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1. Mathematical aspects of molecular replacement. IV. Measure-theoretic decompositions of motion spaces

   https://doi.org/10.1107/S2053273317007227  

   Chirikjian, Gregory S. ; Sajjadi, Sajdeh ; Shiffman, Bernard ; Zucker, Steven M. ( September 2017 , Acta Crystallographica Section A Foundations and Advances)

   In molecular-replacement (MR) searches, spaces of motions are explored for determining the appropriate placement of rigid-body models of macromolecules in crystallographic asymmetric units. The properties of the space of non-redundant motions in an MR search, called a `motion space', are the subject of this series of papers. This paper, the fourth in the series, builds on the others by showing that when the space group of a macromolecular crystal can be decomposed into a product of two space subgroups that share only the lattice translation group, the decomposition of the group provides different decompositions of the corresponding motion spaces. Then an MR search can be implemented by trading off between regions of the translation and rotation subspaces. The results of this paper constrain the allowable shapes and sizes of these subspaces. Special choices result when the space group is decomposed into a product of a normal Bieberbach subgroup and a symmorphic subgroup (which is a common occurrence in the space groups encountered in protein crystallography). Examples of Sohncke space groups are used to illustrate the general theory in the three-dimensional case (which is the relevant case for MR), but the general theory in this paper applies to any dimension. 

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2. Strategies and Discoveries Leading to the Synthesis of Trichoaurantianolide Natural Products

   https://doi.org/10.1016/B978-0-12-822212-6.00002-3  

   Williams, David R ( January 2022 , Strategies and tactics in organic synthesis)

   Harmata, Michael (Ed.)

