Statistics of reversible bond dynamics observed in force-clamp spectroscopy

We present a detailed analysis of two-state trajectories obtained from force-clamp spectroscopy (FCS) of reversibly bonded systems. FCS offers the unique possibility to vary the equilibrium constant in two-state kinetics, for instance the unfolding and refolding of biomolecules, over many orders of magnitude due to the force dependency of the respective rates. We discuss two different kinds of counting statistics, the event-counting usually employed in the statistical analysis of two-state kinetics and additionally the so-called cycle-counting. While in the former case all transitions are counted, cycle-counting means that we focus on one type of transitions. This might be advantageous in particular if the equilibrium constant is much larger or much smaller than unity because in these situations the temporal resolution of the experimental setup might not allow to capture all transitions of an event-counting analysis. We discuss how an analysis of FCS data for complex systems exhibiting dynamic disorder might be performed yielding information about the detailed force-dependence of the transition rates and about the time scale of the dynamic disorder. In addition, the question as to which extent the kinetic scheme can be viewed as a Markovian two-state model is discussed.Comment: 25 pages, 10 figures, Phys. Rev. E, in pres

Force-clamp spectroscopy of reversible bond breakage

We consider reversible breaking of adhesion bonds or folding of proteins under the influence of a constant external force. We discuss the stochastic properties of the unbinding/rebinding events and analyze their mean number and their variance in the framework of simple two-state models. In the calculations, we exploit the analogy to single molecule fluorescence and particularly between unbinding/rebinding and photon emission events. Environmental fluctuation models are used to describe deviations from Markovian behavior. The second moment of the event-number distribution is found to be very sensitive to possible exchange processes and can thus be used to identify temporal fluctuations of the transition rates.Comment: 8 pages, 4 figure

Dynamic force spectroscopy: analysis of reversible bond-breaking dynamics

The problem of diffusive bond-dissociation in a double well potential under application of an external force is scrutinized. We compute the probability distribution of rupture forces and present a detailed discussion of the influence of finite rebinding probabilities on the dynamic force spectrum. In particular, we focus on barrier crossing upon extension, i.e. under linearly increased load, and upon relaxation starting from completely separated bonds. For large loading rates the rupture force and the rejoining force depend on the loading rate in the expected manner determined by the shape of the potential. For small loading rates the mean forces obtained from pull and relax modes approach each other as the system reaches equilibrium. We investigate the dependence of the rupture force distributions and mean rupture forces on external parameters like cantilever stiffness and influence of a soft linker. We find that depending on the implementation of a soft linker the equilibrium rupture force is either unaffected by the presence of the linker or changes in a predictable way with the linker-compliance. Additionally, we show that it is possible to extract the equilibrium constant of the on- and off-rates from the determination of the equilibrium rupture forces.Comment: 32 pages, 14 figure

SNARE-mediated membrane fusion trajectories derived from force-clamp experiments.

Fusion of lipid bilayers is usually prevented by large energy barriers arising from removal of the hydration shell, formation of highly curved structures, and, eventually, fusion pore widening. Here, we measured the force-dependent lifetime of fusion intermediates using membrane-coated silica spheres attached to cantilevers of an atomic-force microscope. Analysis of time traces obtained from force-clamp experiments allowed us to unequivocally assign steps in deflection of the cantilever to membrane states during the SNARE-mediated fusion with solid-supported lipid bilayers. Force-dependent lifetime distributions of the various intermediate fusion states allowed us to propose the likelihood of different fusion pathways and to assess the main free energy barrier, which was found to be related to passing of the hydration barrier and splaying of lipids to eventually enter either the fully fused state or a long-lived hemifusion intermediate. The results were compared with SNARE mutants that arrest adjacent bilayers in the docked state and membranes in the absence of SNAREs but presence of PEG or calcium. Only with the WT SNARE construct was appreciable merging of both bilayers observed

Structural and functional characterization of the two phosphoinositide binding sites of PROPPINs.

