Quantitative Biology

Immunological systems have been an abundant inspiration to contemporary computer scientists. Problem solving strategies, stemming from known immune system phenomena, have been successfully applied to challenging problems of modern computing (MONROY, SAAB, GODINEZ, 2004). Simulation systems and mathematical modeling are also beginning use to answer more complex immunological questions as immune memory process and duration of vaccines, where the regulation mechanisms are not still known sufficiently (LundegaarD, Lund, Kesmir, Brunak, Nielsen, 2007).In this article we studied in machina a approach to simulate the process of antigenic mutation and its implications for the process of memory. Our results have suggested that the durability of the immune memory is affected by the process of antigenic mutation and by populations of soluble antibodies in the blood. The results also strongly suggest that the decrease of the production of antibodies favors the global maintenance of immune memory.

Morphogenesis is a developmental process in which cells organize into shapes and patterns. Complex, multi-factorial models are commonly used to study morphogenesis. It is difficult to understand the relation between the uncertainty in the input and the output of such `black-box' models, giving rise to the need for sensitivity analysis tools. In this paper, we introduce a workflow for a global sensitivity analysis approach to study the impact of single parameters and the interactions between them on the output of morphogenesis models. To demonstrate the workflow, we used a published, well-studied model of vascular morphogenesis. The parameters of the model represent cell properties and behaviors that drive the mechanisms of angiogenic sprouting. The global sensitivity analysis correctly identified the dominant parameters in the model, consistent with previous studies. Additionally, the analysis provides information on the relative impact of single parameters and of interactions between them. The uncertainty in the output of the model was largely caused by single parameters. The parameter interactions, although of low impact, provided new insights in the mechanisms of \emph{in silico} sprouting. Finally, the analysis indicated that the model could be reduced by one parameter. We propose global sensitivity analysis as an alternative approach to study and validate the mechanisms of morphogenesis. Comparison of the ranking of the impact of the model parameters to knowledge derived from experimental data and validation of manipulation experiments can help to falsify models and to find the operand mechanisms in morphogenesis. The workflow is applicable to all `black-box' models, including high-throughput \emph{in vitro} models in which an output measure is affected by a set of experimental perturbations.

Since its introduction in 1952, Turing's (pre-)pattern theory ("the chemical basis of morphogenesis") has been widely applied to a number of areas in developmental biology. The related pattern formation models normally comprise a system of reaction-diffusion equations for interacting chemical species ("morphogens"), whose heterogeneous distribution in some spatial domain acts as a template for cells to form some kind of pattern or structure through, for example, differentiation or proliferation induced by the chemical pre-pattern. Here we develop a hybrid discrete-continuum modelling framework for the formation of cellular patterns via the Turing mechanism. In this framework, a stochastic individual-based model of cell movement and proliferation is combined with a reaction-diffusion system for the concentrations of some morphogens. As an illustrative example, we focus on a model in which the dynamics of the morphogens are governed by an activator-inhibitor system that gives rise to Turing pre-patterns. The cells then interact with morphogens in their local area through either of two forms of chemically-dependent cell action: chemotaxis and chemically-controlled proliferation. We begin by considering such a hybrid model posed on static spatial domains, and then turn to the case of growing domains. In both cases, we formally derive the corresponding deterministic continuum limit and show that that there is an excellent quantitative match between the spatial patterns produced by the stochastic individual-based model and its deterministic continuum counterpart, when sufficiently large numbers of cells are considered. This paper is intended to present a proof of concept for the ideas underlying the modelling framework, with the aim to then apply the related methods to the study of specific patterning and morphogenetic processes in the future.

In this paper we propose a "discrete in continuous" mathematical model for the morphogenesis of the posterior lateral line system in zebrafishes. Our model follows closely the results obtained in recent biological experiments. We rely on a hybrid description: discrete for the cellular level and continuous for the molecular level. We prove the existence of steady solutions consistent with the formation of particular biological structure, the neuromasts. Dynamical numerical simulations are performed to show the behavior of the model and its qualitative and quantitative accuracy to describe the evolution of the cell aggregate.

Current biological knowledge supports the existence of a secondary group of cancer cells within the body of the tumour that exhibits stem cell-like properties. These cells are termed Cancer Stem Cells (CSCs}, and as opposed to the more usual Differentiated Cancer Cells (DCCs), they exhibit higher motility, they are more resilient to therapy, and are able to metastasize to secondary locations within the organism and produce new tumours. The origin of the CSCs is not completely clear; they seem to stem from the DCCs via a transition process related to the Epithelial-Mesenchymal Transition (EMT) that can also be found in normal tissue. In the current work we model and numerically study the transition between these two types of cancer cells, and the resulting "ensemble" invasion of the extracellular matrix. This leads to the derivation and numerical simulation of two systems: an algebraic-elliptic system for the transition and an advection-reaction-diffusion system of Keller-Segel taxis type for the invasion.

