We investigate the effect of valve dynamics, scaffold permeability, and bioreactor length on the scaffold shear stress, and fluxes in the bioreactor. The model is extremely computationally efficient, thus we can quickly simulate its operation under different valve configurations and geometric parameters, to optimise some function of shear stress and fluxes.

Developing a multiscale model that includes relevant mechanical and biological properties of endothelial and tumor cells, it is possible to simulate tumor growth and angiogenesis, in a simplified but realistic way. The present model covers multiple time and spatial scales, including extracellular, cellular and intracellular scales. At the intracellular scale, a Boolean network model is used to implement signaling transduction that determines the cell phenotype. Using an agent-based cellular Potts model, it is possible to simulate the cells' biophysical and molecular interactions. A set of PDEs describes tumor-secreted VEGF, vessel-secreted nutrients and cytotoxic drug pharmacodynamics. Results show that the tumor growth rate increases considerably as new capillaries form around the tumor cells, and the malignant tumor progression leads to a high degree of vascularization. Moreover, a systematic study of chemotherapy allows to evaluate typical clinical protocols in what concern with therapy initiation and dose comparison. Accordingly, a delay in chemotherapy initiation does not have a significant effect in the long term, as the tumor volume continues to increase throughout therapy. However, it has been observed that although the therapeutic efficacy may be not enough to prevent tumor regrowth, there is a significant decrease in the tumor size after chemotherapy.

Extremely preterm infants are at risk of developing chronic lung disease after birth due to factors such as weak intercostal muscles, surfactant deficiency, and a highly compliant (floppy) chest wall. These factors can cause asynchronous volume change between the rib cage and abdomen chest wall components, termed 'thoracoabdominal asynchrony' (TAA), which compromise breathing and could lead to lung volume loss. We constructed a respiratory model that simulates TAA under several clinical conditions by incorporating a chest wall partitioned into independent rib cage and abdominal components with respective intercostal and diaphragm muscle activation functions. Nonlinear compliance functions for the rib cage and abdomen were derived from experimental data. Simulation results indicate that TAA occurs when more than ~80% of driving pressure comes from the diaphragm and when a simulated endotracheal tube increases upper airway resistance ~5-fold. This is the first known explicit simulation of independent chest wall component volume changes with nonlinear compliances and resulting breathing asynchrony.

Ca2+ signalling plays a pivotal role in the generation of vascular tone, which in turn determines the level of blood perfusion within tissues. Despite its implication in the onset of several pathological conditions (such as hypertension, myocardial ischemia), vascular function is still poorly understood and therefore there is an urgent need to develop computer models for providing a mechanistic understanding of the underlying dynamics. Within this context, endothelial cells represent system's sensor able to monitor haemodynamic variables as well as the presence of endogenous agents. This information is then translated by endothelial cells into second messenger molecules (such as Ca2+, IP3) which ultimately may up- or down-regulate the level of contraction of the smooth muscle cells. Here we introduce a model for computing the Ca2+ dynamics in endothelial cells induced by agonist intervention. With respect to its predecessors, this model accounts for a new component describing the interaction between calcium stores and store-operated channels, which constitutes the main way for Ca2+ entry within the cell. Through numerical experiments, a link between this subcellular component and the experimentally recorded Ca2+ oscillations is established. Finally, the developed model is employed for quantifying the variability in Ca2+ response observed within the cell population.

Epithelial organoids are three-dimensional cell culture systems mimicking aspects of organ development and disease. Pancreas organoids are found to be very heterogeneous in culture and exhibit diverse, dynamic behaviour. One example is frequent size oscillations, which are hypothesised to occur in response to an interplay of the elasticity and the production of an osmotic active substance by the cell monolayer, as increasing osmotic pressure can lead to rupture of the cellular contacts, allowing the pressure to relax.Mathematical modelling allowed us to extract core principles driving these size oscillations of the organoids. By deriving a scaling law from the organoid dynamics, we can identify a dependence of the observed size oscillations and the cell proliferation dynamics. Furthermore, size oscillations also depend on the surface-to-volume ratio, hence, on the organoid size. A biomechanical 3D agent-based model confirms these mathematical considerations.The implemented model allows investigation of the interplay of the elasticity of the cells and their production rate in more detail and further observed phenomena such as organoid rotation.

