MMPB Subgroup Contributed Talks

Gabriella Bretti

IAC-CNR

"A mathematical simulation algorithm for the dynamics on cells on microfluidic chips"

The present work was inspired by the recent developments in laboratory experiments made on microfluidic chip, where culturing of multiple human cell species was possible. The model is based on coupled reaction-diffusion-transport equations with chemotaxis, and takes into account the interactions among cell populations and the possibility of drug administration.A simulation tool that is able to reproduce the chemotactic movement was developed and the interactions between different cell species (immune and cancer cells) living in microfluidic chip environment was simulated. The main issues faced in this work are the introduction of mass-preserving and positivity-preserving condition involving the balancing of incoming and outgoing fluxes passing through interfaces between 2D and 1D domains of the chip and the development of mass-preserving and positivity preserving numerical conditions at the external boundaries and at the interfaces between 2D and 1D domains. We finally find that the qualitative behavior of the solutions obtained by our simulation algorithm is comparable with the experimental observations.

Andrew Mair

Heriot-Watt University

"Modelling the influence of plant root systems on soil moisture transport"

Understanding the effect of vegetation on the hydraulic properties of soil is an important aspect of land management. Plants grow complex root systems to acquire water and nutrients. There is strong evidence that the presence of these root systems increases the hydraulic conductivity of soil. The famous Richards' equation is the standard model for moisture transport through soil. In this work we modify Richards' equation to propose a model which incorporates preferential flow along the axes of the roots which occupy the soil. This accounts for the influence of the explicit structure of a root system on soil moisture transport. We calibrate our model with respect to experimental data on the saturated hydraulic conductivity of vegetated soils and use Bayesian optimisation to do this. Our calibration results suggest that preferential moisture flow does occur along root axes. They also support the hypothesis that this preferential flow plays a key role in the observed differences between the hydraulic properties of vegetated and bare soil.

Mohit Dalwadi

University of Oxford

"Emergent robustness of bacterial quorum sensing in fluid flow"

Bacteria use intercellular signalling, or quorum sensing (QS), to share information and respond collectively to aspects of their surroundings. The autoinducers that carry this information are exposed to the external environment. Consequently, they are susceptible to removal through fluid flow, a ubiquitous feature of bacterial habitats ranging from the gut and lungs to lakes and oceans.We develop and apply a general theory that identifies and quantifies the conditions required for QS activation in fluid flow by systematically linking cell- and population-level genetic and physical processes. By exploring the dynamics across an imperfect transcritical bifurcation in the system, we predict that cell-level positive feedback promotes a robust collective response, and can act as a low-pass filter at the population level in oscillatory flow, responding only to changes over slow enough timescales. Moreover, we use our model to predict how bacterial populations can discern between increases in cell density and decreases in flow rate.[1] Emergent robustness of bacterial quorum sensing in fluid flow, MP Dalwadi and P Pearce, PNAS, 118, e2022312118; DOI: 10.1073/pnas.2022312118

Bente Hilde Bakker

Universiteit Leiden

"Cellular Potts model with discrete fibrous extracellular matrix replicates strain-stiffening"

The extracellular matrix is the biological mortar that holds cells together. A major class of matrix proteins form molecularly crosslinked fibres. The fibre network has non-trivial topology and displays strain-stiffening, which affects cell migration. Cell-based models such as cellular Potts generally treat mechanical interactions between cells and the extracellular matrix with mean-field approaches, e.g. finite element models, but these have the downside that they average fibre network topology.To address this gap, we developed a cellular Potts model with discrete extracellular matrix fibres. The model was implemented by interfacing the cellular Potts software library Tissue Simulation Toolkit with the molecular mechanics framework HOOMD-blue via a Python bridge. Fibres are modelled using a bead-spring chain with linear elastic potentials between consecutive beads and linear bending potentials between consecutive bead triplets. Fibres can be mechanically coupled via crosslinkers, and cellular Potts cells link to fibres via discrete focal adhesion-like sites.We simulate how a single contractile cellular Potts cell strains a pre-defined fibre network. We compare how parameters including fibre number, fibre crosslinks, and number of adhesion sites affect network strain and local fibre density. Using in silico atomic force microscopy, we measure spatial variation in network stiffness and detect strain-stiffening.','In this contribution, we present the mathematical modelling tools needed to address an open question in biology: How do interactions between cells and the extracellular matrix affect cell behaviour?Our chosen modelling formalism is a hybrid combination of discrete-space cellular Potts and continuous-space molecular dynamics. These two types of models have been used to great success in isolation to address various biological questions.Combining these techniques is crucial for understanding cell migration during angiogenesis and metastasis.