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DOE OSTI2025

Ligand efficacy shifts a nuclear receptor conformational ensemble between transcriptionally active and repressive states

Abstract Nuclear receptors (NRs) are thought to dynamically alternate between transcriptionally active and repressive conformations, which are stabilized upon ligand binding. Most NR ligand series exhibit limited bias, primarily consisting of transcriptionally active agonists or neutral antagonists, but not repressive inverse agonists—a limitation that restricts understanding of the functional NR conformational ensemble. Here, we report a NR ligand series for peroxisome proliferator-activated receptor gamma (PPARγ) that spans a pharmacological spectrum from repression (inverse agonism) to activation (agonism) where subtle structural modifications switch compound activity. While crystal structures provide snapshots of the fully repressive state, NMR spectroscopy and conformation-activity relationship analysis reveals that compounds within the series shift the PPARγ conformational ensemble between transcriptionally active and repressive conformations that are natively populated in the apo/ligand-free ensemble. Our findings reveal a molecular framework for minimal chemical modifications that enhance PPARγ inverse agonism and elucidate their influence on the dynamic PPARγ conformational ensemble.

Science & Technology - Other Topics↗

DOE OSTI2026

A curated benchmark for cofolding models on kinase conformational states

Abstract Protein kinases are critical drug targets, requiring therapeutics that can modulate their active and inactive conformational states. While cofolding models can generate global folds directly from kinase sequences and ligand SMILES strings, these models have not yet been tested on their ability to recover ligand-induced-fit conformational states of the kinase proteins. Here, we introduce KinConfBench, a curated benchmark of 2225 high-quality human kinase chains to evaluate the ability of four state-of-the-art cofolding models—Boltz-2, Chai-1, Protenix, and RoseTTAFold-All-Atom—to recover both canonical and rare conformational states. We show that geometric success metrics of a ligand pose in the active site do not correlate strongly with the correct kinase conformational state, motivating a new set of dynamical benchmarks for assessing cofolding models. While all four cofolding models achieve ~60–80% prediction accuracy for kinase conformational classification, they exhibit severe mode collapse when performing multiple inferences, show negligible structural diversity in sampling induced-fit motions, and display a prevalent “apo-drift” in which most cofolding models predominantly predict the kinase to be in its ligand-free state. Our results highlight that capturing ligand-induced protein conformational diversity, not just geometric fit, is critical for next-generation structure-based drug discovery.

Sun, Kunyang↗

DOE OSTI2020

Trapping conformational states of a flavin-dependent N-monooxygenase in crystallo reveals protein and flavin dynamics

The siderophore biosynthetic enzyme A (SidA) ornithine hydroxylase from Aspergillus fumigatus is a fungal disease drug target involved in the production of hydroxamate-containing siderophores, which are used by the pathogen to sequester iron. SidA is an N -monooxygenase that catalyzes the NADPH-dependent hydroxylation of l -ornithine through a multistep oxidative mechanism, utilizing a C4a-hydroperoxyflavin intermediate. Here we present four new crystal structures of SidA in various redox and ligation states, including the first structure of oxidized SidA without NADP(H) or l -ornithine bound (resting state). The resting state structure reveals a new out active site conformation characterized by large rotations of the FAD isoalloxazine around the C1–'C2' and N10–C1' bonds, coupled to a 10-Å movement of the Tyr-loop. Additional structures show that either flavin reduction or the binding of NADP(H) is sufficient to drive the FAD to the in conformation. The structures also reveal protein conformational changes associated with the binding of NADP(H) and l -ornithine. Some of these residues were probed using site-directed mutagenesis. Docking was used to explore the active site of the out conformation. These calculations identified two potential ligand-binding sites. Altogether, our results provide new information about conformational dynamics in flavin-dependent monooxygenases. Overall, understanding the different active site conformations that appear during the catalytic cycle may allow fine-tuning of inhibitor discovery efforts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Conformal geometry from entanglement