Nearly immediately after birth, a complex and dynamic ecosystem forms in the human infant gut. The characteristics of this system influence the infant's health in both the short and long term. 2'-FL, the most prevalent prebiotic in most human milk, varies greatly in presence and concentration between individuals. We use a multi-scale spatiotemporal model of the infant colon from birth to three weeks of age to reproduce the effects of variations in nutritional components on the composition and metabolic activity of the microbiota. Using flux balance analysis with molecular crowding on genome-scale metabolic models from the AGORA project, we calculate bacterial fluxes for different locations and time points at a high resolution. The resulting fluxes are integrated together into a model of the ecosystem that feeds back into the flux calculations. The model can give insight and produce predictions for bacterial and metabolic composition of the infant microbiota over time and under different conditions. Our aim is to reach a deeper understanding of the influence that nutrition can have on the development of the infant microbiota. This in turn is the first step towards a comprehensive understanding of the formation of a steady state adult microbial environment.

Recent studies have shown that many functions of multicellular organisms were already present in their unicellular ancestors. For instance, many gene families involved in animal development and cell adhesion can also be found in unicellular relatives. This indicates that the evolutionary transition to multicellularity predominantly required changes in regulation and coordination, more than gene content. We use an evolutionary cell-based model to show that the emergent collective behaviour of multicellular clusters can drive the evolution of adhesion. We then extend this model to investigate how regulation of cell behaviour evolves in concert with the evolution of multicellularity. Cells have an evolvable gene regulatory network that determines when they divide and migrate. We observe that evolution of adhesion changes cell competition dynamics: cells evolve adhesion to migrate collectively and to get closer to resources. Within such cohesive clusters, competition drives cells to divide first, and then migrate to resources. When cells cannot evolve adhesion, cells instead migrate to reach resources first and then divide, blocking their competitors. Thus, the model demonstrates how the transition to multicellularity may have driven a drastic switch in cell behaviour, leading to complex coordinated dynamics compared to the unicellular cousins, without changing the genetic toolkit.

Meiosis, the special cell divisions occurring prior to sexual reproduction, is a crucial process for most organisms.Early during meiosis, the chromosomes encoding the same genes group together to form linear structures.At a small number of points along these structures the DNA strands form crossovers, splicing together chromosomes and exchanging genetic information.These crossovers tend to be much more regularly spaced than would be expected by chance, and the mechanism controlling this is a long-standing open question.We have developed a model for crossover patterning, in which a protein diffuses along the one-dimensional structure, and is able to aggregate at a number of discrete foci.Competition between the foci for the protein leads to coarsening, selecting those foci that will become crossovers.This will allow us to explain many of the elements of crossover positioning in the model plant Arabidopsis thaliana, and we will show that it agrees well with our experimental observations.

Diel vertical migration is the largest daily movement of marine species where animals remain in deep, dark water during daylight hours to avoid visual predators and migrate to upper levels at dusk to feed. The migration of each organism can be rationalized as a trade-off between growth and survival with strategies as spatial distributions of the populations. The dynamics driving vertical migration have broad implications for fluxes through the food-web predator-pray interactions; for vertical transport of carbon in ocean with implications for global climate.I will present ongoing work on a framework for expressing diel vertical migration as a game in terms of partial differential equations. In the base model setup we consider a population of animals distributed in the water column. It is assumed that each animal moves optimally, seeking regions with high growth rate and small mortality, avoiding regions with high population density. The Nash equilibrium for this mean field game is characterized by a system of partial differential equations, which governs the population distribution and migration velocities of animals. I will talk about extension of the base model with added diffusion to cover deep water case.

