hybridization based on the mechanism of the hybridization chain reaction (HCR) has addressed multi-decade challenges that impeded imaging of mRNA expression in diverse organisms, offering a unique combination of multiplexing, quantitation, sensitivity, resolution and versatility. Here, with third-generation HCR, we augment these capabilities using probes and amplifiers that combine to provide automatic background suppression throughout the protocol, ensuring that reagents will not generate amplified background even if they bind non-specifically within the sample. Automatic background suppression dramatically enhances performance and robustness, combining the benefits of a higher signal-to-background ratio with the convenience of using unoptimized probe sets for new targets and organisms. HCR v3.0 enables three multiplexed quantitative analysis modes: (1) qHCR imaging - analog mRNA relative quantitation with subcellular resolution in the anatomical context of whole-mount vertebrate embryos; (2) qHCR flow cytometry - analog mRNA relative quantitation for high-throughput expression profiling of mammalian and bacterial cells; and (3) dHCR imaging - digital mRNA absolute quantitation via single-molecule imaging in thick autofluorescent samples.

In situ hybridization based on the mechanism of hybridization chain reaction (HCR) has addressed multi-decade challenges to imaging mRNA expression in diverse organisms, offering a unique combination of multiplexing, quantitation, sensitivity, resolution, and versatility. Here, with third-generation in situ HCR, we augment these capabilities using probes and amplifiers that combine to provide automatic background suppression throughout the protocol, ensuring that even if reagents bind non-specifically within the sample they will not generate amplified background. Automatic background suppression dramatically enhances performance and robustness, combining the benefits of higher signal-to-background with the convenience of using unoptimized probe sets for new targets and organisms. In situ HCR v3.0 enables multiplexed quantitative mRNA imaging with subcellular resolution in the anatomical context of whole-mount vertebrate embryos, multiplexed quantitative mRNA flow cytometry for high-throughput single-cell expression profiling, and multiplexed quantitative single-molecule mRNA imaging in thick autofluorescent samples.KEYWORDS: in situ HCR v3.0, qHCR imaging, qHCR flow cytometry, dHCR imaging, multiplexed in situ hybridization, quantitative in situ hybridization, single-molecule mRNA imaging, mRNA flow cytometry, whole-mount vertebrate embryos, mammalian cells, bacterial cells, split-initiator probes, automatic background suppression.

We introduce embedded mean-field theory (EMFT), an approach that flexibly allows for the embedding of one mean-field theory in another without the need to specify or fix the number of particles in each subsystem. EMFT is simple, is well-defined without recourse to parameters, and inherits the simple gradient theory of the parent mean-field theories. In this paper, we report extensive benchmarking of EMFT for the case where the subsystems are treated using different levels of Kohn-Sham theory, using PBE or B3LYP/6-31G* in the high-level subsystem and LDA/STO-3G in the low-level subsystem; we also investigate different levels of density fitting in the two subsystems. Over a wide range of chemical problems, we find EMFT to perform accurately and stably, smoothly converging to the high-level of theory as the active subsystem becomes larger. In most cases, the performance is at least as good as that of ONIOM, but the advantages of EMFT are highlighted by examples that involve partitions across multiple bonds or through aromatic systems and by examples that involve more complicated electronic structure. EMFT is simple and parameter free, and based on the tests provided here, it offers an appealing new approach to a multiscale electronic structure.

