Kinetic Model for the Desensitization of G Protein-Coupled Receptor.

Desensitization of G-protein-coupled receptors (GPCR) is a general regulatory mechanism adopted by biological organisms against overstimulation of G protein signaling. Although the details of the mechanism are extensively studied, it is not easy to gain an overarching understanding of the process constituted by a multitude of molecular events with vastly differing time scales. To offer a semiquantitative yet predictive understanding of the mechanism, we formulate a kinetic model for the G protein signaling and desensitization by considering essential biochemical steps from ligand binding to receptor internalization. The internalization, followed by receptor depletion from the plasma membrane, attenuates the downstream signal. Together with the kinetic model and its full numerics of the expression derived for the dose-response relation, an approximated form of the expression clarifies the role played by the individual biochemical processes and allows us to identify four distinct regimes for the downregulation that emerge from the balance between phosphorylation, dephosphorylation, and the cellular level of ß-arrestin.

Dynamic embedding of effective harmonic normal mode vibrations in all-atomistic energy gap fluctuations: Case study of light harvesting 2 complex.

Environmental effects in excitation energy transfer have mostly been modeled by baths of harmonic oscillators, but to what extent such modeling provides a reliable description of actual interactions between molecular systems and environments remains an open issue. We address this issue by investigating fluctuations in the excitation energies of the light harvesting 2 complex using a realistic all-atomistic simulation of the potential energy surface. Our analyses reveal that molecular motions exhibit significant anharmonic features, even for underdamped intramolecular vibrations. In particular, we find that the anharmonicity contributes to the broadening of spectral densities and substantial overlaps between neighboring peaks, which complicates the meaning of mode frequencies constituting a bath model. Thus, we develop a strategy to construct a minimally underdamped harmonic bath that has a clear connection to all-atomistic dynamics by utilizing actual normal modes of molecules but optimizing their frequencies such that the resulting bath model can best reproduce the all-atomistic simulation results. By subtracting the underdamped contribution from the entire fluctuations, we also show that identifying a residual spectral density representing all other contributions with overdamped behavior is possible. We find that this can be fitted well with a well-established analytic form of a spectral density function or, alternatively, modeled as explicit time dependent fluctuations with muti-exponential or power law type correlation functions. We provide an assessment and the implications of these possibilities. The approach presented here can also serve as a general strategy to construct a simplified bath model that can effectively represent the underlying all-atomistic bath dynamics.

Simple and General Unitarity Conserving Numerical Real-Time Propagators of the Time-Dependent Schrödinger Equation Based on Magnus Expansion.

Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. We use this property and explicit integration of Lagrange interpolation formulas for the time-dependent Hamiltonian within each time interval and derive approximations that preserve unitarity for the differential time evolution operators of general time-dependent Hamiltonians. The resulting second-order approximation is the same as using the average of Hamiltonians for two end points of time. We identify three fourth-order approximations involving commutators of Hamiltonians at different times and also derive a sixth-order expression. A test of these approximations along with other available expressions for a two-state time-dependent Hamiltonian with sinusoidal time dependences provides information on the relative performance of these approximations and suggests that the derived expressions can serve as useful numerical tools for time evolution in time-resolved spectroscopy, quantum control, quantum sensing, real-time ab initio quantum dynamics, and open system quantum dynamics.

Nonadiabatic Derivative Couplings through Multiple Franck-Condon Modes Dictate the Energy Gap Law for Near and Short-Wave Infrared Dye Molecules.

