CDEV-06 Contributed Talks

Molly Brennan

University College London

"An asymptotic upscaling of transport across bacterial membranes"

Multiscale problems are prevalent in many real world scenarios, especially in biology, where the behaviour of a single microorganism can have considerable impact over lengthscales much larger than its own. In this work we consider the effect of the membrane microstructure of a bacterial cell on the behaviour of concentration profiles of relevant molecules on bacterial and bacterial colony lengthscales. Transport through the outer membrane of gram-negative bacteria is restricted to specific channels and non-specific porins. These provide a size-restricted passageway for small molecules through an otherwise impermeable membrane. The effects of these channels are important, for example, antibiotics must cross the outer membrane in order to effectively target gram-negative bacteria, and quorum sensing molecules must cross the membrane to allow bacterial colonies to coordinate mass phenotypic changes such as the production of virulence factors. In mathematical models this limiting transport mechanism across the membrane is often represented via phenomenological constitutive boundary conditions. In this work, we systematically derive the correct effective boundary conditions to impose across a bacterial membrane in terms of physical channel and porin properties. We use a hybrid mathematical approach, combining multiscale methodology such as asymptotic homogenisation and boundary layer theory with numerical simulations. More broadly, because we consider a generic membrane geometry and do not impose a specific outer problem, the results that we derive have a wide scope of potential applications beyond bacterial membranes, for example, to model water vapour or heat loss through fabrics, or mass transfer through surface coatings in chemical engineering.

---

Augustinas Sukys

The University of Melbourne

"Cell-cycle dependence of bursty gene expression: insights from fitting mechanistic models to single-cell RNA-seq data"

Many genes are expressed in bursts of transcription, associated with alternating active and inactive promoter states. Such transcriptional bursting is characterised by the burst frequency and burst size, which describe how often a burst occurs and how many transcripts are produced per burst. These two burst parameters offer a simple, intuitive and practical quantitative description of bursty gene expression dynamics. However, a transcriptome-wide picture of how the burst frequency and size are modulated due to gene replication and other cell-cycle dependent factors remains missing. To address this, we fit mechanistic models of gene expression to mRNA count data for thousands of mouse genes, obtained by sequencing of single cells whose cell-cycle position has been inferred previously. Although we observe substantial heterogeneity in transcriptional regulation, we find that upon DNA replication, the genome-wide median burst frequency approximately halves, while the median burst size remains mostly unchanged, thus shedding light on the effect of gene dosage compensation. We show that to accurately estimate the bursting kinetics from sequencing data, mechanistic models must explicitly account for gene copy number variation and extrinsic noise due to factors varying across the cell cycle, whereas correcting for technical noise due to imperfect mRNA capture is less critical.

---

Lucy Ham

The University of Melbourne

"Cell fate control in space and time"

Genetically identical cells can adopt distinct, stable states, playing a crucial role in development and tissue organisation. This talk explores the mechanisms driving cell fate decisions, focusing on the interplay between gene regulatory networks and cell-to-cell communication. Using spatial stochastic models that capture fine-scale regulatory dynamics, we demonstrate how feedback loops and paracrine signalling function as switch-like controllers of cell fate, enabling transitions from transient to stable states. We derive mathematical expressions predicting the threshold signalling strength required to trigger phase transitions and establish a fundamental limit on the spatial spread of phenotypic regions. Specifically, we show that the mean region size scales proportionally to the cubic root of the signalling strength, implying that large, stable domains are prohibitively costly to maintain. This trade-off between robustness and signalling precision highlights the constraints organisms must navigate during development to maintain spatial organisation. Our findings provide key insights into the principles governing multicellular patterning and the regulation of tissue structure.

---