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Cryogenic transmission electron microscopy (cryo-TEM) combined with single particle analysis (SPA) is an emerging imaging approach for soft materials. However, the accuracy of SPA-reconstructed nanostructures, particularly those formed by synthetic polymers, remains uncertain due to potential packing heterogeneity of the nanostructures. In this study, the combination of molecular dynamics (MD) simulations and image simulations is utilized to validate the accuracy of cryo-TEM 3D reconstructions of self-assembled polypeptoid fibril nanostructures. Using CryoSPARC software, image simulations, 2D classifications, ab initio reconstructions, and homogenous refinements are performed. By comparing the results with atomic models, the recovery of molecular details is assessed, heterogeneous structures are identified, and the influence of extraction location on the reconstructions is evaluated. These findings confirm the fidelity of single particle analysis in accurately resolving complex structural characteristics and heterogeneous structures, exhibiting its potential as a valuable tool for detailed structural analysis of synthetic polymers and soft materials.

We investigated the temperature-dependent structural evolution of thermoreversible triblock terpolypeptoid hydrogels, namely poly(N-allyl glycine)-b-poly(N-methyl glycine)-b-poly(N-decyl glycine) (AMD), using small-angle neutron scattering (SANS) with contrast matching in conjunction with X-ray scattering and cryogenic transmission electron microscopy (cryo-TEM) techniques. At room temperature, A100M101D10 triblock terpolypeptoids self-assemble into core-corona-type spherical micelles in aqueous solution. Upon heating above the critical gelation temperature (T gel), SANS analysis revealed the formation of a two-compartment hydrogel network comprising distinct micellar cores composed of dehydrated A blocks and hydrophobic D blocks. At T ≳ T gel, the temperature-dependent dehydration of A block further leads to the gradual rearrangement of both A and D domains, forming well-ordered micellar network at higher temperatures. For AMD polymers with either longer D block or shorter A block, such as A101M111D21 and A43M92D9, elongated nonspherical micelles with a crystalline D core were observed at T < T gel. Although these enlarged crystalline micelles still undergo a sharp sol-to-gel transition upon heating, the higher aggregation number of chains results in the immediate association of the micelles into ordered aggregates at the initial stage, followed by a disruption of the spatial ordering as the temperature further increases. On the other hand, fiber-like structures were also observed for AMD with longer A block, such as A153M127D10, due to the crystallization of A domains. This also influences the assembly pathway of the two-compartment network. Our findings emphasize the critical impact of initial micellar morphology on the structural evolution of AMD hydrogels during the sol-to-gel transition, providing valuable insights for the rational design of thermoresponsive hydrogels with tunable network structures at the nanometer scale.

We introduce a new row insertion algorithm on decreasing tableaux and increasing tableaux, generalizing Edelman-Greene (EG) row insertion. Our row insertion algorithm is a nontrivial variation of Hecke column insertion which generalizes EG column insertion. Similar to Hecke column insertion, our row insertion is bijective and respects Hecke equivalence, and therefore recovers the expansions of stable Grothendieck functions into Grassmannian stable Grothendieck functions.Mathematics Subject Classifications: 05E05Keywords: Hecke insertion, Grothendieck polynomials

Amphiphilic molecules that can crystallize often form molecularly thin nanosheets in aqueous solutions. The possibility of atomic-scale corrugations in these structures has not yet been recognized. We have studied the self-assembly of amphiphilic polypeptoids, a family of bio-inspired polymers that can self-assemble into various crystalline nanostructures. Atomic-scale structure of the crystals in these systems has been inferred using both X-ray diffraction and electron microscopy. Here we use cryogenic electron microscopy to determine the in-plane and out-of-plane structures of a crystalline nanosheet. Data were collected as a function of tilt angle and analyzed using a hybrid single-particle crystallographic approach. The analysis reveals that adjacent rows of peptoid chains, which are separated by 4.5 Å in the plane of the nanosheet, are offset by 6 Å in the direction perpendicular to the plane of the nanosheet. These atomic-scale corrugations lead to a doubling of the unit cell dimension from 4.5 to 9 Å. Our work provides an alternative interpretation for the observed Å X-ray diffraction peak often reported in polypeptoid crystals.

