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  1. Abstract

    Biological evolution has led to precise and dynamic nanostructures that reconfigure in response to pH and other environmental conditions. However, designing micrometre-scale protein nanostructures that are environmentally responsive remains a challenge. Here we describe the de novo design of pH-responsive protein filaments built from subunits containing six or nine buried histidine residues that assemble into micrometre-scale, well-ordered fibres at neutral pH. The cryogenic electron microscopy structure of an optimized design is nearly identical to the computational design model for both the subunit internal geometry and the subunit packing into the fibre. Electron, fluorescent and atomic force microscopy characterization reveal a sharp and reversible transition from assembled to disassembled fibres over 0.3 pH units, and rapid fibre disassembly in less than 1 s following a drop in pH. The midpoint of the transition can be tuned by modulating buried histidine-containing hydrogen bond networks. Computational protein design thus provides a route to creating unbound nanomaterials that rapidly respond to small pH changes.

     
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  2. Free, publicly-accessible full text available August 1, 2024
  3. Free, publicly-accessible full text available June 1, 2024
  4. Abstract

    Current biotechnologies can simultaneously measure multiple high-dimensional modalities (e.g., RNA, DNA accessibility, and protein) from the same cells. A combination of different analytical tasks (e.g., multi-modal integration and cross-modal analysis) is required to comprehensively understand such data, inferring how gene regulation drives biological diversity and functions. However, current analytical methods are designed to perform a single task, only providing a partial picture of the multi-modal data. Here, we present UnitedNet, an explainable multi-task deep neural network capable of integrating different tasks to analyze single-cell multi-modality data. Applied to various multi-modality datasets (e.g., Patch-seq, multiome ATAC + gene expression, and spatial transcriptomics), UnitedNet demonstrates similar or better accuracy in multi-modal integration and cross-modal prediction compared with state-of-the-art methods. Moreover, by dissecting the trained UnitedNet with the explainable machine learning algorithm, we can directly quantify the relationship between gene expression and other modalities with cell-type specificity. UnitedNet is a comprehensive end-to-end framework that could be broadly applicable to single-cell multi-modality biology. This framework has the potential to facilitate the discovery of cell-type-specific regulation kinetics across transcriptomics and other modalities.

     
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    Free, publicly-accessible full text available May 3, 2024
  5. In this Review, we review some recent rigorous results on large N problems in quantum field theory, stochastic quantization, and singular stochastic partial differential equations (SPDEs) and their mean field limit problems. In particular, we discuss the O( N) linear sigma model on a two- and three-dimensional torus. The stochastic quantization procedure leads to a coupled system of N interacting Φ 4 equations. In d = 2, we show uniformity in N bounds for the dynamics and convergence to a mean-field singular SPDE. For large enough mass or small enough coupling, the invariant measures [i.e., the O( N) linear sigma model] converge to the massive Gaussian free field, the unique invariant measure of the mean-field dynamics, in a Wasserstein distance. We also obtain tightness for certain O( N) invariant observables as random fields in suitable Besov spaces as N → ∞, along with exact descriptions of the limiting correlations. In d = 3, the estimates become more involved since the equation is more singular. We discuss in this case how to prove convergence to the massive Gaussian free field. The proofs of these results build on the recent progress of singular SPDE theory and combine many new techniques, such as uniformity in N estimates and dynamical mean field theory. These are based on joint papers with Scott Smith, Rongchan Zhu, and Xiangchan Zhu. 
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  6. Abstract We define a natural state space and Markov process associated to the stochastic Yang–Mills heat flow in two dimensions. To accomplish this we first introduce a space of distributional connections for which holonomies along sufficiently regular curves (Wilson loop observables) and the action of an associated group of gauge transformations are both well-defined and satisfy good continuity properties. The desired state space is obtained as the corresponding space of orbits under this group action and is shown to be a Polish space when equipped with a natural Hausdorff metric. To construct the Markov process we show that the stochastic Yang–Mills heat flow takes values in our space of connections and use the “DeTurck trick” of introducing a time dependent gauge transformation to show invariance, in law, of the solution under gauge transformations. Our main tool for solving for the Yang–Mills heat flow is the theory of regularity structures and along the way we also develop a “basis-free” framework for applying the theory of regularity structures in the context of vector-valued noise – this provides a conceptual framework for interpreting several previous constructions and we expect this framework to be of independent interest. 
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