Oxygen Isotopologues Resolved from Water Oxidation Electrocatalysis by Electron Paramagnetic Resonance Spectroscopy.

Electrocatalytic water oxidation is a key transformation in many strategies designed to harness solar energy and store it as chemical fuels. Understanding the mechanism(s) of the best electrocatalysts for water oxidation has been a fundamental chemical challenge for decades. Here, we quantitate evolved dioxygen isotopologue composition via gas-phase EPR spectroscopy to elucidate the mechanisms of water oxidation on metal oxide electrocatalysts with high precision. Isotope fractionation is paired with computational and kinetic modeling, showing that this technique is sensitive enough to differentiate O-O bond-forming steps. Strong agreement between experiment and theory indicates that for the nickel-iron layered double hydroxide─one of the best earth-abundant electrocatalysts to be studied─water oxidation proceeds via a dioxo coupling mechanism to form a side-bound peroxide rather than a hydroxide attack to form an end-bound peroxide.

Long-distance tmFRET using bipyridyl- and phenanthroline-based ligands.

With the great progress on determining protein structures over the last decade comes a renewed appreciation that structures must be combined with dynamics and energetics to understand function. Fluorescence spectroscopy, specifically Förster resonance energy transfer (FRET), provides a great window into dynamics and energetics due to its application at physiological temperatures and ability to measure dynamics on the ångström scale. We have recently advanced transition metal FRET (tmFRET) to study allosteric regulation of maltose binding protein and have reported measurements of maltose-dependent distance changes with an accuracy of ∼1.5 Å. When paired with the noncanonical amino acid Acd as a donor, our previous tmFRET acceptors were useful over a working distance of 10 to 20 Å. Here, we use cysteine-reactive bipyridyl and phenanthroline compounds as chelators for Fe2+ and Ru2+ to produce novel tmFRET acceptors to expand the working distance to as long as 50 Å, while preserving our ability to resolve even small maltose-dependent changes in distance. We compare our measured FRET efficiencies to predictions based on models using rotameric ensembles of the donors and acceptors to demonstrate that steady-state measurements of tmFRET with our new probes have unprecedented ability to measure conformational rearrangements under physiological conditions.

Measuring conformational equilibria in allosteric proteins with time-resolved tmFRET.

Proteins are the workhorses of biology, orchestrating a myriad of cellular functions through intricate conformational changes. Protein allostery, the phenomenon where binding of ligands or environmental changes induce conformational rearrangements in the protein, is fundamental to these processes. We have previously shown that transition metal Förster resonance energy transfer (tmFRET) can be used to interrogate the conformational rearrangements associated with protein allostery and have recently introduced novel FRET acceptors utilizing metal-bipyridyl derivatives to measure long (>20 Å) intramolecular distances in proteins. Here, we combine our tmFRET system with fluorescence lifetime measurements to measure the distances, conformational heterogeneity, and energetics of maltose-binding protein, a model allosteric protein. Time-resolved tmFRET captures near-instantaneous snapshots of distance distributions, offering insights into protein dynamics. We show that time-resolved tmFRET can accurately determine distance distributions and conformational heterogeneity of proteins. Our results demonstrate the sensitivity of time-resolved tmFRET in detecting subtle conformational or energetic changes in protein conformations, which are crucial for understanding allostery. In addition, we extend the use of metal-bipyridyl compounds, showing that Cu(phen)2+ can serve as a spin label for pulse dipolar electron paramagnetic resonance (EPR) spectroscopy, a method that also reveals distance distributions and conformational heterogeneity. The EPR studies both establish Cu(phen)2+ as a useful spin label for pulse dipolar EPR and validate our time-resolved tmFRET measurements. Our approach offers a versatile tool for deciphering conformational landscapes and understanding the regulatory mechanisms governing biological processes.

Modeling of Cu(II)-based protein spin labels using rotamer libraries.

