The selection of a single molecular handedness among the two possible configurations of a given molecule, or homochirality, is observed across all living matter and is a mystery in the origin of life. Here, we show that large chemical systems, are likely to undergo a spontaneous symmetry breaking toward a homochiral state as the number of chiral species increases [1]. Through an analysis of a large chemical database, we find that there is no need of very large molecules for chiral species to dominate over achiral ones; it already happens when molecules contain about 10 heavy atoms.Refs: G. Laurent, D. Lacoste, and P. Gaspard, PNAS (2021) 118 (3) e2012741118; https://doi.org/10.1073/pnas.2012741118

Gastrulation is a crucial process during embryonic development. During this process, the embryo elongates and cells start rapidly differentiating. We have studied an in vitro model of this process and noticed that the shapes of the resulting tissues had a wide variation. Here we show that a Cellular Potts Model (CPM), based on modified filopodial-tension of convergent extension after Belmonte et al. (P Comput Biol 2016) mimics the variability of the shapes closely. The model periodically places hookian springs between cells, which model filopdia pulling cells close to each other. If cells extend filopida in random polarization directions and align polarizations to their neighbors, the resulting tissues form two or multiple lobes, closely resembling the shapes formed by gastruloids. We analyzed the shapes using lobe contribution elliptic Fourier analysis (LOCO-EFA), which supports the observed qualitative similarities between simulations and gastruloids.

Single celled organisms such as bacteria and yeasts are able to tune enzyme levels that catalyze the reaction pathways by which they eventually make new copies of themselves. Depending on nutrient conditions, more or less enzyme is invested in different parts of their reaction network, so that reaction rates are constantly high, and cellular growth rate is maximised. In this talk I will present an analysis of a reaction network coupled to a set of equations for synthesis and degradation of enzymes involved in this network. These enzyme equations are designed such that the steady state flux through the network is optimal when it is in steady state. The resulting dynamical system is an ODE system with two sets of algebraic equations attached. I will discuss the challenges to analyse this system, including quasi-steady state analysis, local stability, and if we have succeeded by the time of this conference, also global stability.

A deterministic nonlinear ordinary differential equation model for the dynamics of terrestrial forms of the Anopheles sp mosquito population is derived and studied. The model is designed to capture and assess the impact of multiple probing attempts by mosquitoes that quest for blood meals in human populations. There exists a threshold parameter, whose nature is affected by the manner in which we interpret the transitions involving the different classes on the gonotrophic cycle path. The trivial steady state of the system, which always exists, can be globally asymptomatically stable for positive values of the threshold parameter that are less than unity. The non-trivial steady state, when it exist, is stable for a range of values of the threshold parameter but can also be driven to instability via a Hopf bifurcation. Our analysis reveals that waiting class mosquitoes contribute positively in sustaining mosquito populations. A nonlinear analysis, based on the center manifold theorem, is used to derive expressions for the amplitude and phase of the oscillating solutions that arise through Hopf bifurcations. We conclude that to understand the human-mosquito interactions, it is informative to consider multiple feeding attempts that are known to occur when mosquitoes quest for blood meals within humans.

How do cells make efficient collective decisions during tissue morphogenesis? Humans and other organisms use feedback between movement and sensing known as 'sensorimotor coordination' or 'active perception' to inform behaviour. Here we provide the first proof of concept in silico/in vivo study demonstrating that filopodia (actin-rich, dynamic, finger-like cell membrane protrusions) play an unexpected role in speeding up collective endothelial decisions during the time-constrained process of 'tip cell' selection during blood vessel formation (angiogenesis). We first validate simulation predictions in vivo with live imaging of zebrafish intersegmental vessel growth. Further simulation studies then indicate the effect is due to the feedback between movement and sensing on filopodia conferring a bistable switch-like property to Notch lateral inhibition, ensuring tip selection is a rapid and robust process. We then employ measures from computational neuroscience to assess whether filopodia function as a primitive (basal) form of active perception and find evidence in support. By viewing cell behaviour through the 'basal cognitive lens' we acquire a fresh perspective on the tip cell selection process, revealing a hidden, yet vital time-keeping role for filopodia. Finally, we discuss a myriad of new and exciting research directions stemming from our conceptual approach to interpreting cell behaviour.

