Exploring non-linear distance metrics in the structure-activity space: QSAR models for human estrogen receptor.

BACKGROUND: Quantitative structure-activity relationship (QSAR) models are important tools used in discovering new drug candidates and identifying potentially harmful environmental chemicals. These models often face two fundamental challenges: limited amount of available biological activity data and noise or uncertainty in the activity data themselves. To address these challenges, we introduce and explore a QSAR model based on custom distance metrics in the structure-activity space. METHODS: The model is built on top of the k-nearest neighbor model, incorporating non-linearity not only in the chemical structure space, but also in the biological activity space. The model is tuned and evaluated using activity data for human estrogen receptor from the US EPA ToxCast and Tox21 databases. RESULTS: The model closely trails the CERAPP consensus model (built on top of 48 individual human estrogen receptor activity models) in agonist activity predictions and consistently outperforms the CERAPP consensus model in antagonist activity predictions. DISCUSSION: We suggest that incorporating non-linear distance metrics may significantly improve QSAR model performance when the available biological activity data are limited.

Exploring biological electron transfer pathway dynamics with the Pathways plugin for VMD.

We describe the new Pathways plugin for the molecular visualization program visual molecular dynamics. The plugin identifies and visualizes tunneling pathways and pathway families in biomolecules, and calculates relative electronic couplings. The plugin includes unique features to estimate the importance of individual atoms for mediating the coupling, to analyze the coupling sensitivity to thermal motion, and to visualize pathway fluctuations. The Pathways plugin is open source software distributed under the terms of the GNU's Not Unix (GNU) public license.

Steering electrons on moving pathways.

Electron transfer (ET) reactions provide a nexus among chemistry, biochemistry, and physics. These reactions underpin the "power plants" and "power grids" of bioenergetics, and they challenge us to understand how evolution manipulates structure to control ET kinetics. Ball-and-stick models for the machinery of electron transfer, however, fail to capture the rich electronic and nuclear dynamics of ET molecules: these static representations disguise, for example, the range of thermally accessible molecular conformations. The influence of structural fluctuations on electron-transfer kinetics is amplified by the exponential decay of electron tunneling probabilities with distance, as well as the delicate interference among coupling pathways. Fluctuations in the surrounding medium can also switch transport between coherent and incoherent ET mechanisms--and may gate ET so that its kinetics is limited by conformational interconversion times, rather than by the intrinsic ET time scale. Moreover, preparation of a charge-polarized donor state or of a donor state with linear or angular momentum can have profound dynamical and kinetic consequences. In this Account, we establish a vocabulary to describe how the conformational ensemble and the prepared donor state influence ET kinetics in macromolecules. This framework is helping to unravel the richness of functional biological ET pathways, which have evolved within fluctuating macromolecular structures. The conceptual framework for describing nonadiabatic ET seems disarmingly simple: compute the ensemble-averaged (mean-squared) donor-acceptor (DA) tunneling interaction, , and the Franck-Condon weighted density of states, rho(FC), to describe the rate, (2pi/variant Planck's over 2pi)rho(FC). Modern descriptions of the thermally averaged electronic coupling and of the Franck-Condon factor establish a useful predictive framework in biology, chemistry, and nanoscience. Describing the influence of geometric and energetic fluctuations on ET allows us to address a rich array of mechanistic and kinetic puzzles. How strongly is a protein's fold imprinted on the ET kinetics, and might thermal fluctuations "wash out" signatures of structure? What is the influence of thermal fluctuations on ET kinetics beyond averaging of the tunneling barrier structure? Do electronic coupling mechanisms change as donor and acceptor reposition in a protein, and what are the consequences for the ET kinetics? Do fluctuations access minority species that dominate tunneling? Can energy exchanges between the electron and bridge vibrations generate vibronic signatures that label some of the D-to-A pathways traversed by the electron, thus eliminating unmarked pathways that would otherwise contribute to the DA coupling (as in other "which way" or double-slit experiments)? Might medium fluctuations drive tunneling-hopping mechanistic transitions? How does the donor-state preparation, in particular, its polarization toward the acceptor and its momentum characteristics (which may introduce complex rather than pure real relationships among donor orbital amplitudes), influence the electronic dynamics? In this Account, we describe our recent studies that address puzzling questions of how conformational distributions, excited-state polarization, and electronic and nuclear dynamical effects influence ET in macromolecules. Indeed, conformational and dynamical effects arise in all transport regimes, including the tunneling, resonant transport, and hopping regimes. Importantly, these effects can induce switching among ET mechanisms.