The bifunctional spin label double-histidine copper-(II) capped with nitrilotriacetate [dHis-Cu(II)-NTA], used in conjunction with electron paramagnetic resonance (EPR) methods can provide high-resolution distance data for investigating protein structure and backbone conformational diversity. Quantitative utilization of this data is limited due to a lack of rapid and accurate dHis-Cu(II)-NTA modeling methods that can be used to translate experimental data into modeling restraints. Here, we develop two dHis-Cu(II)-NTA rotamer libraries using a set of recently published molecular dynamics simulations and a semi-empirical meta-dynamics-based conformational ensemble sampling tool for use with the recently developed chiLife bifunctional spin label modeling method. The accuracy of both the libraries and the modeling method are tested by comparing model predictions to experimentally determined distance distributions. We show that this method is accurate with absolute deviation between the predicted and experimental modes between 0.0-1.2 Å with an average of 0.6 Å over the test data used. In doing so, we also validate the generality of the chiLife bifunctional label modeling method. Taken together, the increased structural resolution and modeling accuracy of dHis-Cu(II)-NTA over other spin labels promise improvements in the accuracy and resolution of protein models by EPR.

Juvenile downstream migration patterns of an anadromous fish, allis shad (Alosa alosa), before and after the population collapse in the Gironde system, France.

Diadromous fish have exhibited a dramatic decline since the end of the 20th century. The allis shad (Alosa alosa) population in the Gironde-Garonne-Dordogne (GGD) system, once considered as a reference in Europe, remains low despite a fishing ban in 2008. One hypothesis to explain this decline is that the downstream migration and growth dynamics of young stages have changed due to environmental modifications in the rivers and estuary. We retrospectively analysed juvenile growth and migration patterns using otoliths from adults caught in the GGD system 30 years apart during their spawning migration, in 1987 and 2016. We coupled otolith daily growth increments and laser ablation inductively-coupled plasma mass spectrometry measurements of Sr:Ca, Ba:Ca, and Mn:Ca ratios along the longest growth axis from hatching to an age of 100 days (i.e., during the juvenile stage). A back-calculation allowed us to estimate the size of juveniles at the entrance into the brackish estuary. Based on the geochemistry data, we distinguished four different zones that juveniles encountered during their downstream migration: freshwater, fluvial estuary, brackish estuary, and lower estuary. We identified three migration patterns during the first 100 days of their life: (a) Individuals that reached the lower estuary zone, (b) individuals that reached the brackish estuary zone, and (c) individuals that reached the fluvial estuary zone. On average, juveniles from the 1987 subsample stayed slightly longer in freshwater than juveniles from the 2016 subsample. In addition, juveniles from the 2016 subsample entered the brackish estuary at a smaller size. This result suggests that juveniles from the 2016 subsample might have encountered more difficult conditions during their downstream migration, which we attribute to a longer exposure to the turbid maximum zone. This assumption is supported by the microchemical analyses of the otoliths, which suggests based on wider Mn:Ca peaks that juveniles in 2010s experienced a longer period of physiological stress during their downstream migration than juveniles in 1980s. Finally, juveniles from the 2016 subsample took longer than 100 days to exit the lower estuary than we would have expected from previous studies. Adding a new marker (i.e., Ba:Ca) helped us refine the interpretation of the downstream migration for each individual.

Measuring conformational equilibria in allosteric proteins with time-resolved tmFRET.

Proteins are the workhorses of biology, orchestrating a myriad of cellular functions through intricate conformational changes. Protein allostery, the phenomenon where binding of ligands or environmental changes induce conformational rearrangements in the protein, is fundamental to these processes. We have previously shown that transition metal Förster resonance energy transfer (tmFRET) can be used to interrogate the conformational rearrangements associated with protein allostery and have recently introduced novel FRET acceptors utilizing metal-bipyridyl derivatives to measure long (>20 Å) intramolecular distances in proteins. Here, we combine our tmFRET system with fluorescence lifetime measurements to measure the distances, conformational heterogeneity, and energetics of maltose binding protein (MBP), a model allosteric protein. Time-resolved tmFRET captures near-instantaneous snapshots of distance distributions, offering insights into protein dynamics. We show that time-resolved tmFRET can accurately determine distance distributions and conformational heterogeneity of proteins. Our results demonstrate the sensitivity of time-resolved tmFRET in detecting subtle conformational or energetic changes in protein conformations, which are crucial for understanding allostery. In addition, we extend the use of metal-bipyridyl compounds, showing Cu(phen)2+ can serve as a spin label for pulse dipolar electron paramagnetic resonance (EPR) spectroscopy, a method which also reveals distance distributions and conformational heterogeneity. The EPR studies both establish Cu(phen)2+ as a useful spin label for pulse dipolar EPR and validate our time-resolved tmFRET measurements. Our approach offers a versatile tool for deciphering conformational landscapes and understanding the regulatory mechanisms governing biological processes.

