During development, a cell's fate will become increasingly restricted, facilitated by the combined activity of transcription factors and epigenetic modifiers. Single-cell RNA sequencing has greatly improved our appreciation of the transcriptional dynamics underlying lineage specification. However, we still do not fully comprehend how epigenetic modifiers guide this highly dynamic process, as methods that enable us to accurately concatenate a cell's past and present epigenetic state with its current lineage identity are missing. Here, I propose to investigate the combined dynamics and interdependencies of transcription and the polycomb-group of proteins during the differentiation of mouse embryonic stem cells into gastruloids. First, I aim to deploy a protocol that enables the simultaneous quantification of both layers in the same single cell to disentangle epigenetic from transcriptional heterogeneity. Second, I aim to develop a molecular memory system to record the past epigenetic profiles of single cells. This system will be based on the expression of proteins fused to a bacterial Dcm methylase, which will allow for the timed recording and faithful transmission of historic epigenetic profiles. Combined with quantification of transcription of the same single cell, this will enable us to directly integrate past epigenetic states with the current identity of single cells. The proposed work here will therefore allow us to directly assess the role of epigenetic modifiers on establishing cell fate choice and will have important implications on our understanding of the regulation of mammalian development.