Integrative modelling of angiogenesis in the bovine corpus luteum

The corpus luteum (CL) is a tissue formed from the remnants of an ovulated follicle in the ovary, and it produces the progesterone needed for a healthy pregnancy. CL growth is highly dependent on a growing nutrient supply, and can be compared with the most aggressive vascular tumours. Angiogenesis, the growth of new blood vessels from existing ones, plays a key role in the growth and function of the CL. Inadequate angiogenesis has been linked to infertility in cows. The CL is composed of several vascular(e.g. endothelial cells (ECs), pericytes (PCs)), and avascular (e.g. luteal cells (LCs), immune cells) cell types, and several pro-angiogenic factors (e.g. Fibroblast Growth Factor 2, FGF2) found to be important in the angiogenic process. The objective of this thesis is to shed light on the cellular and extracellular level determinants of angiogenesis in the bovine CL. We begin with the relevant biological and mathematical literature in Chapter 1. In Chapter 2, an ordinary differential equation model of CL growth is introduced. We assume that the CL volume is a continuum of three cell types, ECs, LCs, and stromal cells (such as PCs). The fourth variable in the model, FGF2, enhances the EC proliferation rate. The model is able, by varying parameters such as the maximal proliferation rate of the ECs, to distinguish cases where the CL shifts from a ‘normal’ to a ‘pathological’ growth. In Chapter 3, we present in vitro CL published and novel studies from Robinson’s Lab. Preliminary results demonstrate interesting endothelial and pericyte behaviours regarding cell aggregation and sprout formation, which are the motivation for the next two Chapters. In these experimental studies, all the CL cell types were incorporated in the same in vitro culture, hence providing a closer approximation to the in vivo environment compared to other in vitro cultures which use only a single cell type (mainly ECs). However, this complicates matters in terms of distinguishing cell behaviours and factors which contribute on the overall cell dynamics. Therefore, in the Chapters 4 and 5 we use data from literature. In Chapter 4, by using the Cellular Potts Model (CPM) framework, we focus on EC-PC interactions, and particularly on the mechanism which is responsible for the EC growth inhibition. Our model incorporates two possible mechanisms for inhibition. That is, the mechanical cell-cell contact inhibition, and the inhibition mediated from diffusive TGF-b secreted once the two cell types come in contact. Interestingly, our model results suggest that the effective range of TGF-b is a crucial determinant of the degree of EC growth inhibition. Chapter 5, by using a CPM, is devoted to sprouting angiogenesis (the formation of new blood vessel). The dynamic interchange between stalk and tip EC phenotype is incorporated through the Notch signalling pathway, with the leading tip cell moving up macrophage-mediated VEGFA gradients in a non-uniform matrix environment. The model reproduces phenomena in sprouting angiogenesis, including sprout morphology, tip competition, and explains knockout experiments on the Notch signalling pathway. Finally, we close with Chapter 6 where we summarise the ain results from each chapter and propose model extensions for future directions

Integrative modelling of angiogenesis in the bovine corpus luteum

The corpus luteum (CL) is a tissue formed from the remnants of an ovulated follicle in the ovary, and it produces the progesterone needed for a healthy pregnancy. CL growth is highly dependent on a growing nutrient supply, and can be compared with the most aggressive vascular tumours. Angiogenesis, the growth of new blood vessels from existing ones, plays a key role in the growth and function of the CL. Inadequate angiogenesis has been linked to infertility in cows. The CL is composed of several vascular(e.g. endothelial cells (ECs), pericytes (PCs)), and avascular (e.g. luteal cells (LCs), immune cells) cell types, and several pro-angiogenic factors (e.g. Fibroblast Growth Factor 2, FGF2) found to be important in the angiogenic process. The objective of this thesis is to shed light on the cellular and extracellular level determinants of angiogenesis in the bovine CL. We begin with the relevant biological and mathematical literature in Chapter 1. In Chapter 2, an ordinary differential equation model of CL growth is introduced. We assume that the CL volume is a continuum of three cell types, ECs, LCs, and stromal cells (such as PCs). The fourth variable in the model, FGF2, enhances the EC proliferation rate. The model is able, by varying parameters such as the maximal proliferation rate of the ECs, to distinguish cases where the CL shifts from a ‘normal’ to a ‘pathological’ growth. In Chapter 3, we present in vitro CL published and novel studies from Robinson’s Lab. Preliminary results demonstrate interesting endothelial and pericyte behaviours regarding cell aggregation and sprout formation, which are the motivation for the next two Chapters. In these experimental studies, all the CL cell types were incorporated in the same in vitro culture, hence providing a closer approximation to the in vivo environment compared to other in vitro cultures which use only a single cell type (mainly ECs). However, this complicates matters in terms of distinguishing cell behaviours and factors which contribute on the overall cell dynamics. Therefore, in the Chapters 4 and 5 we use data from literature. In Chapter 4, by using the Cellular Potts Model (CPM) framework, we focus on EC-PC interactions, and particularly on the mechanism which is responsible for the EC growth inhibition. Our model incorporates two possible mechanisms for inhibition. That is, the mechanical cell-cell contact inhibition, and the inhibition mediated from diffusive TGF-b secreted once the two cell types come in contact. Interestingly, our model results suggest that the effective range of TGF-b is a crucial determinant of the degree of EC growth inhibition. Chapter 5, by using a CPM, is devoted to sprouting angiogenesis (the formation of new blood vessel). The dynamic interchange between stalk and tip EC phenotype is incorporated through the Notch signalling pathway, with the leading tip cell moving up macrophage-mediated VEGFA gradients in a non-uniform matrix environment. The model reproduces phenomena in sprouting angiogenesis, including sprout morphology, tip competition, and explains knockout experiments on the Notch signalling pathway. Finally, we close with Chapter 6 where we summarise the ain results from each chapter and propose model extensions for future directions

