Semantically Linking In Silico Cancer Models

Multiscale models are commonplace in cancer modeling, where individual models acting on different biological scales are combined within a single, cohesive modeling framework. However, model composition gives rise to challenges in understanding interfaces and interactions between them. Based on specific domain expertise, typically these computational models are developed by separate research groups using different methodologies, programming languages, and parameters. This paper introduces a graph-based model for semantically linking computational cancer models via domain graphs that can help us better understand and explore combinations of models spanning multiple biological scales. We take the data model encoded by TumorML, an XML-based markup language for storing cancer models in online repositories, and transpose its model description elements into a graph-based representation. By taking such an approach, we can link domain models, such as controlled vocabularies, taxonomic schemes, and ontologies, with cancer model descriptions to better understand and explore relationships between models. The union of these graphs creates a connected property graph that links cancer models by categorizations, by computational compatibility, and by semantic interoperability, yielding a framework in which opportunities for exploration and discovery of combinations of models become possible

Bistability and Bacterial Infections

Bacterial infections occur when the natural host defenses are overwhelmed by invading bacteria. The main component of the host defense is impaired when neutrophil count or function is too low, putting the host at great risk of developing an acute infection. In people with intact immune systems, neutrophil count increases during bacterial infection. However, there are two important clinical cases in which they remain constant: a) in patients with neutropenic-associated conditions, such as those undergoing chemotherapy at the nadir (the minimum clinically observable neutrophil level); b) in ex vivo examination of the patient's neutrophil bactericidal activity. Here we study bacterial population dynamics under fixed neutrophil levels by mathematical modelling. We show that under reasonable biological assumptions, there are only two possible scenarios: 1) Bacterial behavior is monostable: it always converges to a stable equilibrium of bacterial concentration which only depends, in a gradual manner, on the neutrophil level (and not on the initial bacterial level). We call such a behavior type I dynamics. 2) The bacterial dynamics is bistable for some range of neutrophil levels. We call such a behavior type II dynamics. In the bistable case (type II), one equilibrium corresponds to a healthy state whereas the other corresponds to a fulminant bacterial infection. We demonstrate that published data of in vitro Staphylococcus epidermidis bactericidal experiments are inconsistent with both the type I dynamics and the commonly used linear model and are consistent with type II dynamics. We argue that type II dynamics is a plausible mechanism for the development of a fulminant infection

The bifurcation diagram: the bacterial equilibrium points (EPs) as a function of neutrophil concentration.

<p>Solid line indicates a branch of stable EPs, and dashed line indicates a branch of unstable EPs. (<b>a</b>) Type I dynamic has a unique stable branch of EPs for all values. The black arrows demonstrate that for any positive initial value of the bacteria, for any , converges to the corresponding unique stable EP (the intersection of the solid black curve with a vertical line). Bifurcation diagram is drawn for Eq. (1) with (<b>b</b>) Type II dynamic has a region of bistability: when , the final state of depends on whether the initial bacterial concentration is above or below the critical bacterial curve of unstable EPs (dashed line). The bifurcation diagram is drawn for Eq. (1) with . (<b>c–d</b>) Time plots of the two initial bacterial concentrations notated by red up and blue down arrows in (b) for a fixed value (notice the different time scales).</p

Bifurcation diagrams with zero and small positive bacterial influx.

<p>Bifurcation curves for Infx  =  are shown in black, magenta and green, respectively. When Infx , the bifurcation curves are shifted to the right. (<b>a</b>) Type I: the zero Infx transcritical bifurcation point at disappears when . (<b>b</b>) Type II: the zero Infx transcritical bifurcation becomes a saddle-node bifurcation that appears at a distance from the transcritical bifurcation point (see Bacterial Influx). (<b>Insert</b>) A close-up around the transcritical bifurcation of (b). This diagram shows that under perturbation (Infx), the transcritical bifurcation becomes a saddle-node bifurcation.</p

The natural bacterial parameter space division into type I and type II dynamics.

<p>The behavior type is found from the derived analytical conditions (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0010010#s2" target="_blank">Methods</a>) for fixed killing-term parameters as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0010010#pone-0010010-g001" target="_blank">Fig. 1</a> (. Notably, most of the parameters give rise to type II behavior. (<b>a</b>) The space is shown for . (<b>b</b>) The space is shown for . The grey region is forbidden, as it corresponds to a reduction in the bacterial population even with no neutrophils, violating A1.</p

Experimental support for the model prediction of bistability.

<p>(<b>a</b>) A phase-space presentation of the data from Li et. al. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0010010#pone.0010010-Li2" target="_blank">[12]</a>. In this experiment, neutrophils and <i>S. epidermidis</i> bacteria were added into a gel and the bacteria were recovered after 90 min. The tail of each of the arrows indicates the bacterial concentration at and the head indicates the concentration at min. Dashed colored lines: the initial bacterial concentrations. Solid colored lines: the corresponding final bacterial concentrations (connecting the corresponding data points). The black bold-dashed line is the estimated critical curve between neutrophil killing and bacterial growth rate. (<b>b</b>) The type II model (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0010010#pone-0010010-g001" target="_blank">Fig. 1b</a>) bifurcation diagram in logarithmic scale.</p