Near infrared (NIR, 700-1000 nm) and short-wave infrared (SWIR, 1000-2000 nm) dye molecules exhibit significant nonradiative decay rates from the first singlet excited state to the ground state. While these trends can be empirically explained by a simple energy gap law, detailed mechanisms of nearly universal behavior have remained unsettled for many cases. Theoretical and experimental results for two representative NIR/SWIR dye molecules reported here clarify the key mechanism for the observed energy gap law behavior. It is shown that the first derivative nonadiabatic coupling terms serve as major coupling pathways for nonadiabatic decay processes from the first excited singlet state to the ground state for these NIR and SWIR dye molecules and that vibrational modes other than the highest frequency modes also make significant contributions to the rate. This assessment is corroborated by further theoretical comparison with possible alternative mechanisms of intersystem crossing to triplet states and also by comparison with experimental data for deuterated molecules.

General Chemical Reaction Network Theory for Olfactory Sensing Based on G-Protein-Coupled Receptors: Elucidation of Odorant Mixture Effects and Agonist-Synergist Threshold.

This work presents a general chemical reaction network theory for olfactory sensing processes that employ G-protein-coupled receptors as olfactory receptors (ORs). The theory can be applied to general mixtures of odorants and an arbitrary number of ORs. Reactions of ORs with G-proteins, in both the presence and absence of odorants, are explicitly considered. A unique feature of the theory is the definition of an odor activity vector consisting of strengths of odorant-induced signals from ORs relative to those due to background G-protein activity in the absence of odorants. It is demonstrated that each component of the odor activity defined this way reduces to a Michaelis-Menten form capable of accounting for cooperation or competition effects between different odorants. The main features of the theory are illustrated for a two-odorant mixture. Known and potential mixture effects, such as suppression, shadowing, inhibition, and synergy, are quantitatively described. Effects of relative values of rate constants, basal activity, and G-protein concentration are also demonstrated.

Modified Fermi's golden rule rate expressions.

Fermi's golden rule (FGR) serves as the basis for many expressions of spectroscopic observables and quantum transition rates. The utility of FGR has been demonstrated through decades of experimental confirmation. However, there still remain important cases where the evaluation of a FGR rate is ambiguous or ill-defined. Examples are cases where the rate has divergent terms due to the sparsity in the density of final states or time dependent fluctuations of system Hamiltonians. Strictly speaking, assumptions of FGR are no longer valid for such cases. However, it is still possible to define modified FGR rate expressions that are useful as effective rates. The resulting modified FGR rate expressions resolve a long standing ambiguity often encountered in using FGR and offer more reliable ways to model general rate processes. Simple model calculations illustrate the utility and implications of new rate expressions.

Partially polaron-transformed quantum master equation for exciton and charge transport dynamics.

Polaron-transformed quantum master equation (PQME) offers a unified framework to describe the dynamics of quantum systems in both limits of weak and strong couplings to environmental degrees of freedom. Thus, the PQME serves as an efficient method to describe charge and exciton transfer/transport dynamics for a broad range of parameters in condensed or complex environments. However, in some cases, the polaron transformation (PT) being employed in the formulation invokes an over-relaxation of slow modes and results in premature suppression of important coherence terms. A formal framework to address this issue is developed in the present work by employing a partial PT that has smaller weights for low frequency bath modes. It is shown here that a closed form expression of a second order time-local PQME including all the inhomogeneous terms can be derived for a general form of partial PT, although more complicated than that for the full PT. All the expressions needed for numerical calculation are derived in detail. Applications to a model of a two-level system coupled to a bath of harmonic oscillators, with test calculations focused on those due to homogeneous relaxation terms, demonstrate the feasibility and the utility of the present approach.

Efficient Free Triplet Generation Follows Singlet Fission in Diketo-pyrrolopyrrole Polymorphs with Goldilocks Coupling.

Microcrystal electron diffraction, grazing incidence wide-angle scattering, and UV-Vis spectroscopy were used to determine the unit cell structure and the relative composition of dimethylated diketopyrrolopyrrole (MeDPP) H- and J-polymorphs within thin films subjected to vapor solvent annealing (VSA) for different times. Electronic structure and excited state deactivation pathways of the different polymorphs were examined by transient absorption spectroscopy, conductive probe atomic force microscopy, and molecular modeling. We find VSA initially converts amorphous films into mixtures of H- and J-polymorphs and promotes further conversion from H to J with longer VSA times. Though both polymorphs exhibit efficient SF to form coupled triplets, free triplet yields are higher in J-polymorph films compared to mixed films because coupling in J-aggregates is lower, and, in turn, more favorable for triplet decoupling.