   Several years ago, a small family of diterpenoid natural products attracted our attention as novel targets for synthesis studies. Initially, four compounds were independently characterized by the research teams of Vidari1 and Steglich.2 Trichoaurantianolides AeD (1e4 of Fig. 9.1) were isolated from fruiting bodies of the mushrooms Tricholoma aurantium and Tricholoma fracticum in 1995. Subsequent efforts of Stermer and coworkers3 described the isolation of the closely related lepistal (5) and lepistol (6) of Fig. 9.2 as the corresponding C8 deoxygenated compounds of this family. In addition, the corresponding acetate of trichoaurantianolide B was discovered and named as 6-O-aetyl- trichoaurantin (7).2 Structure assignments were based upon extensive nuclear magnetic resonance (NMR) studies, and the features of relative stereo- chemistry were confirmed by an X-ray crystallographic analysis of trichoaurantianolide B (2).1b,2 These original investigators described the trichoaurantianolides as examples of a new class of diterpenes named as neodolastanes that signified a structural relationship to the tricyclic metabo- lites of marine origins known as dolastanes as represented by dolatriol (8)4 and the clavularane 95 of Fig. 9.2. Neodolastanes were defined as substances in which the bridgehead methyl substituent appears in a vicinal relationship with respect to the isopropyl group as exemplified in 4,5-deoxyneodolabelline (10) of Fig. 9.2, a related class of marine natural products.6 Steglich and coworkers2 also indicated an assignment of absolute stereo- chemistry for 2 that was based on Hamilton’s applications of linear-hypothesis testing of crystallographic data. This seldom-used technique was in agreement with the proposed absolute configuration of 2 that was advanced by Vidari, based on an assessment of the observed Cotton effects in CD spectroscopy. In 2003, Ohta and coworkers7 reported the discovery of related neodolastanes tricholomalides A, B, and C (structures 11, 12, and 13 of Fig. 9.3) from Tricholoma sp. They concluded that the tricholomalides possessed the opposite absolute configuration claimed for the trichoaurantianolides. This conclusion was based upon the independent analysis of their circular dichroism studies. By application of the octant rule for substituent effects on cisoid a,b- unsaturated ketones,8 Ohta and coworkers suggested a revision of the prior assignment of absolute configuration for the trichoaurantianolides. This asser- tion was advanced in spite of the consistently positive specific rotations recorded in different solvents for trichoaurantianolides A, B, and C1,2 versus the negative values of tricholomalides A (11) and B (12) (compare values in Figs. 9.1 and 9.3). Note that tricholomalide C (13) only differs from trichoaurantianolide B (2) as a C-8 diastereomeric alcohol, presented in the antipodal series. The specific rotation of 13 was of little value since it was recorded as [a]0 (c 0.01, MeOH).7 In 2006, Danishefsky described a pathway for the total synthesis of racemic tricholomalides A and B, and this effort led to a revision of the relative C-2 stereochemistry (Fig. 9.3; revised structures 14 and 15).9 It seemed rather unusual that genetically similar fungi would produce closely related metabolites as enantiomers, but certainly this is not unprecedented. As a starting point, this issue lacked clarity, and we concluded that our synthesis plans must unambig- uously address the issues of absolute configuration. The chemistry of dolabellane and dolastane diterpenes has been reviewed.10 The proposed pathway for biosynthesis of the trichoaurantianolides and related compounds (Fig. 9.4) follows an established sequence from geranyl- geranyl pyrophosphate (16), which undergoes p-cation cyclization to initially form the eleven-membered ring of 17. The event is followed by a second cyclization to form the dolabellane cation 18, and this [9.3.0]cyclotetradecane skeleton is central to several families of natural products. Direct capture or elimination from 18 leads to the 3,7-dolabelladiene 19, which presents the most common pattern of unsaturation within this class. Compounds within this group are traditionally numbered beginning with C-1 as the bridgehead carbon bearing the methyl group rather than following the connectivity presented in ger- anylgeranyl 16. The cation 18 also undergoes a 1,2-hydrogen migration and elimination, which leads to a transannular cyclization yielding the 5e7e6 tri- cyclic dolastane 20. The secodolastanes, represented by 21, are a small collec- tion of marine natural products, which arise from oxidative cleavage of C10eC14 in the parent tricycle 20. In analogous fashion, the neodolabellane structure 22 is produced from 18 by stereospecific backbone migrations that result in the vicinal placement of the bridgehead methyl and isopropyl substituents. Transannular cyclizations, stemming from 22, yield the class of neodolastane diterpenes (23). Trichoaurantianolides and the related lepistal A (5) are the result of oxidations and cleavage of the C-ring (C4eC5) of 23, which leads to the features of an unusual butyrolactone system. The guanacastepenes, such as 24,11 and heptemerones, such as 25,12 are primary examples of the 5e7e6 neodolastane family, and these metabolites have also been isolated from fungi sources. A characteristic structural feature is the vicinal, syn-relationship of the bridgehead methyl and isopropyl sub- stituents as compared with the 1,3-trans relationship found in dolastanes (Fig. 9.2, structures 8 and 9). Guanacastepenes have proven to be attractive targets for synthesis studies.11,13 However, these fungal metabolites exhibit the antipodal, absolute stereochemistry as compared with neodolastanes from marine origins, such as sphaerostanol (26) (Fig. 9.5).14 

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3. Soft interactions and volume exclusion by polymeric crowders can stabilize or destabilize transient structure in disordered proteins depending on polymer concentration

   https://doi.org/10.1002/prot.25307  

   Rusinga, Farai I. ; Weis, David D. ( May 2017 , Proteins: Structure, Function, and Bioinformatics)

