Linear Response Approximation Research Articles

PKa Calculations of GPCRs: Understanding Protonation States in Receptor Activation.

The increase in the available G protein-coupled receptor (GPCR) structures has been pivotal in helping to understand their activation process. However, the role of protonation-conformation coupling in GPCR activation still needs to be clarified. We studied the protonation behavior of the highly conserved Asp2.50 residue in five different class A GPCRs (active and inactive conformations) using a linear response approximation (LRA) pKa calculation protocol. We observed consistent differences (1.3 pK units) for the macroscopic pKa values between the inactive and active states of the A2AR and B2AR receptors, indicating the protonation of Asp2.50 during GPCR activation. This process seems to be specific and not conserved, as no differences were observed in the pKa values of the remaining receptors (CB1R, NT1R, and GHSR).

Machine Learning Approach to Vertical Energy Gap in Redox Processes.

A straightforward approach to calculating the free energy change (ΔG) and reorganization energy of a redox process is linear response approximation (LRA). However, accurate prediction of redox properties is still challenging due to difficulties in conformational sampling and vertical energy-gap sampling. Expensive hybrid quantum mechanical/molecular mechanical (QM/MM) calculations are typically employed in sampling energy gaps using conformations from simulations. To alleviate the computational cost associated with the expensive QM method in the QM/MM calculation, we propose machine learning (ML) methods to predict the vertical energy gaps (VEGs). We tested several ML models to predict the VEGs and observed that simple models like linear regression show excellent performance (mean absolute error ∼0.1 eV) in predicting VEGs in all test systems, even when using features extracted from cheaper semiempirical methods. Our best ML model (extra trees regressor) shows a mean absolute error of around 0.1 eV while using features from the cheapest QM method. We anticipate our approach can be generalized to larger macromolecular systems with more complex redox centers.

Exploring the Light-Emitting Agents in Renilla Luciferases by an Effective QM/MM Approach.

Bioluminescence is a fascinating natural phenomenon, wherein organisms produce light through specific biochemical reactions. Among these organisms, Renilla luciferase (RLuc) derived from the sea pansy Renilla reniformis is notable for its blue light emission and has potential applications in bioluminescent tagging. Our study focuses on RLuc8, a variant of RLuc with eight amino acid substitutions. Recent studies have shown that the luminescent emitter coelenteramide can adopt multiple protonation states, which may be influenced by nearby residues at the enzyme's active site, demonstrating a complex interplay between protein structure and bioluminescence. Herein, using the quantum mechanical consistent force field method and the semimacroscopic protein dipole-Langevin dipole method with linear response approximation, we show that the phenolate state of coelenteramide in RLuc8 is the primary light-emitting species in agreement with experimental results. Our calculations also suggest that the proton transfer (PT) from neutral coelenteramide to Asp162 plays a crucial role in the bioluminescence process. Additionally, we reproduced the observed emission maximum for the amide anion in RLuc8-D120A and the pyrazine anion in the presence of a Na+ counterion in RLuc8-D162A, suggesting that these are the primary emitters. Furthermore, our calculations on the neutral emitter in the engineered AncFT-D160A enzyme, structurally akin to RLuc8-D162A but with a considerably blue-shifted emission peak, aligned with the observed data, possibly explaining the variance in emission peaks. Overall, this study demonstrates an effective approach to investigate chromophores' bimolecular states while incorporating the PT process in emission spectra calculations, contributing valuable insights for future studies of PT in photoproteins.

The role of anharmonicity in single-molecule spin-crossover

We exploit the system-bath paradigm to investigate vibrational-anharmonicity effects on spin-crossover in a single molecule. Focusing on weak coupling, we use the linear response approximation to deal with the nonlinear vibrational bath and propagate the Redfield master equation to obtain the equilibrium high spin fraction. We take both the anharmonicity in the bath potentials and the nonlinearity in the spin-vibration coupling into account and find a strong interplay between these two effects. Further, we show that the spin-crossover in a single molecule is always a gradual transition and the anharmonicity-induced phonon drag greatly affects the transition behavior.

Assessing the Catalytic Role of Native Glucagon Amyloid Fibrils.