A simple generalization of the energy gap law for nonradiative processes.

For more than 50 years, an elegant energy gap (EG) law developed by Englman and Jortner [Mol. Phys. 18, 145 (1970)] has served as a key theory to understand and model the nearly exponential dependence of nonradiative transition rates on the difference of energy between the initial and final states. This work revisits the theory, clarifies the key assumptions involved in the rate expression, and provides a generalization for the cases where the effects of temperature dependence and low-frequency modes cannot be ignored. For a specific example where the low-frequency vibrational and/or solvation responses can be modeled as an Ohmic spectral density, a simple generalization of the EG law is provided. Test calculations demonstrate that this generalized EG law brings significant improvement over the original EG law. Both the original and generalized EG laws are also compared with the stationary phase approximations developed for electron transfer theory, which suggests the possibility of a simple interpolation formula valid for any value of EG.

Frenkel excitons in heat-stressed supramolecular nanocomposites enabled by tunable cage-like scaffolding.

Delocalized Frenkel excitons-coherently shared excitations among chromophores-are responsible for the remarkable efficiency of supramolecular light-harvesting assemblies within photosynthetic organisms. The translation of nature's design principles to applications in optoelectronic devices has been limited by the fragility of the supramolecular structures used and the delicate nature of Frenkel excitons, particularly under mildly changing solvent conditions and elevated temperatures and upon deposition onto solid substrates. Here, we overcome those functionalization barriers through composition of stable supramolecular light-harvesting nanotubes enabled by tunable (~4.3-4.9 nm), uniform (±0.3 nm) cage-like scaffolds. High-resolution cryogenic electron microscopy, combined with scanning electron microscopy, broadband femtosecond transient absorption spectroscopy and near-field scanning optical microscopy revealed that excitons within the cage-like scaffolds are robust, even under extreme heat stress, and control over nanocomposite dimensions is maintained on solid substrates. Our bio-inspired nanocomposites provide a general framework for the development of next-generation organic devices made from stable supramolecular materials.

Theoretical investigation of non-Förster exciton transfer mechanisms in perylene diimide donor, phenylene bridge, and terrylene diimide acceptor systems.

The rates of exciton transfer within dyads of perylene diimide and terrylene diimide connected by oligophenylene bridge units have been shown to deviate significantly from those of Förster's resonance energy transfer theory, according to single molecule spectroscopy experiments. The present work provides a detailed computational and theoretical study investigating the source of such a discrepancy. Electronic spectroscopy data are calculated by time-dependent density functional theory and then compared with experimental results. Electronic couplings between the exciton donor and the acceptor are estimated based on both the transition density cube method and transition dipole approximation. These results confirm that the delocalization of the exciton to the bridge parts contributes to significant enhancement of donor-acceptor electronic coupling. Mechanistic details of exciton transfer are examined by estimating the contributions of the bridge electronic states, vibrational modes of the dyads commonly coupled to both donor and acceptor, inelastic resonance energy transfer mechanism, and dark exciton states. These analyses suggest that the contribution of common vibrational modes serves as the main source of deviation from Förster's spectral overlap expression.

Computational modeling of charge hopping dynamics along a disordered one-dimensional wire with energy gradients in quantum environments.