β-propellers that bind polyphosphoinositides (PROPPINs), a eukaryotic WD-40 motif-containing protein family, bind via their predicted β-propeller fold the polyphosphoinositides PtdIns3P and PtdIns(3,5)P2 using a conserved FRRG motif. PROPPINs play a key role in macroautophagy in addition to other functions. We present the 3.0-Å crystal structure of Kluyveromyces lactis Hsv2, which shares significant sequence homologies with its three Saccharomyces cerevisiae homologs Atg18, Atg21, and Hsv2. It adopts a seven-bladed β-propeller fold with a rare nonvelcro propeller closure. Remarkably, in the crystal structure, the two arginines of the FRRG motif are part of two distinct basic pockets formed by a set of highly conserved residues. In comprehensive in vivo and in vitro studies of ScAtg18 and ScHsv2, we define within the two pockets a set of conserved residues essential for normal membrane association, phosphoinositide binding, and biological activities. Our experiments show that PROPPINs contain two individual phosphoinositide binding sites. Based on docking studies, we propose a model for phosphoinositide binding of PROPPINs

Defect formation of lytic peptides in lipid membranes and their influence on the thermodynamic properties of the pore environment

We present an experimental study of the pore formation processes of small amphipathic peptides in model phosphocholine lipid membranes. We used atomic force microscopy to characterize the spatial organization and structure of alamethicin- and melittin- induced defects in lipid bilayer membranes and the influence of the peptide on local membrane properties. Alamethicin induced holes in gel DPPC membranes were directly visualized at different peptide concentrations. We found that the thermodynamic state of lipids in gel membranes can be influenced by the presence of alamethicin such that nanoscopic domains of fluid lipids form close to the peptide pores, and that the elastic constants of the membrane are altered in their vicinity. Melittin-induced holes were visualized in DPPC and DLPC membranes at room temperature in order to study the influence of the membrane state on the peptide induced hole formation. Also differential scanning calorimetry was used to investigate the effect of alamethicin on the lipid membrane phase behavior.Comment: 11 pages, 7 figures, 1 tabl

Functionalized calix[8]arenes, synthesis and self-assembly on graphite

With the intention of building hollow tubular structures by self-assembly, we have designed and successfully synthesized a series of calix[8]arene derivatives. Their phenolic units were functionalized in p-position by various groups which are able to interact via hydrogen bonding or π-π stacking. Ethynyl, amide, urea, or imide links were chosen for the covalent attachment of these functional groups, to ensure the adjustment of an optimal distance for their interaction. Two different kinds of nanostructures selfassembled on a highly oriented pyrolytic graphite (HOPG) surface were found by scanning force microscopy: parallel aligned nanorods in which the calixarene molecules are adsorbed edge-on on the graphite, providing evidence that these calix[8]arene derivatives stack in a tubular fashion, and micrometer long fiber bundles most probably composed of many nanorods. © 2005 American Chemical Society

Oscillatory Microrheology, Creep Compliance and Stress Relaxation of Biological Cells Reveal Strong Correlations as Probed by Atomic Force Microscopy

The mechanical properties of cells are important for many biological processes, including wound healing, cancers, and embryogenesis. Currently, our understanding of cell mechanical properties remains incomplete. Different techniques have been used to probe different aspects of the mechanical properties of cells, among them microplate rheology, optical tweezers, micropipette aspiration, and magnetic twisting cytometry. These techniques have given rise to different theoretical descriptions, reaching from simple Kelvin-Voigt or Maxwell models to fractional such as power law models, and their combinations. Atomic force microscopy (AFM) is a flexible technique that enables global and local probing of adherent cells. Here, using an AFM, we indented single retinal pigmented epithelium cells adhering to the bottom of a culture dish. The indentation was performed at two locations: above the nucleus, and towards the periphery of the cell. We applied creep compliance, stress relaxation, and oscillatory rheological tests to wild type and drug modified cells. Considering known fractional and semi-fractional descriptions, we found the extracted parameters to correlate. Moreover, the Young’s modulus as obtained from the initial indentation strongly correlated with all of the parameters from the applied power-law descriptions. Our study shows that the results from different rheological tests are directly comparable. This can be used in the future, for example, to reduce the number of measurements in planned experiments. Apparently, under these experimental conditions, the cells possess a limited number of degrees of freedom as their rheological properties change

Supramolecular Structures Formed by Calix[8]arene Derivatives

(Equation presented) Octamethoxy calix[8]arenes substituted in the para position by amide, urea, and imide functions were synthesized from the octamethyl ether of tert-butylcalix[8]arene by ipso nitration, reduction, and acylation. Scanning force microscopy of spin coated samples on graphite suggests that these derivatives self-organize into tubular nanorods via hydrogen bonds between p-amide functions. A single-crystal X-ray structure reveals a centrosymmetric conformation for the octanitro derivative