Glucagon stands out as a pivotal peptide hormone, instrumental in controlling blood glucose levels and lipid metabolism. While the formation of glucagon amyloid fibrils has been documented, their biological functions remain enigmatic. Recently, we demonstrated experimentally that glucagon amyloid fibrils can act as catalysts in several biological reactions including esterolysis, lipid hydrolysis, and dephosphorylation. Herein, we present a multiscale quantum mechanics/molecular mechanics (QM/MM) simulation of the acylation step in the esterolysis of para-nitrophenyl acetate (p-NPA), catalyzed by native glucagon amyloid fibrils, serving as a model system to elucidate their catalytic function. This step entails a concerted mechanism, involving proton transfer from serine to histidine, followed by the nucleophilic attack of the serine oxy anion on the carbonyl carbon of p-NPA. We computed the binding energy and free-energy profiles of this reaction using the protein-dipole Langevin-dipole (PDLD) within the linear response approximation (LRA) framework (PDLD/S-LRA-2000) and the empirical valence bond (EVB) methods. This included simulations of the reaction in an aqueous environment and in the fibril, enabling us to estimate the catalytic effect of the fibril. Our EVB calculations obtained a barrier of 23.4 kcal mol-1 for the enzyme-catalyzed reaction compared to the experimental value of 21.9 kcal mol-1 (and a calculated catalytic effect of 3.2 kcal mol-1 compared to the observed effect of 4.7 kcal mol-1). This close agreement together with the barrier reduction when transitioning from the reference solution reaction to the amyloid fibril provides supporting evidence to the catalytic role of glucagon amyloid fibrils. Moreover, employing the PDLD/S-LRA-2000 approach further reinforced exclusively the enzyme's catalytic role. The results presented in this study contribute significantly to our understanding of the catalytic role of glucagon amyloid fibrils, marking, to the best of our knowledge, the first-principles mechanistic investigation of fibrils using QM/MM methods. Therefore, our findings offer fruitful insights for future research into the mechanisms of related amyloid catalysis.

Directed ultrafast conformational changes accompany electron transfer in a photolyase as resolved by serial crystallography

Charge-transfer reactions in proteins are important for life, such as in photolyases which repair DNA, but the role of structural dynamics remains unclear. Here, using femtosecond X-ray crystallography, we report the structural changes that take place while electrons transfer along a chain of four conserved tryptophans in the Drosophila melanogaster (6-4) photolyase. At femto- and picosecond delays, photoreduction of the flavin by the first tryptophan causes directed structural responses at a key asparagine, at a conserved salt bridge, and by rearrangements of nearby water molecules. We detect charge-induced structural changes close to the second tryptophan from 1 ps to 20 ps, identifying a nearby methionine as an active participant in the redox chain, and from 20 ps around the fourth tryptophan. The photolyase undergoes highly directed and carefully timed adaptations of its structure. This questions the validity of the linear solvent response approximation in Marcus theory and indicates that evolution has optimized fast protein fluctuations for optimal charge transfer.

Lattice response to the radiation damage of molecular crystals: radiation-induced versus thermal expansivity.

The interaction of intense synchrotron radiation with molecular crystals frequently modifies the crystal structure by breaking bonds, producing fragments and, hence, inducing disorder. Here, a second-rank tensor of radiation-induced lattice strain is proposed to characterize the structural susceptibility to radiation. Quantitative estimates are derived using a linear response approximation from experimental data collected on three materials Hg(NO3)2(PPh3)2, Hg(CN)2(PPh3)2 and BiPh3 [PPh3 = triphenylphosphine, P(C6H5)3; Ph = phenyl, C6H5], and are compared with the corresponding thermal expansivities. The associated eigenvalues and eigenvectors show that the two tensors are not the same and therefore probe truly different structural responses. The tensor of radiative expansion serves as a measure of the susceptibility of crystal structures to radiation damage.

Theory of localized light

A theory of the spatially localized light observed by Hau et al. [Nature 397 (1999) 594] is formulated on the basis of the Maxwell equations, where the dynamics of the electron currents due to the electromagnetic fields is also taken into account within the self-consistent linear response approximation. Formulae for the energy, momentum and angular momentum of the localized light are derived.