In a physical system with conformal symmetry, observables depend on cross-ratios, measures of distance invariant under global conformal transformations (conformal geometry for short). We identify a quantum information-theoretic mechanism by which the conformal geometry emerges at the gapless edge of a 2+1D quantum many-body system with a bulk energy gap. We introduce a novel pair of information-theoretic quantities (\mathfrak{c}_{\textrm{tot}}, \eta) ( 𝔠 tot , η ) that can be defined locally on the edge from the wavefunction of the many-body system, without prior knowledge of any distance measure. We posit that, for a topological groundstate, the quantity \mathfrak{c}_{\textrm{tot}} 𝔠 tot is stationary under arbitrary variations of the quantum state, and study the logical consequences. We show that stationarity, modulo an entanglement-based assumption about the bulk, implies (i) \mathfrak{c}_{\textrm{tot}} 𝔠 tot is a non-negative constant that can be interpreted as the total central charge of the edge theory. (ii) \eta η is a cross-ratio, obeying the full set of mathematical consistency rules, which further indicates the existence of a distance measure of the edge with global conformal invariance. Thus, the conformal geometry emerges from a simple assumption on groundstate entanglement. We show that stationarity of \mathfrak{c}_{\textrm{tot}} 𝔠 tot is equivalent to a vector fixed-point equation involving \eta η , making our assumption locally checkable. We also derive similar results for 1+1D systems under a suitable set of assumptions.

Kim, Isaac H.↗

DOE OSTI2026

Continuous Family of Conformal Field Theories and Exactly Marginal Operators

Does a conformal manifold imply the existence of exactly marginal operators? We answer this question affirmatively under the assumption that there exists a conformal interface with certain properties connecting nearby conformal field theories. We show that the exactly marginal operator that connects the conformal field theories can be reconstructed from the interface displacement operator. Our construction is model independent and based on the general principles of conformal symmetry.

conformal field theory↗

DOE OSTI2020

Dynamics of Cation-Induced Conformational Changes in Nanometer-Sized Uranyl Peroxide Clusters

Conformational changes of the pyrophosphate (Pp)-functionalized uranyl peroxide nanocluster [(UO 2 ) 24 (O 2 ) 24 (P 2 O 7 ) 12 ] 48– ({U 24 Pp 12 }), dissolved as a Li/Na salt, can be induced by the titration of alkali cations into solution. The most symmetric conformer of the molecule has idealized octahedral ( O h ) molecular symmetry. One-dimensional 31 P NMR experiments provide direct evidence that both K + and Rb + ions trigger an O h -to- D 4 h conformational change within {U 24 Pp 12 }. Variable-temperature 31 P NMR experiments conducted on partially titrated {U 24 Pp 12 } systems show an effect on the rates; increased activation enthalpy and entropy for the D 4 h -to- O h transition is observed in the presence of Rb + compared to K + . Two-dimensional, exchange spectroscopy 31 P NMR revealed that magnetization transfer links chemically unique Pp bridges that are present in the D 4 h conformation and that this magnetization transfer occurs via a conformational rearrangement mechanism as the bridges interconvert between two symmetries. The interconversion is triggered by the departure and reentry of K (or Rb) cations out of and into the cavity of the cluster. This rearrangement allows Pp bridges to interconvert without the need to break bonds. Cs ions exhibit unique interactions with {U 24 Pp 12 } clusters and cause only minor changes in the solution 31 P NMR signatures, suggesting that O h symmetry is conserved. Single-crystal X-ray diffraction measurements reveal that the mixed Li/Na/Cs salt adopts D 2 h molecular symmetry, implying that while solvated, this cluster is in equilibrium with a more symmetric form. Thus, these results highlight the unusually flexible nature of the actinide-based {U 24 Pp 12 } and its sensitivity to countercations in solution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Polymer Conformations and Diffusion Through a Monolayer of Confining Nanoparticles

