Highlights d The Dpp morphogen gradient of the Drosophila wing disc scales with disc size d Feedback downregulation of receptors and co-receptors is required for gradient scaling d A mathematical model shows how moving boundaries, growth, and feedback work together d The secreted expander Pentagone does not spread sufficiently to explain scaling

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Accurate and reliable forecasting of emerging dominant severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants enables policymakers and vaccine makers to get prepared for future waves of infections. The last three waves of SARS-CoV-2 infections caused by dominant variants, Omicron (BA.1), BA.2, and BA.4/BA.5, were accurately foretold by our artificial intelligence (AI) models built with biophysics, genotyping of viral genomes, experimental data, algebraic topology, and deep learning. On the basis of newly available experimental data, we analyzed the impacts of all possible viral spike (S) protein receptor-binding domain (RBD) mutations on the SARS-CoV-2 infectivity. Our analysis sheds light on viral evolutionary mechanisms, i.e., natural selection through infectivity strengthening and antibody resistance. We forecast that BP.1, BL*, BA.2.75*, BQ.1*, and particularly BN.1* have a high potential to become the new dominant variants to drive the next surge. Our key projection about these variants dominance made on Oct. 18, 2022 (see arXiv:2210.09485) became reality in late November 2022.

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Following injury, skin activates a complex wound healing programme. While cellular and signalling mechanisms of wound repair have been extensively studied, the principles of epidermal‐dermal interactions and their effects on wound healing outcomes are only partially understood. To gain new insight into the effects of epidermal‐dermal interactions, we developed a multiscale, hybrid mathematical model of skin wound healing. The model takes into consideration interactions between epidermis and dermis across the basement membrane via diffusible signals, defined as activator and inhibitor. Simulations revealed that epidermal‐dermal interactions are critical for proper extracellular matrix deposition in the dermis, suggesting these signals may influence how wound scars form. Our model makes several theoretical predictions. First, basal levels of epidermal activator and inhibitor help to maintain dermis in a steady state, whereas their absence results in a raised, scar‐like dermal phenotype. Second, wound‐triggered increase in activator and inhibitor production by basal epidermal cells, coupled with fast re‐epithelialization kinetics, reduces dermal scar size. Third, high‐density fibrin clot leads to a raised, hypertrophic scar phenotype, whereas low‐density fibrin clot leads to a hypotrophic phenotype. Fourth, shallow wounds, compared to deep wounds, result in overall reduced scarring. Taken together, our model predicts the important role of signalling across dermal‐epidermal interface and the effect of fibrin clot density and wound geometry on scar formation. This hybrid modelling approach may be also applicable to other complex tissue systems, enabling the simulation of dynamic processes, otherwise computationally prohibitive with fully discrete models due to a large number of variables.

Directed evolution, a revolutionary biotechnology in protein engineering, optimizes protein fitness by searching an astronomical mutational space via expensive experiments. The cluster learning-assisted directed evolution (CLADE) efficiently explores the mutational space via a combination of unsupervised hierarchical clustering and supervised learning. However, the initial-stage sampling in CLADE treats all clusters equally despite many clusters containing a large portion of non-functional mutations. Recent statistical and deep learning tools enable evolutionary density modeling to access protein fitness in an unsupervised manner. In this work, we construct an ensemble of multiple evolutionary scores to guide the initial sampling in CLADE. The resulting evolutionary score-enhanced CLADE, called CLADE 2.0, efficiently selects a training set within a small informative space using the evolution-driven clustering sampling. CLADE 2.0 is validated by using two benchmark libraries both having 160,000 sequences from four-site mutational combinations. Extensive computational experiments and comparisons with existing cutting-edge methods indicate that CLADE 2.0 is a new state-of-art tool for machine learning-assisted directed evolution.

Due to its high transmissibility, Omicron BA.1 ousted the Delta variant to become a dominating variant in late 2021 and was replaced by more transmissible Omicron BA.2 in March 2022. An important question is which new variants will dominate in the future. Topology-based deep learning models have had tremendous success in forecasting emerging variants in the past. However, topology is insensitive to homotopic shape variations in virus-human protein-protein binding, which are crucial to viral evolution and transmission. This challenge is tackled with persistent Laplacian, which is able to capture both the topology and shape of data. Persistent Laplacian-based deep learning models are developed to systematically evaluate variant infectivity. Our comparative analysis of Alpha,