Dielectric dispersion interpretation of single enzyme dynamic disorder, spectral diffusion, and radiative fluorescence lifetime

On measuring the acoustic state changes in lipid membranes using fluorescent probes

Ultrasound is increasingly being used to modulate the properties of biological membranes for applications in drug delivery and neuromodulation. While various studies have investigated the mechanical aspects of the interaction such as acoustic absorption and membrane deformation, it is not clear how these effects transduce into biological functions, for example, changes in the permeability or the enzymatic activity of the membrane. A critical aspect of the activity of an enzyme is the thermal fluctuations of its solvation or hydration shell. Thermal fluctuations are also known to be directly related to membrane permeability. Here solvation shell changes of lipid membranes subject to an acoustic impulse were investigated using a fluorescence probe, Laurdan. Laurdan was embedded in multi-lamellar lipid vesicles in water, which were exposed to broadband pressure impulses of the order of 1 MPa peak amplitude and 10 µs pulse duration. An instrument was developed to monitor changes in the emission spectrum of the dye at two wavelengths with sub-microsecond temporal resolution. The experiments show that changes in the emission spectrum, and hence the fluctuations of the solvation shell, are related to the changes in the thermodynamic state of the membrane and correlated with the compression and rarefaction of the incident sound wave. The results suggest that acoustic fields affect the state of a lipid membrane and therefore can potentially modulate the kinetics of channels and enzymes embedded in the membrane.

MD + QM correlations with tryptophan fluorescence spectral shifts and lifetimes

Principles behind quenching of tryptophan (Trp) fluorescence are updated and extended in light of recent 100-ns and 1-μs molecular dynamics (MD) trajectories augmented with quantum mechanical (QM) calculations that consider electrostatic contributions to wavelength shifts and quenching. Four studies are summarized, including (1) new insight into the single exponential decay of NATA, (2) a study revealing how unsuspected rotamer transitions affect quenching of Trp when used as a probe of protein folding, (3) advances in understanding the origin of nonexponential decay from 100-ns simulations on 19 Trps in 16 proteins, and (4) the correlation of wavelength with lifetime for decay-associated spectra (DAS). Each study strongly reinforces the concept that-for Trp-electron transfer-based quenching is controlled much more by environment electrostatic factors affecting the charge transfer (CT) state energy than by distance dependence of electronic coupling. In each case, water plays a large role in unexpected ways.

Simulations of tryptophan fluorescence dynamics during folding of the villin headpiece

Protein folding kinetics is commonly monitored by changes in tryptophan (Trp) fluorescence intensity. Considerable recent discussion has centered on whether the fluorescence of the single Trp in the much-studied, fast-folding villin headpiece C-terminal domain (HP35) accurately reflects folding kinetics, given the general view that quenching is by a histidine cation (His(+)) one turn away in an α-helix (helix III) that forms early in the folding process, according to published MD simulations. To help answer this question, we ran 1.0 μs MD simulations on HP35 (N27H) and a faster-folding variant in its folded form at 300 K and used the coordinates and force field charges with quantum calculations to simulate fluorescence quenching caused by electron transfer to the local amide and to the His(+). The simulations demonstrate that quenching by His(+) in the fully formed helix III is possible only during certain Trp and His(+) rotamer and solvent conformations, the propensity of which is a variable that can allow Trp fluorescence to report the global folding rate, as recent experiments imply.

Water and backbone dynamics in a hydrated protein

Rotational immobilization of proteins permits characterization of the internal peptide and water molecule dynamics by magnetic relaxation dispersion spectroscopy. Using different experimental approaches, we have extended measurements of the magnetic field dependence of the proton-spin-lattice-relaxation rate by one decade from 0.01 to 300 MHz for (1)H and showed that the underlying dynamics driving the protein (1)H spin-lattice relaxation is preserved over 4.5 decades in frequency. This extension is critical to understanding the role of (1)H(2)O in the total proton-spin-relaxation process. The fact that the protein-proton-relaxation-dispersion profile is a power law in frequency with constant coefficient and exponent over nearly 5 decades indicates that the characteristics of the native protein structural fluctuations that cause proton nuclear spin-lattice relaxation are remarkably constant over this wide frequency and length-scale interval. Comparison of protein-proton-spin-lattice-relaxation rate constants in protein gels equilibrated with (2)H(2)O rather than (1)H(2)O shows that water protons make an important contribution to the total spin-lattice relaxation in the middle of this frequency range for hydrated proteins because of water molecule dynamics in the time range of tens of ns. This water contribution is with the motion of relatively rare, long-lived, and perhaps buried water molecules constrained by the confinement. The presence of water molecule reorientational dynamics in the tens of ns range that are sufficient to affect the spin-lattice relaxation driven by (1)H dipole-dipole fluctuations should make the local dielectric properties in the protein frequency dependent in a regime relevant to catalytically important kinetic barriers to conformational rearrangements.

A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.