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Impulse control problems, in which a continuously evolving state is modified by discrete control actions, have applications in epidemiology, medicine, and ecology. In this paper, we present a simple method for solving impulse control problems for systems of differential equations. In particular, we show how impulse control problems can be reformulated and solved as discrete optimal control problems. The method is illustrated with two examples. Published 2014. This article has been contributed to by US Government employees and their work is in the public domain in the USA. [ABSTRACT FROM AUTHOR]

Complement receptor 3 (CR3, CD11b/CD18) is a major macrophage phagocytic receptor. The biochemical pathways through which CR3 regulates immunologic responses have not been fully characterized. Francisella tularensis is a remarkably infectious, facultative intracellular pathogen of macrophages that causes tularemia. Early evasion of the host immune response contributes to the virulence of F. tularensis and CR3 is an important receptor for its phagocytosis. Here we confirm that efficient attachment and uptake of the highly virulent Type A F. tularensis spp. tularensis strain Schu S4 by human monocyte-derived macrophages (hMDMs) requires complement C3 opsonization and CR3. However, despite a >40-fold increase in uptake following C3 opsonization, Schu S4 induces limited pro-inflammatory cytokine production compared with non-opsonized Schu S4 and the low virulent F. novicida. This suggests that engagement of CR3 by opsonized Schu S4 contributes specifically to the immune suppression during and shortly following phagocytosis which we demonstrate by CD11b siRNA knockdown in hMDMs. This immune suppression is concomitant with early inhibition of ERK1/2, p38 MAPK and NF-kB activation. Furthermore, TLR2 siRNA knockdown shows that pro-inflammatory cytokine production and MAPK activation in response to non-opsonized Schu S4 depends on TLR2 signaling providing evidence that CR3-TLR2 crosstalk mediates immune suppression for opsonized Schu S4. Deletion of the CD11b cytoplasmic tail reverses the CR3-mediated decrease in ERK and p38 activation during opsonized Schu-S4 infection. The CR3-mediated signaling pathway involved in this immune suppression includes Lyn kinase and Akt activation, and increased MKP-1, which limits TLR2-mediated proinflammatory responses. These data indicate that while the highly virulent F. tularensis uses CR3 for efficient uptake, optimal engagement of this receptor down-regulates TLR2-dependent pro-inflammatory responses by inhibiting MAPK activation though outside-in signaling. CR3-linked immune suppression is an important mechanism involved in the pathogenesis of F. tularensis infection. [ABSTRACT FROM AUTHOR]

Cryptococcus neoformans (Cn) is a common facultative intracellular pathogen that can cause life-threatening fungal meningitis in immunocompromised individuals. Shortly after infection, Cn is detectable as both extra- and intracellular yeast particles, with Cn being capable of establishing long-lasting latent infections within host macrophages. Although recent studies have shown that shed capsular polysaccharides and intact extracellular Cn can compromise macrophage function through modulation of NF-κB signaling, it is currently unclear whether intracellular Cn also affectsNF-κBsignaling. Utilizing live cell imaging andcomputational modeling, we find that extra- and intracellular Cn support distinct modes of NF-κB signaling in cultured murine macrophages. Specifically, in RAW 264.7 murine macrophages treated with extracellular glucuronoxylomannan (GXM), the major Cn capsular polysaccharide, LPS-induced nuclear translocation of p65 is inhibited, whereas in cells with intracellular Cn, LPS-induced nuclear translocation of p65 is both amplifiedandsustained. Mathematical simulations and quantification of nascent protein expression indicate that this is a possible consequence of Cn-induced "translational interference," impeding IκB resynthesis. We also show that long term Cn infection induces stable nuclear localization of p65 and IκB proteins in the absence of additional proinflammatory stimuli. In this case, nuclear localization of p65 is not accompaniedbyTNFor inducibleNOS(iNOS)expression. These results demonstrate that capsular polysaccharides and intact intracellular yeast manipulate NF-κB via multiple distinct mechanisms and provide new insights into how Cn might modulate cellular signaling at different stages of an infection. [ABSTRACT FROM AUTHOR]

Here we study how the structure and growth of a cellular population vary with the distribution of maturation times from each stage. We consider two cell cycle stages. The first represents early G1. The second includes late G1, S, G2, and mitosis. Passage between the two reflects passage of an important cell cycle checkpoint known as the restriction point. We model the population as a system of partial differential equations. After establishing the existence of solutions, we characterize the maturation rates and derive the steady-state age and stage distributions as well as the asymptotic growth rates for models with exponential and inverse Gaussian maturation time distributions. We find that the stable age and stage distributions, transient dynamics, and asymptotic growth rates are substantially different for these two maturation models. We conclude that researchers modeling cellular populations should take care when choosing a maturation time distribution, as the population growth rate and stage structure can be heavily impacted by this choice. Furthermore, differences in the models' transient dynamics constitute testable predictions that can help further our understanding of the fundamental process of cellular proliferation. We hope that our numerical methods and programs will provide a scaffold for future research on cellular proliferation.