The Gillespie algorithm is commonly used to simulate and analyze complex chemical reaction networks. Here, we leverage recent breakthroughs in deep learning to develop a fully differentiable variant of the Gillespie algorithm. The differentiable Gillespie algorithm (DGA) approximates discontinuous operations in the exact Gillespie algorithm using smooth functions, allowing for the calculation of gradients using backpropagation. The DGA can be used to quickly and accurately learn kinetic parameters using gradient descent and design biochemical networks with desired properties. As an illustration, we apply the DGA to study stochastic models of gene promoters. We show that the DGA can be used to: (1) successfully learn kinetic parameters from experimental measurements of mRNA expression levels from two distinct Escherichia coli promoters and (2) design nonequilibrium promoter architectures with desired input–output relationships. These examples illustrate the utility of the DGA for analyzing stochastic chemical kinetics, including a wide variety of problems of interest to synthetic and systems biology.

Mouse oocytes undergo drastic changes in organellar composition and their activities during maturation from the germinal vesicle (GV) to metaphase II (MII) stage. After fertilization, the embryo degrades parts of the maternal components via lysosomal degradation systems, including autophagy and endocytosis, as zygotic gene expression begins during embryogenesis. Here, we demonstrate that endosomal-lysosomal organelles form large spherical assembly structures, termed endosomal-lysosomal organellar assemblies (ELYSAs), in mouse oocytes. ELYSAs are observed in GV oocytes, attaining sizes up to 7–8 μm in diameter in MII oocytes. ELYSAs comprise tubular-vesicular structures containing endosomes and lysosomes along with cytosolic components. Most ELYSAs are also positive for an autophagy regulator, LC3. These characteristics of ELYSA resemble those of ELVA (endolysosomal vesicular assemblies) identified independently. The signals of V1-subunit of vacuolar ATPase tends to be detected on the periphery of ELYSAs in MII oocytes. After fertilization, the localization of the V1-subunit on endosomes and lysosomes increase as ELYSAs gradually disassemble at the 2-cell stage, leading to further acidification of endosomal-lysosomal organelles. These findings suggest that the ELYSA/ELVA maintain endosomal-lysosomal activity in a static state in oocytes for timely activation during early development.