# Research We study biological oscillations and self-organization processes in early embryo development. The local interactions in the form of mechanical and biochemical signals allow individual molecules and cells to generate collective spatio-temporal patterns. To pin down the physical mechanisms behind these processes, we make use of both the cell-free extracts system and live embryos to help us connect the understandings across the molecule, cellular, and tissue levels. **Interdisciplinary Approaches** | We integrate mathematical modeling, time-lapse fluorescence microscopy, biochemical assays, microfluidics, and systems and synthetic biology tools to study the dynamic processes in both in vitro and in vivo systems. ## Research Focus The broad focus of the Yang lab is on the quantitative understanding of early embryo development, a complex pattern formation process that involves proliferation, differentiation, and migration of individual cells, and cell-cell communications through mechanical and chemical signaling. Our strategy is to connect these multi-scale mechanisms by developing complementary in vitro and in vivo systems in the vertebrate zebrafish (Danio rerio) embryos. --- ### Computation---Topology-function mapping

Computational analysis of networks and functions. It remains elusive why networks containing the same core have substantially different abilities to sustain function. We aim to address a fundamental question in the field—what are the ‘simple rules’ that promote the robust performance of biological systems? To identify universal rules independent of any chosen systems, we generate a comprehensive mapping from the entire topology space to the function space. We further integrate the network enumeration with LASSO statistics and Latin Hypercube sampling (LHS) and develop a powerful method to search for hidden network motifs.

--- ### Artificial cells---Minimal design of time control

Bottom-up synthetic biology: build minimal cells to elucidate circuits and functions. Creating synthetic oscillators has drawn extensive interest since the first engineered oscillator, repressilator. Yet, building a non-equilibrium system with robust, tunable, self-sustained functions remains challenging and essential in the field of systems and synthetic biology. A milestone of our lab was to develop a novel synthetic-cell system by encapsulating the cell-free extracts in cell-sized water-in-oil microemulsion droplets. These artificial cells, without or with nuclei, can mimic many dynamic processes just like living cells but allow flexible manipulation of the circuit, which would be difficult in real cells. The system can also be tuned in wide ranges of cell size and oscillation frequency. It enables us to pursue many fascinating questions that would otherwise be hard to answer in living organisms.

--- ### Mitotic waves---Spatial coordination Even when individual molecular clocks are perfectly designed, how they communicate efficiently over long distances in a large embryonic cell (such as a Xenopus embryo of approximately 1.2 mm in diameter) is a question. Diffusion alone cannot achieve such long-range communication. We explore mitotic waves, integrating quantitative experiments and theoretical modeling, with a focus on two types of traveling waves: phase and trigger waves, and their time-dependent behaviors. The bottom-left movie demonstrates a spontaneous Cdk1 chemical wave developed from a homogenous Xenopus cytoplasm in a 1D Teflon tube. Initially, the cytoplasm oscillates synchronously everywhere along the tube, eventually transiting from ultrafast sweep or phase waves into slower trigger waves. Notably, we found that heterogeneous activation, by adding nuclei pacemakers, speeds up this transition. Also, we introduce a novel experimental development of driven waves by dipping a cycling or interphase extract into a metaphase-arrested CSF extract. This setup demonstrates immediate entrainment of the system when metaphase-arrested extracts initiate the waves from the boundary. Our work argues that the transition from fast phase waves to slower trigger waves occurs as a transient effect due to the time required for trigger waves to entrain the system. Both phase and trigger waves are a manifestation of a common biological process undergoing these transient dynamics.
--- ### Growth and patterning---Mechanobiology and synthetic somitogenesis We use zebrafish live embryos, as a system complementary to cell-free extracts, to allow for real-time, multi-scale investigation of developmental processes. We apply in-toto imaging of live embryos as well as presomitic mesoderm (PSM) cells isolated from zebrafish tailbuds and pluripotent stem cells, growing in microfluidics-controlled environments, to track each single cell's 'fate' as the cells divide, differentiate, move, and interact. With mathematical modeling, we explore how these cellular behaviors give rise to tissue-level patterns and eventually develop into the organism. Currently, we focus on the interplay of several biological clocks, namely mitotic oscillators and segmentation clocks, that play essential roles in the somite pattern formation of early vertebrate embryos, and how mechanical signals shape the process.
--- ## Our Funding Resources
These funding resources have supported the past and current research in the Yang Lab. We are grateful to all the funding agencies for their support!