This computational study investigates the effects of energy gradients on charge hopping dynamics along a one-dimensional chain of discrete sites coupled to quantum bath, which is modeled at the level of Pauli master equation (PME). This study also assesses the performance of different approximations for the hopping rates. Three different methods for solving the PME, a fourth order Runge-Kutta method, numerical diagonalization of the rate matrix followed by analytic propagation, and kinetic Monte Carlo simulation method, are tested and confirmed to produce virtually identical values of time dependent mean square displacement, diffusion constant, and mobility. Five different rate expressions, exact numerical evaluation of Fermi's Golden Rule (FGR) rate, stationary phase interpolation (SPI) approximation, semiclassical approximation, classical Marcus rate, and Miller-Abrahams rate, are tested to help understand the effects of approximations in representing quantum environments in the presence of energy gradients. The results based on direct numerical evaluation of FGR rate exhibit transition from diffusive to non-diffusive behavior with the increase in the gradient and show that the charge transport in the quantum bath is more sensitive to the magnitude of the gradient and the disorder than in the classical bath. Among all the four approximations for the hopping rates, the SPI approximation is confirmed to work best overall. A comparison of two different methods to calculate the mobility identifies drift motion of the population distribution as the major source of non-diffusive behavior and provides more reliable information on the contribution of quantum bath.

Comparative Computational Study of Electronic Excitations of Neutral and Charged Small Oligothiophenes and Their Extrapolations Based on Simple Models.

This work reports electronic excitation energies of neutral and charged oligothiophenes (OT n ) with repeat unit n = 2-6 computed by routinely used semiempirical and time-dependent density functional theory (TD-DFT) methods. More specifically, for OT n , OTn +, and OTn -, we calculated vertical transition energies for electronic absorption spectroscopy employing the Zerner's version of intermediate neglect differential overlap method for structures optimized by the PM6 semiempirical method and the TD-DFT method with three different functionals, B3LYP, BVP86, and M06-2X, for structures optimized by the ground-state DFT method employing the same functionals. We also calculated vertical transition energies for the emission spectroscopy from the lowest singlet excited states by employing the TD-DFT method for the structures optimized for the lowest singlet excited states. In addition to computational results in vacuum, solution phase data calculated at the level of polarizable continuum model are reported and compared with available experimental data. Most of the data are fitted reasonably well by two simple model functions, one based on a Frenkel exciton theory and the other based on the model of independent electrons in a box with sinusoidal modulation of potential. Despite similar levels of fitting performance, the two models produce distinctively different asymptotic values of excitation energies. Comparison of these with available experimental and computational data suggests that the values based on the exciton model, while seemingly overestimating, are closer to true values than those based on the other model. This assessment is confirmed by additional calculations for a larger oligomer. The fitting parameters offer new means to understand the relationship between electronic excitations of OTs and their sizes and suggest the feasibility of constructing simple coarse-grained exciton-bath models applicable for aggregates of OTs.

Fourth order expressions for the electronic absorption lineshape of molecular excitons.

The line shape of electronic absorption spectroscopy reflects the information on quantum dynamical processes accompanying the electronic excitation, and its accurate description is an important component for validating theoretical models and assumptions. The present work provides detailed expressions for the absorption line shape of molecular excitons that are valid up to the fourth order of exciton-bath interactions within the quantum master equation approach. These expressions can serve as the basis for developing general and systematic methods to model the line shape for a broad class of molecular exciton systems and environments. For the bath model of linearly coupled harmonic oscillators, more detailed expressions employing the spectral densities of the bath are presented. These expressions are then tested for a linear aggregate of identical chromophores each coupled to the harmonic oscillator bath. Calculation results for a super-Ohmic spectral density with exponential cutoff demonstrate the feasibility of calculations and also offer insights into the utility and difficulty of going beyond the second order approximation.

Robust and Fragile Quantum Effects in the Transfer Kinetics of Delocalized Excitons between B850 Units of LH2 Complexes.

