Molecular jamming - the cystine slipknot mechanical clamp in all-atom simulations

A recent survey of 17 134 proteins has identified a new class of proteins which are expected to yield stretching induced force-peaks in the range of 1 nN. Such high force peaks should be due to forcing of a slip-loop through a cystine ring, i.e. by generating a cystine slipknot. The survey has been performed in a simple coarse grained model. Here, we perform all-atom steered molecular dynamics simulations on 15 cystine knot proteins and determine their resistance to stretching. In agreement with previous studies within a coarse grained structure based model, the level of resistance is found to be substantially higher than in proteins in which the mechanical clamp operates through shear. The large stretching forces arise through formation of the cystine slipknot mechanical clamp and the resulting steric jamming. We elucidate the workings of such a clamp in an atomic detail. We also study the behavior of five top strength proteins with the shear-based mechanostability in which no jamming is involved. We show that in the atomic model, the jamming state is relieved by moving one amino acid at a time and there is a choice in the selection of the amino acid that advances the first. In contrast, the coarse grained model also allows for a simultaneous passage of two amino acids

BSDB: the biomolecule stretching database

We describe the Biomolecule Stretching Data Base that has been recently set up at http://www.ifpan.edu.pl/BSDB/. It provides information about mechanostability of proteins. Its core is based on simulations of stretching of 17 134 proteins within a structure-based model. The primary information is about the heights of the maximal force peaks, the force–displacement patterns, and the sequencing of the contact-rupturing events. We also summarize the possible types of the mechanical clamps, i.e. the motifs which are responsible for a protein's resistance to stretching

Mechanical Strength of 17 134 Model Proteins and Cysteine Slipknots

A new theoretical survey of proteins' resistance to constant speed stretching is performed for a set of 17 134 proteins as described by a structure-based model. The proteins selected have no gaps in their structure determination and consist of no more than 250 amino acids. Our previous studies have dealt with 7510 proteins of no more than 150 amino acids. The proteins are ranked according to the strength of the resistance. Most of the predicted top-strength proteins have not yet been studied experimentally. Architectures and folds which are likely to yield large forces are identified. New types of potent force clamps are discovered. They involve disulphide bridges and, in particular, cysteine slipknots. An effective energy parameter of the model is estimated by comparing the theoretical data on characteristic forces to the corresponding experimental values combined with an extrapolation of the theoretical data to the experimental pulling speeds. These studies provide guidance for future experiments on single molecule manipulation and should lead to selection of proteins for applications. A new class of proteins, involving cystein slipknots, is identified as one that is expected to lead to the strongest force clamps known. This class is characterized through molecular dynamics simulations.Comment: 40 pages, 13 PostScript figure

Deconvolution of dynamic mechanical networks

Time-resolved single-molecule biophysical experiments yield data that contain a wealth of dynamic information, in addition to the equilibrium distributions derived from histograms of the time series. In typical force spectroscopic setups the molecule is connected via linkers to a read-out device, forming a mechanically coupled dynamic network. Deconvolution of equilibrium distributions, filtering out the influence of the linkers, is a straightforward and common practice. We have developed an analogous dynamic deconvolution theory for the more challenging task of extracting kinetic properties of individual components in networks of arbitrary complexity and topology. Our method determines the intrinsic linear response functions of a given molecule in the network, describing the power spectrum of conformational fluctuations. The practicality of our approach is demonstrated for the particular case of a protein linked via DNA handles to two optically trapped beads at constant stretching force, which we mimic through Brownian dynamics simulations. Each well in the protein free energy landscape (corresponding to folded, unfolded, or possibly intermediate states) will have its own characteristic equilibrium fluctuations. The associated linear response function is rich in physical content, since it depends both on the shape of the well and its diffusivity---a measure of the internal friction arising from such processes like the transient breaking and reformation of bonds in the protein structure. Starting from the autocorrelation functions of the equilibrium bead fluctuations measured in this force clamp setup, we show how an experimentalist can accurately extract the state-dependent protein diffusivity using a straightforward two-step procedure.Comment: 9 pages, 3 figures + supplementary material 14 pages, 4 figure

Virus shapes and buckling transitions in spherical shells

We show that the icosahedral packings of protein capsomeres proposed by Caspar and Klug for spherical viruses become unstable to faceting for sufficiently large virus size, in analogy with the buckling instability of disclinations in two-dimensional crystals. Our model, based on the nonlinear physics of thin elastic shells, produces excellent one parameter fits in real space to the full three-dimensional shape of large spherical viruses. The faceted shape depends only on the dimensionless Foppl-von Karman number \gamma=YR^2/\kappa, where Y is the two-dimensional Young's modulus of the protein shell, \kappa is its bending rigidity and R is the mean virus radius. The shape can be parameterized more quantitatively in terms of a spherical harmonic expansion. We also investigate elastic shell theory for extremely large \gamma, 10^3 < \gamma < 10^8, and find results applicable to icosahedral shapes of large vesicles studied with freeze fracture and electron microscopy.Comment: 11 pages, 12 figure

Controlled assembly of SNAP-PNA-fluorophore systems on DNA templates to produce fluorescence resonance energy transfer