Long-distance tmFRET using bipyridyl- and phenanthroline-based ligands.

With the great progress on determining protein structures over the last decade comes a renewed appreciation that structures must be combined with dynamics and energetics to understand function. Fluorescence spectroscopy, specifically Förster resonance energy transfer (FRET), provides a great window into dynamics and energetics due to its application at physiological temperatures and ability to measure dynamics on the ångström scale. We have recently advanced transition metal FRET (tmFRET) to study allosteric regulation of maltose binding protein and have reported measurements of maltose-dependent distance changes with an accuracy of ~1.5 Å. When paired with the noncanonical amino acid Acd as a donor, our previous tmFRET acceptors were useful over a working distance of 10 Å to 20 Å. Here, we use cysteine-reactive bipyridyl and phenanthroline compounds as chelators for Fe2+ and Ru2+ to produce novel tmFRET acceptors to expand the working distance to as long as 50 Å, while preserving our ability to resolve even small maltose-dependent changes in distance. We compare our measured FRET efficiencies to predictions based on models using rotameric ensembles of the donors and acceptors to demonstrate that steady-state measurements of tmFRET with our new probes have unprecedented ability to measure conformational rearrangements under physiological conditions.

Macroscopic sample shape effect on pulse electron double resonance (PELDOR) signal.

Pulse electron double resonance (PELDOR), also called double electron-electron resonance (DEER), is a technique capable of measuring the strength of electron spin dipolar interactions, revealing spin-spin distance distributions in ordered and disordered solid materials. Previous work has shown that PELDOR signals acquire an out-of-phase component under conditions of high electron spin polarization, such as at low temperatures and high fields. In this paper, we show theoretically and experimentally that the size and sign of this effect depends on the macroscopic shape of the sample and its orientation in the external magnetic field. This effect is caused by dipolar interactions between distant spins and provides new insights into the fundamental physics of PELDOR.

Design of stimulus-responsive two-state hinge proteins.

In nature, proteins that switch between two conformations in response to environmental stimuli structurally transduce biochemical information in a manner analogous to how transistors control information flow in computing devices. Designing proteins with two distinct but fully structured conformations is a challenge for protein design as it requires sculpting an energy landscape with two distinct minima. Here we describe the design of "hinge" proteins that populate one designed state in the absence of ligand and a second designed state in the presence of ligand. X-ray crystallography, electron microscopy, double electron-electron resonance spectroscopy, and binding measurements demonstrate that despite the significant structural differences the two states are designed with atomic level accuracy and that the conformational and binding equilibria are closely coupled.

A novel approach to modeling side chain ensembles of the bifunctional spin label RX.

We introduce a novel approach to modeling side chain ensembles of bifunctional spin labels. This approach utilizes rotamer libraries to generate side chain conformational ensembles. Because the bifunctional label is constrained by two attachment sites, the label is split into two monofunctional rotamers which are first attached to their respective sites, then rejoined by a local optimization in dihedral space. We validate this method against a set of previously published experimental data using the bifunctional spin label, RX. This method is relatively fast and can readily be used for both experimental analysis and protein modeling, providing significant advantages over modeling bifunctional labels with molecular dynamics simulations. Use of bifunctional labels for site directed spin labeling (SDSL) electron paramagnetic resonance (EPR) spectroscopy dramatically reduces label mobility, which can significantly improve resolution of small changes in protein backbone structure and dynamics. Coupling the use of bifunctional labels with side chain modeling methods allows for improved quantitative application of experimental SDSL EPR data to protein modeling.

Thermally Ultrarobust S = 1/2 Tetrazolinyl Radicals: Synthesis, Electronic Structure, Magnetism, and Nanoneedle Assemblies on Silicon Surface.

