Germinal centres (GCs) are the histological structures dedicated to the generation and the selection of B cells that produce high-affinity antibodies. However, unexpected malfunctioning in the GCs can cause the appearance of different pathologies, including the malignant transformation of B cell. Understanding the Gene Regulatory Networks (GRNs) which orchestrate that response is therefore a critical task. GRNs describe how the genomic sequence encodes the regulation of expression sets of genes that are responsible for generation of developmental patterns and execution of the multiple states of differentiation. Inferring and evaluating GRNs from gene expression data is a long-standing and challenging task in systems biology. Novel technology allows us to measure mRNA levels in individual cells, which promise significant increase of GRNs precision, but will require relevant models. Our aim was to assess the use of a new stochastic executable model for GRNs made from coupled Piecewise Deterministic Markov Process (PDMP) to fit single cell transcriptomic data from the GCs B cells differentiation sequence. We showed that our PDMP model, which was build from the coupling of three transcription factors and two cell surface receptors, can qualitatively estimate the distributions of the mRNA at different stages of GC B cell differentiation. A partial quantitative agreement was obtained through systematic parameter tuning but a full quantitative agreement proved to be highly challenging. PDMP allows to evaluate the structure of the GRN, and in the future may lead to further understanding of the different types of dysfunctions of the regulatory mechanisms.