Effective statistical control strategies for complex turbulent dynamical systems

Control of complex turbulent dynamical systems involving strong nonlinearity and high degrees of internal instability is an important topic in practice. Different from traditional methods for controlling individual trajectories, controlling the statistical features of a turbulent system offers a more robust and efficient approach. Crude first-order linear response approximations were typically employed in previous works for statistical control with small initial perturbations. This paper aims to develop two new statistical control strategies for scenarios with more significant initial perturbations and stronger nonlinear responses, allowing the statistical control framework to be applied to a much wider range of problems. First, higher-order methods, incorporating the second-order terms, are developed to resolve the full control-forcing relation. The corresponding changes to recovering the forcing perturbation effectively improve the performance of the statistical control strategy. Second, a mean closure model for the mean response is developed, which is based on the explicit mean dynamics given by the underlying turbulent dynamical system. The dependence of the mean dynamics on higher-order moments is closed using linear response theory but for the response of the second-order moments to the forcing perturbation rather than the mean response directly. The performance of these methods is evaluated extensively on prototype nonlinear test models, which exhibit crucial turbulent features, including non-Gaussian statistics and regime switching with large initial perturbations. The numerical results illustrate the feasibility of different approaches due to their physical and statistical structures and provide detailed guidelines for choosing the most suitable method based on the model properties.

Thermoelectric transport properties of single quantum dot systems in the presence of Majorana states

We present theoretical results for the thermoelectric transport properties in a single quantum dot system side coupled to a Majorana nanowire. The system’s electrical conductivity G , and the fundamental thermoelectric parameters such as the Seebeck coefficient S and thermal conductivity κ are numerically estimated based on a linear response approximation. Our results prove that the Majorana states in the side nanowire play an important role in the system’s thermoelectric response. In particular, a proper choice of the quantum dot — Majorana nanowire tunneling rate ξ and of the Majorana states overlap amplitude ɛ M can provide the appropriate physical environment for the experimental detection of Majorana states via thermoelectrical experimental measurements. • We considered the effects of Majorana states on the thermoelectric response of a single quantum dot system. • We present numerical results for the system electrical conductivity, Seebeck coefficient, thermal conductivity, and figure of merit. • The system thermoelectric response is strongly dependent on the quantum dot — Majorana nanowire tunneling rate ξ and of the Majorana states overlap amplitude ɛ M .

Conductance of a One and Double-Level Quantum Dot

"We analytically study the expression of the electric charge current through a two-terminal quantum dot in the linear response approximation. We analyse the one-level and the two-level quantum dot scaled conductance taking into account the relevant parameters. We also present the results for the conductance in the Sommerfeld approximation. Keywords: Electrical conductance, Quantum dots, Linear response "

Quantum transport of strongly interacting fermions in one dimension far out of equilibrium

In the study of quantum transport, much has been known about dynamics near thermal equilibrium. However, quantum transport far away from equilibrium is much less well understood---the linear response approximation does not hold for physics far out of equilibrium in general. In this work, motivated by recent cold atom experiments on probing quantum many-body dynamics of a one-dimensional XXZ spin chain, where a transition from ballistic to diffusive dynamics has been established by increasing the interaction strengths, we study the strong interaction limit of the one-dimensional spinless fermion model, which is dual to the XXZ spin chain. We develop a highly efficient computation algorithm for simulating the nonequilibrium dynamics of this system exactly, and examine the nonequilibrium dynamics starting from a density modulation quantum state. We find ballistic transport in this strongly correlated setting and show that a plane-wave description emerges at long-time evolution. We also observe a sharp distinction between transport velocities in short and long times as induced by interaction effects and provide a quantitative interpretation for the long-time transport velocity. We expect our results to shed light on the understanding of the dynamics of the XXZ spin chain in the strong interaction regime.

