Analytical approach for the Floquet theory of delay differential equations

We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To this end we start with approximately determining such reference states by extending the Poincaré-Lindstedt and the Shohat expansions, which were originally developed for ordinary differential equations. Then we systematically elaborate a linear stability analysis around a time periodic reference state. This allows us to approximately calculate the Floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions.

IL-12 is dispensable for innate and adaptive immunity against low doses of Listeria monocytogenes

We have studied IL-12p35-deficient (IL-12p35(-/-)) mice to evaluate the role of IL-12 in resistance against Listeria monocytogenes. In the absence of bioactive IL-12p75, mutant mice acquired higher bacterial organ burden than wild-type mice and died during the first week following infection with normally sublethal doses of Listeria. Moreover, blood IFN-gamma levels were strikingly reduced in mutant mice at day 2 post-infection. These results suggest that in IL-12p35-deficient mice impaired production of IFN-gamma which is crucial for activation of listericidal effector functions of macrophages leads to defective innate immunity against Listeria. In contrast to mice deficient for IFN-gamma or IFN-gamma receptor which are unable to resist very low infection doses of Listeria, IL-12p35(-/-) mice resisted up to 1000 c.f.u. and were able to eliminate Listeria. Spleen cells from mutant mice re-stimulated with heat-killed Listeria produced considerable amounts of IFN-gamma, suggesting that at low dose infection sufficient IFN-gamma is produced independently of IL-12. Subsequent challenge of these immunized mice with high doses of L. monocytogenes resulted in sterile elimination demonstrating efficient memory responses. These results demonstrate for the first time that at low doses of Listeria IL-12 is neither critical for innate immunity nor for the development of protective T cell-dependent acquired immunity.

Interleukin-12 is essential for a protective Th1 response in mice infected with Cryptococcus neoformans

To analyze the roles of interleukin-12 (IL-12) and the IL-12-dependent Th1 response in resistance to Cryptococcus neoformans, we have established a chronic infection model in wild-type mice and in mice with targeted disruptions of the genes for the IL-12p35 and IL-12p40 subunits (IL-12p35(-/-) and IL-12p40(-/-) mice, respectively) as well as in mice with a targeted disruption of the IL-4 gene. Long-term application of exogenous IL-12 prevented death of infected wild-type mice for the entire period of the experiment (up to 180 days) but did not resolve the infection. Infected IL-12p35(-/-) and IL-12p40(-/-) mice died significantly earlier than infected wild-type mice, whereas infection of IL-4-deficient mice led to prolonged survival. Interestingly, infected IL-12p40(-/-) mice died earlier and developed higher organ burdens than IL-12p35(-/-) mice, which, for the first time in an infection model, suggests a protective role of the IL-12p40 subunit independent of the IL-12 heterodimer. The fungal organ burdens of IL-4-deficient mice and IL-12-treated wild-type mice were significantly reduced compared to those of untreated wild-type mice and IL-12-deficient mice. Histopathological analysis revealed reduction of the number of granulomatous lesions following treatment with IL-12. Susceptibility of both IL-12p35(-/-) and IL-12p40(-/-) mice was associated with marginal production of gamma interferon and elevated levels of IL-4 from CD4(+) T cells, which indicates Th2 polarization in the absence of IL-12, whereas wild-type mice developed a Th1 response. Taken together, our data emphasize the essential role of IL-12 for protective Th1 responses against C. neoformans.