Mathematical analysis of a model for the growth of the bovine corpus luteum

The corpus luteum (CL) is an ovarian tissue that grows in the wound space created by follicular rupture. It produces the progesterone needed in the uterus to maintain pregnancy. Rapid growth of the CL and progesterone transport to the uterus require angiogenesis, the creation of new blood vessels from pre-existing ones, a process which is regulated by proteins that include fibroblast growth factor 2 (FGF2).\ud \ud In this paper we develop a system of time-dependent ordinary differential equations to model CL growth. The dependent variables represent FGF2, endothelial cells (ECs), luteal cells, and stromal cells (like pericytes), by assuming that the CL volume is a continuum of the three cell types. We assume that if the CL volume exceeds that of the ovulated follicle, then growth is inhibited. This threshold volume partitions the system dynamics into two regimes, so that the model may be classified as a Filippov (piecewise smooth) system.\ud \ud We show that normal CL growth requires an appropriate balance between the growth rates of luteal and stromal cells. We investigate how angiogenesis influences CL growth by considering how the system dynamics depend on the dimensionless EC proliferation rate, p5. We find that weak (low p5) or strong (high p5) angiogenesis leads to ‘pathological’ CL growth, since the loss of CL constituents compromises progesterone production or delivery. However, for intermediate values of p5, normal CL growth is predicted. The implications of these results for cow fertility are also discussed. For example, inadequate angiogenesis has been linked to infertility in dairy cows

Mathematical analysis of a model for the growth of the bovine corpus luteum.

The corpus luteum (CL) is an ovarian tissue that grows in the wound space created by follicular rupture. It produces the progesterone needed in the uterus to maintain pregnancy. Rapid growth of the CL and progesterone transport to the uterus require angiogenesis, the creation of new blood vessels from pre-existing ones, a process which is regulated by proteins that include fibroblast growth factor 2 (FGF2). In this paper we develop a system of time-dependent ordinary differential equations to model CL growth. The dependent variables represent FGF2, endothelial cells (ECs), luteal cells, and stromal cells (like pericytes), by assuming that the CL volume is a continuum of the three cell types. We assume that if the CL volume exceeds that of the ovulated follicle, then growth is inhibited. This threshold volume partitions the system dynamics into two regimes, so that the model may be classified as a Filippov (piecewise smooth) system. We show that normal CL growth requires an appropriate balance between the growth rates of luteal and stromal cells. We investigate how angiogenesis influences CL growth by considering how the system dynamics depend on the dimensionless EC proliferation rate, ρ₅. We find that weak (low ρ₅) or strong (high ρ₅) angiogenesis leads to 'pathological' CL growth, since the loss of CL constituents compromises progesterone production or delivery. However, for intermediate values of ρ₅, normal CL growth is predicted. The implications of these results for cow fertility are also discussed. For example, inadequate angiogenesis has been linked to infertility in dairy cows

A proliferation saturation index to predict radiation response and personalize radiotherapy fractionation

