Efficient use of single molecule time traces to resolve kinetic rates, models and uncertainties

Single molecule time traces reveal the time evolution of unsynchronized kinetic systems. Especially single molecule F\"orster resonance energy transfer (smFRET) provides access to enzymatically important timescales, combined with molecular distance resolution and minimal interference with the sample. Yet the kinetic analysis of smFRET time traces is complicated by experimental shortcomings - such as photo-bleaching and noise. Here we recapitulate the fundamental limits of single molecule fluorescence that render the classic, dwell-time based kinetic analysis unsuitable. In contrast, our Single Molecule Analysis of Complex Kinetic Sequences (SMACKS) considers every data point and combines the information of many short traces in one global kinetic rate model. We demonstrate the potential of SMACKS by resolving the small kinetic effects caused by different ionic strengths in the chaperone protein Hsp90. These results show an unexpected interrelation between conformational dynamics and ATPase activity in Hsp90.Comment: 17 pages, 6 figure

Experiment-friendly kinetic analysis of single molecule data in and out of equilibrium

We present a simple and robust technique to extract kinetic rate models and thermodynamic quantities from single molecule time traces. SMACKS (Single Molecule Analysis of Complex Kinetic Sequences) is a maximum likelihood approach that works equally well for long trajectories as for a set of short ones. It resolves all statistically relevant rates and also their uncertainties. This is achieved by optimizing one global kinetic model based on the complete dataset, while allowing for experimental variations between individual trajectories. In particular, neither a priori models nor equilibrium have to be assumed. The power of SMACKS is demonstrated on the kinetics of the multi-domain protein Hsp90 measured by smFRET (single molecule F\"orster resonance energy transfer). Experiments in and out of equilibrium are analyzed and compared to simulations, shedding new light on the role of Hsp90's ATPase function. SMACKS pushes the boundaries of single molecule kinetics far beyond current methods.Comment: 11 pages, 8 figure