The ability to engineer synthetic polymers with the same structural precision as biomacromolecules is crucial to enable the de novo design of robust nanomaterials with biomimetic function. Peptoids, poly(N-substituted) glycines, are a highly controllable bio-inspired polymer family that can assemble into a variety of functional, crystalline nanostructures over a wide range of sequences. Extensive investigation on the molecular packing in these lattices has been reported; however, many key atomic-level details of the molecular structure remain underexplored. Here, we use cryo-TEM 3D reconstruction to directly visualize the conformation of an individual polymer chain within a peptoid nanofiber lattice in real space at 3.6 Å resolution. The backbone in the N-decylglycine hydrophobic core is shown to clearly adopt an extended, all-cis-sigma strand conformation, as previously suggested in many peptoid lattice models. We also show that packing interactions (covalent and noncovalent) at the solvent-exposed N-termini have a dominant impact on the local chain ordering and hence the ability of the chains to pack into well-ordered lattices. Peptoids in pure water form fibers with limited growth in the a direction (

Lascoux polynomials generalize Grassmannian stable Grothendieck polynomials and may be viewed as K-theoretic analogs of key polynomials. The latter two polynomials have combinatorial formulas involving tableaux: Lascoux and Schützenberger gave a combinatorial formula for key polynomials using right keys; Buch gave a set-valued tableau formula for Grassmannian stable Grothendieck polynomials. We establish a novel combinatorial description for Lascoux polynomials involving right keys and set-valued tableaux. Our description generalizes the tableaux formulas of key polynomials and Grassmannian stable Grothendieck polynomials. To prove our description, we construct a new abstract Kashiwara crystal structure on set-valued tableaux. This construction answers an open problem of Monical, Pechenik and Scrimshaw.Mathematics Subject Classifications: 05E05Keywords: Lascoux polynomials, set-valued tableaux, crystal operators

BackgroundSupportive parenting during childhood has been associated with many positive developmental outcomes for offspring in adulthood, including fewer health-risk behaviors. Little is known about the neural mechanisms underlying these associations.MethodsThe present study followed rural African Americans (n = 91, 52% female) from late childhood (11-13 years of age) to emerging adulthood (25 years of age). Parent-child communication was assessed at 11, 12, and 13 years of age. Functional magnetic resonance imaging was used at 25 years of age to measure resting-state functional connectivity of the anterior salience network (ASN). Harmful alcohol use and emotional eating were also assessed at 25 years of age. Structural equation modeling was used to test pathways from parent-child communication at 11 to 13 years of age to harmful alcohol use and emotional eating at 25 years of age via resting-state functional connectivity of the ASN.ResultsGreater parent-child communication between 11 and 13 years of age forecast greater resting-state functional connectivity of the ASN at 25 years of age which, in turn, was associated with lower harmful alcohol use and emotional eating at 25 years of age. Significant indirect effects through the ASN were present for both outcomes.ConclusionsThese findings indicate the importance of parenting in late childhood for adaptive behaviors and suggest a pathway via higher ASN coherence. This network was implicated in both harmful alcohol use and emotional eating, corroborating evidence of overlap in brain regions for dysregulated substance use and eating behaviors and revealing divergent pathways. These findings support the value of prevention and intervention efforts targeting parenting skills in childhood toward fostering long-term, adaptive neurocognitive development.

ImportanceThis study was designed to determine whether a preventive intervention focused on enhancing supportive parenting could ameliorate the association between exposure to poverty and brain development in low socioeconomic status African American individuals from the rural South.ObjectiveTo determine whether participation in an efficacious prevention program designed to enhance supportive parenting for rural African American children will ameliorate the association between living in poverty and reduced hippocampal and amygdalar volumes in adulthood.Design, setting, and participantsIn the rural southeastern United States, African American parents and their 11-year-old children were assigned randomly to the Strong African American Families randomized prevention trial or to a control condition. Parents provided data used to calculate income-to-needs ratios when children were aged 11 to 13 years and 16 to 18 years. When the participants were aged 25 years, hippocampal and amygdalar volumes were measured using magnetic resonance imaging.ExposuresHousehold poverty was measured by income-to-needs ratios.Main outcomes and measuresYoung adults' whole hippocampal, dentate gyrus, and CA3 hippocampal subfields as well as amygdalar volumes were assessed using magnetic resonance imaging.ResultsOf the 667 participants in the Strong African American Families randomized prevention trial, 119 right-handed African American individuals aged 25 years living in rural areas were recruited. Years lived in poverty across ages 11 to 18 years forecasted diminished left dentate gyrus (simple slope, -14.20; standard error, 5.22; P = .008) and CA3 (simple slope, -6.42; standard error, 2.42; P = .009) hippocampal subfields and left amygdalar (simple slope, -34.62; standard error, 12.74; P = .008) volumes among young adults in the control condition (mean [SD] time, 2.04 [1.88] years) but not among those who participated in the Strong African American Families program (mean [SD] time, 2.61 [1.77] years).Conclusions and relevanceIn this study, we described how participation in a randomized clinical trial designed to enhance supportive parenting ameliorated the association of years lived in poverty with left dentate gyrus and CA3 hippocampal subfields and left amygdalar volumes. These findings are consistent with a possible role for supportive parenting and suggest a strategy for narrowing social disparities.