Session T11: Focus Session: Single Molecule Biophysics and Chemical Physics V

Single Molecule Force Spectroscopy using Optical Traps and AFMs

Force spectroscopy is an important single-molecule technique to study the energetics and dynamics of biological systems. Both optical traps and atomic force microscopes (AFMs) can measure the dynamics of individual molecules. My talk will focus on two intellectually distinct ways to improve these experiments: passive force clamps and an optically stabilized AFM. To increase measurement precision, feedback is used to maintain a constant force on a molecule -- often called a force clamp. Precise yet rapid active feedback is limited by Brownian motion. This limited bandwidth leads to significant fluctuations in force that are particularly pronounced for the rapid, large changes in extension seen in nucleic acid structures (e.g. DNA hairpins, ribozymes, riboswitches). Here, we show that the dynamics determined in active force clamps are five-to-seven fold different than in a passive force clamp, which has a $\sim $30-fold faster control of force. Thus, the dynamics of biological molecules can be significantly altered by the mechanism of force feedback. In AFM-based force spectroscopy experiments, force versus extension curves are generated by retracting the tip using a PZT stage while measuring force via cantilever deflection. Extension is inferred, not measured, and therefore convolved with drift in the AFM assembly ($\sim $10 nm/min). We developed an ultrastable AFM by scattering a laser off the apex of a commercial AFM tip to measure and thereby stabilize the tip in 3D. A second laser stabilized the sample, leading to a 100-fold improvement in tip-sample stability compared to the previous state-of-the-art at ambient conditions (in air at room temperature). We next demonstrated simultaneous and independent measurement of extension and force in liquid. Preliminary studies of bacteriorhodopsin, a model membrane protein, highlight this instrument's unique force- and position-clamp modes.   

Characterization of mechanical properties of Type IV pili (Tfp) using atomic force microscopy

Type IV pili (Tfp) are thin flexible protein filaments that extend from the cell envelope of Gram- negative bacteria. The mechanical properties of Tfp are important since they allow bacteria to establish contact with various surfaces, as a first step in the formation of biofilms. We have used atomic force microscopy (AFM) for both imaging and pulling on Tfp filaments from hyper-piliated mutants of \textit{P. aeruginosa} PAO1 that cannot retract their pili. Bacterial cells were adhered to AFM probes using poly-L-lysine. Force-extension curves were obtained for single pili and were fitted using the worm-like-chain (WLC) model. The statistical distributions obtained for pili contour length and persistence length were used to evaluate the mechanical properties of a single pilus and the biogenesis functions of different proteins (pilA, pilT) involved in its assembly and disassembly. The difference in rupture force between Tfp and different surfaces (mica, gold) was also measured. Our results shed new light on the role of mechanical forces that mediate bacteria-surface interactions and biofilm formation.   

Direct measurement of mechanical susceptibility in single-molecule proteins

A protein acquires its function through the specific structure of its polypeptide chain. A mechanical force of only a few tens of picoNewtons is sufficient to disrupt this structure and cause the protein to unfold. Conventional rheology of complex fluids seeks to understand a materials internal structures, energy landscape, and time scales of relaxation by measuring its bulk mechanical response to applied stress and strain as a function of frequency. By analogy, we propose a nano-rheological study of single-molecule proteins. To this end we report on a new AFM design, targeted at high speed force and position controlled measurements of single-molecule proteins. Using this new tool we are able to measure previously inaccessible properties of mechanically stable proteins. Using a broad spectrum force excitation technique we have measured the frequency dependent mechanical susceptibility of both folded and unfolded proteins as a function of applied force. Using these measurements we can begin to characterize the sources of dissipation or ``friction'' present in the protein.   

Semi-flexible polymer with heterogeneous bending rigidity adsorbed at interfaces

We study a generalization of the worm-like chain model to the case where different parts of the chain have different persistence length. This model is developed to analyze the effect of adsorbed proteins on semi-flexible chains. The relative fraction of heterogeneous component is controlled by adding a chemical potential term to the free energy. We present the analytic solution and several numerical examples in two dimensions.   