The plant cell wall is a versatile material that can meet a wide range of mechanical requirements. The banded patterns in protoxylem form a striking example, enabling these vessels withstand substantial negative pressure and allow for extension at the same time. The required anisotropic material properties largely derive from the location and orientation of the constituting cellulose microfibrils. These, in turn are deposited along the cortical microtubule cytoskeleton. So, using the case of protoxylem as a model system for complex cell wall patterns, the question becomes how cortical microtubules can self-organize into banded patterns. This happens in interaction with another well-known patterning system, the ROP proteins. Studying their interaction provides interesting methodological challenges, as cortical microtubules are most often studied in ``particle based'' stochastic simulations, whereas ROPs, or their animal/yeast counterparts, are typically described in terms of partial differential equations. We, therefore, started by addressing both parts of the interaction in isolation: how can dynamic microtubules collectively adjust to a predefined ROP pattern and how can an –implicitly microtubule derived– field of diffusion anisotropy orient and change ROP patterns? Despite the very different modelling frameworks, our ROP work provided critical insights into a problem in the stochastic microtubule simulations.

Efficient energy use and storage is crucial in living organisms. In the context of evolution, energy management is continuously optimized to ensure an individual's ability to successfully compete. This is especially true for oviparous species, as all required energy has to be provided at the moment of oviposition in order to give rise to a fully functional organism. Based on our preliminary imaging data in the emerging insect model Tribolium castaneum, we formulate the hypothesis that extra-embryonic serosa cells utilize shape change during gastrulation to allocate and store energy that is later on required for their extensive movement during dorsal closure. To investigate this possible functional connection, we want to gain further insights into the multi- scale effects of force propagation from cellular to tissue level. Spatial and temporal dynamics of forces are calculated using non-invasive Force Inference (FI). FI utilizes a biomechanical model, a mathematical inverse method and a Bayesian framework to estimate cell and tissue stress from segmented image data and for the whole system simultaneously. Here we highlight our workflow from obtaining 3D time-lapse light sheet-based fluorescent microscopy images of live Tribolium embryos to multi-scale estimation of tensions and pressures acting in the serosa membrane.

Efficient energy use and storage is crucial in living organisms. In the context of evolution, energy management is continuously optimized to ensure an individual's ability to successfully compete. This is especially true for oviparous species, as all required energy has to be provided at the moment of oviposition in order to give rise to a fully functional organism. Based on our preliminary imaging data in the emerging insect model Tribolium castaneum, we formulate the hypothesis that extra-embryonic serosa cells utilize shape change during gastrulation to allocate and store energy that is later on required for their extensive movement during dorsal closure. To investigate this possible functional connection, we want to gain further insights into the multi- scale effects of force propagation from cellular to tissue level. Spatial and temporal dynamics of forces are calculated using non-invasive Force Inference (FI). FI utilizes a biomechanical model, a mathematical inverse method and a Bayesian framework to estimate cell and tissue stress from segmented image data and for the whole system simultaneously. Here we highlight our workflow from obtaining 3D time-lapse light sheet-based fluorescent microscopy images of live Tribolium embryos to multi-scale estimation of tensions and pressures acting in the serosa membrane.

This contribution analyzes the existence and minimal complexity of positive subharmonics of arbitrary order in the planar periodic Volterra predator-prey model. If the support of the birth rate of the prey intersects the support of the death rate of the predator, then the existence of positive subharmonics can be derived with a refinement of the Poincaré-Birkhoff theorem. However, in the “degenerate” case when these supports do not intersect, then, the last Poincaré theorem can fails. Still in these degenerate situations, some local and global bifurcations techniques combined with a refinement of the Poincaré-Birkhoff theorem provide us with the existence of positive subharmonics of arbitrary order.