Population structure is an important aspect of natural populations and has a large impact on population dynamics. In theoretical models, populations are generally structured by age or size. As long as individuals follow a fixed growth curve, age- and size structured models are virtually similar, but if individual growth rates become plastic (e.g. depend on the environment), age- and size structured models start to differ. In nature, individuals of various species differ strongly in the plasticity of their somatic growth rate as well. To explore the effect of plasticity in somatic growth we formulated a physiologically structured population model in which growth plasticity can be varied from entirely plastic to entirely non-plastic. The life history rates in this model were based on a Dynamic energy budget model to ensure closed individual energy dynamics. From the analysis of our model it became clear that changes in growth plasticity provoke a complex trade-off between energy allocation to somatic growth and reproduction. This tradeoff results in two distinct parameter regions which differ in their ecological and evolutionary dynamics. These results can gain insight in the different ways a population can respond to human impact and the different ways population structure can be modelled.

Foraging is often modeled as a sequence of patch-leaving decisions. An animal enters a patch of food, harvests resources, and then decides when to leave and search for other patches. Foraging strategies shape experimental observables like patch residence time, inter-patch travel time, as well as rate of energy intake. Models of foraging as an evidence accumulation process accounts for learning processes involved in determining resource availability within and across patches by associating evidence for leaving a patch with a deterministic drift term and the stochasticity of food encounters and memory with diffusive noise (Davidson & El Hady A, 2019). My work extends these individual evidence accumulation models to consider patch foraging decisions of multi-agent systems sharing social information.

Multi-channel food webs are shaped by the ability of apex predators to link asymmetric energy flows in mesohabitats differing in productivity and community traits. While body size is a fundamental trait underlying life histories and demography, its implications for structuring multi-channel food webs are unexplored. To fill this gap, we develop a model that links population responses to predation and resource availability to community-level patterns using a tri-trophic food web model with two populations of intermediate consumers and a size-selective top predator. We show that asymmetries in mesohabitat productivities and consumer body sizes drive food web structure, merging previously separate theory on apparent competition and emergent Allee effects (i.e., abrupt collapses of top predator populations). Our results yield theoretical support for empirically observed stability of asymmetric multi-channel food webs and discover three novel types of emergent Allee effects involving intermediate consumers, multiple populations or multiple alternative stable states.

Gene drives are predicted to increase in frequency within a population even when harmful to individuals carrying them. This allows associated desirable genetic material to also increase in frequency, potentially allowing their use against globally important issues including disease vectors, crop pests and invasive species. The most high-profile - CRISPR-based gene drives - bias inheritance by “cutting” a target DNA sequence and tricking the system into using the gene drive as a repair template – converting drive heterozygotes into homozygotes. Unfortunately, alternate repair mechanisms can create cut-resistant alleles, causing drive failure. A commonly stated solution is multiplexing – targeting multiple DNA sequences – since this requires resistance at all target sites for drive failure. However, simultaneous DNA “cuts” can lead to the deletion of large DNA sequences and thus the removal of multiple (or all) target sequences within a single event. Here we consider novel approaches for overcoming these issues by multiplexing at the population rather than the individual level. Stochastic mathematical models demonstrate that significant performance improvements can be obtained from these approaches. Based on technical feasibility, we further investigate one approach – demonstrating robustness to key performance parameters and the potential for control of biologically relevant population sizes.

Dispersal is one of the fundamental life-history strategies of organisms, so understanding the selective forces shaping the dispersal traits is important. In the Wright's island model, dispersal evolves due to kin competition even when dispersal is costly, and it has traditionally been assumed that the living conditions are the same everywhere. In order to study the effect of spatial heterogeneity, we extend the model so that patches may receive different amounts of immigrants, foster different number of individuals and give different reproduction efficiency to individuals therein. We obtain an analytical expression for the fitness gradient, which shows that directional selection consists of three components: as in the homogeneous case, direct cost of dispersal selects against dispersal and kin competition promotes dispersal. The new component, spatial heterogeneity, more precisely the variance of so-called relative reproductive potential, tends to select against dispersal. We also obtain an expression for the second derivative of fitness, which can be used to determine whether there is disruptive selection: Unlike the homogeneous case, we found that divergence of traits through evolutionary branching is possible in the heterogeneous case. Existing spatial heterogeneity in the real world is a key determinant in dispersal evolution.

