Novel multiscale modeling tool applied to Pseudomonas aeruginosa biofilm formation

Abstract

Multiscale modeling is used to represent biological systems with increasing frequency and success. Multiscale models are often hybrids of different modeling frameworks and programming languages. We present the MATLAB-NetLogo extension (MatNet) as a novel tool for multiscale modeling. We demonstrate the utility of the tool with a multiscale model of Pseudomonas aeruginosa biofilm formation that incorporates both an agent-based model (ABM) and constraint-based metabolic modeling. The hybrid model correctly recapitulates oxygen-limited biofilm metabolic activity and predicts increased growth rate via anaerobic respiration with the addition of nitrate to the growth media. In addition, a genome-wide survey of metabolic mutants and biofilm formation exemplifies the powerful analyses that are enabled by this computational modeling tool.

Figure 1. MATLAB-NetLogo Extension (MatNet) diagram and example code.

MATLAB and NetLogo are both Java-based applications and are able to pass data via the Java Serial library. The user is insulated from the details of data passing, and can call MATLAB functions (native or user-defined) from within NetLogo using simple commands. In the example above, a list of numbers is created in NetLogo and passed to MATLAB where the numbers are summed. The answer is retrieved from MATLAB and displayed in NetLogo.

Figure 2. Oxygen-dependent metabolic activity in P. aeruginosa biofilms.

(A) Progression of biofilm growth in a multiscale model with the associated time step (time steps represent 5 minute intervals). Each circle represents a cluster of P. aeruginosa cells. (B) Snapshot from multiscale biofilm model in glucose minimal media at time step 2000. (C) in vitro P. aeruginosa biofilm cross section grown in glucose MOPS media for four days (modified from Xu et al. [22]). The oxygen gradient through the biofilm limits metabolic activity. Only with high O₂ (near the surface) can cells actively synthesize protein. The multiscale model recapitulates this pattern of oxygen-limited metabolic activity throughout the biofilm.

Figure 3. ABM simulations of nitrate-dependent growth rates.

(A) Predicted biofilm formation in the presence of nitrate (NO₃) shows higher proportion of active cells when compared to glucose minimal media control (Figure 2). (B) Predicted biofilm growth with and without nitrate (3 independent runs each). Addition of nitrate is predicted to increase biofilm growth rate by enabling anaerobic growth deeper in the biofilm. Note that for simulations in glucose minimal media (blue lines), slower growth increases the impact of random cell spacing and resultant heterogeneous nutrient usage such that the model resulted in differing final cell counts for the same 15 hour simulation times.

Figure 4. Single-gene deletion screen.

Models of several single-deletion mutants were evaluated for biofilm formation after 200 time steps in nitrate-supplemented glucose minimal media. The wild-type (WT) model serves as a positive control. ΔlysS is known to be lethal, and provides a negative control. As such, the six initial cells seeded in the model never produced any additional biomass. (A) Snapshots of each multiscale simulation at time step 200. (B) Proportions of active and inactive biomass for each ABM at time step 200. ΔsdhD, ΔaceE and ΔatpD grew more slowly than wild-type. Δgcd and Δpgm appeared to have significant growth defects (final biomass only slightly more than that initially seeded). This screen is an example of a powerful analysis that is enabled by the multiscale simulations integrating spatial modeling with NetLogo and the metabolic network analysis performed in MATLAB.