QCT-based spatio-temporal aging atlas of the proximal femur BMD and cortical geometry

Aging is associated with an increased risk of fragility fractures at the hip, resulting from a loss of bone mass. While this loss is typically reported as a decreased mean areal bone mineral density (aBMD) in the proximal femur or the femoral neck, its evolution is spatially inhomogeneous, which might also contribute to the increased risk of fractures. Yet, little is known about the evolution of BMD distribution and cortical thickness with age in the proximal femur. We propose a 3D spatio-temporal atlas of the proximal femur to identify regions with high BMD losses and cortical thinning. The atlas is based on 532 post-mortem QCT scans from donors aged 20 to 94, including 179 female subjects. A point cloud with anatomically corresponding positions was defined for each femur based on a personalized coordinate system. The evolution of BMD and cortical thickness was computed as a multiple linear regression with age and BMI, for female and male subjects separately. The average BMD decrease with age was significant in all subregions for both sexes but higher in females. High BMD losses were observed in the superior and middle neck regions, in the medial part of the head, and in the trochanteric trabecular bone. BMD was well preserved in the inferior neck and, for males, in cortical regions. In both sexes, the cortical thickness decreased significantly in the superior and posterior neck cortex and increased significantly in the inferior neck. Higher BMI was associated with increased BMD in the inferior neck and medial shaft cortex, as well as with increased cortical thickness in all neck and shaft regions for both sexes. The spatio-temporal atlas showed the evolution of BMD distribution and cortical thickness in the proximal femur, with high losses in typical fracture locations, such as the femoral neck and pertrochanteric regions.</p

Supporting Information: Quantum Chemical Roots of Machine-Learning Molecular Similarity Descriptors

This document contains the supporting information published together with the article "Quantum Chemical Roots of Machine-Learning Molecular Similarity Descriptors" (J. Chem. Theory Comput., 2022, 18, 6670)

Quantum chemical roots of machine-learning molecular similarity descriptors

In this work, we explore the quantum chemical foundations of descriptors for molecular similarity. Such descriptors are key for traversing chemical compound space with machine learning. Our focus is on the Coulomb matrix and on the smooth overlap of atomic positions (SOAP). We adopt a basic framework that allows us to connect both descriptors to electronic structure theory. This framework enables us then to define two new descriptors that are more closely related to electronic structure theory, which we call Coulomb lists and smooth overlap of electron densities (SOED). By investigating their usefulness as molecular similarity descriptors, we gain new insights in how and why Coulomb matrix and SOAP work. Moreover, Coulomb lists avoid the somewhat mysterious diagonalization step of the Coulomb matrix and might provide a direct means to extract subsystem information that can be compared across Born-Oppenheimer surfaces of varying dimension. For the electron density we derive the necessary formalism to create the SOED measure in close analogy to SOAP. Since this formalism is more involved than that of SOAP, we review the essential theory, but also introduce a set of approximations that eventually allow us to work with SOED in terms of the same implementation available for the evaluation of SOAP. We focus our analysis on elementary reaction steps, where transition state structures are more similar to either reactant or product structures than the latter two are with respect to one another. The prediction of electronic energies of transition state structures can, however, be more difficult than that of stable intermediates due to multi-configurational effects. The question arises to what extent molecular similarity descriptors rooted in electronic structure theory can resolve these intricate effects.Comment: 41 pages, 10 figure

Quantum Chemical Roots of Machine-Learning Molecular Similarity Descriptors

In this work, we explore the quantum chemical foundations of descriptors for molecular similarity. Such descriptors are key for traversing chemical compound space with machine learning. Our focus is on the Coulomb matrix and on the smooth overlap of atomic positions (SOAP). We adopt a basic framework that allows us to connect both descriptors to electronic structure theory. This framework enables us to then define two new descriptors that are more closely related to electronic structure theory, which we call Coulomb lists and smooth overlap of electron densities (SOED). By investigating their usefulness as molecular similarity descriptors, we gain new insights into how and why Coulomb matrix and SOAP work. Moreover, Coulomb lists avoid the somewhat mysterious diagonalization step of the Coulomb matrix and might provide a direct means to extract subsystem information that can be compared across Born-Oppenheimer surfaces of varying dimension. For the electron density, we derive the necessary formalism to create the SOED measure in close analogy to SOAP. Because this formalism is more involved than that of SOAP, we review the essential theory as well as introduce a set of approximations that eventually allow us to work with SOED in terms of the same implementation available for the evaluation of SOAP. We focus our analysis on elementary reaction steps, where transition state structures are more similar to either reactant or product structures than the latter two are with respect to one another. The prediction of electronic energies of transition state structures can, however, be more difficult than that of stable intermediates due to multi-configurational effects. The question arises to what extent molecular similarity descriptors rooted in electronic structure theory can resolve these intricate effects.ISSN:1549-9618ISSN:1549-962

Enumeration of de novo Inorganic Complexes for Chemical Discovery and Machine Learning

Despite being attractive targets for functional materials, the discovery of transition metal complexes with high-throughput computational screening is challenged by the amount of feasible coordination numbers, spin states, or oxidation states and the potentially large sizes of ligands. To overcome these limitations, we take inspiration from organic chemistry where full enumeration of neutral, closed shell molecules under the constraint of size has enriched discovery efforts. We design monodentate and bidentate ligands from scratch for the construction of mononuclear, octahedral transition metal complexes with up to 13 heavy atoms (i.e., metal, C, N, O, P, or S). From > 11,000 theoretical ligands, we develop a heuristic score for ranking a chemically feasible 2,500 ligand subset, only 71 of which were previously included in common organic molecule databases. We characterize the top 20% of scored ligands with density functional theory (DFT) in an octahedral homoleptic ligand database (OHLDB). The OHLDB contains i) the geometry optimized structures of 1,250 homoleptic octahedral complexes obtained from the enumerated pool of ligands and an open-shell transition metal (M(II)/M(III), M = Cr, Mn, Fe, or Co), and ii) the resulting high-spin/low-spin adiabatic electronic energies (ΔEH-L) obtained with hybrid DFT. Over the OHLDB, we observe structure–property (i.e., ΔEH-L) relationships different from those expected on the basis of ligand field arguments or from our prior data sets. Finally, we demonstrate how incorporating OHLDB data into artificial neural network (ANN) training improves ANN out-of-sample performance on much larger transition metal complexes.</p

Enumeration of de novo inorganic complexes for chemical discovery and machine learning

Vapor phase deposition is typically used to apply thin films and coatings onto solid substrates. Deposition of materials onto liquid substrates provides complexity due to surface tension, viscosity, and solubility effects. Understanding the interactions between the deposited material and the liquid substrate can lead to the formation of materials with new structures and compositions. In this review, we will discuss the interactions associated with initiated chemical vapor deposition of polymers onto liquid substrates including silicone oils and ionic liquids. We will provide guidelines for selecting liquid properties to control the formation of polymer particles, films, and gels. We will conclude by discussing recent work on combining polymer and metal deposition to create hybrid organic/inorganic structures and actively moving the liquid during polymer deposition. ©2019Office of Naval Research (grant no. N00014-17-1-2956)Office of Naval Research (grant no. N00014-18-1-2434