Mathematical modeling and its analysis for instability of the immune system induced by chemotaxis

Viral infection dynamics with immune chemokines and CTL mobility modulated by the infected cell density

We study a viral infection model incorporating both cell-to-cell infection and immune chemokines. Based on experimental results in the literature, we make a standing assumption that the cytotoxic T lymphocytes (CTL) will move toward the location with more infected cells, while the diffusion rate of CTL is a decreasing function of the density of infected cells. We first establish the global existence and ultimate boundedness of the solution via a priori energy estimates. We then define the basic reproduction number of viral infection R 0 and prove (by the uniform persistence theory, Lyapunov function technique and LaSalle invariance principle) that the infection-free steady state E 0 is globally asymptotically stable ifR 0 < 1 . WhenR 0 > 1 , then E 0 becomes unstable, and another basic reproduction number of CTL response R 1 becomes the dynamic threshold in the sense that ifR 1 < 1 , then the CTL-inactivated steady state E 1 is globally asymptotically stable; and ifR 1 > 1 , then the immune response is uniform persistent and, under an additional technical condition the CTL-activated steady state E 2 is globally asymptotically stable. To establish the global stability results, we need to prove point dissipativity, obtain uniform persistence, construct suitable Lyapunov functions, and apply the LaSalle invariance principle.

Global well-posedness and pattern formations of the immune system induced by chemotaxis

This paper studies a reaction-diffusion-advection system describing a directed movement of immune cells toward chemokines during the immune process. We investigate the global solvability of the model based on the bootstrap argument for minimal chemotaxis models. We also examine the stability of nonconstant steady states and the existence of periodic orbits from theoretical aspects of bifurcation analysis. Through numerical simulations, we observe the occurrence of steady or time-periodic pattern formations.

Integrative Computational Modeling of the Lymph Node Stromal Cell Landscape

Adaptive immune responses develop in secondary lymphoid organs such as lymph nodes (LNs) in a well-coordinated series of interactions between migrating immune cells and resident stromal cells. Although many processes that occur in LNs are well understood from an immunological point of view, our understanding of the fundamental organization and mechanisms that drive these processes is still incomplete. The aim of systems biology approaches is to unravel the complexity of biological systems and describe emergent properties that arise from interactions between individual constituents of the system. The immune system is greater than the sum of its parts, as is the case with any sufficiently complex system. Here, we review recent work and developments of computational LN models with focus on the structure and organization of the stromal cells. We explore various mathematical studies of intranodal T cell motility and migration, their interactions with the LN-resident stromal cells, and computational models of functional chemokine gradient fields and lymph flow dynamics. Lastly, we discuss briefly the importance of hybrid and multi-scale modeling approaches in immunology and the technical challenges involved.

Chemokine Transport Dynamics and Emerging Recognition of Their Role in Immune Function

Leukocyte migration is critically important during all protective and pathological immune and inflammatory responses. Chemokines play fundamental roles in this process, and chemokine concentration gradients stimulate the directional migration of leukocytes. The formation and regulation of these gradients is poorly understood. These are complex processes that depend on the specific properties of each chemokine and interactions between physical, biological and biochemical processes, including production, diffusion, advection, scavenging, post-translational modification, and extracellular matrix (ECM) binding. While some of these mechanisms have been investigated in isolation or limited combinations, more integrative research is required to provide a quantitative knowledge base that explains how chemokine gradients are established and maintained, and how cells respond to, and modify, these gradients.