The SNAP protein is a widely used self-labeling tag that can be used for tracking protein localization and trafficking in living systems. A model system providing controlled alignment of SNAP-tag units can provide a new way to study clustering of fusion proteins. In this work, fluorescent SNAP-PNA conjugates were controllably assembled on DNA frameworks forming dimers, trimers, and tetramers. Modification of peptide nucleic acid (PNA) with the O6-benzyl guanine (BG) group allowed the generation of site-selective covalent links between PNA and the SNAP protein. The modified BG-PNAs were labeled with fluorescent Atto dyes and subsequently chemo-selectively conjugated to SNAP protein. Efficient assembly into dimer and oligomer forms was verified via size exclusion chromatography (SEC), electrophoresis (SDS-PAGE), and fluorescence spectroscopy. DNA directed assembly of homo- and hetero-dimers of SNAP-PNA constructs induced homo- and hetero-FRET, respectively. Longer DNA scaffolds controllably aligned similar fluorescent SNAP-PNA constructs into higher oligomers exhibiting homo-FRET. The combined SEC and homo-FRET studies indicated the 1:1 and saturated assemblies of SNAP-PNA-fluorophore:DNA formed preferentially in this system. This suggested a kinetic/stoichiometric model of assembly rather than binomially distributed products. These BG-PNA-fluorophore building blocks allow facile introduction of fluorophores and/or assembly directing moieties onto any protein containing SNAP. Template directed assembly of PNA modified SNAP proteins may be used to investigate clustering behavior both with and without fluorescent labels which may find use in the study of assembly processes in cells

Extraction of Accurate Biomolecular Parameters from Single-Molecule Force Spectroscopy Experiments

The atomic force microscope (AFM) is able to manipulate biomolecules and their complexes with exquisite force sensitivity and distance resolution. This capability, complemented by theoretical models, has greatly improved our understanding of the determinants of mechanical strength in proteins and revealed the diverse effects of directional forces on the energy landscape of biomolecules. In unbinding experiments, the interacting partners are usually immobilized on their respective substrates via extensible linkers. These linkers affect both the force and contour length (Lc) of the complex at rupture. Surprisingly, while the former effect is well understood, the latter is largely neglected, leading to incorrect estimations of Lc, a parameter that is often used as evidence for the detection of specific interactions and remodeling events and for the inference of interaction regions. To address this problem, a model that predicts contour length measurements from single-molecule forced-dissociation experiments is presented that considers attachment position on the AFM tip, geometric effects, and polymer dynamics of the linkers. Modeled data are compared with measured contour length distributions from several different experimental systems, revealing that current methods underestimate contour lengths. The model enables nonspecific interactions to be identified unequivocally, allows accurate determination of Lc, and, by comparing experimental and modeled distributions, enables partial unfolding events before rupture to be identified unequivocally

Single-molecule experiments in biological physics: methods and applications

I review single-molecule experiments (SME) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SME it is possible to: manipulate molecules one at a time and measure distributions describing molecular properties; characterize the kinetics of biomolecular reactions and; detect molecular intermediates. SME provide the additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SME it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level emphasizing the importance of SME to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques. The review discusses SME from an experimental perspective, first exposing the most common experimental methodologies and later presenting various molecular systems where such techniques have been applied. I briefly discuss experimental techniques such as atomic-force microscopy (AFM), laser optical tweezers (LOT), magnetic tweezers (MT), biomembrane force probe (BFP) and single-molecule fluorescence (SMF). I then present several applications of SME to the study of nucleic acids (DNA, RNA and DNA condensation), proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discuss applications of SME to the study of the nonequilibrium thermodynamics of small systems and the experimental verification of fluctuation theorems. I conclude with a discussion of open questions and future perspectives.Comment: Latex, 60 pages, 12 figures, Topical Review for J. Phys. C (Cond. Matt

Force unfolding kinetics of RNA using optical tweezers. II. Modeling experiments

By exerting mechanical force it is possible to unfold/refold RNA molecules one at a time. In a small range of forces, an RNA molecule can hop between the folded and the unfolded state with force-dependent kinetic rates. Here, we introduce a mesoscopic model to analyze the hopping kinetics of RNA hairpins in an optical tweezers setup. The model includes different elements of the experimental setup (beads, handles and RNA sequence) and limitations of the instrument (time lag of the force-feedback mechanism and finite bandwidth of data acquisition). We investigated the influence of the instrument on the measured hopping rates. Results from the model are in good agreement with the experiments reported in the companion article (1). The comparison between theory and experiments allowed us to infer the values of the intrinsic molecular rates of the RNA hairpin alone and to search for the optimal experimental conditions to do the measurements. We conclude that long handles and soft laser traps represent the best conditions to extract rate estimates that are closest to the intrinsic molecular rates. The methodology and rationale presented here can be applied to other experimental setups and other molecules.Comment: PDF file, 32 pages including 9 figures plus supplementary materia

Conformational rearrangements in the transmembrane domain of CNGA1 channels revealed by single-molecule force spectroscopy

Cyclic nucleotide-gated (CNG) channels are activated by binding of cyclic nucleotides. Although structural studies have identified the channel pore and selectivity filter, conformation changes associated with gating remain poorly understood. Here we combine single-molecule force spectroscopy (SMFS) with mutagenesis, bioinformatics and electrophysiology to study conformational changes associated with gating. By expressing functional channels with SMFS fingerprints in Xenopus laevis oocytes, we were able to investigate gating of CNGA1 in a physiological-like membrane. Force spectra determined that the S4 transmembrane domain is mechanically coupled to S5 in the closed state, but S3 in the open state. We also show there are multiple pathways for the unfolding of the transmembrane domains, probably caused by a different degree of \u3b1-helix folding. This approach demonstrates that CNG transmembrane domains have dynamic structure and establishes SMFS as a tool for probing conformational change in ion channels