We present coarse-grained molecular dynamics simulations to probe chain-scale polymer conformations and diffusion between confining nanoparticles (NPs). By constructing a monolayer of hexagonally-packed NPs in a polymer melt with athermal interactions, we observe the magnitude and length-scale over which homogeneously confining NPs impact the polymer behavior, which provides fundamental insights into more complex polymer nanocomposites. We show that polymer conformations are more perturbed under strong confinement (i.e. when the interparticle distance, ID, is less than twice the polymer radius of gyration, 2R g ) as compared to around an isolated NP, and the effect depends on the ratio of R NP /R g rather than either independently. In fact, these conformations can be quantitatively replicated by executing a simple random walk in a similarly confining environment. We also show that polymer diffusion is slowed by the presence of NPs and the slowing persists far beyond the length-scale over which polymer conformations are perturbed. Although the slowing is strongest ~R g from the NPs, the diffusion coefficient is slower even beyond ~5R g from the NPs. Furthermore, by analyzing the directional van Hove distributions, we show polymer diffusion away from the NP monolayer is bulk-like while diffusion through the monolayer is slower with increasing NP confinement. Furthermore, these molecular dynamics simulations provide fundamental insights into the temporal and spatial effect of confining, athermal NPs on chain-scale polymer conformations and diffusion.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Chain Conformations of TEMPO-Based Organic Radical Polymers with Varying Radical Loading and Temperature in Battery-Relevant Solvents

Poly(2,2,6,6-tetramethylpiperidinyloxy-4-yl methacrylate) (PTMA) is an organic radical polymer that is a promising active material in organic batteries. The proximity of the radical groups impacts the nature of charge transfer, in which closer packing promotes electron exchange; however, the chain conformation of PTMA is not well understood. Here, the conformation of PTMA in, and its thermodynamic interactions with, battery-relevant solvents is determined using small-angle neutron scattering (SANS). N-methyl-2-pyrrolidone (NMP) and 50:50 (wt %) ethylene carbonate/dimethyl carbonate (EC/DMC) mixtures with PTMA of varying radical content (68 vs 98%) and temperature (25 and 60 °C) are examined. Both solvents are theta solvents for PTMA irrespective of radical loading and temperature. PTMA attains an expanded chain conformation in NMP and a more compact polymer chain conformation in EC/DMC. Lastly, the electrochemical performance of PTMA films formed from EC/DMC shows improved performance relative to those cast from NMP, which is interpreted to indicate that the compact conformation of PTMA in EC/DMC enables improved inter- and intrachain charge transfer.

25 ENERGY STORAGE↗

DOE OSTI2025

Resonant Tender X-ray Scattering for Disclosing the Backbone Conformation of Conjugated Polymers

The backbone conformation of conjugated polymers (CPs) is essential to their performance in electronic applications. Contrast-variation small-angle neutron scattering (CV-SANS) techniques were used to assess the CP’s backbone conformation, which relies on synthesis of deuterated polymers. Such a technique has been proven mature and effective. One drawback is that deuteration labeling might subtly alter polymer’s physical properties due to structural modifications. To address these challenges, we introduce a novel approach utilizing tender Xray scattering near the sulfur K-edge to distinctly evaluate the backbone versus whole chain conformation for a low-bandgap donor−acceptor CP, poly[(5,6-difluoro- 2,1,3-benzothiadiazol-4,7-diyl)-alt-(3,3‴-dialkyl-2,2′;5′,2″;5″,2‴-quaterthiophen-5,5‴- diyl)] (PffBT4T). For PffBT4T dissolved in trimethylbenzene (TMB), the sulfur K-edge is identified at approximately 2477 eV using near-edge X-ray absorption fine structure spectroscopy (NEXAFS). Tender X-ray scattering conducted at presulfur K-edge and on-sulfur K-edge at elevated temperatures facilitated the distinction between the backbone and whole chain conformations. The results demonstrate that for highly flexible polymer, the backbone’s persistence length could be lower than that of the whole chains, suggesting a more flexible backbone. This rapid, label-free method enhances our ability to characterize CP’s backbone conformation efficiently, offering significant implications for the design and optimization of CPs for advanced electronics.

36 MATERIALS SCIENCE↗

DOE OSTI2025

From sequence to protein structure and conformational dynamics with artificial intelligence/machine learning

