Reaction Cycle of Operating Pump Protein Studied with Single-Molecule Spectroscopy.

Biological machinery relies on nonequilibrium dynamics to maintain stable directional fluxes through complex reaction cycles. For such reaction cycles, the presence of microscopically irreversible conformational transitions of the protein, and the accompanying entropy production, is of central interest. In this work, we use multidimensional single-molecule fluorescence lifetime correlation spectroscopy to measure the forward and reverse conformational transitions of bacteriorhodopsin during trans-membrane H+ pumping. We quantify the flux, affinity, enthalpy and entropy production through portions of the reaction cycle as a function of temperature. We find that affinity of irreversible conformational transitions decreases with increasing temperature, resulting in diminishing flux and entropy production. We show that the temperature dependence of the transition affinity is well fit by the Gibbs-Helmholtz relation, allowing the ΔHtrans to be experimentally extracted.

Protein-Bath Coupling of an Internal Reaction Coordinate at Intermediate Time Scales.

Thermally activated barrier-crossing processes are central to protein reaction kinetics. A determining factor for such kinetics is the extent to which the protein's motions are coupled to the surrounding bath. It is understood that slow large-scale conformational motions are strongly coupled to the environment, while fast librational motions are uncoupled. However, less is known about protein-bath coupling of reaction coordinates located on the interior of a protein and with dynamics on intermediate time scales. In this work, we use single molecule 2D fluorescence lifetime correlation spectroscopy to study the microsecond chemical reaction occurring in the chromophore pocket of eGFP. The equilibrium reaction involves a dihedral rotation of a glutamic acid residue and a rearrangement of the local hydrogen-bonding network surrounding the endogenous chromophore, with no accompanying large-scale conformational changes. We observe that the internal chemical reaction is coupled to the solvent viscosity, though the scaling deviates from Kramers' behavior. We attribute this deviation to the internal friction of the protein, which weakens the protein-solvent coupling at high viscosity and intermediate time scales.

Fast and robust two-dimensional inverse Laplace transformation of single-molecule fluorescence lifetime data.

Fluorescence spectroscopy at the single-molecule scale has been indispensable for studying conformational dynamics and rare states of biological macromolecules. Single-molecule two-dimensional (2D) fluorescence lifetime correlation spectroscopy is an emerging technique that holds promise for the study of protein and nucleic acid dynamics, as the technique is 1) capable of resolving conformational dynamics using a single chromophore, 2) resolves forward and reverse transitions independently, and 3) has a dynamic window ranging from microseconds to seconds. However, the calculation of a 2D fluorescence relaxation spectrum requires an inverse Laplace transform (ILT), which is an ill-conditioned inversion that must be estimated numerically through a regularized minimization. Current methods for performing ILTs of fluorescence relaxation can be computationally inefficient, sensitive to noise corruption, and difficult to implement. Here, we adopt an approach developed for NMR spectroscopy (T1-T2 relaxometry) to perform one-dimensional (1D) and 2D-ILTs on single-molecule fluorescence spectroscopy data using singular-valued decomposition and Tikhonov regularization. This approach provides fast, robust, and easy to implement Laplace inversions of single-molecule fluorescence data. We compare this approach to the widely used maximal entropy method.

The nano-scale viscoelasticity using atomic force microscopy in liquid environment.

We measured viscoelasticity of two nanoscale systems, single protein molecules and molecular layers of water confined between solid walls. In order to quantify the viscoelastic response of these nanoscale systems in liquid environment, the measurements are performed using two types of atomic force microscopes (AFMs), which employ different detection schemes to measure the cantilever response. We used a deflection detection scheme, available in commercial AFMs, that measures cantilever bending and a fibre-interferometer based detection which measures cantilever displacement. The hydrodynamics of the cantilever is modelled using Euler-Bernoulli equation with appropriate boundary conditions which accommodate both detection schemes. In a direct contradiction with many reports in the literature, the dissipation coefficient of a single octomer of titin I278 is found to be immeasurably low. The upper bound on the dissipation coefficient is 5 × 10-7 kg s-1, which is much lower than the reported values. The entropic stiffness of single unfolded domains of protein measured using both methods is in the range of 10 mN m-1. We show that in a conventional deflection detection measurement, the phase of the bending signal can be a primary source of artefacts in the dissipation estimates. It is recognized that the measurement of cantilever displacement, which has negligibly small phase lag due to hydrodynamics of the cantilever at low excitation frequencies, is better suited for ensuring artefact-free measurement of viscoelasticity compared to the measurement of the cantilever bending. Further, it was possible to measure dissipation in molecular layers of water confined between the tip and the substrate using fibre interferometer based AFM with similar experimental parameters. It confirms that the dissipation coefficient of a single I278 is below the detection limit of AFM. The results shed light on the discrepancy observed in the measured diffusional dynamics of protein collapse measured using Force spectroscopic techniques and single-molecule optical techniques.