[Mathematical modelling for cellular processes].

Biomanufacturing harnesses engineered cells for the large-scale production of biochemicals, biopharmaceuticals, biofuels, and biomaterials, playing a vital role in mitigating global environmental crises, achieving carbon peaking and neutrality, and driving the green transformation of the economy and society. The effective design and construction of these engineered cells require precise and comprehensive computational models. Recent technological breakthroughs including high-throughput sequencing, mass spectrometry, spectroscopy, and microfluidic devices, coupled with advances in data science, artificial intelligence, and automation, have enabled the rapid acquisition of large-scale biological datasets, thereby facilitating a deeper understanding of cellular dynamics and the construction of mechanism-based models with enhanced accuracy. This review systematically summarises the mathematical frameworks employed in cellular modelling. It begins by evaluating prevalent mathematical paradigms, such as network topology analyses, stochastic processes, and kinetic equations, critically assessing their applicability across various contexts. The discussion then categorises modelling strategies for specific cellular processes, including cellular growth and division, morphogenesis, DNA replication, transcriptional regulation, metabolism, signal transduction, and quorum sensing. We also examine the recent progress in developing whole-cell models through the integration of diverse cellular processes. The review concludes by addressing key challenges such as data scarcity, unknown mechanisms, multi-dimensional data integration, and exponentially escalating computational complexity. Overall, this work consolidates the mathematical models for the precise simulation of cellular processes, thereby enhancing our understanding of the molecular mechanisms governing cellular functions and contributing to the future design and optimisation of engineered organisms.