The kinetics of biomolecular systems can be quantified by calculating the stochastic rate constants that govern the biomolecular state versus time trajectories (i.e., state trajectories) of individual biomolecules. To do so, the experimental signal versus time trajectories (i.e., signal trajectories) obtained from observing individual biomolecules are often idealized to generate state trajectories by methods such as thresholding or hidden Markov modeling. Here, we discuss approaches for idealizing signal trajectories and calculating stochastic rate constants from the resulting state trajectories. Importantly, we provide an analysis of how the finite length of signal trajectories restrict the precision of these approaches, and demonstrate how Bayesian inference-based versions of these approaches allow rigorous determination of this precision. Similarly, we provide an analysis of how the finite lengths and limited time resolutions of signal trajectories restrict the accuracy of these approaches, and describe methods that, by accounting for the effects of the finite length and limited time resolution of signal trajectories, substantially improve this accuracy. Collectively, therefore, the methods we consider here enable a rigorous assessment of the precision, and a significant enhancement of the accuracy, with which stochastic rate constants can be calculated from single-molecule signal trajectories.
A quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulation has been carried out using CP2K for a hole introduced into a B-form DNA molecule consisting of 10 adenine-thymine (A/T) pairs in water. At the beginning of the simulation, the hole wave function is extended over several adenines. Within 20-25 fs, the hole wave function contracts so that it is localized on a single A. At 300 K, it stays on this A for the length of the simulation, several hundred fs, with the wave function little changed. In a range of temperatures below 300 K, proton transfer from A to T is seen to take place within the A/T occupied by the hole; it is completed by ∼40 fs after the contraction. We show that the contraction is due to polarization of the water by the hole. This polarization also plays a role in the proton transfer. Implications for transport are considered.
ATP-Binding Cassette (ABC) Transporters employ homologous ATPase domains to drive transmembrane transport of diverse substrates ranging from small molecules to large polymers. Bacterial ABC importers require an extramembranous substrate binding protein (SBP) to deliver the transport substrate to the extracellular side of the transporter complex. Previous studies suggest significant differences in the transport mechanisms of type I vs. type II bacterial ABC importers, which contain unrelated transmembrane domains. We herein use ensemble fluorescence resonance energy transfer (FRET) experiments to characterize the kinetics of SBP interaction in the E. coli BtuCD-F complex, a canonical type II ABC importer that transports vitamin B12 . We demonstrate that, in the absence of B12 , BtuF (the SBP) forms a 'locked' (kinetically hyper-stable) complex with nanodisc-reconstituted BtuCD that can only be dissociated by ATP hydrolysis, which represents a futile reaction cycle. Notably, no type I importer has been observed to form an equivalent locked complex. We also show that either ATP or vitamin B12 binding substantially slows formation of the locked BtuCD-F complex, which will limit the occurrence of futile hydrolysis under physiological conditions. Mutagenesis experiments demonstrate that efficient locking requires concerted interaction of BtuCD with residues on both sides of the B12 binding pocket in BtuF. Combined with the kinetic inhibition of locking by ATP binding, these observations imply that the transition state for the locking reaction involves a global alteration in the conformation of BtuCD that extends from its BtuF binding site in the periplasm to its ATP-binding sites on the opposite side of the membrane in the cytoplasm. These observations suggest that locking, which seals the extracellular B12 entry site of the transporter, may help push B12 through the transporter and directly contribute to the transport mechanism in type II ABC importers.
The optical confinement generated by metal-based nanoapertures fabricated on a silica substrate has recently enabled single-molecule fluorescence measurements to be performed at physiologically relevant background concentrations of fluorophore-labeled biomolecules. Nonspecific adsorption of fluorophore-labeled biomolecules to the metallic cladding and silica bottoms of nanoapertures, however, remains a critical limitation. To overcome this limitation, we have developed a selective functionalization chemistry whereby the metallic cladding of gold nanoaperture arrays is passivated with methoxy-terminated, thiol-derivatized polyethylene glycol (PEG), and the silica bottoms of those arrays are functionalized with a binary mixture of methoxy- and biotin-terminated, silane-derivatized PEG. This functionalization scheme enables biotinylated target biomolecules to be selectively tethered to the silica nanoaperture bottoms via biotin-streptavidin interactions, and reduces the non-specific adsorption of fluorophore-labeled ligand biomolecules. This, in turn, enables the observation of ligand biomolecules binding to their target biomolecules even under greater than 1 µM background concentrations of ligand biomolecules, thereby rendering previously impracticable biological systems accessible to single-molecule fluorescence investigations.
On the basis of pK a measurements, it has been predicted that proton transfer will not occur in the radical cation of the A/T base pair (A: adenine, T: thymine). Testing this prediction, we have performed simulations as a function of time on an A/T oligomer missing one electron, in solution, using the code CP2K. We find that proton transfer occurs rapidly at temperatures below room temperature. We suggest that the difference in behavior of (A/T)·+ from that predicted on the basis of pK a measurements is the effect of hydration. Hydration also appears to have effects not previously considered on hole motion in solution.
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