The Cellular-Potts model is a powerful and ubiquitous framework for developing computational models for simulating complex multicellular biological systems. Cellular-Potts models (CPMs) are often computationally expensive due to the explicit modeling of interactions among large numbers of individual model agents and diffusive fields described by partial differential equations (PDEs). In this work, we develop a convolutional neural network (CNN) surrogate model using a U-Net architecture that accounts for periodic boundary conditions. We use this model to accelerate the evaluation of a mechanistic CPM previously used to investigate in vitro vasculogenesis. The surrogate model was trained to predict 100 computational steps ahead (Monte-Carlo steps, MCS), accelerating simulation evaluations by a factor of 562 times compared to single-core CPM code execution on CPU. Over short timescales of up to 3 recursive evaluations, or 300 MCS, our model captures the emergent behaviors demonstrated by the original Cellular-Potts model such as vessel sprouting, extension and anastomosis, and contraction of vascular lacunae. This approach demonstrates the potential for deep learning to serve as a step toward efficient surrogate models for CPM simulations, enabling faster evaluation of computationally expensive CPM simulations of biological processes.

With the generation of spatially resolved transcriptomics of microbial biofilms, computational tools can be used to integrate this data to elucidate the multi-scale mechanisms controlling heterogeneous biofilm metabolism. This work presents a Multi-scale model of Metabolism In Cellular Systems (MiMICS) which is a computational framework that couples a genome-scale metabolic network reconstruction (GENRE) with Hybrid Automata Library (HAL), an existing agent-based model and reaction-diffusion model platform. A key feature of MiMICS is the ability to incorporate multiple -omics-guided metabolic models, which can represent unique metabolic states that yield different metabolic parameter values passed to the extracellular models. We used MiMICS to simulate Pseudomonas aeruginosa regulation of denitrification and oxidative stress metabolism in hypoxic and nitric oxide (NO) biofilm microenvironments. Integration of P. aeruginosa PA14 biofilm spatial transcriptomic data into a P. aeruginosa PA14 GENRE generated four PA14 metabolic model states that were input into MiMICS. Characteristic of aerobic, denitrification, and oxidative stress metabolism, the four metabolic model states predicted different oxygen, nitrate, and NO exchange fluxes that were passed as inputs to update the agent's local metabolite concentrations in the extracellular reaction-diffusion model. Individual bacterial agents chose a PA14 metabolic model state based on a combination of stochastic rules, and agents sensing local oxygen and NO. Transcriptome-guided MiMICS predictions suggested microscale denitrification and oxidative stress metabolic heterogeneity emerged due to local variability in the NO biofilm microenvironment. MiMICS accurately predicted the biofilm's spatial relationships between denitrification, oxidative stress, and central carbon metabolism. As simulated cells responded to extracellular NO, MiMICS revealed dynamics of cell populations heterogeneously upregulating reactions in the denitrification pathway, which may function to maintain NO levels within non-toxic ranges. We demonstrated that MiMICS is a valuable computational tool to incorporate multiple -omics-guided metabolic models to mechanistically map heterogeneous microbial metabolic states to the biofilm microenvironment.

[This corrects the article DOI: 10.1371/journal.pcbi.1010701.].

Antibiotic resistance poses mounting risks to human health, as current antibiotics are losing efficacy against increasingly resistant pathogenic bacteria. Of particular concern is the emergence of multidrug-resistant strains, which has been rapid among Gram-negative bacteria such as Escherichia coli. A large body of work has established that antibiotic resistance mechanisms depend on phenotypic heterogeneity, which may be mediated by stochastic expression of antibiotic resistance genes. The link between such molecular-level expression and the population levels that result is complex and multi-scale. Therefore, to better understand antibiotic resistance, what is needed are new mechanistic models that reflect single-cell phenotypic dynamics together with population-level heterogeneity, as an integrated whole. In this work, we sought to bridge single-cell and population-scale modeling by building upon our previous experience in "whole-cell" modeling, an approach which integrates mathematical and mechanistic descriptions of biological processes to recapitulate the experimentally observed behaviors of entire cells. To extend whole-cell modeling to the "whole-colony" scale, we embedded multiple instances of a whole-cell E. coli model within a model of a dynamic spatial environment, allowing us to run large, parallelized simulations on the cloud that contained all the molecular detail of the previous whole-cell model and many interactive effects of a colony growing in a shared environment. The resulting simulations were used to explore the response of E. coli to two antibiotics with different mechanisms of action, tetracycline and ampicillin, enabling us to identify sub-generationally-expressed genes, such as the beta-lactamase ampC, which contributed greatly to dramatic cellular differences in steady-state periplasmic ampicillin and was a significant factor in determining cell survival.