Intralocus sexual conflict, or sexual antagonism, occurs when alleles have opposing fitness effects in the two sexes. Previous theory suggests that sexual antagonism is a driver of genetic variation by generating balancing selection. However, most of these studies assume that populations are well-mixed, neglecting the effects of spatial subdivision. Here we use mathematical modelling to show that limited dispersal changes evolution at sexually antagonistic autosomal and X-linked loci due to inbreeding and sex-specific kin competition. We find that if the sexes disperse at different rates, kin competition within the philopatric sex biases intralocus conflict in favour of the more dispersive sex. Furthermore, kin competition diminishes the strength of balancing selection relative to genetic drift, reducing genetic variation in small subdivided populations. Meanwhile, by decreasing heterozygosity, inbreeding reduces the scope for sexually antagonistic polymorphism due to non-additive allelic effects, and this occurs to a greater extent on the X-chromosome than autosomes. Overall, our results indicate that spatial structure is a relevant factor in predicting where sexually antagonistic alleles might be observed. We suggest that sex-specific dispersal ecology and demography can contribute to interspecific and intragenomic variation in sexual antagonism.

The standard viral dynamics model explains HIV viral dynamics during acute infection reasonably well. However, the model makes simplifying assumptions, neglecting some aspects of HIV pathogenesis. For example, in the standard model, target cells are infected by a single HIV virion. Yet, cellular multiplicity of infection (MOI) may have considerable effects in pathogenesis and viral evolution. Further when using the standard model, we take constant infected cell death rates, simplifying the dynamic immune responses. Here, we use four models—1) the standard viral dynamics model, 2) an alternate model incorporating cellular MOI, 3) a model assuming density-dependent death rate of infected cells and 4) a model combining (2) and (3)—to investigate acute infection dynamics among study participants in the RV217 dataset. We find that all models explain the data, but different models describe differing features of the dynamics more accurately. For example, while the standard viral dynamics model may be the most parsimonious model, viral peaks are better explained by a model allowing for cellular MOI. These results suggest that heterogeneity in within-host viral dynamics cannot be captured by a single model but depending on the aspect of interest, a corresponding model should be employed.

A virus sample's infectivity is measured by the number of the infections it causes per unit volume, via a plaque or focus forming assay (PFU or FFU) or an endpoint dilution (ED) assay (TCID50, EID50, etc.). The plaque and focus assays have several technical and experimental limitations we will outline in this presentation, but yield a simple measure: one plaque equals one infectious dose. The ED assay does not suffer from these limitations, but as we will show, the measure it yields, the TCID50, is calculated using biased and antiquated approximations that relate poorly to the number of infectious doses in the sample. We propose taking the best of both: (1) preferring the ED assay over the more subjective plaque or focus forming assay; and (2) replacing the TCID50 with an accurate, robust and meaningful measure we call Specific INfections or SIN, corresponding to the most likely number of infections a virus sample will cause. We will demonstrate how the measure of SIN compares to current measures (FFU, TCID50) under typical experimental conditions, and how experimental protocols can be altered to yield even more accurate measures.

During inhalational anthrax infection, Bacillus anthracis spores are ingested by alveolar macrophages, and begin to germinate and then proliferate inside them, which may eventually lead to death of the host cell and the release of bacteria into the extracellular environment. Alternatively, some macrophages may be successful in eliminating the intracellular bacteria and will recover. In this talk, we consider a stochastic model of the intracellular infection dynamics of B. anthracis in macrophages. We explore the potential for heterogeneity in the spore germination rate, with the consideration of two extreme cases for the rate distribution: continuous Gaussian and discrete Bernoulli. This model has been calibrated by means of approximate Bayesian computation, using experimental measurements. We use the calibrated stochastic model to predict the probability of rupture, mean time until rupture, and rupture size distribution, of a macrophage that has been infected with one spore. We also obtain the mean spore and bacterial loads over time for a population of cells, each assumed to be initially infected with a single spore. Our results support the existence of significant heterogeneity in the germination rate across different spores, with a subset of spores expected to germinate much later than the majority.