Open-shell organic molecules, including S = 1/2 radicals, may provide enhanced properties for several emerging technologies; however, relatively few synthesized to date possess robust thermal stability and processability. We report the synthesis of S = 1/2 biphenylene-fused tetrazolinyl radicals 1 and 2. Both radicals possess near-perfect planar structures based on their X-ray structures and density-functional theory (DFT) computations. Radical 1 possesses outstanding thermal stability as indicated by the onset of decomposition at 269 °C, based on thermogravimetric analysis (TGA) data. Both radicals possess very low oxidation potentials <0 V (vs. SCE) and their electrochemical energy gaps, Ecell ≈ 0.9 eV, are rather low. Magnetic properties of polycrystalline 1 are characterized by superconducting quantum interference device (SQUID) magnetometry revealing a one-dimensional S = 1/2 antiferromagnetic Heisenberg chain with exchange coupling constant J'/k ≈ -22.0 K. Radical 1 in toluene glass possesses a long electron spin coherence time, Tm ≈ 7 µs in the 40-80 K temperature range, a property advantageous for potential applications as a molecular spin qubit. Radical 1 is evaporated under ultrahigh vacuum (UHV) forming assemblies of intact radicals on a silicon substrate, as confirmed by high-resolution X-ray photoelectron spectroscopy (XPS). Scanning electron microscope (SEM) images indicate that the radical molecules form nanoneedles on the substrate. The nanoneedles are stable for at least 64 hours under air as monitored by using X-ray photoelectron spectroscopy. Electron paramagnetic resonance (EPR) studies of the thicker assemblies, prepared by UHV evaporation, indicate radical decay according to first-order kinetics with a long half-life of 50 ± 4 days at ambient conditions.

Magnetically Detected Protein Binding Using Spin-Labeled Slow Off-Rate Modified Aptamers.

Recent developments in aptamer chemistry open up opportunities for new tools for protein biosensing. In this work, we present an approach to use immobilized slow off-rate modified aptamers (SOMAmers) site-specifically labeled with a nitroxide radical via azide-alkyne click chemistry as a means for detecting protein binding. Protein binding induces a change in rotational mobility of the spin label, which is detected via solution-state electron paramagnetic resonance (EPR) spectroscopy. We demonstrate the workflow and test the protocol using the SOMAmer SL5 and its protein target, platelet-derived growth factor B (PDGF-BB). In a complete site scan of the nitroxide over the SOMAmer, we determine the rotational mobility of the spin label in the absence and presence of target protein. Several sites with sufficiently tight affinity and large rotational mobility change upon protein binding are identified. We then model a system where the spin-labeled SOMAmer assay is combined with fluorescence detection via diamond nitrogen-vacancy (NV) center relaxometry. The NV center spin-lattice relaxation time is modulated by the rotational mobility of a proximal spin label and thus responsive to SOMAmer-protein binding. The spin label-mediated assay provides a general approach for transducing protein binding events into magnetically detectable signals.

Ultrafast Bioorthogonal Spin-Labeling and Distance Measurements in Mammalian Cells Using Small, Genetically Encoded Tetrazine Amino Acids.

Site-directed spin-labeling (SDSL)─in combination with double electron-electron resonance (DEER) spectroscopy─has emerged as a powerful technique for determining both the structural states and the conformational equilibria of biomacromolecules. DEER combined with in situ SDSL in live cells is challenging since current bioorthogonal labeling approaches are too slow to allow for complete labeling with low concentrations of spin label prior to loss of signal from cellular reduction. Here, we overcome this limitation by genetically encoding a novel family of small, tetrazine-bearing noncanonical amino acids (Tet-v4.0) at multiple sites in proteins expressed in Escherichia coli and in human HEK293T cells. We achieved specific and quantitative spin-labeling of Tet-v4.0-containing proteins by developing a series of strained trans-cyclooctene (sTCO)-functionalized nitroxides─including a gem-diethyl-substituted nitroxide with enhanced stability in cells─with rate constants that can exceed 106 M-1 s-1. The remarkable speed of the Tet-v4.0/sTCO reaction allowed efficient spin-labeling of proteins in live cells within minutes, requiring only sub-micromolar concentrations of sTCO-nitroxide. DEER recorded from intact cells revealed distance distributions in good agreement with those measured from proteins purified and labeled in vitro. Furthermore, DEER was able to resolve the maltose-dependent conformational change of Tet-v4.0-incorporated and spin-labeled MBP in vitro and support assignment of the conformational state of an MBP mutant within HEK293T cells. We anticipate the exceptional reaction rates of this system, combined with the relatively short and rigid side chains of the resulting spin labels, will enable structure/function studies of proteins directly in cells, without any requirements for protein purification.

Effects of high and low flows on abundances of fish species in Central European headwater streams: The role of ecological species traits.

