Cell-fate determination is a complex process involving intricate regulation of gene expression at multiple levels, including chromatin accessibility, transcription, and alternative splicing (AS). Despite significant progress in understanding these processes, current modelling studies often focus on transcription or AS in isolation, overlooking their interplay and the influence of spatial dynamics within the cell nucleus.

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This project aims to develop a comprehensive multilevel modelling framework that integrates molecular kinetics, spatial dynamics, and boundary conditions to elucidate the impact of transcriptomic complexity on cell-fate determination. Our approach encompasses three key aspects:

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1. Chromatin Accessibility and Transcription Dynamics: We will develop a non-Markov-based framework to describe DNA transcriptions, incorporating the transitions between closed and open chromatin states, and the influence of chromatin modifiers on RNA-Pol II elongation rates.
    

2. Co-transcriptional Splicing and Isoform Expression: We will develop a Markov-based representation of co-transcriptional splicing, considering the strength of splicing factor binding to donor, acceptor, and branchpoint sites, along with transition probabilities based on binding strength. We will also investigate the impact of various factors, such as pre-mRNA length, exon and intron numbers/lengths, GC content, and the distance between splicing sites, on alternative splicing outcomes and isoform expression. Subsequently, by integrating transcription, AS, and mRNA degradation, we will comprehensively describe the process of isoform expression.
    

3. Spatial Dynamics and Constraints in the Cell Nucleus: We will develop a Partial Differential Equation (PDE) model to account for the impact of molecular movement and spatial constraints in the cell nucleus on transcription and AS. The model will represent the nucleus as a bounded spatial domain, incorporating its shape and volume, and include both absorbing and reflective boundary conditions.
    

Our multilevel modelling framework will provide novel insights into the complex interplay of these processes in shaping the transcriptomic complexity and determining cell fate. The outcomes of this project are expected to advance our understanding of the regulatory mechanisms of transcription and AS processes underlying cell-fate determination and contribute to the development of new mathematical modelling frameworks for studying gene expression mechanisms.