Dynamic programming algorithms within the NUPACK software suite enable analysis of nucleic acid sequences over complex and test tube ensembles containing arbitrary numbers of interacting strand species, serving the needs of researchers in molecular programming, nucleic acid nanotechnology, synthetic biology, and across the life sciences. Here, to enhance the underlying physical model, ensure scalability for large calculations, and achieve dramatic speedups when calculating diverse physical quantities over complex and test tube ensembles, we introduce a unified dynamic programming framework that combines three ingredients: (1) recursions that specify the dependencies between subproblems and incorporate the details of the structural ensemble and the free energy model, (2) evaluation algebras that define the mathematical form of each subproblem, (3) operation orders that specify the computational trajectory through the dependency graph of subproblems. The physical model is enhanced using new recursions that operate over the complex ensemble including coaxial and dangle stacking subensembles. The recursions are coded generically and then compiled with a quantity-specific evaluation algebra and operation order to generate an executable for each physical quantity: partition function, equilibrium base-pairing probabilities, MFE energy and proxy structure, suboptimal proxy structures, and Boltzmann sampled structures. For large complexes (e.g., 30 000 nt), scalability is achieved for partition function calculations using an overflow-safe evaluation algebra, and for equilibrium base-pairing probabilities using a backtrack-free operation order. A new blockwise operation order that treats subcomplex blocks for the complex species in a test tube ensemble enables dramatic speedups (e.g., 20–120× ) using vectorization and caching. With these performance enhancements, equilibrium analysis of substantial test tube ensembles can be performed in ≤ 1 min on a single computational core (e.g., partition function and equilibrium concentration for all complex species of up to six strands formed from two strand species of 300 nt each, or for all complex species of up to two strands formed from 80 strand species of 100 nt each). A new sampling algorithm simultaneously samples multiple structures from the complex ensemble to yield speedups of an order of magnitude or more as the number of structures increases above ≈103. These advances are available within the NUPACK 4.0 code base () which can be flexibly scripted using the all-new NUPACK Python module.

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NUPACK is a growing software suite for the analysis and design of nucleic acid structures, devices, and systems serving the needs of researchers in the fields of nucleic acid nanotechnology, molecular programming, synthetic biology, and across the life sciences. NUPACK algorithms are unique in treating complex and test tube ensembles containing arbitrary numbers of interacting strand species, providing crucial tools for capturing concentration effects essential to analyzing and designing the intermolecular interactions that are a hallmark of these fields. The all-new NUPACK web app (nupack.org) has been re-architected for the cloud, leveraging a cluster that scales dynamically in response to user demand to enable rapid job submission and result inspection even at times of peak user demand. The web app exploits the all-new NUPACK 4 scientific code base as its backend, offering enhanced physical models (coaxial and dangle stacking subensembles), dramatic speedups (20-120x for test tube analysis), and increased scalability for large complexes. NUPACK 4 algorithms can also be run locally using the all-new NUPACK Python module.

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Iron formations (IFs) are chemical sedimentary rocks that were widely deposited before the Great Oxidation Event (GOE) around 2.4–2.2 Ga. It is generally thought that IFs precipitated as hydrated Fe3+ oxides (HFOs) such as ferrihydrite following surface oxidation of Fe2+-rich, anoxic deep waters. This model often implicates biological oxidation and underpins reconstructions of marine nutrient concentrations. However, nanoscale petrography indicates that an Fe2+ silicate, greenalite, is a common primary mineral in well-preserved IFs, motivating an alternative depositional model of anoxic ferrous silicate precipitation. It is unclear, however, if Fe2+-rich silicates can produce the Fe isotopic variations in IFs that are well explained by Fe2+ oxidation. To address this question, we constrain the equilibrium Fe isotopic (56Fe/54Fe) fractionation of greenalite and ferrihydrite by determining the iron phonon densities of states for those minerals. We use ab initio density functional theory (DFT + U) calculations and nuclear resonant inelastic X-ray scattering spectroscopy to show that ferrous greenalite should be isotopically lighter than ferrihydrite by ∼1–1.2‰ at equilibrium, and fractionation should scale linearly with increasing Fe3+ content in greenalite. By anchoring ferrihydrite–greenalite mineral pair fractionations to published experimental Fe isotopic fractionations between HFOs and aqueous Fe2+, we show that ferrous greenalite may produce all but the heaviest pre-GOE Fe isotopic compositions and mixed valence greenalites can produce the entire record. Our results suggest that heavy Fe isotope enrichments alone are not diagnostic of primary IF mineralogies, and ferrihydrite and partially oxidized or even purely ferrous greenalite are all viable primary IF mineralogies.