Optical diffraction for measurements of nano-mechanical bending.

We explore and exploit diffraction effects that have been previously neglected when modelling optical measurement techniques for the bending of micro-mechanical transducers such as cantilevers for atomic force microscopy. The illumination of a cantilever edge causes an asymmetric diffraction pattern at the photo-detector affecting the calibration of the measured signal in the popular optical beam deflection technique (OBDT). The conditions that avoid such detection artefacts conflict with the use of smaller cantilevers. Embracing diffraction patterns as data yields a potent detection technique that decouples tilt and curvature and simultaneously relaxes the requirements on the illumination alignment and detector position through a measurable which is invariant to translation and rotation. We show analytical results, numerical simulations and physiologically relevant experimental data demonstrating the utility of the diffraction patterns. We offer experimental design guidelines and quantify possible sources of systematic error in OBDT. We demonstrate a new nanometre resolution detection method that can replace OBDT, where diffraction effects from finite sized or patterned cantilevers are exploited. Such effects are readily generalized to cantilever arrays, and allow transmission detection of mechanical curvature, enabling instrumentation with simpler geometry. We highlight the comparative advantages over OBDT by detecting molecular activity of antibiotic Vancomycin.

Probability of observing a number of unfolding events while stretching polyproteins.

The mechanical stretching of single polyproteins is an emerging tool for the study of protein (un)folding, chemical catalysis and polymer physics at the single molecule level. The observed processes, i.e., unfolding or reduction events, are typically considered to be stochastic and by nature are susceptible to be censored by the finite duration of the experiment. A formal analytical and experimental description on the number of observed events under various conditions of practical interest is developed. Rules of thumb are provided to define an optimal experiment protocol duration. Finally, a methodology is described to accurately estimate the real number of stretched molecules based on the number of observed unfolding events. The model-free numerical analysis applied to experimental data confirms that poly-ubiquitin binds at a random position both to the substrate and to the pulling probe.

Rate limit of protein elastic response is tether dependent.

The elastic restoring force of tissues must be able to operate over the very wide range of loading rates experienced by living organisms. It is surprising that even the fastest events involving animal muscle tissues do not surpass a few hundred hertz. We propose that this limit is set in part by the elastic dynamics of tethered proteins extending and relaxing under a changing load. Here we study the elastic dynamics of tethered proteins using a fast force spectrometer with sub-millisecond time resolution, combined with Brownian and Molecular Dynamics simulations. We show that the act of tethering a polypeptide to an object, an inseparable part of protein elasticity in vivo and in experimental setups, greatly reduces the attempt frequency with which the protein samples its free energy. Indeed, our data shows that a tethered polypeptide can traverse its free-energy landscape with a surprisingly low effective diffusion coefficient D(eff) ~ 1,200 nm(2)/s. By contrast, our Molecular Dynamics simulations show that diffusion of an isolated protein under force occurs at D(eff) ~ 10(8) nm(2)/s. This discrepancy is attributed to the drag force caused by the tethering object. From the physiological time scales of tissue elasticity, we calculate that tethered elastic proteins equilibrate in vivo with D(eff) ~ 10(4)-10(6) nm(2)/s which is two to four orders magnitude smaller than the values measured for untethered proteins in bulk.

Dwell-time distribution analysis of polyprotein unfolding using force-clamp spectroscopy.

Using the recently developed single molecule force-clamp technique we quantitatively measure the kinetics of conformational changes of polyprotein molecules at a constant force. In response to an applied force of 110 pN, we measure the dwell times of 1647 unfolding events of individual ubiquitin modules within each protein chain. We then establish a rigorous method for analyzing force-clamp data using order statistics. This allows us to test the success of a history-independent, two-state model in describing the kinetics of the unfolding process. We find that the average unfolding trajectory is independent of the number of protein modules N in each trajectory, which varies between 3 and 12 (the engineered protein length), suggesting that the unfolding events in each chain are uncorrelated. We then derive a binomial distribution of dwell times to describe the stochastic dynamics of protein unfolding. This distribution successfully describes 81% of the data with a single rate constant of alpha = 0.6 s(-1) for all N. The remainder of the data that cannot be accounted for suggests alternative unfolding barriers in the energy landscape of the protein. This method investigates the statistical features of unfolding beyond the average measurement of a single rate constant, thus providing an attractive alternative for measuring kinetics by force-clamp spectroscopy.