Bats play an important role in the UK ecosystem, but their populations are declining due to many reasons, including loss of habitat from human activity. As a result, ecological surveys are legally required when undertaking large-scale building work to locate breeding, or resting places (roosts). However, locating roosts is generally a difficult task, requiring many hours of manual searching. In collaboration with ecological experts we propose a novel approach for modelling bat motion dynamics and use it to predict roost locations using data from static acoustic detectors. Specifically, radio tracking studies of Greater Horseshoe bats demonstrate that bat movement can be split into two phases: dispersion and return. Dispersion is easily understood and can be modelled as simple random motion. The return phase is much more complex, as it requires intelligent directed motion and results in all agents returning home in a stereotypical manner. Critically, combining reaction-diffusion theory and domain shrinking we deterministically and stochastically model a ``leap-frogging'' motion, which fits favourably with the observed tracking data.

Different species of scavengers may compete for the same food in an ecosystem. This case study considers the competition between jackals, vultures and anthrax outbreaks in Etosha National Park in Namibia. While jackals are facultative scavengers, able to hunt for food if necessary, vultures are obligate scavengers wholly dependent on carcasses of animals like zebras for persistence. This competition is further affected by outbreaks of infections such as anthrax, which temporarily increase the number of carcasses but lower the zebra population, acting in some ways as a third competitor. We use a dynamical system to model the interplay between competition dynamics and infection dynamics, and how it is affected by the nature of the competition: indirect (exploitative) or direct (interference). A bifurcation analysis using reproduction numbers shows how vultures' survival may depend on their direct competitive edge in reaching carcasses faster than jackals, and how the infection and the scavengers complicate each other's persistence.

Bacterial biofilms are surface-adhering multicellular collectives embedded in a self-produced extracellular matrix. They can have both beneficial and detrimental effects on the surrounding environment. For example, the soil-dwelling bacterium Bacillus subtilis forms biofilms on the roots of plants, where some strains promote the growth of plants. However, to fully realise their potential as biocontrol agents, strains need to be capable of coexisting with (or outcompeting) other biofilm-forming strains in the rhizosphere. Many antagonistic interaction mechanisms require spatial colocation of competing strains. In this talk, we discuss the crucial role of spatial dynamics on competitive interactions within biofilms using an interdisciplinary approach. Mathematical modelling using a continuum approach predicts that the density of biofilm founder cells has a profound impact on competitive outcome and that randomly allocated cell locations in the biofilm inoculum significantly affect competitive dynamics. We define a predictor for competitive outcome that quantifies a strain's “access to free space” in the initial condition and show that a favourable initial cell placement can lead to domination of a weaker strain (in the sense of interactions of well-mixed populations) in the biofilm. Finally, we present validation of model hypotheses through biofilm assays using strains of B. subtilis.

All sexually reproducing organisms are faced with a fundamental decision: to invest valuable resources and energy in reproduction or in their own survival. This trade-off between reproduction and survival represents the 'cost of reproduction' and occurs across a diverse range of organisms. It is widely assumed that cooperative breeding behavior in vertebrates — when individuals care for young who are not their own — results in part from costly parental care. When caring for young is too costly, parents need help from related or unrelated individuals to successfully raise their offspring. Cooperatively breeding birds and mammals are also more commonly found in unpredictable environments than non-cooperative species, suggesting that decisions about when to breed or help may represent complex yet critical choices that depend on the energy individuals have available to dedicate to reproduction given the harshness of the current environment. Here, we introduce a novel, socially-tiered model of a cooperatively breeding species that incorporates the influence environmental stochasticity. Through numerical and analytical methods, we use this model to show that costly reproduction and environmental variability are compounding factors in the evolution and maintenance of cooperation.

In studying the dynamics of drug resistance, many models have used net growth rates of cell populations. However, we have discovered that cell populations with the same net growth rate but different birth and death rates have dramatically different tendencies to escape extinction and develop drug resistance. Therefore, it is important to identify birth and death rates separately. We develop a method to parse out birth and death rates from cell count time series of populations that follow logistic birth-death processes. We validate our method on in-silico data generated using the tau-leaping approximation. With separate birth and death rates, we infer different underlying mechanisms and drug effects for the same observed population dynamics. From our results, we propose to replace a one-dimensional 'fitness' phenotype (net growth rate) with a two-dimensional 'fitness vector' phenotype (birth and death rates).