Cells crawling through tissues migrate inside a complex fibrous environment called the extracellular matrix (ECM), which provides signals regulating motility. Here we investigate one such well-known pathway, involving mutually antagonistic signalling molecules (small GTPases Rac and Rho) that control the protrusion and contraction of the cell edges (lamellipodia). Invasive melanoma cells were observed migrating on surfaces with topography (array of posts), coated with adhesive molecules (fibronectin, FN) by Park et al., 2016. Several distinct qualitative behaviors they observed included persistent polarity, oscillation between the cell front and back, and random dynamics. To gain insight into the link between intracellular and ECM signaling, we compared experimental observations to a sequence of mathematical models encoding distinct hypotheses. The successful model required several critical factors. (1) Competition of lamellipodia for limited pools of GTPases. (2) Protrusion / contraction of lamellipodia influence ECM signaling. (3) ECM-mediated activation of Rho. A model combining these elements explains all three cellular behaviors and correctly predicts the results of experimental perturbations. This study yields new insight into how the dynamic interactions between intracellular signaling and the cell's environment influence cell behavior.

Within the human respiratory tract (HRT), viruses diffuse through the periciliary fluid (PCF) bathing the epithelium, and travel upwards via advection towards the nose and mouth, as the mucus escalator entrains the PCF. While many mathematical models (MMs) to date have described the course of influenza A virus (IAV) infections in vivo, none have considered the impact of both diffusion and advection on the kinetics and localization of the infection. The MM herein represents the HRT as a one-dimensional track extending from the nose down to a depth of 30 cm, wherein stationary cells interact with the concentration of IAV which move along within the PCF. When IAV advection and diffusion are both considered, the former is found to dominate infection kinetics, and a 10-fold increase in the virus production rate is required to counter its effects. The MM predicts that advection prevents infection from disseminating below the depth at which virus first deposits. Because virus is entrained upwards, the upper HRT sees the most virus, whereas the lower HRT sees far less. As such, infection peaks and resolves faster in the upper than in the lower HRT, making it appear as though infection progresses from the upper towards the lower HRT. When the spatial MM is expanded to include cellular regeneration and an immune response, it can capture the time course of infection with a seasonal and an avian IAV strain by shifting parameters in a manner consistent with what is expected to differ between these two types of infection. The impact of antiviral therapy with neuraminidase inhibitors was also investigated. This new MM offers a convenient and unique platform from which to study the localization and spread of respiratory viral infections within the HRT.

Cell migration is often accompanied by collisions with other cells, which can lead to cessation of movement, repolarization, and migration away from the contact site - a process termed contact inhibition of locomotion (CIL). During CIL, the coupling between actomyosin contractilityand cell-substrate adhesions is modified. However, mathematical models describing stochastic cell migration and collision outcomes as a result of the coupling remain elusive. Here, we extend our previously developed stochastic model of single cell migration to include CIL. Our simulation results explain, in terms of the modified contractility and adhesion dynamics, several experimentally observed findings regarding CIL. These include response modulation in the presence of an external cue and alterations of group migration in the absence of CIL. Together with our previous findings, our work is able to explain a wide range of observations about single and collective cell migration.

We develop a physiological model of granulopoiesis which includes explicit modelling of the kinetics of the cytokine granulocyte colony-stimulating factor (G-CSF) incorporating both the freely circulating concentration and the concentration of the cytokine bound to mature neutrophils. G-CSF concentrations are used to directly regulate neutrophil production, with the rate of differentiation of stem cells to neutrophil precursors, the effective proliferation rate in mitosis, the maturation time, and the release rate from the mature marrow reservoir into circulation all dependent on the level of G-CSF in the system. The dependence of the maturation time on the cytokine concentration introduces a state-dependent delay into our differential equation model, and we show how this is derived from an age-structured partial differential equation model of the mitosis and maturation, and also detail the derivation of the rest of our model. The model and its estimated parameters are shown to successfully predict the neutrophil and G-CSF responses to a variety of treatment scenarios, including the combined administration of chemotherapy and exogenous G-CSF. This concomitant treatment was reproduced without any additional fitting to characterise drug-drug interactions.

Complete understanding of the mechanisms regulating the proliferation and differentiation that takes place during human immune CD8+ T cell responses is still lacking. Human clinical data is usually limited to blood cell counts, yet the initiation of these responses occurs in the draining lymph nodes; antigen-specific effector and memory CD8+ T cells generated in the lymph nodes migrate to those tissues where they are required. We use approximate Bayesian computation with deterministic mathematical models of CD8+ T cell populations (naive, central memory, effector memory and effector) and yellow fever virus vaccine data to infer the dynamics of these CD8+ T cell populations in three spatial compartments: draining lymph nodes, circulation and skin. We have made use of the literature to obtain rates of division and death for human CD8+ T cell population subsets and thymic export rates. Under the decreasing potential hypothesis for differentiation during an immune response, we find that, as the number of T cell clonotypes driven to an immune response increases, there is a reduction in the number of divisions required to differentiate from a naive to an effector CD8+ T cell, supporting the "division of labour" hypothesis observed in murine studies. We have also considered the reverse differentiation scenario, the increasing potential hypothesis. The decreasing potential model is better supported by the yellow fever virus vaccine data.