An Agent-Based Model of Cellular Dynamics and Circadian Variability in Human Endotoxemia

<div><p>As cellular variability and circadian rhythmicity play critical roles in immune and inflammatory responses, we present in this study an agent-based model of human endotoxemia to examine the interplay between circadian controls, cellular variability and stochastic dynamics of inflammatory cytokines. The model is qualitatively validated by its ability to reproduce circadian dynamics of inflammatory mediators and critical inflammatory responses after endotoxin administration <em>in vivo</em>. Novel computational concepts are proposed to characterize the cellular variability and synchronization of inflammatory cytokines in a population of heterogeneous leukocytes. Our results suggest that there is a decrease in cell-to-cell variability of inflammatory cytokines while their synchronization is increased after endotoxin challenge. Model parameters that are responsible for IκB production stimulated by NFκB activation and for the production of anti-inflammatory cytokines have large impacts on system behaviors. Additionally, examining time-dependent systemic responses revealed that the system is least vulnerable to endotoxin in the early morning and most vulnerable around midnight. Although much remains to be explored, proposed computational concepts and the model we have pioneered will provide important insights for future investigations and extensions, especially for single-cell studies to discover how cellular variability contributes to clinical implications.</p> </div

Dynamics patterns of selected components under circadian control.

<p>Circadian control is regulated by the rhythms of cortisol (F) and melatonin (M), which in turn drive the patterns of other components in the system. Pro-inflammatory cytokines (P), driven by melatonin secretion, are up-regulated to peak around ∼4:00AM whereas anti-inflammatory cytokines (A) are down regulated due to the increase of pro-inflammatory cytokines and then up-regulated under the effects of cortisol rhythms. These behaviors result in the circadian variation of bio-energetic proteins (E) and others.</p

Model components.

*<p>the initial corresponding number of molecules within a cell; ^$: the status of P, A, F, and M change to active when they are imported to the cytoplasm (cells) or brain compartment</p

Cellular variability and synchronization behaviors.

<p>The top-panel displays the pattern of variability-based fitness of a simulated day in the homeostatic system and of the day where endotoxin is treated at 9:00AM. Two parallel curves present corresponding standard errors of N simulations (N = 100 in this study). The bottom panel shows the synchronization level of specific behaviors among all cells of the system in the interval [t – 3 hr, t], t = 3, 6…24 hr. The error bars are corresponding standard errors of N simulations.</p

Correspondence between <i>in vivo-</i> and <i>in silico-</i> system responses to endotoxin.

<p>The left-panel presents average expression patterns of critical inflammatory responses under endotoxin treatment at 9:00AM. Early-up (red) and middle-up (black) patterns are characterized for pro-inflammatory responses, late-up pattern (magenta) for anti-inflammatory responses, and down pattern (green) for energetic responses. The right-panel displays corresponding simulated responses. The patterns between <i>in vivo-</i> and <i>in silico-</i> responses are matched to define the time-scale for the system.</p

Effects of production parameters on system behaviors.

*<p>decrease/increase 75% of the current value; if greater than 1.0, set to 1.0.</p

Model production parameters.

*<p>x (Y Z): x is the probability that a single unit Y can produce an individual unit Z when Y is in the nucleus (or brain) compartment.</p

<i>In silico</i> human endotoxemia model accounting for circadian variability.

<p>(a) The rule system representation. At the cellular level, molecular interactions involve the propagation of LPS signaling on the transcriptional response level (P, A, E) through the activation of NF-kB signaling module. At the systemic level, circulating stress hormones are released from the neuro-endocrine system coupled with their circadian rhythms. The dynamics of cortisol (F) and melatonin (M) signaling from the systemic level involve molecular behaviors at the cellular level. The activities of each agent are characterized by its corresponding color. (b) A snapshot of the implemented model. Molecules are displayed with solid circles (P: red-; A: magenta-; F: blue-; M: cyan-; NFkB: yellow-; E: green-; TLR & GR: white-; IkB, IKK, NFkB.IkB: black- circles). Cells are displayed with solid squares where green squares represent for cells with an approximate number of P and A, red squares for those with the number of P greater than 1.5 fold of the number of A and magenta squares for those with A more than 1.5 fold of P.</p

Stochastic dynamics in cell population.

<p>The stochastic behaviors of pro-inflammatory cytokines (a) and anti-inflammatory cytokines (b) in three different cells are shown in the top-panel. Although cellular patterns are different from cell to cell and from day to day, the average pattern still exhibits some daily common pattern. The dynamics of the homeostatic system in a simulated day are present in (c). Cells are displayed with solid squares where green squares represent for cells with an approximate number of P and A, red squares for those with the number of P much greater than the number of A and magenta squares for those with A >> P.</p