The interaction between T-cell receptors (TCRs) and peptides is highly degenerate: a single TCR may recognize about one million different peptides in the context of a single MHCI molecule. On the other hand, TCR recognition is fundamentally peptide- and/or MHC-specific: the functional sensitivity, which can be viewed as experimental realisation of the TCR triggering rate, is large enough only for minute fraction of all possible ligands. TCR triggering rate and degeneracy are mathematical concepts that are fundamental for an approach that uses length-matched combinatorial peptide library (CPL) scan data to search protein databases and to rank peptides in order of likelihood recognition. This CPL-based database screening can, to a large extent, accurately identify self-peptides that triggered the CD8 T-cell. The computational time required for peptide searching can be significantly reduced by using graphics processing units (GPUs). Adoption of GPU-accelerated prediction of T-cell agonists has the capacity to revolutionise our understanding of cancer immunity by identifying potential targets for tumor-specific T-cells.

Protecting health professionals is crucial to maintain a functioning healthcare system. However, little is known about the risk factors affecting healthcare personnel during the COVID-19 pandemic. We implemented a weekly testing regime on the cohort to identify pre- and asymptomatic individuals at a department of Bern University Hospital among a cohort of 330 healthcare professionals. We have developed a mathematical model of SARS-CoV-2 transmission that integrates the infection dynamics among the cohort. We used our model to study how regular testing and a shift work protocol are effective in preventing transmission of COVID-19 infection at work, and compared both strategies in terms of workforce availability and cost-effectiveness. We showed that case incidence among health workers is higher than would be explained solely by community infection. Furthermore, while both strategies are effective in preventing nosocomial transmission, regular testing allows work productivity to be maintained while keeping implementation costs lower than shift work.

Early-warning signals are widely used in many fields to anticipate a critical threshold prior to reaching it. A systems undergoes the phenomenon known as critical slowing down as it crosses through a bifurcation. Theory predicts that fluctuations away from the mean will recover more slowly as the system approaches a critical transition. This is key in infectious disease modelling to assess when the basic reproduction number is reduced below the threshold of one. Theoretical advances have shown indicators of critical transitions in epidemiology, such as measuring the rising lag-1 autocorrelation in synthetic disease data. An effective early-warning signal would be able to predict an impending critical transition of this type with a suitable 'lead time' in order to act on the current path of the disease.We validate several empirical studies which offer lead time predictions for ecological and infectious diseases systems when using this theory practice. Our work highlights several challenges when applying lead time methodologies to simulated models. We find poor specificity, falsely reporting a critical transition in simulations at steady state.In this talk we present an extension to these methods and our results show promising potential for calculating early-warning signals of elimination on real-world noisy data.

In March 2020, a multidisciplinary task force (so-called Basque Modelling Task Force, BMTF) was created to assist the Basque health managers and Government during the COVID-19 responses. BMTF is a modelling team, working on different approaches, including stochastic processes, statistical methods and artificial intelligence. Here we describe the efforts and challenges to develop a flexible modeling framework able to describe the dynamics observed for the tested positive cases, including the modelling development steps. The results obtained by a new stochastic SHARUCD model framework are presented. Our models differentiate mild and asymptomatic from severe infections prone to be hospitalized and were able to predict the course of the epidemic, providing important projections on the national health system's necessities during the increased population demand on hospital admissions. Short and longer-term predictions were tested with good results adjusted to the available epidemiological data. We have shown that the partial lockdown measures were effective and enough to slow down disease transmission in the Basque Country. This framework is now being used to monitor disease transmission while the country lockdown was gradually lifted, with insights to specific programs for a general policy of “social distancing” and home quarantining.