   The effects of macromolecular crowding on the transient structure of intrinsically disordered proteins is not well‐understood. Crowding by biological molecules inside cells could modulate transient structure and alter IDP function. Volume exclusion theory and observations of structured proteins suggest that IDP transient structure would be stabilized by macromolecular crowding. Amide hydrogen exchange (HX) of IDPs in highly concentrated polymer solutions would provide valuable insights into IDP transient structure under crowded conditions. Here, we have used mass spectrometry to measure HX by a transiently helical random coil domain of the activator of thyroid and retinoid receptor (ACTR) in solutions containing 300 g L⁻¹and 400 g L⁻¹of Ficoll, a synthetic polysaccharide, using a recently‐developed strong cation exchange‐based cleanup method [Rusinga, et al., Anal Chem 2017;89:1275–1282]. Transiently helical regions of ACTR exchanged faster in 300 g L⁻¹Ficoll than in dilute buffer. In contrast, one transient helix exchanged more slowly in 400 g L⁻¹Ficoll. Nonspecific interactions destabilize ACTR helicity in 300 g L⁻¹Ficoll because ACTR engages with the Ficoll polymer mesh. In contrast, 400 g L⁻¹Ficoll is a semi‐dilute solution where ACTR cannot engage the Ficoll mesh. At this higher concentration, volume exclusion stabilizes ACTR helicity because ACTR is compacted in interstitial spaces between Ficoll molecules. Our results suggest that the interplay between nonspecific interactions and volume exclusion in different cellular compartments could modulate IDP function by altering the stability of IDP transient structures. Proteins 2017; 85:1468–1479. © 2017 Wiley Periodicals, Inc.

    

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4. Molecular dynamics inferred transfer learning models for finite‐strain hyperelasticity of monoclinic crystals: Sobolev training and validations against physical constraints

   https://doi.org/10.1002/nme.6992  

   Vlassis, Nikolaos N. ; Zhao, Puhan ; Ma, Ran ; Sewell, Tommy ; Sun, WaiChing ( May 2022 , International Journal for Numerical Methods in Engineering)

   We present a machine learning framework to train and validate neural networks to predict the anisotropic elastic response of a monoclinic organic molecular crystal known as ‐HMX in the geometrical nonlinear regime. A filtered molecular dynamic (MD) simulations database is used to train neural networks with a Sobolev norm that uses the stress measure and a reference configuration to deduce the elastic stored free energy functional. To improve the accuracy of the elasticity tangent predictions originating from the learned stored free energy, a transfer learning technique is used to introduce additional tangential constraints from the data while necessary conditions (e.g., strong ellipticity, crystallographic symmetry) for the correctness of the model are either introduced as additional physical constraints or incorporated in the validation tests. Assessment of the neural networks is based on (1) the accuracy with which they reproduce the bottom‐line constitutive responses predicted by MD, (2) the robustness of the models measured by detailed examination of their stability and uniqueness, and (3) the admissibility of the predicted responses with respect to mechanics principles in the finite‐deformation regime. We compare the training efficiency of the neural networks under different Sobolev constraints and assess the accuracy and robustness of the models against MD benchmarks for ‐HMX.

    

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5. A computational method for the design of nested proteins by loop‐directed domain insertion

   https://doi.org/10.1002/prot.25445  

   Blacklock, Kristin M. ; Yang, Lu ; Mulligan, Vikram K. ; Khare, Sagar D. ( January 2018 , Proteins: Structure, Function, and Bioinformatics)

   The computational design of novel nested proteins—in which the primary structure of one protein domain (insert) is flanked by the primary structure segments of another (parent)—would enable the generation of multifunctional proteins. Here we present a new algorithm, called Loop‐Directed Domain Insertion (LooDo), implemented within the Rosetta software suite, for the purpose of designing nested protein domain combinations connected by flexible linker regions. Conformational space for the insert domain is sampled using large libraries of linker fragments for linker‐to‐parent domain superimposition followed by insert‐to‐linker superimposition. The relative positioning of the two domains (treated as rigid bodies) is sampled efficiently by a grid‐based, mutual placement compatibility search. The conformations of the loop residues, and the identities of loop as well as interface residues, are simultaneously optimized using a generalized kinematic loop closure algorithm and Rosetta EnzymeDesign, respectively, to minimize interface energy. The algorithm was found to consistently sample near‐native conformations and interface sequences for a benchmark set of structurally similar but functionally divergent domain‐inserted enzymes from the α/β hydrolase superfamily, and discriminates well between native and nonnative conformations and sequences, although loop conformations tended to deviate from the native conformations. Furthermore, in cross‐domain placement tests, native insert‐parent domain combinations were ranked as the best‐scoring structures compared to nonnative domain combinations. This algorithm should be broadly applicable to the design of multi‐domain protein complexes with any combination of inserted or tandem domain connections.

    

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