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Bimolecular binding rate constants are often used to describe the association of large molecules, such as proteins. In this paper, we analyze a model for such binding rates that includes the fact that pairs of molecules can bind only in certain orientations. The model considers two spherical molecules, each with an arbitrary number of small binding sites on their surface, and the two molecules bind if and only if their binding sites come into contact (such molecules are often called "patchy particles" in the biochemistry literature). The molecules undergo translational and rotational diffusion, and the binding sites are allowed to diffuse on their surfaces. Mathematically, the model takes the form of a high-dimensional, anisotropic diffusion equation with mixed boundary conditions. We apply matched asymptotic analysis to derive the bimolecular binding rate in the limit of small, well-separated binding sites. The resulting binding rate formula involves a factor that depends on the electrostatic capacitance of a certain four-dimensional region embedded in five dimensions. We compute this factor numerically by modifying a recent kinetic Monte Carlo algorithm. We then apply a quasi chemical formalism to obtain a simple analytical approximation for this factor and find a binding rate formula that includes the effects of binding site competition/saturation. We verify our results by numerical simulation. [ABSTRACT FROM AUTHOR]

We present a simple and versatile single-molecule-based method for the accurate determination of binding rates to surfaces or surface bound receptors. To quantify the reversible surface attachment of fluorescently labeled molecules, we have modified previous schemes for fluorescence correlation spectroscopy with total internal reflection illumination (TIR-FCS) and camera-based detection. In contrast to most modern applications of TIR-FCS, we completely disregard spatial information in the lateral direction. Instead, we perform correlation analysis on a spatially integrated signal, effectively converting the illuminated surface area into the measurement volume. In addition to providing a high surface selectivity, our new approach resolves association and dissociation rates in equilibrium over a wide range of time scales. We chose the transient hybridization of fluorescently labeled single-stranded DNA to the complementary handles of surface-immobilized DNA origami structures as a reliable and well-characterized test system. We varied the number of base pairs in the duplex, yielding different binding times in the range of hundreds of milliseconds to tens of seconds, allowing us to quantify the respective surface affinities and binding rates. [ABSTRACT FROM AUTHOR]

Background: The calculation of diffusion-controlled ligand binding rates is important for understanding enzyme mechanisms as well as designing enzyme inhibitors. Methods: We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) BC, is considered on the reactive boundaries. This new BC treatment allows for the analysis of enzymes with "imperfect" reaction rates. Results: The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to a mouse acetylcholinesterase (mAChE) monomer. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Conclusions: Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature. [ABSTRACT FROM AUTHOR]

Abstract: Previous kinetic studies of photoinitiated transition metal–dinitrogen bond forming reactions are reviewed, with an emphasis on room temperature reactivity, and in particular, the techniques of time-resolved infrared (TRIR) spectroscopy and UV–vis flash photolysis. Our recent results on the reactivity of the formally 16-electron, but agostically stabilized, complex, mer,trans-W(CO)3(PCy3)2 (W) (Cy=cyclohexyl) toward N2 in toluene and n-hexane solution are then discussed. Laser flash photolysis of a toluene solution of W-N2 in the presence of excess N2 resulted in the photoejection of N2. The back reaction of W with N2 was followed by monitoring the decay of the transient absorption of W at 600nm. The second-order rate constant for the reaction of N2 with W in toluene to generate W–N2 was found to be (3.0±0.2)×105 M−1 s−1. The rate of the reverse reaction was found to be 100±10s−1, allowing an estimation of the equilibrium constant, . Time-resolved step-scan FTIR (s2-FTIR) spectroscopy was also used to spectroscopically characterize the W intermediate and monitor its back-reaction with N2 in n-hexane solution. The rate of formation of W–N2 measured by s2-FTIR agreed well with that measured by flash photolysis. Finally, density functional theory (DFT) calculations have been performed on the model complexes, mer,trans-W(CO)3(PH3)2(L) (L=none and N2) in order to understand the observed IR and UV–vis spectra of W and W–N2 and to determine the nature of the frontier molecular orbitals of W and W–N2, allowing their lowest energy excited states to be assigned. [Copyright &y& Elsevier]

Molecular dynamics simulations can now routinely access the microsecond timescale, making feasible direct sampling of ligand association events. While Markov State Model (MSM) approaches offer a useful framework for analyzing such trajectory data to gain insight into binding mechanisms, accurate modeling of ligand association pathways and kinetics must be done carefully. We describe methods and good practices for constructing MSMs of ligand binding from unbiased trajectory data and discuss how to use time-lagged independent component analysis (tICA) to build informative models, using as an example recent simulation work to model the binding of phenylalanine to the regulatory ACT domain dimer of phenylalanine hydroxylase. We describe a variety of methods for estimating association rates from MSMs and discuss how to distinguish between conformational selection and induced-fit mechanisms using MSMs. In addition, we review some examples of MSMs constructed to elucidate the mechanisms by which p53 transactivation domain (TAD) and related peptides bind the oncoprotein MDM2.

Background: The calculation of diffusion-controlled ligand binding rates is important for understanding enzyme mechanisms as well as designing enzyme inhibitors., Methods: We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) BC, is considered on the reactive boundaries. This new BC treatment allows for the analysis of enzymes with "imperfect" reaction rates., Results: The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to a mouse acetylcholinesterase (mAChE) monomer. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates., Conclusions: Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.