Hydrological variability is considered a major structuring factor for biotic and abiotic processes in freshwater ecosystems and is of particular importance to fish communities. We used hydrological indices to investigate the short intermediate-and long-term effects of high- and low-flow patterns on the population abundances of 17 fish species in headwater streams in Germany. Generalized linear models, on average, explained 54 % of the variability in fish abundance, whereas long-term hydrological indices performed better than indices based on shorter periods. Three clusters of species were differentiated in their response patterns to low-flow conditions. Cold stenotherm and demersal species were susceptible to high frequency and long duration but tolerant to the magnitude of low-flow events. In contrast, species with a more benthopelagic habitat preference and tolerance to warmer water were susceptible to magnitude but tolerated larger frequencies of low-flow events. The euryoecious chub (Squalius cephalus), tolerating both long durations and large magnitudes of low-flow events, formed its own cluster. Species responses to high flows were more complex and five clusters of species were differentiated. Species with an equilibrium life history strategy were positively affected by longer durations of high-flow conditions, which may allow them to take advantage of the extended floodplain, whereas opportunistic and periodic species significantly differed by thriving in events characterized by high magnitude and frequency. These response patterns of fish species to high and low flows help understand species-specific risks when hydrological conditions are altered by climate change or direct human intervention.

Taxonomic and functional reorganization in Central European stream macroinvertebrate communities over 25 years.

Climate warming can lead to a replacement of species that favour cold temperatures by species that favour warm temperatures. However, the implications of such thermic shifts for the functioning of ecosystems remain poorly understood. Here, we used stream macroinvertebrate biological and ecological traits to quantify the relative contribution of cold, intermediate and warm temperature-adapted taxa to changes in community functional diversity (FD) using a dataset of 3781 samples collected in Central Europe over 25 years, from 1990 to 2014. Our analyses indicated that functional diversity of stream macroinvertebrate communities increased over the study period. This gain was driven by a net 39 % increase in the richness of taxa that favour intermediate temperatures, which comprise the highest share in the community, and to a 97 % increase in the richness of taxa that favour warm temperatures. These warm temperature-adapted taxa displayed a distinct and more diverse suite of functional traits compared to the cold temperature-adapted group and thus contributed disproportionately to local FD on a per-taxon basis. At the same time, taxonomic beta-diversity declined significantly within each thermal group, in association with increasing local taxon richness. This study shows that over recent decades, small low-mountain streams in Central Europe have experienced a process of thermophilization and increasing functional diversity at local scales. However, a progressive homogenisation occurred at the regional scale, with communities converging towards similar taxonomic composition. As the reported increase in local functional diversity can be attributed mostly to the intermediate temperature-adapted taxa and a few expanding warm temperature-adapted taxa, these patterns could mask more subtle loss of sensitive cold temperature-adapted taxa with irreplaceable functional traits. In light of increasing climate warming, preservation of cold habitat refuges, should be considered a priority in river conservation.

Computational tools for the simulation and analysis of spin-polarized EPR spectra.

The EPR spectra of paramagnetic species induced by photoexcitation typically exhibit enhanced absorptive and emissive features resulting from sublevel populations that differ from thermal equilibrium. The populations and the resulting spin polarization of the spectra are dictated by the selectivity of the photophysical process generating the observed state. Simulation of the spin-polarized EPR spectra is crucial in the characterization of both the dynamics of formation of the photoexcited state as well as its electronic and structural properties. EasySpin, the simulation toolbox for EPR spectroscopy, now includes extended support for the simulation of the EPR spectra of spin-polarized states of arbitrary spin multiplicity and formed by a variety of different mechanisms, including photoexcited triplet states populated by intersystem crossing, charge recombination or spin polarization transfer, spin-correlated radical pairs created by photoinduced electron transfer, triplet pairs formed by singlet fission and multiplet states arising from photoexcitation in systems containing chromophores and stable radicals. In this paper, we highlight EasySpin's capabilities for the simulation of spin-polarized EPR spectra on the basis of illustrative examples from the literature in a variety of fields ranging across chemistry, biology, material science and quantum information science.

chiLife: An open-source Python package for in silico spin labeling and integrative protein modeling.

