Zhenyi Zhang

Reconstructing dynamics using samples from sparsely time-resolved snapshots is an important problem in both natural sciences and machine learning. Here, we introduce a new deep learning approach for solving regularized unbalanced optimal transport (RUOT) and inferring continuous unbalanced stochastic dynamics from observed snapshots. Based on the RUOT form, our method models these dynamics without requiring prior knowledge of growth and death processes or additional information, allowing them to be learnt directly from data. Theoretically, we explore the connections between the RUOT and Schrödinger bridge problem and discuss the key challenges and potential solutions. The effectiveness of our method is demonstrated with a synthetic gene regulatory network. Compared with other methods, our approach accurately identifies growth and transition patterns, eliminates false transitions, and constructs the Waddington developmental landscape.

Noninvasive preimplantation genetic testing for aneuploidy based on embryonic cell-free DNA (cfDNA) released in spent embryo culture media (SECM) has brought hope in selecting embryos that are most likely to implant and grow into healthy babies during assisted reproduction. However, maternal DNA contamination in SECM significantly hampers the reliability of embryonic chromosome ploidy profiles, leading to false negative results, particularly at high contamination levels. Here, we present DECENT (deep copy number variation (CNV) reconstruction), a deep learning method to reconstruct embryonic CNVs and mitigate maternal contamination in SECM from single-cell methylation sequencing of cfDNA. DECENT integrates sequence features and methylation patterns by combining convolution modules, long-short memory, and attention mechanisms to infer the origin of cfDNA reads. The benchmarking study demonstrated DECENT’s ability to estimate contamination proportions and restore embryonic chromosome aneuploidies in samples with varying contamination levels. In contaminated SECM clinical samples, including one with more than 80% maternal reads, DECENT achieved consistent CNV recovery with invasive tests. Overall, DECENT contributes to enhancing the diagnostic accuracy and effectiveness of cfDNA-based noninvasive preimplantation genetic testing, establishing a robust groundwork for its extensive clinical utilization in the field of reproductive medicine.

Understanding the dynamic nature of biological systems is fundamental to deciphering cellular behavior, developmental processes, and disease progression. Single-cell RNA sequencing (scRNA-seq) has provided static snapshots of gene expression, offering valuable insights into cellular states at a single time point. Recent advancements in temporally resolved scRNA-seq, spatial transcriptomics (ST), and time-series spatial transcriptomics (temporal-ST) have further revolutionized our ability to study the spatiotemporal dynamics of individual cells. These technologies, when combined with computational frameworks such as Markov chains, stochastic differential equations (SDEs), and generative models like optimal transport and Schrödinger bridges, enable the reconstruction of dynamic cellular trajectories and cell fate decisions. This review discusses how these dynamical system approaches offer new opportunities to model and infer cellular dynamics from a systematic perspective.

Modeling the dynamics from sparsely time-resolved snapshot data is crucial for understanding complex cellular processes and behavior. Existing methods leverage optimal transport, Schrödinger bridge theory, or their variants to simultaneously infer stochastic, unbalanced dynamics from snapshot data. However, these approaches remain limited in their ability to account for cell-cell interactions. This integration is essential in real-world scenarios since intercellular communications are fundamental life processes and can influence cell state-transition dynamics. To address this challenge, we formulate the Unbalanced Mean-Field Schrödinger Bridge (UMFSB) framework to model unbalanced stochastic interaction dynamics from snapshot data. Inspired by this framework, we further propose CytoBridge, a deep learning algorithm designed to approximate the UMFSB problem. By explicitly modeling cellular transitions, proliferation, and interactions through neural networks, CytoBridge offers the flexibility to learn these processes directly from data. The effectiveness of our method has been extensively validated using both synthetic gene regulatory data and real scRNA-seq datasets. Compared to existing methods, CytoBridge identifies growth, transition, and interaction patterns, eliminates false transitions, and reconstructs the developmental landscape with greater accuracy.