Some forms of reproductive division of labor, e.g. multicellular organisation in eukaryotes, are coordinated through differential gene expression. Recent experiments have shown an alternative mechanism in antibiotic producing bacteria, where division of labor is coordinated by mutations. Somatic cells are generated from a germline through genomic deletions. These mutants produce antibiotics but their replication rate is strongly reduced. To understand the evolutionary origin of these findings, we have built a spatial model of bacteria evolution. Bacteria are given a genome, represented as beads on a string, which determines replication and antibiotic production. We find that bacterial genomes evolve to incorporate several fragile sites which increases the rate of deletions. Concurrently, genomes become structured such that fragile sites-induced deletions generate antibiotic-producing mutants from a non-producing germline. These mutants protect their colony from competitors, but they are unable to grow because they lack growth-promoting genes. Altogether, our model suggests a novel mechanism for the evolution of reproductive division of labor in Streptomyces through genome reorganization. Through this mechanism, social conflicts become impossible because altruists lack the genetic means to replicate. These results also help conceptualise the many examples of division of labor through genome manipulation found in other microorganisms and multicellular life.

Population dynamics including a strong Allee effect describe the situation where long-term population survival or extinction depends on the initial population density. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to extinction, whereas initial densities above the threshold lead to survival. Mean-field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as competition and dispersal. The influence of non-mean-field effects has not been studied in the presence of an Allee effect. To address this, we develop an individual-based model that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure neglected by mean-field models. For example, there are cases where the mean-field model predicts extinction but the population actually survives. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.

The innate immune system responds to bacterial infections first by activating the fastest defense mechanism called the complement system. This system is controlled by more than 30 different proteins that work as a team to damage the invader and to alert other immune systems. However, this defense mechanism is perilous if the activation is abnormal, inefficient, and overstimulated, or if there are deficiencies in a surface-bound with receptors of the invaders. It is therefore vital that the complement system binds with an invading bacterium successfully allowing the cascade of events that will enable a proper stimulation of the defensive mechanism by the complement system. Here, we propose a mathematical model which describes the dynamics of the complement system against bacterial infection. We further investigate the mathematical and numerical analysis of the model which generates and explains conditions for normal, efficient, and properly stimulated concentration of the complement system proteins. We also perform sensitivity analysis to identify the critical parameters that affect the direct action of the complement system on the bacterial infection.

Autoimmune myocarditis, or inflammation of cardiac muscle tissue, is a rare but potentially fatal side effect of cancer treatment with immune checkpoint inhibitors. Of patients receiving this type of treatment, approximately 1% develop myocarditis, and the disease proves to be fatal in about 25-50% of these cases. Despite the severity of this side effect and the large volume of cancer patients eligible for treatment with immune checkpoint inhibitors, no preclinical assay currently exists that tests new compounds for myocarditis-related cardiotoxicity. Our aim is to use mathematical modelling to develop a better understanding of the immune cell types and mechanisms involved in the development and progression of autoimmune myocarditis and the effects that immune checkpoint inhibitors have on this. To this end, we have developed the first mathematical model of this disease. By employing parameter sensitivity methods and examining the bifurcation structures in the model, we aim to pinpoint the critical cell types that have to be included in the preclinical test for it to reflect well the mechanisms involved in the development of drug-induced autoimmune myocarditis in vivo.

We present a multi-scale model of the within-phagocyte, within-host and population-level infection dynamics of Francisella tularensis, which extends the mechanistic one proposed by Wood et al. (2014). Our multi-scale model incorporates key aspects of the interaction between host phagocytes and extracellular bacteria, accounts for inter-phagocyte variability in the number of bacteria released upon phagocyte rupture, and allows one to compute the probability of response, and mean time until response, of an infected individual as a function of the initial infection dose. A Bayesian approach is applied to parameterize both the within-phagocyte and within-host models using infection data. Finally, we show how dose response probabilities at the individual level can be used to estimate the airborne exposure to Francisella tularensis in indoor settings (such as a microbiology laboratory) at the population level, by means of a deterministic zonal ventilation model.

