Davide Cusseddu (GFM, University of Lisbon)
Title: A bulk-surface reaction-diffusion model for cell polarisation with membrane-cytosolic interactions
Abstract: The bulk-surface wave-pinning (BSWP) model is a reaction-diffusion system developed for studying cell polarisation in three-dimensional domains. The model describes the switching between active and inactive state of a representative protein from the GTPase family. The bulk-surface framework allows the spatial compartmentalisation of the active proteins, which are bounded to the cell membrane, and inactive proteins, generally found internally in the interior of the cell. Interactions are described by a bistable reaction term on the surface.
Cell polarisation arises as the surface component forms specific patterns, by developing propagating front solutions with non-constant speed. Since proteins diffuse much faster in the cell interior than on the membrane, in the literature, the bulk component is often assumed to be spatially homogeneous, and the model reduces to a single surface equation. However, a spatially non-uniform bulk component might be an important player to take into account.
We will discuss, through numerical computations, the role of the bulk component and, more specifically, how different bulk diffusion rates might affect the polarisation response. We find that the bulk component is indeed a key factor in defining the final position of the polarised surface area. Moreover, for certain geometries, it is the spatial heterogeneity of the bulk component that triggers the polarisation response, which might not be possible in a minimal surface model.
Understanding how polarisation depends on bulk diffusivity might be crucial when studying models of migrating cells, which are naturally subject to domain deformation.
_______________________________________________________________________________
Wolfram Erlhagen (CMAT, University of Minho)
Title: Dynamic Neural Fields as a Mathematical Framework to model Cognitive Brain Functions
Abstract: Dynamic Neural Fields (DNFs) formalized by nonlinear integro-differential equations have been originally introduced as a model framework for explaining basic principles of neural information processing in which the interactions of billions of neurons are treated as a continuum. The intention is to reduce the enormous complexity of neural interactions to simpler population properties that are tractable by mathematical analysis. DNF models explain the existence of stable neural activity patterns which are initially triggered by transient sensory inputs. Such persistent activity is commonly believed to play a fundamental role in higher cognitive functions such as working memory, planning, decision making and learning.
In my talk, I will give an overview about the physiological motivation of DNFs, the mathematical analysis of their dynamic behaviors, and some applications in cognitive neuroscience. I will also present an example how we further develop Dynamic Field theory to address new experimental findings which are not well captures by classical DNF models.
_______________________________________________________________________________
Carla Moreira (CMAT, University of Minho)
Title: Statistical methods for doubly truncated data
Abstract: Truncation is a well-known phenomenon that may be present in observational studies of time-to-event data. For example, when the sample restricts to those individuals with event falling between two particular dates, they are subject to selection bias due to the simultaneous presence of left and right truncation, also known as interval sampling, leading to a double truncation. When time-to-event data is doubly truncated, the sampling information includes the variable of interest X and left-truncation and right-truncation variables U and V, but the observable population reduces to those individuals for which the variable of interest lies between left-truncation and right-truncation variables. In this case, both large and small values of X are observed in principle with a relatively small probability. The problem of estimating the distribution of X and other related curves such as kernel density and kernel hazard functions, using nonparametric and semiparametric approaches, from a set of iid triplets with distribution of (X, U, V) given the double truncation restriction will be presented. Several epidemiological scenarios where the effect of ignoring double truncation appears in practice will be reported. Possible limitations of the nonparametric and semiparametric estimators will be discussed.
_______________________________________________________________________________
João Oliveira (CMAT, University of Minho)
Title: Microscopic equilibria in an autoimmune disease model
Abstract: There are many types of autoimmune disease, from organ specific to general immunological dysfunction involving multiple organs. These diseases can have significant impact on the short and long term health of individuals. It is then our interest to mathematically model the evolution of these kinds of diseases, in order to better predict and control how a patient's state will develop.
In this talk we discuss how we can model the dynamics and interactions between cell populations using a kinetic theory model, and how that can be used to model autoimmune disease evolution. We then discuss the distinctions between the micro and macro counterparts of the model and end with an analytical study of the equilibrium solutions of the microscopic model.
_______________________________________________________________________________
José Joaquim Oliveira (CMAT, University of Minho)
Title: A mathematical periodic model for the hematopoiesis process with predictable abrupt changes
Abstract: Hematopoiesis is the process of production, multiplication, regulation and specialization of blood cells in the bone marrow, until they become mature blood cells for release in the circulation bloodstream. By one hand, this is a biological process, thus it is better modeled if the periodicity of the environment is taken into account. On the other hand, some evolutionary systems go through abrupt changes, due to predictable or sudden external phenomena such as drugs administration or radiation. These phenomena are better described by impulsive differential equations.
In this presentation, we explain a mathematical model to describe the hematopoises process taking into account the periodicity of the environment and predictable abrupt changes. Sufficient conditions for the existence and global asymptotic stability of a periodic solution are given.
This is a joint work with Teresa Faria.
_______________________________________________________________________________
Cristiana João da Silva (CIDMA, University Institute of Lisbon)
Title: Mathematical modeling of epidemics: one possible way to get there
Abstract: In this talk we show one possible way to construct epidemic mathematical models, using systems of ordinary differential equations, complex networks and agent-based models. Coupling these three mathematical tools, we construct hybrid models which allow us to integrate the microscopic dynamics of individual behaviors into the macroscopic evolution of various population dynamics models. In each step, the models will be applied to real data from recent outbreaks.
_______________________________________________________________________________
Liliana Garrido da Silva (CMUP, University of Porto, Portugal)
Title: Heteroclinic attractors in biological dynamical systems
Abstract: Differential equations on R^n that leave certain hyperplanes invariant can arise as models in mathematical biology. In such systems heteroclinic cycles occur in a robust way. A heteroclinic cycle is a sequence of trajectories connecting a set of equilibrium points (or more general invariant subsets) in a topological circle. An interest is taken in their dynamic behaviour determined by the way they are stable. The stability of heteroclinic trajectories can be quantified by the local stability index. We develop a method to compute this index for a general class of robust heteroclinic cycles called quasi-simple heteroclinic cycles. A heteroclinic cycle is quasi-simple if its heteroclinic connections are one-dimensional and contained in flow-invariant spaces of equal dimensions. We apply our techniques to study the role of competition in the spatial system of five species governed by Rock-Paper-Scissors-LizardSpock (RPSLS) game. We identify regions of parameter space in which distinct survival states emerge.
_______________________________________________________________________________
Egídio Torrado (ICVS, University of Minho)
Title: Regulation of CD4+ T cell responses to Mycobacterium tuberculosis infection
Abstract: CD4+ T cells play a crucial role in the control of Mycobacterium tuberculosis infection; however, there is a delayed appearance of effector T cells in the lungs following aerosol infection. In this work, we showed that IL-10 plays a key role in preventing the migration of newly activated CD4+ T cells into the lung parenchyma. Specifically, CD4+ T cells primed and differentiated in an IL-10-enriched environment displayed reduced expression of the chemokine receptor CXCR3 and, because they did not migrate into the lung parenchyma, their ability to control infection was limited. Importantly, these CD4+ T cells maintained their vasculature phenotype and were unable to control infection, even after adoptive transfer into low IL-10 settings. Together our data support a model wherein, during M. tuberculosis infection, IL-10 acts intrinsically on T cells, impairing their parenchymal migratory capacity and ability to engage with infected phagocytic cells, thereby impeding control of infection.