Abstract: 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.

Abstract: The conformational energy landscape of a protein out of equilibrium is poorly understood. We use single-molecule force-clamp spectroscopy to measure the kinetics of unfolding of the protein ubiquitin under a constant force. We discover a surprisingly broad distribution of unfolding rates that follows a power law with no characteristic mean. The structural fluctuations that give rise to this distribution reveal the architecture of the protein’s energy landscape. Following models of glassy dynamics, this complex kinetics implies large fluctuations in the energies of the folded protein, characterized by an exponential distribution with a width of 5-10k(B)T. Our results predict the existence of a ’glass transition’ force below which the folded conformations interconvert between local minima on multiple timescales. These techniques offer a new tool to further test statistical energy landscape theories experimentally.

Abstract: Conventional Raman spectroscopy on BaTiO3 determines vibrational modes by integrating over a macroscopic sample volume. In domain-rich materials and to account for microscopic surface domains, an experimental study of the domain distribution is desirable. We applied polarized light microscopy (PLM) and piezo-response force microscopy (PFM) to 40 mum thick BaTiO3 single crystals in order to get an exact model of the domain distribution, which allows to allocate the laser spot of a micro-Raman spectrograph within a specific domain type. We are able to assign most of the Raman-active normal modes in polarized measurements, which are free of ferroelastic domain walls but not necessarily free of ferroelectric walls. We propose to study the influence of ferroelectric walls on the asymmetric peak shapes by an in situ combination of PFM and micro-Raman spectroscopy. (C) 2003 Elsevier Science B.V. All rights reserved.

Abstract: We report the 100% correlation between polarized light microscopy (PLM), piezoresponse force microscopy (PFM), and micro-Raman spectroscopy when investigating domain-rich ferroelectric systems. In order to allocate the desired spot on a submicrometer scale, both PLM and PFM were combined to elucidate the effective three-dimensional ferroelectric domain distribution. With PFM we observe spike-like a and c domains well inside extended a and c-polarized areas, which were not conclusive with PLM. The knowledge on such a domain distribution is essential when addressing quantitative micro-Raman spectroscopy. In addition, we show the unambiguous differentiation between a and c domains on the submicrometer scale using the B-2 mode of lattice vibrations. (C) 2001 American Institute of Physics.