The severity of the COVID19 pandemic creates an emerging need to investigate the long-term effect of infection on healing patients. Many individuals are at the risk of suffering pulmonary fibrosis due to pathogenesis of lung injury and impairment in the healing mechanism. SARS-CoV-2 enters the host cells via binding its spike protein with the ACE2 receptor which is a key component in modulating the balance of the renin-angiotensin system (RAS). The dysregulation of ACE2 by the viral infection can shift the balance of RAS towards pro-inflammation and pro-fibrosis. We developed a multiscale agent-based model to investigate the dynamics of viral infection, immune cell response, and fibrosis in lung tissue. The model can simulate the dynamics of ACE2 and collagen deposition in the 2D lung tissue at different severity of infections. We use the ACE2 dynamics as input in a separate model of RAS to predict the change in ANGII, which is a mediator for pro-inflammation and collagen deposition which is a mediator for pro-fibrosis from homeostasis for normotensive and hypertensive patients. Our model also reveals that the variation in available ACE2 due to age and gender can lead to significant change in inflammation, tissue damage, and fibrosis.

In this paper we will consider a mathematical model that aims to better describe the transmissionof malaria. The transmission model is an interaction model between mosquitoes and humans thatdescribes the progress of the infectious disease malaria in the human population. It accounts for thedifferent stages of the disease, showing how the infection develops in both humans and mosquitoes,together with treatment of both sick and partially immune humans. Partially immune humans, whichare termed as asymptomatic, have recovered from the worst stages of the infection, but can still passon the disease to other humans. I will present a mathematical model that consists of a system ofordinary differential equations that describes the evolution of humans and mosquitoes in a range ofdifferent stages of the disease.A new part of the model that I have added, in what turns out to be a key part of the system, is the consideration of asymptomatic humans that have been reinfected again with malaria. Studying the model I will be able to provide a better timeframe in which possible interventions, in the infected region, may produce better results.

A question of major importance at this moment in time of the ongoing COVID-19 epidemic is the momentary growth rate (exponential growthwith positive growth factor or restriction to limited spreading subcritically), in the public discussed as momentary epidemiological reproduction ratio above or belowunity. In the presentation we investigate stochastic processes which are in their community spreading still controlled, but close to the epidemiologicalthreshold. Such models show large fluctuations, mimicking variations of reproduction numbers oscillating around the threshold of unity, sometimes below,sometimes above threshold due to large fluctuations expected from theories of percolation. Any transition from susecptible individuals to infected not mediatedby the currently infected persons in the study community, here called 'import', will lead to an epidemiological situation under community control but proneto large subcritical fluctuations. We analyse simple models and transfer the notion to well calibrated models of COVID-19, e.g. in the Basque Country, whereexcellent data can be obtained. Reference: medRxiv preprint doi: https://doi.org/10.1101/2020.12.25.20248840, and updates.

Modelers of an emerging pathogen can typically assume that a population is entirely susceptible to the infection. In contrast, the dynamics of an endemic infection are highly dependent on the fraction of the population that is susceptible. This has important implications for the short and long-term success of control measures targeting an endemic infection (the ''honeymoon effect'') and can lead to perverse outcomes of transient non-immunizing control measures (the ''divorce effect''). We discuss recent examples of these phenomena in the context of the impacts of non-pharmaceutical interventions aimed at COVID-19 on other directly transmitted respiratory infections, and on the interpretation of large-scale trials of non-vaccine controls of mosquito-borne viral infections.

We propose and analyse a mathematical model of epidemiological dynamics coupled with vaccination to assess under which conditions delaying the application of the second dose in a two-dose vaccination effort during an ongoing epidemic reduces the number of cases and deaths. We use delay differential equations to accurately describe the timing between doses, and calculate optimal vaccination rate under several scenarios of production and maximum vaccination rates, and initial vaccine storage. Vaccine parameters are based on published second dose efficacy values of three main vaccine platforms - inactivated virus, adenovirus and mRNA - and the key parameter related to first dose efficacy is varied to assess the critical value over which it is better to delay the application of the second dose. We evaluate the dependency of this critical value on vaccine production and maximum rate of vaccination, as well as the initial growth rate of the epidemic.

