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The authors have declared that no competing interests exist.

Conceived and designed the experiments: MBB JAP. Performed the experiments: MBB. Analyzed the data: MBB JAP. Contributed reagents/materials/analysis tools: MBB. Wrote the manuscript: MBB JAP.

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

Multiscale modeling is a broad class of hybrid modeling techniques that attempt to represent physical systems that span multiple spatial or time scales. Spatial and time scales are particularly interdependent in biological applications and there is increasing utility for multiscale models that capture this interdependency [

The hybrid nature of many multiscale models creates a need for software tools in which to implement the models. Different software packages offer unique strengths (e.g. R provides vast statistics capabilities [

Here, we present a novel software tool that fills a need in biomedical and biological multiscale modeling. The MATLAB-NetLogo extension (MatNet) provides new functions within NetLogo that allow data passing between NetLogo and MATLAB, and the calling of any valid, one-line MATLAB commands from within NetLogo. The need for this tool is demonstrated by publications that have used NetLogo and MATLAB (as the most appropriate software platforms) to implement biomedical multiscale models [

To demonstrate the utility of this tool, we present a multiscale model of

Here, we briefly describe the structure and processes of the ABM and refer the reader to our publicly-available model as well as corresponding citations for further details. The rules for the two-dimensional ABM of biofilm growth were implemented in NetLogo essentially as described by Pizarro et al. [

The key difference in our model from the Pizarro et al. formulation is a change from representative “food particles” to concentrations of all 105 extracellular metabolites used in the genome-scale metabolic network reconstruction of

The multiscale modeling of the biofilm is an iterative process involving analysis in MATLAB and NetLogo. First, constraints on exchange fluxes for the FBA problem in MATLAB are scaled to local nutrient concentrations. This simplifying assumption can be relaxed with more detailed flux constraints implemented as such data is available. However, these simplified constraints are sufficient to illustrate the value of the modeling tool presented here. After solving the FBA problem in MATLAB, local nutrient concentrations are calculated and returned, along with the growth rate, to the NetLogo environment. The nutrient concentrations are updated in NetLogo, agents with accumulated biomass divide in two and rearrange according to the shoving rule, nutrients diffuse, and the new nutrient concentrations are passed to MATLAB. These steps constitute one time step of the simulation, which simulates a 5 minute interval of biofilm growth. A single simulation of 200 time steps simulates biofilm growth over a period of ~17 hours.

Our implementation of the biofilm model in NetLogo displays the same behavior as the Pizarro et al. model (

Initial conditions simulating glucose minimal media were generated by including negative, non-zero lower bounds for the extracellular metabolite exchange reactions: Iron (Fe and Fe_{3+}), Oxygen (O_{2}), D-Glucose (C_{6}H_{12}O_{6}), Cadmium (Cd), Carbon Dioxide (CO_{2}), Sulfate (H_{2}O_{4}S), Copper (Cu), Water (H_{2}O), Manganese (Mn), Cobalt (Co), Ammonium (NH_{4}+), Sodium (Na), Nitrogen (N_{2}), Magnesium (Mg), Orthophosphate (H_{3}O_{4}P), and Zinc (Zn). For the anaerobic respiration simulation, an additional negative, non-zero lower bound was included for the Nitrate (HNO_{3}) exchange reaction. The metabolic model and accompanying constraints were previously described [

MatNet, example code, and the biofilm model are available from:

Simulations were performed on a 64-bit Sony Vaio laptop with 6 GB of RAM and a 2.8 GHz dual-core processor running Windows 7, NetLogo version 5.0.3 and MATLAB version 2012b. The duration of single simulations of biofilm growth ranged from 5 to 15 hours, depending on model settings.

MatNet was written in Java, utilizing the NetLogo Extensions API (

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.

Individual simulations were performed over 5 to 15 hours. We evaluated the computational time for each of the functions in a given simulation. A large fraction of the simulation run time is claimed by the metabolite diffusion simulations in NetLogo and the repeated FBA simulations in MATLAB. The slower run time of these steps is expected, given that both processes are called frequently during each time step, and both are computationally intensive. While an appreciable portion of the computational time was spent passing data between MATLAB and NetLogo, this computational time is attributable to the high frequency with which these functions were called. The passing of data between the two environments via MatNet did not add undue computational overhead. Among all the functions in the simulation, each MatNet function was listed among the fastest on a per-function-call basis.

The ABM correctly recapitulates oxygen-limited metabolic activity in a biofilm. Biofilm formation was simulated under glucose minimal media conditions. Metabolic activity was defined as an increase in biomass (> 0.01 mass dry weight) associated with a particular agent in the two-dimensional space. Metabolites were allowed to diffuse in from the top to mimic fresh media being washed over the biofilm as done by Pizarro et al [

(_{2} (near the surface) can cells actively synthesize protein. The multiscale model recapitulates this pattern of oxygen-limited metabolic activity throughout the biofilm.

Our multiscale model recapitulated increased biofilm growth rate in nitrate-supplemented media. Addition of nitrate (NO_{3}) to the _{3}) is reduced to dinitrogen (N_{2}), and nitrate replaces gaseous oxygen as the terminal electron acceptor. Anaerobic respiration prolongs active growth deeper in the biofilm after oxygen is removed from the microenvironment. The model prediction of increased growth rate was subsequently validated via literature search; Borriello et al. report increased biofilm growth with the addition of nitrate [

(_{3}) shows higher proportion of active cells when compared to glucose minimal media control (

An

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. Δ

We present the hybrid model results for nine models: wild-type, Δ

This model framework correctly recapitulated known biofilm characteristics and yielded useful predictions that may guide future experimental design. Future development of the models presented here could include an accounting of extracellular polymeric substances in the ABM [

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We thank our colleagues Joanna Goldberg, Shayn Peirce-Cottler, John Varga, Jennifer Bartell, and Phillip Yen for their helpful suggestions during the writing of this manuscript.