Here we introduce chiLife, a Python package for site-directed spin label (SDSL) modeling for electron paramagnetic resonance (EPR) spectroscopy, in particular double electron-electron resonance (DEER). It is based on in silico attachment of rotamer ensemble representations of spin labels to protein structures. chiLife enables the development of custom protein analysis and modeling pipelines using SDSL EPR experimental data. It allows the user to add custom spin labels, scoring functions and spin label modeling methods. chiLife is designed with integration into third-party software in mind, to take advantage of the diverse and rapidly expanding set of molecular modeling tools available with a Python interface. This article describes the main design principles of chiLife and presents a series of examples.

Ultra-Fast Bioorthogonal Spin-Labeling and Distance Measurements in Mammalian Cells Using Small, Genetically Encoded Tetrazine Amino Acids.

Studying protein structures and dynamics directly in the cellular environments in which they function is essential to fully understand the molecular mechanisms underlying cellular processes. Site-directed spin-labeling (SDSL)-in combination with double electron-electron resonance (DEER) spectroscopy-has emerged as a powerful technique for determining both the structural states and the conformational equilibria of biomacromolecules. In-cell DEER spectroscopy on proteins in mammalian cells has thus far not been possible due to the notable challenges of spin-labeling in live cells. In-cell SDSL requires exquisite biorthogonality, high labeling reaction rates and low background signal from unreacted residual spin label. While the bioorthogonal reaction must be highly specific and proceed under physiological conditions, many spin labels display time-dependent instability in the reducing cellular environment. Additionally, high concentrations of spin label can be toxic. Thus, an exceptionally fast bioorthogonal reaction is required that can allow for complete labeling with low concentrations of spin-label prior to loss of signal. Here we utilized genetic code expansion to site-specifically encode a novel family of small, tetrazine-bearing non-canonical amino acids (Tet-v4.0) at multiple sites in green fluorescent protein (GFP) and maltose binding protein (MBP) expressed both in E. coli and in human HEK293T cells. We achieved specific and quantitative spin-labeling of Tet-v4.0-containing proteins by developing a series of strained trans -cyclooctene (sTCO)-functionalized nitroxides-including a gem -diethyl-substituted nitroxide with enhanced stability in cells-with rate constants that can exceed 10 6 M -1 s -1 . The remarkable speed of the Tet-v4.0/sTCO reaction allowed efficient spin-labeling of proteins in live HEK293T cells within minutes, requiring only sub-micromolar concentrations of sTCO-nitroxide added directly to the culture medium. DEER recorded from intact cells revealed distance distributions in good agreement with those measured from proteins purified and labeled in vitro . Furthermore, DEER was able to resolve the maltose-dependent conformational change of Tet-v4.0-incorporated and spin-labeled MBP in vitro and successfully discerned the conformational state of MBP within HEK293T cells. We anticipate the exceptional reaction rates of this system, combined with the relatively short and rigid side chains of the resulting spin labels, will enable structure/function studies of proteins directly in cells, without any requirements for protein purification.

Dipolar pathways in multi-spin and multi-dimensional dipolar EPR spectroscopy.

Dipolar electron paramagnetic resonance (EPR) experiments, such as double electron-electron resonance (DEER), measure distributions of nanometer-scale distances between unpaired electrons, which provide valuable information for structural characterization of proteins and other macromolecular systems. We present an extension to our previously published general model based on dipolar pathways valid for multi-dimensional dipolar EPR experiments with more than two spin-1/2 labels. We examine the 4-pulse DEER and TRIER experiments in terms of dipolar pathways and show experimental results confirming the theoretical predictions. This extension to the dipolar pathways model allows the analysis of previously challenging datasets and the extraction of multivariate distance distributions.

Comparative evaluation of spin-label modeling methods for protein structural studies.

Site-directed spin-labeling electron paramagnetic resonance spectroscopy is a powerful technique for the investigation of protein structure and dynamics. Accurate spin-label modeling methods are essential to make full quantitative use of site-directed spin-labeling electron paramagnetic resonance data for protein modeling and model validation. Using a set of double electron-electron resonance data from seven different site pairs on maltodextrin/maltose-binding protein under two different conditions using five different spin labels, we compare the ability of two widely used spin-label modeling methods, based on accessible volume sampling and rotamer libraries, to predict experimental distance distributions. We present a spin-label modeling approach inspired by canonical side-chain modeling methods and compare modeling accuracy with the established methods.