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The cell cycle is a highly regulated process that ensures the accurate replication and transmission of genetic information from one generation of cells to the next. It is a fundamental biological process and plays a crucial role in development, growth, and maintenance of all living organisms, and its dysregulation can lead to a number of pathologies such as autoimmune diseases, neurodegenerative diseases, and cancer. In this work we present a novel approach to study the gene expression and chromatin accessibility dynamics during the cell cycle in mouse embryonic stem cells. To achieve this, we combined high-depth single-cell multiome sequencing, biophysical modeling, and deep learning techniques. First, we used DeepCycle, a deep learning tool that assigns a cell cycle phase to every cell based on its spliced and unspliced mRNA levels. We then developed a biophysical model that describes the dynamics of gene-specific mRNA transcription, nuclear export, and degradation rates during the cell cycle. Our model obtains genome-wide estimates of mRNA transcription, nuclear retention, and degradation half-lives of genes exhibiting oscillatory dynamics in mESCs. The key feature of single-cell multiome sequencing is that it simultaneously provides readouts for gene expression as well as chromatin accessibility in the same cells. By applying our approach to these data we showcase first-of-its-kind exploration of chromatin accessibility during the cell cycle at high temporal resolution. We believe that our work will be pivotal in formulating a coherent quantitative description of mRNA metabolism.