Effect of nucleon effective mass and symmetry energy on the neutrino mean free path in a neutron star

The Korea-IBS-Daegu-SKKU energy density functional (KIDS-EDF) models, constructed from the perturbative expansion of the energy density in nuclear matter, have been successfully and widely applied in describing the properties of finite nuclei and infinite nuclear matter. In the present work, we extend the applications of the KIDS-EDF models to investigate the implications of the nucleon effective mass and nuclear symmetry energy for the properties of neutron stars (NSs) and neutrino interaction with the NS constituent matter in the linear response approximation (LRA). At fixed neutrino energy and momentum transfer, we analyze the total differential cross section of neutrinos, the neutrino mean free path (NMFP), and the NS mass-radius (M-R) relations. Remarkable results are given by the KIDS0-m*87 and SLy4 models, in which ${M}_{n}^{*}/M\ensuremath{\lesssim}1$, and their NMFPs are quite higher in comparison with those obtained from the KIDS0, KIDS-A, and KIDS-B models, which result in ${M}_{n}^{*}/M\ensuremath{\gtrsim}1$. For the KIDS0, KIDS-A, and KIDS-B models, we obtain $\ensuremath{\lambda}\ensuremath{\lesssim}{R}_{\text{NS}}$, indicating that these models could predict the slow NS cooling and neutrino trapping in NSs. In contrast, the KIDS0-m*87 and SLy4 models yield $\ensuremath{\lambda}\ensuremath{\gtrsim}{R}_{\text{NS}}$ and thus we expect faster NS cooling and a small possibility of neutrino trapping within NSs. We also calculate the NMFP as a function of the neutrino energy and the nuclear matter density and find that the NMFP decreases as the density and neutrino energy increase, which is consistent with the result obtained in the Brussels-Montreal Skyrme (BSk17 and BSk18) models at saturation density.

Changes in polarization dictate necessary approximations for modeling electronic deexcitation intensity: Application to x-ray emission

We systematically investigate the underlying relations among different levels of approximation for simulating electronic de-excitations, with a focus on modeling X-ray emission spectroscopy (XES). Using Fermi's golden rule and explicit modeling of the initial, core-excited state and the final, valence-hole state, we show that XES can be accurately modeled by using orbital optimization for the various final states within a Slater-determinant framework. However, in this paper, we introduce a much cheaper approach reliant only on a single self-consistent field for all the final states, and show that it is typically sufficient. Further approximations reveal that these fundamentally many-body transitions can be reasonably approximated by projections of ground state orbitals, but that the ground state alone is insufficient. Furthermore, except in cases where the core-ionization induces negligible changes in polarization, linear-response approaches within the adiabatic approximation will have difficulty in accurately modeling de-excitation to the core level. Therefore, change in the net dipole moment of the valence electrons can serve as a metric for the validity of the linear-response approximation.

Pseudo pair potential between protons in dense hydrogen from first principles

Calculating the underlying quantum behaviour of dense hydrogen has proven to be difficult due to subtle electronic effects and also the lightness of the proton leading to large quantum motion. The analytical form of the contribution from the nuclear and electronic degrees of freedom (DOF) is integrated out of the Schödinger equation by way of the generated pseudo pair potential in this paper. This is accomplished through the adiabatically linear response approximation of an electron gas-jellium model to the perturbations induced by discrete hydrogen ions in the absence of an external field. This pair potential for the hydrogen ions can then be fitted to generate first-principles data. From these pair potentials, computational time can be drastically reduced for larger systems of dense hydrogen to determine their various properties.

Polar liquids at charged interfaces: A dipolar shell theory.

The structure of polar liquids and electrolytic solutions, such as water and aqueous electrolytes, at interfaces underlies numerous phenomena in physics, chemistry, biology, and engineering. In this work, we develop a continuum theory that captures the essential features of dielectric screening by polar liquids at charged interfaces, including decaying spatial oscillations in charge and mass, starting from the molecular properties of the solvent. The theory predicts an anisotropic dielectric tensor of interfacial polar liquids previously studied in molecular dynamics simulations. We explore the effect of the interfacial polar liquid properties on the capacitance of the electrode/electrolyte interface and on hydration forces between two plane-parallel polarized surfaces. In the linear response approximation, we obtain simple formulas for the characteristic decay lengths of molecular and ionic profiles at the interface.