BACKGROUND: Although altered protocols that challenge conventional radiation fractionation have been tested in prospective clinical trials, we still have limited understanding of how to select the most appropriate fractionation schedule for individual patients. Currently, the prescription of definitive radiotherapy is based on the primary site and stage, without regard to patient-specific tumor or host factors that may influence outcome. We hypothesize that the proportion of radiosensitive proliferating cells is dependent on the saturation of the tumor carrying capacity. This may serve as a prognostic factor for personalized radiotherapy (RT) fractionation. METHODS: We introduce a proliferation saturation index (PSI), which is defined as the ratio of tumor volume to the host-influenced tumor carrying capacity. Carrying capacity is as a conceptual measure of the maximum volume that can be supported by the current tumor environment including oxygen and nutrient availability, immune surveillance and acidity. PSI is estimated from two temporally separated routine pre-radiotherapy computed tomography scans and a deterministic logistic tumor growth model. We introduce the patient-specific pre-treatment PSI into a model of tumor growth and radiotherapy response, and fit the model to retrospective data of four non-small cell lung cancer patients treated exclusively with standard fractionation. We then simulate both a clinical trial hyperfractionation protocol and daily fractionations, with equal biologically effective dose, to compare tumor volume reduction as a function of pretreatment PSI. RESULTS: With tumor doubling time and radiosensitivity assumed constant across patients, a patient-specific pretreatment PSI is sufficient to fit individual patient response data (R(2) = 0.98). PSI varies greatly between patients (coefficient of variation >128 %) and correlates inversely with radiotherapy response. For this study, our simulations suggest that only patients with intermediate PSI (0.45–0.9) are likely to truly benefit from hyperfractionation. For up to 20 % uncertainties in tumor growth rate, radiosensitivity, and noise in radiological data, the absolute estimation error of pretreatment PSI is <10 % for more than 75 % of patients. CONCLUSIONS: Routine radiological images can be used to calculate individual PSI, which may serve as a prognostic factor for radiation response. This provides a new paradigm and rationale to select personalized RT dose-fractionation

IL-2 sensitivity and exogenous IL-2 concentration gradient tune the productive contact duration of CD8+ T cell-APC: a multiscale modeling study

International audienceAbstractBackgroundThe CD8+ T cell immune response fights acute infections by intracellular pathogens and, by generating an immune memory, enables immune responses against secondary infections. Activation of the CD8+ T cell immune response involves a succession of molecular events leading to modifications of CD8+ T cell population. To understand the endogenous and exogenous mechanisms controlling the activation of CD8+ T cells and to investigate the influence of early molecular events on the long-term cell population behavior, we developed a multiscale computational model. It integrates three levels of description: a Cellular Potts model describing the individual behavior of CD8+ T cells, a system of ordinary differential equations describing a decision-making molecular regulatory network at the intracellular level, and a partial differential equation describing the diffusion of IL-2 in the extracellular environment.ResultsWe first calibrated the model parameters based on in vivo data and showed the model’s ability to reproduce early dynamics of CD8+ T cells in murine lymph nodes after influenza infection, both at the cell population and intracellular levels. We then showed the model’s ability to reproduce the proliferative responses of CD5hi and CD5lo CD8+ T cells to exogenous IL-2 under a weak TCR stimulation. This stressed the role of short-lasting molecular events and the relevance of explicitly describing both intracellular and cellular scale dynamics. Our results suggest that the productive contact duration of CD8+ T cell-APC is influenced by the sensitivity of individual CD8+ T cells to the activation signal and by the IL-2 concentration in the extracellular environment.ConclusionsThe multiscale nature of our model allows the reproduction and explanation of some acquired characteristics and functions of CD8+ T cells, and of their responses to multiple stimulation conditions, that would not be accessible in a classical description of cell population dynamics that would not consider intracellular dynamics

Multiscale Modeling of the Early CD8 T-Cell Immune Response in Lymph Nodes: An Integrative Study

International audienceCD8 T-cells are critical in controlling infection by intracellular pathogens. Upon encountering antigen presenting cells, T-cell receptor activation promotes the differentiation of naïve CD8 T-cells into strongly proliferating activated and effector stages. We propose a 2D-multiscale computational model to study the maturation of CD8 T-cells in a lymph node controlled by their molecular profile. A novel molecular pathway is presented and converted into an ordinary differential equation model, coupled with a cellular Potts model to describe cell-cell interactions. Key molecular players such as activated IL2 receptor and Tbet levels control the differentiation from naïve into activated and effector stages, respectively, while caspases and Fas-Fas ligand interactions control cell apoptosis. Coupling this molecular model to the cellular scale successfully reproduces qualitatively the evolution of total CD8 T-cell counts observed in mice lymph node, between Day 3 and 5.5 post-infection. Furthermore, this model allows us to make testable predictions of the evolution of the different CD8 T-cell stages

Additional file 7: of IL-2 sensitivity and exogenous IL-2 concentration gradient tune the productive contact duration of CD8+ T cell-APC: a multiscale modeling study

This zip file contains the simulation files used to generate the results presented in this manuscript. One may note that CompuCell3D must be installed in order to run the files. (ZIP 122 kb