Towards Synthetic Molecular Motors Interfaced by AFM

Molecular machines are at the ultimate limit of miniaturization. Living organisms provide a variety of examples for such molecular machines, but in order to utilize and to control them, they need to be interfaced with the macroscopic world. On the other h and, there are synthetic molecular machines. Some have been interfaced already but usually in high vacuum at very low temperatures, which is clearly not desirable for technical applications. In this thesis, AFM-based single molecule force spectroscopy (S M FS) was utilized to investigate the mechanical change in single synthetic molecules upon environmental changes (external stimuli) in liquid environment at room temperature. The molecules are either from theory or from bulk experiments supposed to be ab le to convert such an external stimulus into mechanical work, which is a prerequisite for molecular motors. Three different types of molecules and various external energy inputs were investigated which led to the realization of a light driven synthetic mo le cular machine: - Polyelectrolytes should, by OSF-theory, change their persistence length (and therefore the overall length at a constant force) with the Debye screening length of the solvent (which is manipulated by the salt concentration). Therefore, t he elasticity of the polyelectrolyte polyvinylamine, which could be covalently attached to the substrate and the AFM tip, was investigated in dependence on the salt concentration. It was found that the dependence of persistence length on salt concentr atio n is much smaller than expected from OSF-theory, which made this system less attractive for a molecular machine, but led to new theoretical insights. - The adhesive properties of polyelectrolytes onto charged solid supports in aqueous solution are a subj ect of current research in industry and academia. A manipulation of polymer – substrate adhesion, e. g. at an AFM tip, could lead to a molecular 'grab and release' device. Therefore, the desorption force of single polyvinylamine-molecules from solid suppo rts was investigated. Polyvinylamine was physisorbed to a glass substrate and covalently attached to the cantilever. Then, the charge-charge interaction was manipulated by variation in salt concentration and polymer charge. While this has not led t o a sin gle molecule device yet, it gave new insights into the desorption of polyelectrolytes from charged substrates. The measurements performed here revealed that van der Waals forces and other non-covalent chemical interactions such as hydrogen and coo rdinative bonds can by far outweigh the electrostatic coulomb force (namely at short distances), and are therefore a more promising candidate for the tuning of adhesion forces. - Elastin-based polypeptides have proven various kinds of energy conversion i n cross-linked bulk samples. The mechanism is based on a hydrophobic folding transition, which can be manipulated by temperature, salt, pH, electrochemistry, and/or by the composition (hydrophobicity) of the polymers. The difference between the folded and random state could be detected and investigated here at the level of individual polymer chains and characterized by the force-extension traces of the two polypeptides (GVGVP)nx251 and (GVGIP)nx260. Because of their different hydophobicity their folding t emperatu res lie above and below room temperature, respectively. With the polypeptide (GVGIP)nx260 the folded state was investigated extensively. All observations support the conjecture, that intermolecular aggregation dominates intramolecular aggregatio n. This i s further supported by the finding that neither a change in temperature nor the treatment with sodium dodecyl sulfate or guanidinium hydrochloride could force any of the two polypeptides from the folded to the random state or vice versa within a n experime nt, which in turn would be a prerequisite for a polypeptide based molecular motor. - The most successful approach to building an AFM-interfaced molecular machine was in taking advantage of reversible configurational changes in azobenzene poly mer molecul es upon irradiation with light. Azobenzene can be driven from a shorter 'cis' to a longer 'trans' configuration by illumination with l = 420 nm light and vice versa by l = 365 nm. In order to utilize azobenzene, a setup had to be developed and built, whic h allows for the coupling of light into the AFM experiment. Total internal reflection geometry was necessary to avoid any artifacts due to direct effects of the light on the cantilever. A polypeptide chain with multiple functional azobenzene units was cov alently fixed to both, a gold coated cantilever and a flint glass substrate. In the force-extension traces lengthening as well as shortening of the polyazopeptide was observed even under an applied external force. This is not only a proof of principle for the first single molecule motor interfaced to the macroscopic world, but also generates discussion concerning potential energy landscapes under external force.Molekulare Maschinen stellen eine Grenze der Miniaturisierung dar. Lebende Organismen beinhalten eine Vielzahl solcher molekularer Maschinen, aber um diese zu nutzen und zu kontrollieren, müssen sie mit der makroskopischen Welt verbunden werden, was immer noch außerordentlich schwierig ist. Außerdem wird deren kontrollierter Einsatz durch ein oft unvollständiges Verständnis der Funktion und der Struktur erschwert. Andererseits gibt es synthetische molekulare Maschinen, diese können gezielt konstruiert wer den und erlauben einfache Funktionen auszuführen. In dieser Arbeit wurde Einzelmolekül-Kraftspektroskopie dazu verwendet, die mechanische Antwort einzelner synthetischer Moleküle auf externe Anregungen in flüssiger Umgebung bei Raumtemperatur zu messen. V on den untersuchten Molekülen wurde erwartet, dass sie eine externe Anregung in mechanische Arbeit umwandeln können. Es wurden drei verschiedenartige Moleküle und viele verschiedene Anregungen untersucht: Zuerst wurde die Elastizität des Polyelektroly te n Polyvinylamin in Abhängigkeit von der Salzkonzentration untersucht. Theoretisch sollten Polyelektrolyte ihre Persistenzlänge (und damit die Länge bei konstanter Kraft) mit der Salzkonzentration ändern. Die Experimente zeigten, dass diese Abhängigkeit de utlich geringer ist als erwartet. Dies macht das System für eine molekulare Maschine ungeeignet, führte aber zu neuen Einsichten bei der Beschreibung von Polyelektrolyten. Außerdem konnte das Verständnis der Adhäsion (einzelner) Polyelektrolyte an ge lade nen festen Oberflächen in wässriger Lösung erweitert werden. Die durchgeführten Messungen zeigten, dass van der Waals Kräfte und andere chemische Wechselwirkungen (z. B. Wasserstoffbrücken, koordinative Bindungen) die Coulomb Wechselwirkungen bei wei tem ü bertreffen können. Mit Peptiden, die auf Elastin basieren, wurden in vernetzten Sytemen vielfältige Energieumwandlungen demonstriert. Der Mechanismus basiert auf einem hydrophoben Faltungsübergang, der durch äußere Einflüsse kontrolliert werden ka nn. In dieser Arbeit wurden der gefaltete und der ungefalteten Zustand auf molekularer Ebene mit den beiden Polypeptiden (GVGVP)nx251 und (GVGIP)nx260 charakterisiert. Die Messungen weisen darauf hin, dass in diesen Systemen intermolekulare Aggregation ei ne Vor aussetzung zur hydrophoben Faltung ist. Dies erschwert eine Verwendung dieser Peptide als molekulare Maschinen. Schließlich wurde ein Polymer mit mehreren funktionellen Azobenzol-Einheiten untersucht. Azobenzol kann reversibel mit Licht verschiede ner Wellenlängen von einer kürzeren 'cis' in eine längere 'trans' Konfiguration geschaltet werden. Diese Isomerisation ist die Grundlage für die erfolgreiche Konstruktion einer molekularen Maschine, die mit dem AFM verbunden ist. Ein einzelnes Azobenzol-P olymer wurde kovalent an den Cantilever und die Unterlage gebunden. Das Licht einer Blitzlampe wurde in 'Totaler Interner Reflexions Geometrie' in einen Glas-Objektträger eingekoppelt, um Artefakte durch direkte Bestrahlung des Cantilevers zu vermeiden. I n Kraft-Abstands Kurven konnte bei Bestrahlung mit Licht der entsprechenden Wellenlänge sowohl die Verkürzung als auch die Verlängerung des Polymers auch gegen eine äußere Kraft beobachtet werden. Dies ist der erste lichtgetriebenen Einzelmolekül-Motor, der mit der makroskopischen Welt verbunden werden konnte. Außerdem haben diese Experimente zu neuen Erkenntnisse über Potential-Landschaften unter einer externen Kraft geführt

