Theoretical Studies On The Dynamic Aspects Of Macromolecular Function

点击翻译按钮获取中文摘要

In this reporting period four papers were published dealing with (1) Free energy surfaces extracted from single-molecule force spectroscopy experiments:(2) Analysis of three photon color Forster energy transfer experiments (3) The theory of NMR solvent paramagnetic relaxation to propel the interaction of denaturants with proteins and (4) Diffusion influenced ligand binding to proteins with multiple sites in membranes and in solution. These are briefly explained in turn/ below. (1) In single-molecule force spectroscopy experiments, a biomolecule is attached to a force probe via polymer linkers and the total extension of the molecule plus apparatus is monitored as a function of time. In a typical unfolding experiment at constant force, the total extension jumps between two values that correspond to the folded and unfolded states of the molecule. For several biomolecular systems, the committor, which is the probability to fold starting from a given extension, has been used to extract the molecular activation barrier. We studied the influence of the force probe, which is much larger than the molecule being measured, on the activation barrier obtained by this procedure by numerically solving the Onsager equation and using Brownian dynamics simulations. We analyzed the dependence of the extracted barrier on the linker stiffness, molecular barrier height, and diffusion anisotropy and thus established the range of validity of this procedure, which much simpler than any other and thus is expected to be widely used. (2) Single-molecule Forster resonance energy transfer (FRET) between fluorescent donor and acceptor labels attached to a protein or nucleic acid is widely used to probe intramolecular distances and study the structure, dynamics and function of macromolecules. In these experiments, a molecule is illuminated by a laser, and the donor fluorophore is excited. The donor can emit a photon or transfer the excitation to an acceptor which then can emit a photon of a different color. The rate of transfer depends on the inter-dye distance and this is why there is information about conformational dynamics. The output of these experiments is a sequence of photons with recorded colors and arrival times. The distances between fluorescence labels attached to a molecule fluctuate due to conformational dynamics on a wide range of time scales. During the last year, we continued our work on the theory and analyses of single-molecule FRET in collaboration with Dr. H. S. Chung from LCP. We have extended our previous work to three-color FRET in which three dyes are attached to the protein of interest (one donor and two acceptors). These experiments contain more information (three instead of one distances) than the usual two-color FRET, but the theory required to analyze them is also more challenging. The theory and analysis of three-color FRET have been applied to probe sub-millisecond conformational dynamics of two systems, a fast-folding protein, a3D, and binding of a disordered protein, the N-terminal transactivation domain (TAD), to a binding partner, the nuclear coactivator binding domain (NCBD). TAD is disordered in the unbound state and folds upon binding NCBD. Since the states of the proteins cannot be distinguished in binned fluorescence trajectories, the proton sequences were analyzed without binning using a maximum likelihood method. In order to determine all three distances in three-color FRET, additional information was extracted from two-color photon sequences collected in the same experiment. Three FRET efficiencies in the folded/unfolded and bound/unbound states and kinetic parameters were determined from a global maximum likelihood analysis of three-color and two-color photon sequences. The extracted kinetic parameters agree very well with the previously measured parameters for the same protein with two-color FRET. From the extracted fractions of acceptor photon counts, the FRET efficiencies for all three dye pairs were calculated after various corrections. In the binding experiment, the three-color parameters explicitly demonstrate the coupling between binding and folding. (3) Protein-small cosolute molecule (e.g a denaturant like urea) interactions modulate the solubility, stability, and function of many proteins. Characterization of such transient weak interactions at atomic resolution remains challenging. We developed a simple and practical NMR method for extracting both energetic and dynamic information on protein-cosolute interactions from solvent paramagnetic relaxation enhancement measurements. Our procedure is based on an approximate spectral density that is exact at both high and low frequencies and contains two parameters, one global, and the other residue specific. These parameters can be readily determined from experimental data and then used to analytically calculate an equilibrium average of the interspin distance and an effective correlation time, which provide measures of the energetics and dynamics of the interaction. We compare our approach with existing ones that are extremely complicated and demonstrate the its utility using experimental results for the protein ubiquitin in the presence of two different nitroxide radicals. Because of its simplicity and accuracy, our approach is expected to be widely used to deepen our understanding of extremely weak, nonspecific protein-cosolute interactions. (4) Translational diffusion of reactants can modify the kinetics of coupled association and dissociation of biomolecules. Traditional approach to describe the influence of diffusion on the kinetics of bimolecular reactions is to replace the rate constants in the conventional chemical kinetics by the diffusion-influenced ones. However, when the reactions are coupled, not only the rate constants, but also the reaction scheme can be modified by introducing new reaction channels between the bound complexes. This happens because a ligand that just dissociated from one site of a macromolecule can diffuse and bind to the other site rather than diffusing away into the bulk. Previously, we developed a general theory for a diffusion-influenced network of coupled reversible association-dissociation. Our main result is a set of non-Markovian rate equations involving stoichiometric matrices and net reaction rates (fluxes), in which these rates are coupled by a time-dependent matrix of pair association fluxes. Here we considered various implementations of the general theory in two and three dimensions for two-site reversible binding and established their range of validity. When the concentrations of the reactants change on the time scale much longer that the diffusion time (i.e., the time required to diffuse through the distance of closest approach), the Markovian equations with time-independent rate constants appropriately describe the kinetics of the reaction. However, the Markovian equations are not valid for reactions on the surface of membranes since the rate coefficients in two dimensions never achieve a steady state. Nevertheless, the kinetics can be approximated by the Markovian kinetics, and we suggest a simple procedure for doing this.