The “pace” of host life history is an important driver of pathogen transmission dynamics in wildlife populations. Populations of species with a faster pace-of-life (generally associated with more frequent reproduction and a shorter lifespan) are often the most competent reservoirs for zoonoses and present a greater risk of spillover to human populations. However, the role of pace in systems of mosquito-borne pathogen transmission, where temperature also plays a crucial role in the population dynamics of mosquitoes, has not been previously studied. By considering a compartmental model of pathogen transmission, which incorporates important features of mosquito and vertebrate life history, we investigate how temperature and pace interact to determine zoonotic potential in these systems, measured through the basic reproduction number. We determine that the relationship between zoonotic potential, pace, and temperature as predicted by the “pace-of-life” and “warmer-means-sicker” hypotheses occurs only in some cases, depending on how host traits vary with the pace of their life history. Overall, incorporating realistic assumptions about mosquito-host contact rates and variations in host life history, pace and temperature interact in complex ways to drive transmission dynamics.

The Gillespie algorithm is commonly applied for simulating memoryless processes that follow an exponential waiting-time. However, stochastic processes governing biological interactions, such as cell apoptosis and epidemic spreading, are empirically known to exhibit properties of memory, an inherently non-Markovian feature. The presence of such non-Markovian processes can significantly influence the outcome of a simulation. While several extensions to the Gillespie algorithm have been proposed, most of them suffer from either a high computational cost, or are only applicable to a narrow selection of probability distributions that do not match the experimentally observed biological data distributions. To tackle the aforementioned issues, we developed a Rejection Gillespie for non-Markovian Reactions (REGINR) that is capable of generating simulations with non-exponential waiting-times, while remaining an order of magnitude faster than alternative approaches. REGINR uses the Weibull distribution, which interpolates between the exponential, normal, and heavy-tailed distributions. We applied our algorithm to a mouse stem cell dataset with known non-Markovian dynamics and found it to faithfully recapitulate the underlying biological processes. We conclude that our algorithm is suitable for gaining insight into the role of molecular memory in stochastic models, as well as for accurately simulating real-world biological processes.

Mathematical models are standard tools for understanding the underlying mechanisms of biological systems. Generally, the parameters of these models are unknown and they need to be inferred from experimental data using statistical methods. Most common measurement techniques only provide relative information about the absolute molecular state and often data is noise-corrupted. Therefore, introducing scaling and noise parameters in the model observables is necessary. Since frequently these parameters are also unknown, the dimensionality of the estimation problem is augmented. Sampling methods are widely used in systems biology to assess parameter and prediction uncertainties. However, the evaluation of sampling methods is usually demanding and often on the border of computational feasibility. Hence, efficient sampling algorithms are required.We propose a marginal sampling scheme for estimating the parameter uncertainties of mechanistic models with relative data. We integrate out the scaling and noise parameters from the original problem, leading to a dimension reduction of the parameter space. Herewith, only reaction rate constants have to be sampled. We find that the marginal sampling scheme retrieves the same parameter probability distributions and outperforms sampling on the full parameter space by substantially increasing the effective sample size and smoothing the transition probability between posterior modes.

A core challenge of modern mathematical biology is fitting models to the ever increasing quantities of biological data. Frequently, the data is affected by both measurement noise and stochasticity intrinsic to the underlying system in ways that are difficult to disentangle. Building on prior work addressing the two kinds of stochasticity independently, we present a method for inferring dynamics without assuming either noise-free measurements or an underlying deterministic system. Our approach is motivated by measurement techniques available in single-cell sequencing and generically applicable for learning stochastic differential equations from noisy data.

Insights in cell dynamics and tissue development are constantly changing our understanding of fundamental biological processes including embryogenesis, wound healing, and tumorigenesis. The availability of high-quality microscopy data and an increasing understanding of single-cell effects are speeding up discoveries. However, many computational models still describe either a few cells in high detail or larger cell ensembles and tissues in rather coarse detail. We combine these two scales, therefore we developed a highly parallel version of the cellular Potts model and provides an agent-based model for controlling cellular events. The model can be modularly extended to a multimodel simulation at both scales. Based on the NAStJA framework, we implemented a scalable version that runs efficiently on high-performance computing systems.Our model scales beyond 10,000 cores in an approximately linear manner, enabling the simulation of large three-dimensional tissues. The strictly modular design allows flexible configuration of arbitrary models and enables applications in a wide range of research questions. Cells in Silico can be easily adapted to different modeling assumptions and helps computational scientists to extend their simulations to a new area of tissue simulations. As an example, we show a 1000^3 voxel cancer tissue simulation with sub-cellular resolution.

