Leah Band

I am currently a Leverhulme Early Career Fellow based at the Centre for Plant Integrative Biology at the University of Nottingham, with joint affiliation to the School of Biosciences and the School of Mathematical Sciences. My research focusses on creating and using multiscale mathematical models to investigate aspects of hormone-regulated plant growth and development.

One aspect of my work investigates the transport of the hormone auxin, which moves within the root tissue in a polar manner due to spatially distributed membrane proteins. I am using multiscale asymptotic techniques to determine how the membrane-protein distribution determines the effective tissue-scale transport. I am also interested in how the auxin-transport dynamics affect downstream processes at the subcellular scale, such as signal transduction and gene regulation. As well as using analytical techniques, I am adapting the transport and gene-network models to produce vertex-based simulations using the OpenAlea software, which enable us to investigate the dynamics using realistic tissue geometries.

Another focus of my work is the hormone GA’s regulation of cell growth. We have constructed a multiscale model to investigate the interplay between growth regulatory processes on multiple scales, including hormone transport, gene regulation, cell-wall remodelling and cell growth. Considering wild type, treated and mutant roots, the model provides an explanation for why the particular phenotype is observed, and we have validated the model results experimentally by performing detailed morphological analysis.

Prior to CPIB, my research was in the fields of mathematical medicine and biomechanics. In my previous postdoctoral position, I modelled the encrustation of urethral catheters to understand the dynamics of the crystal clusters that aggregate and deposit on the catheter surface, reducing the catheter’s lumen and inhibiting the urine flow. By incorporating Smoluchowski coagulation theory into a fluid-mechanical model, we obtained a system of reaction–advection–diffusion equations that describe the spatially inhomogeneous concentrations of crystal clusters. We used the model to predict the crystal dynamics, and suggest methods to reduce catheter encrustation.

I completed my PhD at the University of Nottingham, under the supervision of Dr Sarah Waters and Prof. David Riley. In my thesis, I developed models of arterial plaques, modelling the cholesterol region of a plaque as a thin film of viscous fluid lining a cylindrical tube and capturing the variations in the properties of the plaque by prescribing an azimuthally varying interfacial tension. Exploiting the symmetries of the evolution equation, we identified a number of unstable steady solutions using asymptotic methods, whereas numerical investigations of the large-time film dynamics revealed steady solutions featuring a drained region. Such drained-region steady states are reminiscent of the arc-shaped cholesterol regions that are commonly seen within arterial plaques, and therefore the model provides a possible explanation for the prevalence of this plaque configuration.

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