The 2024 Nobel Prize in Chemistry was awarded in part for de novo protein structure prediction using AlphaFold2, an artificial intelligence/machine learning (AI/ML) model trained on vast amounts of sequence and three-dimensional structure data. AlphaFold2 and related models, including RoseTTAFold and ESMFold, employ specialized neural network architectures driven by attention mechanisms to infer relationships between sequence and structure. At a fundamental level, these AI/ML models operate on the long-standing hypothesis that the structure of a protein is determined by its amino acid sequence. More recently, AlphaFold2 has been adapted for the prediction of multiple protein conformations by subsampling multiple sequence alignments. Herein, we provide an overview of the deterministic relationship between sequence and structure, which was hypothesized over half a century ago with profound implications for the biological sciences ever since. We postulate that protein conformational dynamics are also determined, at least in part, by amino acid sequence and that this relationship may be leveraged for construction of AI/ML models dedicated to predicting protein conformational ensembles. Accordingly, we describe a conceptual model architecture, which may be trained on sequence data in combination with conformationally sensitive structural information, coming primarily from nuclear magnetic resonance (NMR) spectroscopy. Notwithstanding certain limitations in this context, NMR offers abundant structural heterogeneity conducive to conformational ensemble prediction. As NMR and other data continue to accumulate, sequence-informed prediction of protein structural dynamics with AI/ML has the potential to emerge as a transformative capability across the biological sciences.

Artificial intelligence↗

DOE OSTI2024

Precision Computations in Strongly Coupled Conformal Field Theories (Final Technical Report)

Conformal Field Theories (CFTs) are quantum field theories that are invariant under the conformal symmetry group (which includes translations and rotations, but also local rescalings of spacetime). They are building blocks of general quantum field theories, and appear in many areas of physics, including statistical physics, condensed matter physics, particle physics, and quantum gravity. Because of their extra symmetries, the mathematical structure of CFTs is tightly constrained, and this leads to the idea of the ``conformal bootstrap," which is to use these mathematical structures to constrain, and in some cases determine, CFT observables. A new numerical implementation of the conformal bootstrap idea appeared in 2008 with the work of Rattazzi, Rychkov, Tonni, and Vichi. Their observation was that certain bootstrap constraints (conformal symmetry and unitarity) could be combined to yield a convex optimization problem that constraints CFT data. By solving this convex optimization problem on a computer, one could obtain bounds on observables like critical exponents and operator product expansion (OPE) coefficients. Over the course of this award, the PI has improved numerical bootstrap techniques by optimizing known algorithms and finding new ones for performing the required convex optimization computations. The PI has applied these techniques to compute high-precision observables in several important strongly-coupled systems. The PI has also explored both analytical and numerical bootstrap methods for constraining the space of low energy effective field theories of quantum gravity, and developed new analytical techniques for CFT and QFT more broadly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Similarity Downselection: Finding the n Most Dissimilar Molecular Conformers for Reference-Free Metabolomics

Computational methods for creating in silico libraries of molecular descriptors (e.g., collision cross sections) are becoming increasingly prevalent due to the limited number of authentic reference materials available for traditional library building. These so-called “reference-free metabolomics” methods require sampling sets of molecular conformers in order to produce high accuracy property predictions. Due to the computational cost of the subsequent calculations for each conformer, there is a need to sample the most relevant subset and avoid repeating calculations on conformers that are nearly identical. The goal of this study is to introduce a heuristic method of finding the most dissimilar conformers from a larger population in order to help speed up reference-free calculation methods and maintain a high property prediction accuracy. Finding the set of the n items most dissimilar from each other out of a larger population becomes increasingly difficult and computationally expensive as either n or the population size grows large. Because there exists a pairwise relationship between each item and all other items in the population, finding the set of the n most dissimilar items is different than simply sorting an array of numbers. For instance, if you have a set of the most dissimilar n = 4 items, one or more of the items from n = 4 might not be in the set n = 5. An exact solution would have to search all possible combinations of size n in the population exhaustively. We present an open-source software called similarity downselection (SDS), written in Python and freely available on GitHub. SDS implements a heuristic algorithm for quickly finding the approximate set(s) of the n most dissimilar items. We benchmark SDS against a Monte Carlo method, which attempts to find the exact solution through repeated random sampling. We show that for SDS to find the set of n most dissimilar conformers, our method is not only orders of magnitude faster, but it is also more accurate than running Monte Carlo for 1,000,000 iterations, each searching for set sizes n = 3–7 out of a population of 50,000. We also benchmark SDS against the exact solution for example small populations, showing that SDS produces a solution close to the exact solution in these instances. Using theoretical approaches, we also demonstrate the constraints of the greedy algorithm and its efficacy as a ratio to the exact solution.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Structure of the Diphtheria Toxin at Acidic pH: Implications for the Conformational Switching of the Translocation Domain