Estimation of parameters in differential equation models can be achieved by applying learning algorithms to quantitative time-series data. However, sometimes it is only possible to measure qualitative changes of a system in response to a controlled condition. In dynamical systems theory, such change points are known as bifurcations and lie on a function of the controlled condition called the bifurcation diagram. In this work, we propose a gradient-based semi-supervised approach for inferring the parameters of differential equations that produce a user-specified bifurcation diagram. The cost function contains a supervised error term that is minimal when the model bifurcations match the specified targets and an unsupervised bifurcation measure which has gradients that push optimisers towards bifurcating parameter regimes. The gradients can be computed without the need to differentiate through the operations of the solver that was used to compute the diagram. We demonstrate parameter inference with minimal models which explore the space of saddle-node and pitchfork diagrams and the genetic toggle switch from synthetic biology. Furthermore, the cost landscape allows us to organise models in terms of topological and geometric equivalence.

Effector T cells rely on the cytokine IL-7 to receive receptor-mediated signalling for their survival. The IL-7 receptor (IL-7R), composed of the common gamma chain and the specific alpha chain, is also associated with the kinase JAK3, which triggers its signalling pathway. Recently, study of cell-to-cell variability and flow cytometry data yielded a seemingly paradoxical observation: increased expression of gamma chains reduces the IL-7 response. We introduce a mathematical model of cytokine IL-7 and IL-7R signalling that provides an explanation for this empirical observation. Our results show the formation of dummy complexes (those receptors that are bound to ligand but not to the JAK3 kinase, and are thus, unable to signal) and indicate that the balance between the number of IL-7R subunits in one cell is crucial for optimal signalling. We make use of a method in algebraic geometry, the Groebner basis, to compute exact analytical expressions for the maximum IL-7 response (or amplitude) and for the half-maximal effective concentration of ligand (EC50) of our mathematical models of cytokine-receptor signalling. While predicted amplitudes agree with the experimental data, measurements of EC50 exhibit more complicated behaviour than we have managed to capture with a variation of our IL-7R model.

Mathematical modelling is a vital tool in coping with complexity on numerous spatial and temporal scales, and a key goal of modelling is to be able to predict future outcomes using model analysis and simulation. The challenge for this dream scenario is the difficulty of validating a particular model, and it is often achieved by attempting to fit the model to observed data. However, often there are multiple candidate models available which renders the task of knowing which description is “correct” very difficult. In order to encode physical properties of the studied system in the construction phase of a model, a novel mathematical technique called symmetry methods can be used. The method of symmetries originates from mathematical physics, and they are transformations that encode physical properties, often formulated as conservation laws. Symmetries have been used with huge success in theoretical physics, but are relatively unexplored in a biological context. Here, the application of symmetries for finding analytical solutions to partial differential equation models of cell migration is showcased, as well as a methodology for model selection. Finally, the difficulties of finding symmetries of large biological models in an automated fashion are discussed.

Many cells of the immune system have molecules which are produced in the nucleus and these move under the influence of diffusion until they reach the outer membrane of the cell. Depending on the type of molecule, they might also diffuse on the surface of the cell until either a certain period of time has passed or the molecule forms a complex. After either of these events the molecules re-enter the cytoplasm and diffuse until they are absorbed by the nucleus. We are interested in the first passage properties of the molecules. For this purpose, we derive an analytic expression for the Green's function of the Laplace equation for a domain bounded by non-concentric surfaces in two dimensions and three dimensions subject to mixed boundary conditions. Utilizing the Green's function we derive an exact expression for the mean time for a Brownian molecule to return to the nuclear surface given that it hit the cellular surface and compare with previous results in the literature. Furthermore, using the Green's function we calculate an exact formula for the hitting density of molecules on the cellular surface and compare it with numerical results.