Aggregates of light harvesting 2 (LH2) complexes form the major exciton-relaying domain in the photosynthetic unit of purple bacteria. Application of a generalized master equation to pairs of the B850 units of LH2 complexes, where excitons predominantly reside, provides quantitative information on how the inter-LH2 exciton transfer depends on the distance, relative rotational angle, and the relative energies of the two LH2s. The distance dependence demonstrates significant enhancement of the rate due to quantum delocalization of excitons, the qualitative nature of which remains robust against the disorder. The angle dependence reflects isotropic nature of exciton transfer, which remains similar for the ensemble of disorder. The variation of the rate on relative excitation energies of LH2 exhibits resonance peaks, which, however, is fragile as the disorder becomes significant. Overall, the average transfer times between two LH2s are estimated to be in the range of 4-25 ps for physically plausible inter-LH2 distances.

Implications for human odor sensing revealed from the statistics of odorant-receptor interactions.

Binding of odorants to olfactory receptors (ORs) elicits downstream chemical and neural signals, which are further processed to odor perception in the brain. Recently, Mainland and colleagues have measured more than 500 pairs of odorant-OR interaction by a high-throughput screening assay method, opening a new avenue to understanding the principles of human odor coding. Here, using a recently developed minimal model for OR activation kinetics, we characterize the statistics of OR activation by odorants in terms of three empirical parameters: the half-maximum effective concentration EC50, the efficacy, and the basal activity. While the data size of odorants is still limited, the statistics offer meaningful information on the breadth and optimality of the tuning of human ORs to odorants, and allow us to relate the three parameters with the microscopic rate constants and binding affinities that define the OR activation kinetics. Despite the stochastic nature of the response expected at individual OR-odorant level, we assess that the confluence of signals in a neuron released from the multitude of ORs is effectively free of noise and deterministic with respect to changes in odorant concentration. Thus, setting a threshold to the fraction of activated OR copy number for neural spiking binarizes the electrophysiological signal of olfactory sensory neuron, thereby making an information theoretic approach a viable tool in studying the principles of odor perception.

Computational Modeling of Exciton-Bath Hamiltonians for Light Harvesting 2 and Light Harvesting 3 Complexes of Purple Photosynthetic Bacteria at Room Temperature.

Light harvesting 2 (LH2) complex is the primary component of the photosynthetic unit of purple bacteria that is responsible for harvesting and relaying excitons. The electronic absorption line shape of LH2 contains two major bands at 800 and 850 nm wavelength regions. Under low light conditions, some species of purple bacteria replace LH2 with light harvesting 3 (LH3), a variant form with almost the same structure as the former but with distinctively different spectral features. The major difference between the absorption line shapes of LH2 and LH3 is the shift of the 850 nm band of the former to a new 820 nm region. The microscopic origin of this difference has been the subject of some theoretical/computational investigations. However, the genuine molecular level source of such a difference is not clearly understood yet. This work reports a comprehensive computational study of LH2 and LH3 complexes so as to clarify different molecular level features of LH2 and LH3 complexes and to construct simple exciton-bath models with a common form. All-atomistic molecular dynamics simulations of both LH2 and LH3 complexes provide detailed molecular level structural differences of bacteriochlorophylls (BChls) in the two complexes, in particular, in their patterns of hydrogen bonding (HB) and torsional angles of the acetyl group. Time-dependent density functional theory calculation of the excitation energies of BChls for structures sampled from the MD simulations suggests that the observed differences in the HB and torsional angles cannot fully account for the experimentally observed spectral shift of LH3. Potential sources that can explain the actual spectral shift of LH3 are discussed, and their magnitudes are assessed through fitting of experimental line shapes. These results demonstrate the feasibility of developing simple exciton-bath models for both LH2 and LH3, which can be employed for large-scale exciton quantum dynamics in their aggregates.

Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space.

Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present work revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [Jang and Voth, J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does not provide a derivation of RPMD-TST in general and points to a new ambiguity of HA-QTST with respect to its justification for general cyclically invariant dividing surfaces defined in the space of imaginary time path integrals. Our analysis also offers new insights into similar path integral based QTST approaches.