A survey of adaptive cell population dynamics models of emergence of drug resistance in cancer, and open questions about evolution and cancer

This article is a proceeding survey (deepening a talk given by the first author at the BioMath 2019 International Conference on Mathematical Models and Methods, held in Będlewo, Poland) of mathematical models of cancer and healthy cell population adaptive dynamics exposed to anticancer drugs, to describe how cancer cell populations evolve toward drug resistance. Such mathematical models consist of partial differential equations (PDEs) structured in continuous phenotypes coding for the expression of drug resistance genes; they involve different functions representing targets for different drugs, cytotoxic and cytostatic, with complementary effects in limiting tumour growth. These phenotypes evolve continuously under drug exposure, and their fate governs the evolution of the cell population under treatment. Methods of optimal control are used, taking inevitable emergence of drug resistance into account, to achieve the best strategies to contain the expansion of a tumour. This evolutionary point of view, which relies on biological observations and resulting modelling assumptions, naturally extends to questioning the very nature of cancer as evolutionary disease, seen not only at the short time scale of a human life, but also at the billion year-long time scale of Darwinian evolution, from unicellular organisms to evolved multicellular organs such as animals and man. Such questioning, not so recent, but recently revived, in cancer studies, may have consequences for understanding and treating cancer. Some open and challenging questions may thus be (non exhaustively) listed as:-May cancer be defined as a spatially localised loss of coherence between tissues in the same mul-ticellular organism, 'spatially localised' meaning initially starting from a given organ in the body, but also possibly due to flaws in an individual's rms of evolution towards drug resistance governed by the phenotypes which determine landscape such as imperfect epigenetic control of differentiation genes?-If one assumes that "The genes of cellular cooperation that evolved with multicellularity about a billion years ago are the same genes that malfunction in cancer." (Davies and Lineweaver, 2011), how can these genes be systematically investigated, looking for zones of fragility-that depend on individuals-in the 'tinkering' (F. Jacob, 1977) evolution is made of, tracking local defaults of coherence?-What is such coherence made of and to what extent is the immune system responsible for it (the self and differentiation within the self)? Related to this question of self, what parallelism can be established between the development of multicellularity in different species proceeding from the same origin and the development of the immune system in these different species

A survey of adaptive cell population dynamics models of emergence of drug resistance in cancer, and open questions about evolution and cancer

This article is a proceeding survey (deepening a talk given by the first author at the Biomath 2019 International Conference on Mathematical Models and Methods, held in Bedlewo, Poland) of mathematical models of cancer and healthy cell population adaptive dynamics exposed to anticancer drugs, to describe how cancer cell populations evolve toward drug resistance. Such mathematical models consist of partial differential equations (PDEs) structured in continuous phenotypes coding for the expression of drug resistance genes; they involve different functions representing targets for different drugs, cytotoxic and cytostatic, with complementary effects in limiting tumour growth. These phenotypes evolve continuously under drug exposure, and their fate governs the evolution of the cell population under treatment. Methods of optimal control are used, taking inevitable emergence of drug resistance into account, to achieve the best strategies to contain the expansion of a tumour. This evolutionary point of view, which relies on biological observations and resulting modelling assumptions, naturally extends to questioning the very nature of cancer as evolutionary disease, seen not only at the short time scale of a human life, but also at the billion year-long time scale of Darwinian evolution, from unicellular organisms to evolved multicellular organs such as animals and man. Such questioning, not so recent, but recently revived, in cancer studies, may have consequences for understanding and treating cancer. Some open and challenging questions may thus be (non exhaustively) listed as: - May cancer be defined as a spatially localised loss of coherence between tissues in the same multicellular organism, `spatially localised' meaning initially starting from a given organ in the body, but also possibly due to flaws in an individual's rms of evolution towards drug resistance governed by the phenotypes which determine landscape such as imperfect epigenetic control of differentiation genes? - If one assumes that ''The genes of cellular cooperation that evolved with multicellularity about a billion years ago are the same genes that malfunction in cancer.'', how can these genes be systematically investigated, looking for zones of fragility - that depend on individuals - in the 'tinkering' evolution is made of, tracking local defaults of coherence? - What is such coherence made of and to what extent is the immune system responsible for it (the self and differentiation within the self)? Related to this question of self, what parallelism can be established between the development of multicellularity in different species proceeding from the same origin and the development of the immune system in these different species

Nonlinear Control and Estimation of an Infammatory Immune Response

The immune response is a complex mechanism that can be triggered by biological or physical stresses on the organism. However an excessive and dys-regulated inflammatory response may lead to sepsis, a critical state, promoting tissue damage, organ dysfunction or even death.The main objective in this dissertation is to derive a strategy consisting of manipulating pro and anti-inflammatory mediators in order to direct the state of a virtual patient to a healthy equilibrium, after some disturbance from health due to infection. Two key challenges need to be addressed in solving such a problem: estimating the unmeasurable states of the inflammatory model as well as the model\u27s unknown rate parameters; and second, determining an appropriate strategy to effectively control the response.We initially study the nonlinear controllability, observability and identifiability of the inflammatory immune model. Then, we address the first challenge by comparing the performance of various nonlinear filters for state estimation in the presence of noise and incomplete information. For parameter estimation, a recently introduced approximate Markov chain Monte Carlo approach known as the Particle Metropolis- Hastings method is used. To control the highly nonlinear model, various model-based optimization approaches were investigated in which the control strategy is derived in terms of pro-inflammatory and anti-inflammatory response doses. Due to parameter variability and the difficult practical task of obtaining accurate state and parameter estimates in real time, a new model-free control methodology and its intelligent controllers is explored. The method does not rely on any precise modeling and the identification of each parameter of the inflammatory immune model is no longer needed for control design. The various methods are compared for performance to adequately control the responses in a diverse patient population as well as the clinical feasibility of the derived control protocol from the approach used

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

A numerical approach to studying cell dynamics

The focus of this thesis is to propose and implement a highly efficient numerical method to study cell dynamics. Three key phases are covered: mathematical modelling, linear stability analytical theory and numerical simulations using the moving grid finite element method. This aim is to study cell deformation and cell movement by considering both the mechanical and biochemical properties of the cortical network of actin filaments and its concentration. These deformations are assumed to be a result of the cortical actin dynamics through its interaction with a protein known as myosin II in the cell cytoskeleton. The mathematical model that we consider is a continuum model that couples the mechanics of the network of actin filaments with its bio-chemical dynamics. Numerical treatment of the model is carried out using the moving grid finite element method. By assuming slow deformations of the cell boundary, we verify the numerical simulation results using linear stability theory close to bifurcation points. Far from bifurcation points, we show that the model is able to describe the deformation of cells as a function of the contractile tonicity of the complex formed by the association of actin filaments with the myosin II motor proteins. Our results show complex cell deformations and cell movements such as cell expansion, contraction, translation and protrusions in accordance with experimental observations. The migratory behaviour of cells plays a crucial role in many biological events such as immune response, wound healing, development of tissues, embryogenesis, inflammation and the formation of tumours