Modeling the Snoek peak in bct-martensite

Snoek relaxation in bcc crystals is the delayed strain response to an applied stress resulting from the interaction of the interstitial atoms with the stress field. It is responsible for the Snoek peak observed in internal friction measurements of ferrite. However, although martensite is carbon supersaturated, several authors denied the possibility of Snoek relaxation in bct-martensite. We investigated this matter by means of Monte Carlo simulations and mean-field thermo-kinetic modeling. Our results show that Snoek relaxation does occur in bct-martensite. The computed Snoek profiles of temperature-dependent and frequency-dependent internal friction exhibit unexpected features: both peak height and peak temperature decrease when the carbon content is increased. We explain this behavior in the frame of the linear-response approximation. Our theoretical predictions are in qualitative agreement with experiments.

NNMT: Mean-Field Based Analysis Tools for Neuronal Network Models.

Mean-field theory of neuronal networks has led to numerous advances in our analytical and intuitive understanding of their dynamics during the past decades. In order to make mean-field based analysis tools more accessible, we implemented an extensible, easy-to-use open-source Python toolbox that collects a variety of mean-field methods for the leaky integrate-and-fire neuron model. The Neuronal Network Mean-field Toolbox (NNMT) in its current state allows for estimating properties of large neuronal networks, such as firing rates, power spectra, and dynamical stability in mean-field and linear response approximation, without running simulations. In this article, we describe how the toolbox is implemented, show how it is used to reproduce results of previous studies, and discuss different use-cases, such as parameter space explorations, or mapping different network models. Although the initial version of the toolbox focuses on methods for leaky integrate-and-fire neurons, its structure is designed to be open and extensible. It aims to provide a platform for collecting analytical methods for neuronal network model analysis, such that the neuroscientific community can take maximal advantage of them.

Multidimensional minimum-work control of a 2D Ising model.

A system's configurational state can be manipulated using dynamic variation of control parameters, such as temperature, pressure, or magnetic field; for finite-duration driving, excess work is required above the equilibrium free-energy change. Minimum-work protocols in multidimensional control-parameter space have the potential to significantly reduce work relative to one-dimensional control. By numerically minimizing a linear-response approximation to the excess work, we design protocols in control-parameter spaces of a 2D Ising model that efficiently drive the system from the all-down to all-up configuration. We find that such designed multidimensional protocols take advantage of more flexible control to avoid control-parameter regions of high system resistance, heterogeneously input and extract work to make use of system relaxation, and flatten the energy landscape, making accessible many configurations that would otherwise have prohibitively high energy and, thus, decreasing spin correlations. Relative to one-dimensional protocols, this speeds up the rate-limiting spin-inversion reaction, thereby keeping the system significantly closer to equilibrium for a wide range of protocol durations and significantly reducing resistance and, hence, work.

All-electron real-time and imaginary-time time-dependent density functional theory within a numeric atom-centered basis function framework.

Real-time time-dependent density functional theory (RT-TDDFT) is an attractive tool to model quantum dynamics by real-time propagation without the linear response approximation. Sharing the same technical framework of RT-TDDFT, imaginary-time time-dependent density functional theory (it-TDDFT) is a recently developed robust-convergence ground state method. Presented here are high-precision all-electron RT-TDDFT and it-TDDFT implementations within a numerical atom-centered orbital (NAO) basis function framework in the FHI-aims code. We discuss the theoretical background and technical choices in our implementation. First, RT-TDDFT results are validated against linear-response TDDFT results. Specifically, we analyze the NAO basis sets' convergence for Thiel's test set of small molecules and confirm the importance of the augmentation basis functions for adequate convergence. Adopting a velocity-gauge formalism, we next demonstrate applications for systems with periodic boundary conditions. Taking advantage of the all-electron full-potential implementation, we present applications for core level spectra. For it-TDDFT, we confirm that within the all-electron NAO formalism, it-TDDFT can successfully converge systems that are difficult to converge in the standard self-consistent field method. We finally benchmark our implementation for systems up to ∼500 atoms. The implementation exhibits almost linear weak and strong scaling behavior.