Direct Observation of Single-Protein Transition State Passage by Nanopore Ionic Current Jumps

Hydrogen bonding heterogeneity correlates with protein folding transition state passage time as revealed by data sonification

Protein-protein and protein-water hydrogen bonding interactions play essential roles in the way a protein passes through the transition state during folding or unfolding, but the large number of these interactions in molecular dynamics (MD) simulations makes them difficult to analyze. Here, we introduce a state space representation and associated "rarity" measure to identify and quantify transition state passage (transit) events. Applying this representation to a long MD simulation trajectory that captured multiple folding and unfolding events of the GTT WW domain, a small protein often used as a model for the folding process, we identified three transition categories: Highway (faster), Meander (slower), and Ambiguous (intermediate). We developed data sonification and visualization tools to analyze hydrogen bond dynamics before, during, and after these transition events. By means of these tools, we were able to identify characteristic hydrogen bonding patterns associated with "Highway" versus "Meander" versus "Ambiguous" transitions and to design algorithms that can identify these same folding pathways and critical protein-water interactions directly from the data. Highly cooperative hydrogen bonding can either slow down or speed up transit. Furthermore, an analysis of protein-water hydrogen bond dynamics at the surface of WW domain shows an increase in hydrogen bond lifetime from folded to unfolded conformations with Ambiguous transitions as an outlier. In summary, hydrogen bond dynamics provide a direct window into the heterogeneity of transits, which can vary widely in duration (by a factor of 10) due to a complex energy landscape.

A Marcus-Type Inverted Region in the Translocation Kinetics of a Knotted Protein

Knotted proteins are rare but important species, yet how their complex topologies affect their physical properties is not fully understood. Here we combine single molecule nanopore experiments and all-atom MD simulations to study the electric-field-driven unfolding during the translocation through a model pore of individual protein knots important for methylating tRNA. One of these knots shows an unusual behavior that resembles the behavior of electrons hopping between two potential surfaces: as the electric potential driving the translocation reaction is increased, the rate eventually plateaus or slows back down in the "Marcus inverted regime". Our results shed light on the influence of topology in knotted proteins on their forced translocation through a pore connecting two electrostatic potential wells.

Ultrafast Polymer Dynamics through a Nanopore

Ultrathin nanopore sensors allow single-molecule and polymer measurements at sub-microsecond time resolution enabled by high current signals (∼10-30 nA). We demonstrate for the first time the experimental probing of the ultrafast translocation and folded dynamics of double-stranded DNA (dsDNA) through a nanopore at 10 MHz bandwidth with acquisition of data points per 25 ns (150 MB/s). By introducing a rigorous algorithm, we are able to accurately identify each current level present within translocation events and elucidate the dynamic folded and unfolded behaviors. The remarkable sensitivity of this system reveals distortions of short-lived folded states at a lower bandwidth. This work revisits probing of dsDNA as a model polymer and develops broadly applicable methods. The combined improvements in sensor signals, instrumentation, and large data analysis methods uncover biomolecular dynamics at unprecedentedly small time scales.

Microscopic origin of diffusive dynamics in the context of transition path time distributions for protein folding and unfolding

Experimentally measured transition path time distributions are usually analyzed theoretically in terms of a diffusion equation over a free energy barrier. It is though well understood that the free energy profile separating the folded and unfolded states of a protein is characterized as a transition through many stable micro-states which exist between the folded and unfolded states. Why is it then justified to model the transition path dynamics in terms of a diffusion equation, namely the Smoluchowski equation (SE)? In principle, van Kampen has shown that a nearest neighbor Markov chain of thermal jumps between neighboring microstates will lead in a continuum limit to the SE, such that the friction coefficient is proportional to the mean residence time in each micro-state. However, the practical question of how many microstates are needed to justify modeling the transition path dynamics in terms of an SE has not been addressed. This is a central topic of this paper where we compare numerical results for transition paths based on the diffusion equation on the one hand and the nearest neighbor Markov jump model on the other. Comparison of the transition path time distributions shows that one needs at least a few dozen microstates to obtain reasonable agreement between the two approaches. Using the Markov nearest neighbor model one also obtains good agreement with the experimentally measured transition path time distributions for a DNA hairpin and PrP protein. As found previously when using the diffusion equation, the Markov chain model used here also reproduces the experimentally measured long time tail and confirms that the transition path barrier height is ∼3k_BT. This study indicates that in the future, when attempting to model experimentally measured transition path time distributions, one should perhaps prefer a nearest neighbor Markov model which is well defined also for rough energy landscapes. Such studies can also shed light on the minimal number of microstates needed to unravel the experimental data.

