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Population mechanics: A mathematical framework to study T cell homeostasis.

ABSTRACT: Unlike other cell types, T cells do not form spatially arranged tissues, but move independently throughout the body. Accordingly, the number of T cells in the organism does not depend on physical constraints imposed by the shape or size of specific organs. Instead, it is determined by competition for interleukins. From the perspective of classical population dynamics, competition for resources seems to be at odds with the observed high clone diversity, leading to the so-called diversity paradox. In this work we make use of population mechanics, a non-standard theoretical approach to T cell homeostasis that accounts for clone diversity as arising from competition for interleukins. The proposed models show that carrying capacities of T cell populations naturally emerge from the balance between interleukins production and consumption. These models also suggest remarkable functional differences in the maintenance of diversity in naïve and memory pools. In particular, the distribution of memory clones would be biased towards clones activated more recently, or responding to more aggressive pathogenic threats. In contrast, permanence of naïve T cell clones would be determined by their affinity for cognate antigens. From this viewpoint, positive and negative selection can be understood as mechanisms to maximize naïve T cell diversity.

SUBMITTER: Arias CF

PROVIDER: S-EPMC5573381 | biostudies-literature | 2017 Aug

REPOSITORIES: biostudies-literature

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Population mechanics: A mathematical framework to study T cell homeostasis.

Arias Clemente F CF Herrero Miguel A MA Acosta Francisco J FJ Fernandez-Arias Cristina C

Scientific reports 20170825 1

Unlike other cell types, T cells do not form spatially arranged tissues, but move independently throughout the body. Accordingly, the number of T cells in the organism does not depend on physical constraints imposed by the shape or size of specific organs. Instead, it is determined by competition for interleukins. From the perspective of classical population dynamics, competition for resources seems to be at odds with the observed high clone diversity, leading to the so-called diversity paradox. ...[more]

PMID: 28842645

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Project description:Mechanics plays a key role in the development of higher organisms. However, understanding this relationship is complicated by the difficulty of modeling the link between local forces generated at the subcellular level and deformations observed at the tissue and whole-embryo levels. Here we propose an approach first developed for lipid bilayers and cell membranes, in which force-generation by cytoskeletal elements enters a continuum mechanics formulation for the full system in the form of local changes in preferred curvature. This allows us to express and solve the system using only tissue strains. Locations of preferred curvature are simply related to products of gene expression. A solution, in that context, means relaxing the system's mechanical energy to yield global morphogenetic predictions that accommodate a tendency toward the local preferred curvature, without a need to explicitly model force-generation mechanisms at the molecular level. Our computational framework, which we call SPHARM-MECH, extends a 3D spherical harmonics parameterization known as SPHARM to combine this level of abstraction with a sparse shape representation. The integration of these two principles allows computer simulations to be performed in three dimensions on highly complex shapes, gene expression patterns, and mechanical constraints. We demonstrate our approach by modeling mesoderm invagination in the fruit-fly embryo, where local forces generated by the acto-myosin meshwork in the region of the future mesoderm lead to formation of a ventral tissue fold. The process is accompanied by substantial changes in cell shape and long-range cell movements. Applying SPHARM-MECH to whole-embryo live imaging data acquired with light-sheet microscopy reveals significant correlation between calculated and observed tissue movements. Our analysis predicts the observed cell shape anisotropy on the ventral side of the embryo and suggests an active mechanical role of mesoderm invagination in supporting the onset of germ-band extension.

Dataset Information

Population mechanics: A mathematical framework to study T cell homeostasis.

Publications

Population mechanics: A mathematical framework to study T cell homeostasis.

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