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.

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.

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

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.

We develop a three-dimensional hybrid atomistic-continuum model that describes the invasive growth dynamics of individual cancer cells in tissue. The framework explicitly accounts for phenotypic variation by distinguishing between cancer cells of an epithelial-like and a mesenchymal-like phenotype. It also describes mutations between these cell phenotypes in the form of epithelial-mesenchymal transition (EMT) and its reverse process mesenchymal-epithelial transition (MET). The model consists of a hybrid system of partial and stochastic differential equations that describe the evolution of epithelial-like and mesenchymal-like cancer cells, respectively, under the consideration of matrix-degrading enzyme concentrations and the extracellular matrix density. With the help of inverse parameter estimation and a sensitivity analysis, this three-dimensional model is then calibrated to an in vitro organotypic invasion assay experiment of oral squamous cell carcinoma cells.

In heterogeneous tumors, cell types of different properties compete over the available resources, that are nutrients and space. Rapid expansion leads to solid stress in in-vivo tumors that can collapse blood vessels, which together with angiogenesis leads to fluctuations in nutrient availability. Here, we observe the influence of such fluctuations on tumor evolution.We developed a 3D computational model that simulates the evolutionary trajectories of an evolving tumor. Cell motility and cell-cell adhesion are observed as free evolving parameters in tumor cells that grow in a medium of surrounding cells. A nutrient dependent cell cycle is introduced and constant and dynamic nutrient surroundings are compared.We find an evolutionary advantage of low adhesion cells independent of the surrounding. Furthermore we find a dependency between the evolution speed and the frequency of the nutrient fluctuations, with a significant increase of evolutionary speed for a frequency domain.

In ex vivo drug-sensitivity assays, cells are treated with varying drug concentrations and viable cells are measured at one or more time points. Viability curves, and their characteristics (e.g. IC50), allow comparing drug sensitivity across multiple drugs and cell samples. However, the interpretation of those curves is confounded by the presence of cellular heterogeneity in each sample. The presence of several subclones with different drug sensitivities results in an aggregated drug-sensitivity profile that does not represent the cell population complexity, and thus hinders the design of precise treatment strategies.Here we show how to infer on the presence of cellular subclones with differential drug response, using standard cell viability data at total population level. We build cell population dynamic models of the evolution of individual subclones over time and dose. We estimate the number of subclones, their mixture frequencies and drug-response profiles. We validate our methodology on data from admixtures of synthetic and actual cancer cells at known frequencies. Finally, we explore the clinical usefulness of the method for multiple myeloma patients.This is joint work with J. Foo, K. Leder, A. Frigessi, E.M. Myklebust, J. Noory, S. Mumenthaler, D.S. Tadele, M. Giliberto, F. Schjesvold, J. Enserink and K. Tasken.

It is largely recognized that tumours consist of a diverse population of cancer cells. Treatment exerts selection on the phenotype and may shift the distribution of characteristic functional traits within the population. Taking the underlying phenotypic trait distribution into account, given for example by the growth rate of individual cells, allows to predict and compare the performance of different treatment options. Here, we investigate how treatment that is either growth rate selective or unselective affects a population of cancer cells with diverse growth rates. We find that different treatment types result in different cancer cell population dynamics and trait distributions. Further, we find that accounting for phenotypic diversity allows to select optimal treatment patterns for specific targets. To increase the likelihood of tumour eradication, the maximum mortality should be exerted on the cancer cell population. If tumour eradication is not achievable, maximizing the time until relapse may be achieved by a very different treatment strategy that aims not for maximum cancer cell mortality but rather for a specific, desirable trait distribution. It thus becomes evident that combining a trait-based approach with considering the phenotypic diversity of cancer allows for mechanistic understanding of cancer dynamics and optimization of personalized treatment.