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Abstract Protein engineering is an emerging field in biotechnology that has the potential to revolutionize various areas, such as antibody design, drug discovery, food security, ecology, and more. However, the mutational space involved is too vast to be handled through experimental means alone. Leveraging accumulative protein databases, machine learning (ML) models, particularly those based on natural language processing (NLP), have considerably expedited protein engineering. Moreover, advances in topological data analysis (TDA) and artificial intelligence-based protein structure prediction, such as AlphaFold2, have made more powerful structure-based ML-assisted protein engineering strategies possible. This review aims to offer a comprehensive, systematic, and indispensable set of methodological components, including TDA and NLP, for protein engineering and to facilitate their future development. 

Abstract Time-series single-cell RNA sequencing (scRNA-seq) datasets provide unprecedented opportunities to learn dynamic processes of cellular systems. Due to the destructive nature of sequencing, it remains challenging to link the scRNA-seq snapshots sampled at different time points. Here we present TIGON, a dynamic, unbalanced optimal transport algorithm that reconstructs dynamic trajectories and population growth simultaneously as well as the underlying gene regulatory network from multiple snapshots. To tackle the high-dimensional optimal transport problem, we introduce a deep learning method using a dimensionless formulation based on the Wasserstein–Fisher–Rao (WFR) distance. TIGON is evaluated on simulated data and compared with existing methods for its robustness and accuracy in predicting cell state transition and cell population growth. Using three scRNA-seq datasets, we show the importance of growth in the temporal inference, TIGON’s capability in reconstructing gene expression at unmeasured time points and its applications to temporal gene regulatory networks and cell–cell communication inference. 

In biology, cell-fate decisions are controlled by complex gene regulation. Although gene expression data may be collected at multiple time points, it remains difficult to construct the continuous dynamics from the data. In this work, we developed a data-driven approach, NeuralGene, a model based on neural ordinary differential equations (ODEs), to reconstruct continuous dynamical systemsgoverning gene regulation from temporal gene expression data. In addition, NeuralGene has the flexibility of incorporating partial prior biological information in the model to further improve its accuracy. For a given cell at a static time point, the NeuralGene model can impute its continuous gene expression dynamics and predict its cell fate. We applied NeuralGene to a simulation toggle-switch model to verify its utility in modeling and reconstructing temporal dynamics. In addition, NeuralGene was applied to experimental single-cell qPCR data to show its ability for gene expression imputation and cell-fate prediction. 

The vertebrate hindbrain is segmented into rhombomeres (r) initially defined by distinct domains of gene expression. Previous studies have shown that noise-induced gene regulation and cell sorting are critical for the sharpening of rhombomere boundaries, which start out rough in the forming neural plate (NP) and sharpen over time. However, the mechanisms controlling simultaneous formation of multiple rhombomeres and accuracy in their sizes are unclear. We have developed a stochastic multiscale cell-based model that explicitly incorporates dynamic morphogenetic changes (i.e. convergent-extension of the NP), multiple morphogens, and gene regulatory networks to investigate the formation of rhombomeres and their corresponding boundaries in the zebrafish hindbrain. During pattern initiation, the short-range signal, fibroblast growth factor (FGF), works together with the longer-range morphogen, retinoic acid (RA), to specify all of these boundaries and maintain accurately sized segments with sharp boundaries. At later stages of patterning, we show a nonlinear change in the shape of rhombomeres with rapid left-right narrowing of the NP followed by slower dynamics. Rapid initial convergence improves boundary sharpness and segment size by regulating cell sorting and cell fate both independently and coordinately. Overall, multiple morphogens and tissue dynamics synergize to regulate the sizes and boundaries of multiple segments during development. 

Abstract 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.