Peripheral vascular disease (PVD) is an abnormal condition of blood vessels, where they become completely or partially blocked due to atherosclerosis, which is associated with increased serum levels of fibrinogen. High levels of fibrinogen may result in increased erythrocyte aggregation, leading to changes in blood rheology. Here we combine experimental micropipette assays with mathematical modeling to gain insight into the role of fibrinogen in mediating erythrocyte adhesion. The micropipette assay permits the direct visualization of the deformation of two erythrocytes as a function of fibrinogen concentration as they adhere while being pulled apart. The computational phase-field model we implement permits us to relate the morphology of the adhered erythrocytes with the pulling force they exert on each other. By comparing the erythrocyte deformations observed in the two methodologies we are able to estimate the forces the two cells exert on each other during the micropipette assay. We further compare this value with the forces measured by AFM between fibrinogen covered spheres and erythrocytes.

In response to a mechanical or other stimuli, vascular endothelial cells release superoxide to the extracellular medium. Part of this superoxide is readily dismutated into hydrogen peroxide, which can act as an autocrine and/or a paracrine signalling agent. In this work we developed a computer simulation to quantify the restrictions of hydrogen peroxide signalling in capillaries and arterioles. This computer simulation considered the following processes: the superoxide dismutation; the superoxide/hydrogen peroxide release by endothelial cells and uptake by erythrocytes and endothelial cells; and the diffusion and transport of hydrogen peroxide/superoxide by the blood flow. It is assumed that superoxide is produced in a ring of endothelial cells with 20μm length. For plausible cellular rates of superoxide production, local hydrogen peroxide concentrations in blood plasma may reach ~0.1 μM. Maximal concentrations occur within 10 μm and 500μm of the start of the superoxide production domains, in capillaries and arterioles, respectively. We conclude that (i) signalling through superoxide/hydrogen peroxide release to the circulation can only be autocrine in the case of the capillaries and may be paracrine in arterioles; (ii) hypothetical signalling mechanisms must be sensitive to sub-μM extracellular hydrogen peroxide concentrations, which requires peroxiredoxins or peroxidases acting as hydrogen peroxide receptors.

Data-driven methods via machine learning have been useful for predicting the behavior of several complex systems in science and engineering. Recently, the Sparse Identification of Nonlinear Dynamical Systems (SINDy) method has been proposed to discover underlying governing equations from measurement data. This approach assumes that most physical systems have only a few relevant terms to the dynamics and depends on determining the best value for a threshold parameter, which eliminates non-important terms of the governing equations. However, this choice needs to be performed exhaustively, evaluating the Pareto frontier that balances model complexity and accuracy. On the other hand, sensitivity analysis (SA) is a technique that allows ranking the importance of the parameters with respect to the quantity of interest. In this work, we modify the original SINDy implementation replacing the definition of the threshold parameter with a sensitivity analysis method. The SINDy-SA method is applied to capture the dynamical system from time evolution data of different tumor phenotypes. The data are collected from a simulation of a hybrid multiscale model for tumor growth. Besides retrieving the governing equations from data, the proposed approach is automated and able to reduce high complexity models to low complexity systems of ordinary differential equations.

Cell movement involves the coordination between mechanical forces, biochemical regulatory pathways and environmental cues. In particular, epithelial cancer cells have to employ mechanical strategies in order to migrate through the tissue's basement membrane and infiltrate the bloodstream during the invasion stage of metastasis. In this work we explore how mechanical interactions such as spatial restriction and adhesion affect migration of a self-propelled droplet in dense fibrous media. We have performed a systematic analysis using the phase-field model and a vertex model, and we propose a novel approach to simulate cell migration with dissipative particle dynamics modelling. With this purpose we have measured in our simulation the cell's velocity and quantified its morphology as a function of the fibre density and of its adhesiveness to the matrix fibres. Furthermore, we have compared our results to a previous in vitro migration assay of fibrosarcoma cells in fibrous matrices. Our results indicate that adhesiveness is critical for cell migration, by modulating cell morphology in crowded environments and by enhancing cell velocity. In addition, we explore the morphology of epithelial tissues after multiple events of cell extrusion.