Sequence-Dependent Force Response During Peeling of Single Stranded DNA from Graphite

We have analyzed the statistical thermodynamics of peeling single- stranded DNA (ssDNA) from the surface of graphite. Using parameters obtained from recently reported single-molecule peeling experiments, we model ssDNA as a polymer chain strongly adsorbed to a frictionless substrate. Three polymer models were analyzed, namely, freely jointed chain, worm-like chain and rotational isomeric state models. All three models predict similar thermodynamics of peeling - steady peeling force under force control, in agreement with single-molecule experiments, and measurable spikes in force under displacement control for finite length chains ($<$25). A simple transition model was developed to predict, quantitatively, the decay in the peak and valley values of force spikes with increasing end-to-end distance of the desorbed chain. These force spikes carry information about the underlying sequence of ssDNA, which might thus be measurable with a sufficiently stiff loading system. In the case of the freely jointed chain model, under force control, we have obtained several exact closed-form results and provide relations between the measured peel force and the underlying adhesion free energy.   

Dynamics of polymer expansion out of spherical capsids

We present simulations investigating the dynamics of expanding flexible polymers while ejecting from a spherical capsid. Recent theoretical models predict that for a good solvent the number of ejected beads, $N$, follows a power law with time, $N \sim (1 + at)^{-1}$ ($a$ is a constant). Our simulation results agree with these predictions for shorter ejection times. However, we find that at larger times the remaining beads eject at a faster rate than predicted. A possible explanation is that models neglect of the polymer's entropy outside the capsid, which can contribute an additional force that aids in pulling the beads remaining in the capsid outside.   

Probing the Mechanical Properties of Plasma von Willebrand Factor Using Atomic Force Microscopy

Single-molecule manipulation allows us to study the real time kinetics of many complex cellular processes. The mechanochemistry of different forms of von Willebrand factor (VWF) and their receptor-ligand binding kinetics can be unraveled by atomic force microscopy (AFM). Since plasma VWF can be activated upon shear, the structural and functional properties of VWF are critical in mediating thrombus formation become important. Here we characterized the mechanical resistance to domain unfolding of VWF to determine the conformational states of VWF. We found the shear induced conformational, hence mechanical property changes can be detected by the change in unfolding forces. The relaxation rate of such effect is much longed than expected. This supports the model of lateral association VWF under shear stress. Our results offer an insight in establishing strategies for regulating VWF adhesion activity, increasing our understanding of surface-induced thrombosis as mediated by VWF.   

Immobilization dynamics of a tethered membrane by peptide binding - a coarse-grained computer simulation model

A coarse-grained description is used to model a tethered membrane (also a representation of a clay platelet) immersed in peptide solutions (CR3-1: \textit{Trp-Pro-Ser-Ser-Tyr-Leu-Ser-Pro-Lle-Pro-Tyr-Ser} and S2: \textit{His-Gly-Lle-Asn-Thr-Thr-Lys-Pro-Phe-Lys-ser-Val}) on a cubic lattice. Using all-atom simulations, X-ray crystallographic data, and the hydrophobicity of each residue as input, an interaction matrix is developed for residue--residue and residue-clay interactions. Dynamics of the membrane and CR3-1 or S2 peptides is examined as a function of peptide concentration among other quantities such as density profiles, binding energy of each residue, mobility and their proximity profile around the membrane. Simulations show that S2 binds to the membrane anchored by Lysine interactions while CR3-1 does not. Binding of S2 slows down the membrane, leading to its pinning. How fast the immobilization of the membrane occurs depends on the peptide concentration.   

Fluid Flows and Their Role in the Regulation of Biological Molecules in the Bloodstream

We use computer simulations to elucidate the physics underlying blood clotting mechanisms. A straightforward and general model for the behavior of proteins such as von Willebrand Factor (vWF) under various flow conditions has been developed. The particular case of vWF is considered in depth, since it demonstrates the counter-intuitive behavior of adsorbing to a surface at higher flow rates. We use the globule-stretch transition of a collapsed polymer to explain this phenomenon, and have identified the conditions necessary to induce this transition. We have also developed a theory to explain the mechanism of this transition, which is based on the nucleation and growth of large thermal protrusions. Upon the consideration of the specific length and time scales present under biological conditions, it is apparent that vWF is strongly regulated by elongational flows. We can show how phenomena from the molecular to physiological levels are supplemented by this understanding of vWF function.