flagellar filament by ion translocation through membrane-bound stator complexes. We used the light-driven proton pump proteorhodopsin (pR) to control the proton-motive force (PMF) in vivo by illumination. pR excitation was shown to be sufficient to replace native PMF generation, and when excited in cells with intact native PMF generation systems increased motor speed beyond the physiological norm. We characterized the effects of rapid in vivo PMF changes on the flagellar motor. Transient PMF disruption events from loss of illumination caused motors to stop, with rapid recovery of their previous rotation rate after return of illumination. However, extended periods of PMF loss led to stepwise increases in rotation rate upon PMF return as stators returned to the motor. The rate constant for stator binding to a putative single binding site on the motor was calculated to be 0.06 s(-1). Using GFP-tagged MotB stator proteins, we found that transient PMF disruption leads to reversible stator diffusion away from the flagellar motor, showing that PMF presence is necessary for continued motor integrity, and calculated a stator dissociation rate of 0.038 s(-1).