A spatial mathematical model investigates how well-known tumor traits: increased resource consumption and angiogenesis, may alter tumor growth in different densities of normal tissue, using CT scan data to initialize the model.A novel modeling paradigm was developed specifically to model tissue at the resolution of CT imaging: the population-based model (PBM). The PBM uses discrete agents, however agents are compartmentalized into homogenous populations, which simplifies computation and allows modeling much larger populations than with conventional agent-based modeling. This PBM method allows us to seed a model with individual cells that operates at the CT scale of cubic millimeters. A virtual tumor can then be grown in this environment.Extensive parameter sweeping was done on different tumor phenotypes and normal tissue densities to assess how these affect marginal tumor growth rate and cell count.We find an optimal balance between angiogenesis and resource consumption by the tumor is needed to maximize invasiveness and tumor bulk, and that this balance changes depending on surrounding tissue density. These results suggest that such a balance may evolve in patient tumors and change depending on the density of the tissue on the tumor margin.

The prostate is an exocrine gland of the male reproductive system dependent on androgens (testosterone and dihydrotestosterone) for development and maintenance. Since prostate cells and their malignant counterparts require androgen stimulation to grow, prostate cancer can be treated by androgen deprivation therapy (ADT). A significant problem in a continuous PCa ADT treatment at the maximum tolerable dose is the insurgence of cancer cell resistance; thus, intermittent adaptive therapy (IAT) is invoked to delay time to progression (TTP).Several mathematical models with different biological resistance mechanisms have been considered to simulate intermittent ADT treatment response dynamics. We present a comparison between 12 of these intermittent prostate-specific antigens (PSA) dynamical models over the Canadian Prospective Phase II Trial of IADT for locally advanced prostate cancer.We identified a few models with critical abilities to disentangle between relapsing and not relapsing patients, which can be exploited for clinical purposes. Finally, within the Bayesian framework, we detected the most compelling models in the trial description.

Conservation is broadly used to identify biologically important genomic regions. Indeed, preferential DNA methylation conservation during tumor growth can indicate areas of particular functional importance to the tumor. In a cohort of 21 colorectal cancer (CRC) patients with multiple tissue samples per patient, we measured methylation at over 850,000 CpG sites using the Infinium Methylation EPIC microarray. Next, we developed a Bayesian hierarchical model that allows for variance decomposition of methylation on 3 hierarchical levels built around the multiple tissue sampling. We fit the model to the CRC data using a Monte Carlo Markov Chain algorithm (Stan). Based on the posterior parameter distributions of the fits, we defined a conservation score to indicate reduced within-tumor variation of methylation relative to between-patient normal variation, thereby quantifying preferential methylation conservation at single CpG sites, individual genes, and molecular pathways. Across gene regulatory regions, preferential conservation was highest in the vicinity of gene transcription start sites and lowest at exon boundaries. Genes belonging to CRC gene sets exhibited increased preferential conservation, suggesting the model's ability to identify functionally relevant regions based on methylation conservation. A pathway analysis of significantly preferentially conserved genes implicated several CRC relevant pathways and pathways related to immune evasion.

Cachexia is the loss of muscle and adipose tissues that directly correlates with patient energy levels, strength, and general quality of life. Chemotherapy is a standard cancer treatment with notorious side effects including nausea, diarrhea, anorexia, and fatigue. Unfortunately, chemotherapy can also induce severe muscle loss. Cancer presence itself can induce cachexia, leading to a double-barrelled attack on healthy lean mass, and thus patient life quality.In this work, we develop a novel mathematical framework to investigate the response of muscle tissue to 5-FU chemotherapy. We model the role of stem cells in tissue maintenance and use the model to examine potential mechanisms of chemotherapy induced muscle loss, including disruption of the differentiation pathway. We confront our model to various treatment doses and dose schedules in an attempt to understand several qualitative features of chemotherapy-induced cachexia. In this talk I will review the model mechanisms we used to capture the qualitative features of the experimental data and discuss some of the computational challenges including parameterization of this dynamic process.