Competition between transients in the rate of approach to a fixed point

Dynamical systems studies of differential equations often focus on the behavior of solutions near critical points and on invariant manifolds, to elucidate the organization of the associated flow. In addition, effective methods, such as the use of Poincare maps and phase resetting curves, have been developed for the study of periodic orbits. However, the analysis of transient dynamics associated with solutions on their way to an attracting fixed point has not received much rigorous attention. This paper introduces methods for the study of such transient dynamics. In particular, we focus on the analysis of whether one component of a solution to a system of differential equations can overtake the corresponding component of a reference solution, given that both solutions approach the same stable node. We call this phenomenon tolerance, which derives from a certain biological effect. Here, we establish certain general conditions, based on the initial conditions associated with the two solutions and the properties of the vector field, that guarantee that tolerance does or does not occur in two-dimensional systems. We illustrate these conditions in particular examples, and we derive and demonstrate additional techniques that can be used on a case by case basis to check for tolerance. Finally, we give a full rigorous analysis of tolerance in two-dimensional linear systems.Comment: Resolution on the figures of the paper has been reduced to conserve file space. Animation files are viewable at: http://people.mbi.ohio-state.edu/jday/Tol_Animations.htm

Cellular Mechanisms That Cause Suppressed Gamma Interferon Secretion in Endotoxin-Tolerant Mice

Endotoxin (lipopolysaccharide [LPS]) tolerance is a state of altered immunity characterized, in part, by suppression of LPS-induced gamma interferon (IFN-γ) expression. However, the cellular mediators regulating LPS-induced production of IFN-γ in normal mice and the effect of LPS tolerance on these mediators has not been well characterized. Our studies show that macrophage dysfunction is the primary factor causing suppressed IFN-γ expression in LPS-tolerant mice. Specifically, LPS-tolerant macrophages have a markedly impaired ability to induce IFN-γ secretion by T cells and NK cells obtained from either control or LPS-tolerant mice. However, T cells and NK cells isolated from LPS-tolerant mice produce normal levels of IFN-γ when cocultured with control macrophages or exogenous IFN-γ-inducing factors. Assessment of important IFN-γ-regulating factors showed that interleukin-12 (IL-12) and costimulatory signals provided by IL-15, IL-18, and CD86 are largely responsible for LPS-induced IFN-γ expression in control mice. IL-10 is an inhibitor of IFN-γ production in both the control and LPS-tolerant groups. Expression of IL-12 and the IL-12 receptor β1 (IL-12Rβ1) and IL-12Rβ2 subunits are suppressed in the spleens of LPS-tolerant mice. LPS-tolerant splenocytes also exhibit decreased production of IL-15 and IL-15Rα. However, expression of IL-18 and the B7 proteins CD80 and CD86 are unchanged or increased compared to controls after induction of LPS tolerance. CD28, a major receptor for B7 proteins, is also increased in the spleens of LPS-tolerant mice. Expression of the inhibitory cytokine IL-10 and the IL-10R are sustained after induction of LPS tolerance. These data show that suppression of IFN-γ production in LPS-tolerant mice is largely due to macrophage dysfunction and provide insight into the cellular alterations that occur in LPS tolerance. This study also better defines the factors that mediate LPS-induced IFN-γ production in normal mice

CpG oligodeoxynucleotides promote the host protective response against infection with Cryptococcus neoformans through induction of interferon-gamma production by CD4(+) T cells

In the present study, we elucidated the effect of synthetic CpG-containing oligodeoxynucleotides (ODN) on pulmonary and disseminated infection caused by Cryptococcus neoformans. CDF-1 mice were inoculated intratracheally with a highly virulent strain of this pathogen, which resulted in massive bacterial growth in the lung, dissemination to the brain and death. Administration of CpG-ODN promoted the clearance of C. neoformans in the lungs, decreased their dissemination to brain and prolonged the survival of infected mice. These effects correlated well with the enhanced production of interleukin (IL)-12 and interferon (IFN)-γ and attenuated secretion of IL-4 in bronchoalveolar lavage fluids (BALF) and promoted development of Th1 cells, as indicated by the increased production of IFN-γ by paratracheal lymph node cells upon restimulation with cryptococcal antigens. The IFN-γ synthesis in BALF was inhibited by depletion of CD8(+) and CD4(+) T cells on days 7 and 14 after infection, respectively, but not by depletion of NK and γδ T cells. Consistent with these data, intracellular expression of IFN-γ was detected predominantly in CD8(+) and CD4(+) T cells in the lung on days 7 and 14, respectively. The protective effect of CpG-ODN, as shown by the prolonged survival, was completely and partially inhibited by depletion of CD4(+) or CD8(+) T cells, respectively, but not by depletion of other cells. Finally, TNF-α was markedly induced by CpG-ODN, and the protective effect of this agent was strongly inhibited by neutralizing anti-TNF-α MoAb. Our results indicate that CpG-ODN alters the Th1–Th2 cytokine balance and promotes host resistance against infection with C. neoformans