A Mathematical Model of Stroma-Supported Allometric Tumor Growth.

Mounting empirical research suggests that the stroma, or interface between healthy and cancerous tissue, is a critical determinate of cancer invasion. At the same time, a cancer cell's location and potential to proliferate can influence its sensitivity to cancer treatments. In this paper, we use ordinary differential equations to develop spatially structured models for solid tumors wherein the growth of tumor components is coordinated. The model tumors feature two components, a proliferating peripheral growth region, which potentially includes a mix of cancerous and noncancerous stroma cells, and a solid tumor core. Mathematical and numerical analysis are used to investigate how coordinated expansion of the tumor growth region and core can influence overall growth dynamics in a variety of tumor types. Model assumptions, which are motivated by empirical and in silico solid tumor research, are evaluated through comparison to tumor volume data and existing models of tumor growth.

The impact of maturation time distributions on the structure and growth of cellular populations.

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.

A drift-diffusion checkpoint model predicts a highly variable and growth-factor-sensitive portion of the cell cycle G1 phase.

Even among isogenic cells, the time to progress through the cell cycle, or the intermitotic time (IMT), is highly variable. This variability has been a topic of research for several decades and numerous mathematical models have been proposed to explain it. Previously, we developed a top-down, stochastic drift-diffusion+threshold (DDT) model of a cell cycle checkpoint and showed that it can accurately describe experimentally-derived IMT distributions [Leander R, Allen EJ, Garbett SP, Tyson DR, Quaranta V. Derivation and experimental comparison of cell-division probability densities. J. Theor. Biol. 2014;358:129-135]. Here, we use the DDT modeling approach for both descriptive and predictive data analysis. We develop a custom numerical method for the reliable maximum likelihood estimation of model parameters in the absence of a priori knowledge about the number of detectable checkpoints. We employ this method to fit different variants of the DDT model (with one, two, and three checkpoints) to IMT data from multiple cell lines under different growth conditions and drug treatments. We find that a two-checkpoint model best describes the data, consistent with the notion that the cell cycle can be broadly separated into two steps: the commitment to divide and the process of cell division. The model predicts one part of the cell cycle to be highly variable and growth factor sensitive while the other is less variable and relatively refractory to growth factor signaling. Using experimental data that separates IMT into G1 vs. S, G2, and M phases, we show that the model-predicted growth-factor-sensitive part of the cell cycle corresponds to a portion of G1, consistent with previous studies suggesting that the commitment step is the primary source of IMT variability. These results demonstrate that a simple stochastic model, with just a handful of parameters, can provide fundamental insights into the biological underpinnings of cell cycle progression.

Modulation of Macrophage Inflammatory Nuclear Factor κB (NF-κB) Signaling by Intracellular Cryptococcus neoformans.

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 affects NF-κB signaling. Utilizing live cell imaging and computational 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 amplified and sustained. Mathematical simulations and quantification of nascent protein expression indicate that this is a possible consequence of Cn-induced "translational interference," impeding IκBα resynthesis. We also show that long term Cn infection induces stable nuclear localization of p65 and IκBα proteins in the absence of additional pro-inflammatory stimuli. In this case, nuclear localization of p65 is not accompanied by TNFα or inducible NOS (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.

Fine tuning inflammation at the front door: macrophage complement receptor 3-mediates phagocytosis and immune suppression for Francisella tularensis.

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-κB 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 pro-inflammatory 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 through outside-in signaling. CR3-linked immune suppression is an important mechanism involved in the pathogenesis of F. tularensis infection.

A mathematical model of CR3/TLR2 crosstalk in the context of Francisella tularensis infection.

Complement Receptor 3 (CR3) and Toll-like Receptor 2 (TLR2) are pattern recognition receptors expressed on the surface of human macrophages. Although these receptors are essential components for recognition by the innate immune system, pathogen coordinated crosstalk between them can suppress the production of protective cytokines and promote infection. Recognition of the virulent Schu S4 strain of the intracellular pathogen Francisella tularensis by host macrophages involves CR3/TLR2 crosstalk. Although experimental data provide evidence that Lyn kinase and PI3K are essential components of the CR3 pathway that influences TLR2 activity, additional responsible upstream signaling components remain unknown. In this paper we construct a mathematical model of CR3 and TLR2 signaling in response to F. tularensis. After demonstrating that the model is consistent with experimental results we perform numerical simulations to evaluate the contributions that Akt and Ras-GAP make to ERK inhibition. The model confirms that phagocytosis-associated changes in the composition of the cell membrane can inhibit ERK activity and predicts that Akt and Ras-GAP synergize to inhibit ERK.