Diphtheria toxin, an exotoxin secreted by Corynebacterium that causes disease in humans by inhibiting protein synthesis, enters the cell via receptor-mediated endocytosis. The subsequent endosomal acidification triggers a series of conformational changes, resulting in the refolding and membrane insertion of the translocation (T-)domain and ultimately leading to the translocation of the catalytic domain into the cytoplasm. Here, we use X-ray crystallography along with circular dichroism and fluorescence spectroscopy to gain insight into the mechanism of the early stages of pH-dependent conformational transition. For the first time, we present the high-resolution structure of the diphtheria toxin at a mildly acidic pH (5–6) and compare it to the structure at neutral pH (7). We demonstrate that neither catalytic nor receptor-binding domains change their structure upon this acidification, while the T-domain undergoes a conformational change that results in the unfolding of the TH2–3 helices. Surprisingly, the TH1 helix maintains its conformation in the crystal of the full-length toxin even at pH 5. This contrasts with the evidence from the new and previously published data, obtained by spectroscopic measurements and molecular dynamics computer simulations, which indicate the refolding of TH1 upon the acidification of the isolated T-domain. The overall results imply that the membrane interactions of the T-domain are critical in ensuring the proper conformational changes required for the preparation of the diphtheria toxin for the cellular entry.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS2014

Arcjet Testing of Advanced Conformal Ablative TPS

A conformable TPS over a rigid aeroshell has the potential to solve a number of challenges faced by traditional rigid TPS materials (such as tiled Phenolic Impregnated Carbon Ablator (PICA) system on MSL. The compliant (high strain to failure) nature of the conformable ablative materials will allow integration of the TPS with the underlying aeroshell structure much easier and enable monolithic-like configuration and larger segments (or parts) to be used. In May of 2013 the CA250 project executed an arcjet test series in the Ames IHF facility to evaluate a phenolic-based conformal system (named Conformal-PICA) over a range of test conditions from 40-400Wcm2. The test series consisted of four runs in the 13-inch diameter nozzle. Test models were based on SPRITE configuration (a 55-deg sphere cone), as it was able to provide a combination of required heat flux, pressure and shear within a single entry. The preliminary in-depth TC data acquired during that test series allowed a mid-fidelity thermal response model for conformal-PICA to be created while testing of seam models began to address TPS attachment and joining of multiple segments for future fabrication of large-scale aeroshells. Discussed in this paper are the results.

Arcjet Testing↗

DOE OSTI2020

Over 15% Efficiency Polymer Solar Cells Enabled by Conformation Tuning of Newly Designed Asymmetric Small‐Molecule Acceptors

Abstract The prosperous period of polymer solar cells (PSCs) has witnessed great progress in molecule design methods to promote power conversion efficiency (PCE). Designing asymmetric structures has been proved effective in tuning energy level and morphology, which has drawn strong attention from the PSC community. Two hepta‐ring and octa‐ring asymmetric small molecular acceptors (SMAs) (IDTP‐4F and IDTTP‐4F) with S‐shape and C‐shape confirmations are developed to study the relationship between conformation shapes and PSC efficiencies. The similarity of absorption and energy levels between two SMAs makes the conformation a single variable. Additionally, three wide‐bandgap polymer donors (PM6, S1, and PM7) are chosen to prove the universality of the relationship between conformation and photovoltaic performance. Consequently, the champion PCE afforded by PM7: IDTP‐4F is as high as 15.2% while that of PM7: IDTTP‐4F is 13.8%. Moreover, the S‐shape IDTP‐4F performs obviously better than their IDTTP‐4F counterparts in PSCs regardless of the polymer donors, which confirms that S‐shape conformation performs better than the C‐shape one. This work provides an insight into how conformations of asymmetric SMAs affect PCEs, specific functions of utilizing different polymer donors to finely tune the active‐layer morphology and another possibility to reach an excellent PCE over 15%.