Investigation of α-Synuclein and Amyloid-β(42)-E22Δ Oligomers Using SiN Nanopore Functionalized with L-Dopa

Solid-state nanopores are an emerging technology used as a high-throughput, label-free analytical method for the characterization of protein aggregation in an aqueous solution. In this work, we used Levodopamine to coat a silicon nitride nanopore surface that was fabricated through a dielectric breakdown in order to reduce the unspecific adsorption. The coating of inner nanopore wall by investigation of the translocation of heparin. The functionalized nanopore was used to investigate the aggregation of amyloid-β and α-synuclein, two biomarkers of degenerative diseases. In the first application, we demonstrate that the α-synuclein WT is more prone to form dimers than the variant A53T. In the second one, we show for the Aβ(42)-E22Δ (Osaka mutant) that the addition of Aβ(42)-WT monomers increases the polymorphism of oligomers, while the incubation with Aβ(42)-WT fibrils generates larger aggregates.

The Effect of Time Resolution on Apparent Transition Path Times Observed in Single-Molecule Studies of Biomolecules

Single-molecule experiments have now achieved a time resolution allowing observation of transition paths, the brief trajectory segments where the molecule undergoing an unfolding or folding transition enters the energetically or entropically unfavorable barrier region from the folded/unfolded side and exits to the unfolded/folded side, thereby completing the transition. This resolution, however, is yet insufficient to identify the precise entrance/exit events that mark the beginning and the end of a transition path: the nature of the diffusive dynamics is such that a molecular trajectory will recross the boundary between the barrier region and the folded/unfolded state, multiple times, at a time scale much shorter than that of the typical experimental resolution. Here we use theory and Brownian dynamics simulations to show that, as a result of such recrossings, the apparent transition path times are generally longer than the true ones. We quantify this effect using a simple model where the observed dynamics is a moving average of the true dynamics and discuss experimental implications of our results.

Threading single proteins through pores to compare their energy landscapes

Protein function correlates with its structural dynamics. While theoretical approaches to studying protein energy landscapes are well developed, experimental methods that enable probing these landscapes of proteins remain challenging. We used solid-state nanopores to study the translocation behavior of three mutants of a helix bundle protein and quantified the number of energetically accessible conformational states for each mutant. We found that a slower-folding mutant with access to more conformational states translocates faster than a faster-folding mutant with a smaller number of accessible states, suggesting that ease of folding and ease of translocation are at odds in this case.

Translocation of proteins is correlated with structural fluctuations that access conformational states higher in free energy than the folded state. We use electric fields at the solid-state nanopore to control the relative free energy and occupancy of different protein conformational states at the single-molecule level. The change in occupancy of different protein conformations as a function of electric field gives rise to shifts in the measured distributions of ionic current blockades and residence times. We probe the statistics of the ionic current blockades and residence times for three mutants of the λ-repressor family in order to determine the number of accessible conformational states of each mutant and evaluate the ruggedness of their free energy landscapes. Translocation becomes faster at higher electric fields when additional flexible conformations are available for threading through the pore. At the same time, folding rates are not correlated with ease of translocation; a slow-folding mutant with a low-lying intermediate state translocates faster than a faster-folding two-state mutant. Such behavior allows us to distinguish among protein mutants by selecting for the degree of current blockade and residence time at the pore. Based on these findings, we present a simple free energy model that explains the complementary relationship between folding equilibrium constants and translocation rates.

A Generalized Transformer-Based Pulse Detection Algorithm

Pulse-like signals are ubiquitous in the field of single molecule analysis, e.g., electrical or optical pulses caused by analyte translocations in nanopores. The primary challenge in processing pulse-like signals is to capture the pulses in noisy backgrounds, but current methods are subjectively based on a user-defined threshold for pulse recognition. Here, we propose a generalized machine-learning based method, named pulse detection transformer (PETR), for pulse detection. PETR determines the start and end time points of individual pulses, thereby singling out pulse segments in a time-sequential trace. It is objective without needing to specify any threshold. It provides a generalized interface for downstream algorithms for specific application scenarios. PETR is validated using both simulated and experimental nanopore translocation data. It returns a competitive performance in detecting pulses through assessing them with several standard metrics. Finally, the generalization nature of the PETR output is demonstrated using two representative algorithms for feature extraction.