Adsorption mechanism and valency of catechol-functionalized hyperbranched polyglycerols

Nature often serves as a model system for developing new adhesives. In aqueous environments, mussel-inspired adhesives are promising candidates. Understanding the mechanism of the extraordinarily strong adhesive bonds of the catechol group will likely aid in the development of adhesives. With this aim, we study the adhesion of catechol-based adhesives to metal oxides on the molecular level using atomic force microscopy (AFM). The comparison of single catechols (dopamine) with multiple catechols on hyperbranched polyglycerols (hPG) at various pH and dwell times allowed us to further increase our understanding. In particular, we were able to elucidate how to achieve strong bonds of different valency. It was concluded that hyperbranched polyglycerols with added catechol end groups are promising candidates for durable surface coatings

Single Lipid Extraction: The Anchoring Strength of Cholesterol in Liquid-Ordered and Liquid-Disordered Phases

AbstractCholesterol is important for the formation of microdomains in supported lipid bilayers and is enriched in the liquid-ordered phase. To understand the interactions leading to this enrichment, we developed an AFM-based single-lipid-extraction (SLX) approach that enables us to determine the anchoring strength of cholesterol in the two phases of a phase-separated lipid membrane. As expected, the forces necessary for extracting a single cholesterol molecule from liquid-ordered phases are significantly higher than for extracting it from the liquid-disordered phases. Interestingly, application of the Bell model shows two energy barriers that correlate with the head and full length of the cholesterol molecule. The resulting lifetimes for complete extraction are 90 s and 11 s in the liquid-ordered and liquid-disordered phases, respectively. Molecular dynamics simulations of the very same experiment show similar force profiles and indicate that the stabilization of cholesterol in the liquid-ordered phase is mainly due to nonpolar contacts