Guo, Qing↗

DOE OSTI2024

SEC ‐ SAXS / MC Ensemble Structural Studies of the Microtubule Binding Protein Cdt1 Show Monomeric, Folded‐Over Conformations

ABSTRACT Cdt1 is a mixed folded protein critical for DNA replication licensing and it also has a “moonlighting” role at the kinetochore via direct binding to microtubules and the Ndc80 complex. However, it is unknown how the structure and conformations of Cdt1 could allow it to participate in these multiple, unique sets of protein complexes. While robust methods exist to study entirely folded or unfolded proteins, structure–function studies of combined, mixed folded/disordered proteins remain challenging. In this work, we employ orthogonal biophysical and computational techniques to provide structural characterization of mitosis‐competent human Cdt1. Thermal stability analyses shows that both folded winged helix domains1 are unstable. CD and NMR show that the N‐terminal and linker regions are intrinsically disordered. DLS shows that Cdt1 is monomeric and polydisperse, while SEC‐MALS confirms that it is monomeric at high concentrations, but without any apparent inter‐molecular self‐association. SEC‐SAXS enabled computational modeling of the protein structures. Using the program SASSIE, we performed rigid body Monte Carlo simulations to generate a conformational ensemble of structures. We observe that neither fully extended nor extremely compact Cdt1 conformations are consistent with SAXS. The best‐fit models have the N‐terminal and linker disordered regions extended into the solution and the two folded domains close to each other in apparent “folded over” conformations. We hypothesize the best‐fit Cdt1 conformations could be consistent with a function as a scaffold protein that may be sterically blocked without binding partners. Our study also provides a template for combining experimental and computational techniques to study mixed‐folded proteins.

Cell Biology↗

DOE OSTI2025

Aromatic Amide Foldamers Show Conformation‐Dependent Electronic Properties

Electron transport in organic molecules and biomolecules is governed by electronic structure and molecular conformations. Despite recent progress, key challenges remain in understanding the role of intramolecular interactions and three-dimensional (3D) conformations on the electron transport behavior of organic molecules. In this work, the electronic properties of aromatic amide foldamers are characterized that organize into distinct 3D structures, including an extended secondary amide that adopts a trans-conformation and a folded N-methylated tertiary amide that adopts a cis-conformation. Results from single-molecule electronic experiments show that the extended secondary amide exhibits a fourfold enhancement in molecular conductance compared to the folded N-methylated tertiary amide, despite a longer contour length. The results show that extended amide molecules are governed by a through-bond electron transport mechanism, whereas folded amide molecules are dominated by through-space transport. Bulk spectroscopic characterization and density functional theory calculations further reveal that extended amides have a smaller HOMO–LUMO gap and larger transmission values compared to folded amides, consistent with single-molecule electronic experiments. Overall, this work shows that 3D molecular conformations significantly influence the electronic properties of single-molecule junctions.

electron transport↗

DOE OSTI2021

Effects of pH on an IDP conformational ensemble explored by molecular dynamics simulation

The conformational ensemble of intrinsically disordered proteins, such as α-synuclein, are responsible for their function and malfunction. Misfolding of α-synuclein can lead to neurodegenerative diseases, and the ability to study their conformations and those of other intrinsically disordered proteins under varying physiological conditions can be crucial to understanding and preventing pathologies. In contrast to well-folded peptides, a consensus feature of IDPs is their low hydropathy and high charge, which makes their conformations sensitive to pH perturbation. We examine a prominent member of this subset of IDPs, α-synuclein, using a divide-and-conquer scheme that provides enhanced sampling of IDP structural ensembles. We constructed conformational ensembles of α-synuclein under neutral (pH ~ 7) and low (pH ~ 3) pH conditions and compared our results with available information obtained from smFRET, SAXS, and NMR studies. Specifically, α-synuclein has been found to in a more compact state at low pH conditions and the structural changes observed are consistent with those from experiments. We also characterize the conformational and dynamic differences between these ensembles and discussed the implication on promoting pathogenic fibril formation. We find that under low pH conditions, neutralization of negatively charged residues leads to compaction of the C-terminal portion of α-synuclein while internal reorganization allows α-synuclein to maintain its overall end-to-end distance. Here, we also observe different levels of intra-protein interaction between three regions of α-synuclein at varying pH and a shift towards more hydrophilic interactions with decreasing pH.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