Coarse-grained modeling of allosteric regulation in protein receptors.

Allosteric regulation provides highly specific ligand recognition and signaling by transmembrane protein receptors. Unlike functions of protein molecular machines that rely on large-scale conformational transitions, signal transduction in receptors appears to be mediated by more subtle structural motions that are difficult to identify. We describe a theoretical model for allosteric regulation in receptors that addresses a fundamental riddle of signaling: What are the structural origins of the receptor agonism (specific signaling response to ligand binding)? The model suggests that different signaling pathways in bovine rhodopsin or human beta(2)-adrenergic receptor can be mediated by specific structural motions in the receptors. We discuss implications for understanding the receptor agonism, particularly the recently observed "biased agonism" (selected activation of specific signaling pathways), and for developing rational structure-based drug-design strategies.

Persistence of structure over fluctuations in biological electron-transfer reactions.

In the soft-wet environment of biomolecular electron transfer, it is possible that structural fluctuations could wash out medium-specific electronic effects on electron tunneling rates. We show that beyond a transition distance (2-3 A in water and 6-7 A in proteins), fluctuation contributions to the mean-squared donor-to-acceptor tunneling matrix element are likely to dominate over the average matrix element. Even though fluctuations dominate the tunneling mechanism at larger distances, we find that the protein fold is "remembered" by the electronic coupling, and structure remains a key determinant of electron transfer kinetics.

The nature of aqueous tunneling pathways between electron-transfer proteins.

Structured water molecules near redox cofactors were found recently to accelerate electron-transfer (ET) kinetics in several systems. Theoretical study of interprotein electron transfer across an aqueous interface reveals three distinctive electronic coupling mechanisms that we describe here: (i) a protein-mediated regime when the two proteins are in van der Waals contact; (ii) a structured water-mediated regime featuring anomalously weak distance decay at relatively close protein-protein contact distances; and (iii) a bulk water-mediated regime at large distances. Our analysis explains a range of otherwise puzzling biological ET kinetic data and provides a framework for including explicit water-mediated tunneling effects on ET kinetics.

Protein dynamics and electron transfer: electronic decoherence and non-Condon effects.

We compute the autocorrelation function of the donor-acceptor tunneling matrix element for six Ru-azurin derivatives. Comparison of this decay time to the decay time of the time-dependent Franck-Condon factor {computed by Rossky and coworkers [Lockwood, D. M., Cheng, Y.-K. & Rossky, P. J. (2001) Chem. Phys. Lett. 345, 159-165]} reveals the extent to which non-Condon effects influence the electron-transfer rate. is studied as a function of donor-acceptor distance, tunneling pathway structure, tunneling energy, and temperature to explore the structural and dynamical origins of non-Condon effects. For azurin, the correlation function is remarkably insensitive to tunneling pathway structure. The decay time is only slightly shorter than it is for solvent-mediated electron transfer in small organic molecules and originates, largely, from fluctuations of valence angles rather than bond lengths.

Insights into the molecular mechanism of rotation in the Fo sector of ATP synthase.

F(1)F(o)-ATP synthase is a ubiquitous membrane protein complex that efficiently converts a cell's transmembrane proton gradient into chemical energy stored as ATP. The protein is made of two molecular motors, F(o) and F(1), which are coupled by a central stalk. The membrane unit, F(o), converts the transmembrane electrochemical potential into mechanical rotation of a rotor in F(o) and the physically connected central stalk. Based on available data of individual components, we have built an all-atom model of F(o) and investigated through molecular dynamics simulations and mathematical modeling the mechanism of torque generation in F(o). The mechanism that emerged generates the torque at the interface of the a- and c-subunits of F(o) through side groups aSer-206, aArg-210, and aAsn-214 of the a-subunit and side groups cAsp-61 of the c-subunits. The mechanism couples protonation/deprotonation of two cAsp-61 side groups, juxtaposed to the a-subunit at any moment in time, to rotations of individual c-subunit helices as well as rotation of the entire c-subunit. The aArg-210 side group orients the cAsp-61 side groups and, thereby, establishes proton transfer via aSer-206 and aAsn-214 to proton half-channels, while preventing direct proton transfer between the half-channels. A mathematical model proves the feasibility of torque generation by the stated mechanism against loads typical during ATP synthesis; the essential model characteristics, e.g., helix and subunit rotation and associated friction constants, have been tested and furnished by steered molecular dynamics simulations.