The effect of temperature on single-polypeptide adsorption

The hydrophobic attraction (HA) is believed to be one of the main driving forces for protein folding. Understanding its temperature dependence promises a deeper understanding of protein folding. Herein, we present an approach to investigate the HA with a combined experimental and simulation approach, which is complementary to previous studies on the temperature dependence of the solvation of small hydrophobic spherical particles. We determine the temperature dependence of the free-energy change and detachment length upon desorption of single polypeptides from hydrophobic substrates in aqueous environment. Both the atomic force microscopy (AFM) based experiments and the molecular dynamics (MD) simulations show only a weak dependence of the free energy change on temperature. In fact, depending on the substrate, we find a maximum or a minimum in the temperature-dependent free energy change, meaning that the entropy increases or decreases with temperature for different substrates. These observations are in contrast to the solvation of small hydrophobic particles and can be rationalized by a compensation mechanism between the various contributions to the desorption force. On the one hand this is reminiscent of the protein folding process, where large entropic and enthalpic contributions compensate each other to result in a small free energy difference between the folded and unfolded state. On the other hand, the protein folding process shows much stronger temperature dependence, pointing to a fundamental difference between protein folding and adsorption. Nevertheless such temperature dependent single molecule desorption studies open large possibilities to study equilibrium and non-equilibrium processes dominated by the hydrophobic attraction

Hydration effects turn a highly stretched polymer from an entropic into an energetic spring

Polyethylene glycol (PEG) is a structurally simple and nontoxic water-soluble polymer that is widely used in medical and pharmaceutical applications as molecular linker and spacer. In such applications, PEG’s elastic response against conformational deformations is key to its function. According to text-book knowledge, a polymer reacts to the stretching of its end-to-end separation by a decrease in entropy that is due to the reduction of available conformations, which is why polymers are commonly called entropic springs. By a combination of single-molecule force spectroscopy experiments with molecular dynamics simulations in explicit water, we show that entropic hydration effects almost exactly compensate the chain conformational entropy loss at high stretching. Our simulations reveal that this entropic compensation is due to the stretching-induced release of water molecules that in the relaxed state form double hydrogen bonds with PEG. As a consequence, the stretching response of PEG is predominantly of energetic, not of entropic, origin at high forces and caused by hydration effects, while PEG backbone deformations only play a minor role. These findings demonstrate the importance of hydration for the mechanics of macromolecules and constitute a case example that sheds light on the antagonistic interplay of conformational and hydration degrees of freedom

Conformational dynamics of a single protein monitored for 24 hours at video rate

We use plasmon rulers to follow the conformational dynamics of a single protein for up to 24 h at a video rate. The plasmon ruler consists of two gold nanospheres connected by a single protein linker. In our experiment, we follow the dynamics of the molecular chaperone heat shock protein 90, which is known to show open and closed conformations. Our measurements confirm the previously known conformational dynamics with transition times in the second to minute time scale and reveals new dynamics on the time scale of minutes to hours. Plasmon rulers thus extend the observation bandwidth 3/4 orders of magnitude with respect to single-molecule fluorescence resonance energy transfer and enable the study of molecular dynamics with unprecedented precision

On the relationship between peptide adsorption resistance and surface contact angle: a combined experimental and simulation single-molecule study

The force-induced desorption of single peptide chains from mixed OH/CH3-terminated self-assembled monolayers is studied in closely matched molecular dynamics simulations and atomic force microscopy experiments with the goal to gain microscopic understanding of the transition between peptide adsorption and adsorption resistance as the surface contact angle is varied. In both simulations and experiments, the surfaces become adsorption resistant against hydrophilic as well as hydrophobic peptides when their contact angle decreases below θ ≈ 50°-60°, thus confirming the so-called Berg limit established in the context of protein and cell adsorption. Entropy/enthalpy decomposition of the simulation results reveals that the key discriminator between the adsorption of different residues on a hydrophobic monolayer is of entropic nature and thus is suggested to be linked to the hydrophobic effect. By pushing a polyalanine peptide onto a polar surface, simulations reveal that the peptide adsorption resistance is caused by the strongly bound water hydration layer and characterized by the simultaneous gain of both total entropy in the system and total number of hydrogen bonds between water, peptide, and surface. This mechanistic insight into peptide adsorption resistance might help to refine design principles for anti-fouling surfaces