Multi-scale, Multi-cellular simulations of nutrient limitation effects on

It has been previously shown that nutrient limitation and cell culture density affect the propensity of B. subtilis cells to enter the competent state [17]. Our goal was to leverage the intracellular model into a multi-scale model of both intra- and inter-cellular interactions, to examine the cellular population level effects on competence. The model consists of two layers--an intracellular layer and an extracellular layer. The first layer consists of the intracellular model previously described (Within-Cell Model, Figure 5.4). The second layer consists of cell agents representing the whole cell's interaction with extracellular environmental factors such as nutrients and the quorum sensing pheromones (Culture Model, Figure 5.4).

Thus, the model is a multi-scale ABM consisting of an overall ABM of agent ABMs running within it.

To model nutrients and quorum sensing pheromones in the extracellular environment, diffusion equation layers were used (Nutrient and Peptide Layers, Figure 5.4). One of the layers represents the local concentration of the ComX pheromone, an intracellular signaling molecule that is involved in quorum sensing and regulation of the competence circuit (Figure 5.2). The Cell agents produce and consume ComX throughout the simulation. Consumption of ComX by a Cell agent

decreases its concentration at the culture level, while resulting in the creation of a new ComX agent in the intracellular ABM. Likewise, the ComX peptide is produced at a constant intracellular rate [96] and is transferred stochastically to the

extracellular environment for uptake by other cells (details in Materials and

Methods). As concentrations of cell agents grow, extracellular ComX concentrations increase, thereby increasing the likelihood of ComX uptake by other cells.

Figure 5.4. The multi-scale agent based model of competence, representing both the intracellular pathways (bottom) and the multicellular environment (top). There are two layers that represent the ComX quorum sensing pheromone and nutrient concentrations.

A second layer represents consumable nutrients required for cell growth and division in the model. Cell agents at the culture level consume nutrients from the nutrient layer, depleting the quantity available in the nutrient layer. The consumption of a nutrient molecule is input to the cell growth equation, based on the Logistic Map equation, that governs growth and division (Methods and Materials). The cellular agents could divide if sufficient growth has occurred according to the equation. As the cell agents grow and divide, daughter agents are placed at a randomly

determined adjacent location to the parent. If there is not a free adjacent location, agents are "shoved" to the side to make room for the new cell agent. When nutrients become depleted at a Cell Agent's location, the agent will move in the direction of an increasing nutrient gradient if present, or move randomly otherwise, simulating chemotaxis. If insufficient nutrients are present, a Cell Agent's probability of death is increased. In addition, these starvation conditions are transferred to the intracellular model by reducing the number of agents that repress comK and comS

transcription, Figure 5.2. In this manner, extracellular environmental conditions influence the intracellular conditions, and intracellular conditions feed back upon the environment and other agents within it.

Like the intracellular model, the multi-scale model agents are placed

randomly in a 2-D grid environment. However, in this case the initial concentrations of ComK, ComS, and ComX agents for the intracellular models are randomly

determined within pre-defined threshold levels (Materials and Methods). There are no ComK mRNA agents placed at the start of a model run, but these agents can be generated via transcription during a simulation.

Since individual simulations would often result in distinct outcomes, we ran the model repeatedly to obtain average statistics for competence-switching behavior. Out of 6 simulations, the model typically reached an average of 867 cells. We necessarily limited the available “plate size” and nutrient concentration for culture growth to limit the computing to feasible time spans. For each of the cell agents, a complete intracellular model was running, which meant that a full simulation running on a fast desktop computer may take three weeks or more to complete. Improved parallelism may reduce run times in the future.

Figure 5.5. A) Growth curve of modeled cell culture. 1-lag phase, 2-exponential growth phase, 3-stationary phase and 4-death phase. B) 2-D agent-based model showing nutrient (green) consumption by cell models (blue) early in the growth phase of the culture. C) A view of the intra-cellular ABM.

Figure 5.5a shows the growth curve for an example multi-scale simulation, with the resulting count of competent cells as they switched to the competence phenotype. In an example simulation, the model was run with an initial seed of 20 randomly placed cell agents that grew to a maximum of about 865 cell agents, with 160 exhibiting the competence phenotype (18.5%) by the end of stationary phase (Figure 5.5a). Execution halted within the death phase of the growth curve after approximately 43,000 iterations. Figure 5.5b shows a snapshot of the simulation, with the blue dots representing cell agents running an independent intracellular ABM. The nutrient gradient is represented in green, with the lighter shade indicating a full nutrient concentration and transitions to darker green indicating nutrient

depletion.

The model resulted in classical bacterial growth curves with the standard phases of bacterial culture: lag phase, exponential growth phase, stationary phase, and death phase (Figure 5.5a). It has been shown in vitro that competence begins to emerge in abundance during stationary growth phase [17]. As shown in Figure 5.5a, the model demonstrated similar emergence of competence during stationary phase, even though there was no explicit programming instructing it to do so. After cell division ceased due to nutrient limitation, ComK transcripts and protein

accumulation increased the likelihood of competence transition. Out of 6 simulations, the intracellular B. subtilis ABM demonstrated the emergence of 16.3% (on average) competent cells by the end of stationary phase. This compares with in