MOTIVATION: This article introduces Vivarium-software born of the idea that it should be as easy as possible for computational biologists to define any imaginable mechanistic model, combine it with existing models and execute them together as an integrated multiscale model. Integrative multiscale modeling confronts the complexity of biology by combining heterogeneous datasets and diverse modeling strategies into unified representations. These integrated models are then run to simulate how the hypothesized mechanisms operate as a whole. But building such models has been a labor-intensive process that requires many contributors, and they are still primarily developed on a case-by-case basis with each project starting anew. New software tools that streamline the integrative modeling effort and facilitate collaboration are therefore essential for future computational biologists. RESULTS: Vivarium is a software tool for building integrative multiscale models. It provides an interface that makes individual models into modules that can be wired together in large composite models, parallelized across multiple CPUs and run with Vivarium's discrete-event simulation engine. Vivarium's utility is demonstrated by building composite models that combine several modeling frameworks: agent-based models, ordinary differential equations, stochastic reaction systems, constraint-based models, solid-body physics and spatial diffusion. This demonstrates just the beginning of what is possible-Vivarium will be able to support future efforts that integrate many more types of models and at many more biological scales. AVAILABILITY AND IMPLEMENTATION: The specific models, simulation pipelines and notebooks developed for this article are all available at the vivarium-notebooks repository: https://github.com/vivarium-collective/vivarium-notebooks. Vivarium-core is available at https://github.com/vivarium-collective/vivarium-core, and has been released on Python Package Index. The Vivarium Collective (https://vivarium-collective.github.io) is a repository of freely available Vivarium processes and composites, including the processes used in Section 3. Supplementary Materials provide with an extensive methodology section, with several code listings that demonstrate the basic interfaces. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Physiological and pathological processes including embryogenesis and tumorigenesis rely on the ability of individual cells to work collectively to form multicell patterns. In these heterogeneous multicell systems, cell-cell signaling induces differential adhesion between cells that leads to tissue-level patterning. However, the sensitivity of pattern formation to changes in the strengths of signaling or cell adhesion processes is not well understood. Prior work has explored these issues using synthetically engineered heterogeneous multicell spheroid systems, in which cell subpopulations engage in bidirectional intercellular signaling to regulate the expression of different cadherins. While engineered cell systems provide excellent experimental tools to observe pattern formation in cell populations, computational models of these systems may be leveraged to explore more systematically how specific combinations of signaling and adhesion parameters can drive the emergence of unique patterns. We developed and validated two- and three-dimensional agent-based models (ABMs) of spheroid patterning for previously described cells engineered with a bidirectional signaling circuit that regulates N- and P-cadherin expression. Systematic exploration of model predictions, some of which were experimentally validated, revealed how cell seeding parameters, the order of signaling events, probabilities of induced cadherin expression, and homotypic adhesion strengths affect pattern formation. Unsupervised clustering was also used to map combinations of signaling and adhesion parameters to these unique spheroid patterns predicted by the ABM. Finally, we demonstrated how the model may be deployed to design new synthetic cell signaling circuits based on a desired final multicell pattern.

Skeletal muscle possesses a remarkable capacity for repair and regeneration following a variety of injuries. When successful, this highly orchestrated regenerative process requires the contribution of several muscle resident cell populations including satellite stem cells (SSCs), fibroblasts, macrophages and vascular cells. However, volumetric muscle loss injuries (VML) involve simultaneous destruction of multiple tissue components (e.g., as a result of battlefield injuries or vehicular accidents) and are so extensive that they exceed the intrinsic capability for scarless wound healing and result in permanent cosmetic and functional deficits. In this scenario, the regenerative process fails and is dominated by an unproductive inflammatory response and accompanying fibrosis. The failure of current regenerative therapeutics to completely restore functional muscle tissue is not surprising considering the incomplete understanding of the cellular mechanisms that drive the regeneration response in the setting of VML injury. To begin to address this profound knowledge gap, we developed an agent-based model to predict the tissue remodeling response following surgical creation of a VML injury. Once the model was able to recapitulate key aspects of the tissue remodeling response in the absence of repair, we validated the model by simulating the tissue remodeling response to VML injury following implantation of either a decellularized extracellular matrix scaffold or a minced muscle graft. The model suggested that the SSC microenvironment and absence of pro-differentiation SSC signals were the most important aspects of failed muscle regeneration in VML injuries. The major implication of this work is that agent-based models may provide a much-needed predictive tool to optimize the design of new therapies, and thereby, accelerate the clinical translation of regenerative therapeutics for VML injuries.

Motivation: Colocalization of structures in biomedical images can lead to insights into biological behaviors. One class of colocalization problems is examining an annular structure (disk-shaped such as a cell, vesicle or molecule) interacting with a network structure (vascular, neuronal, cytoskeletal, organellar). Examining colocalization events across conditions is often complicated by changes in density of both structure types, confounding traditional statistical approaches since colocalization cannot be normalized to the density of both structure types simultaneously. We have developed a technique to measure colocalization independent of structure density and applied it to characterizing intercellular colocation with blood vessel networks. This technique could be used to analyze colocalization of any annular structure with an arbitrarily shaped network structure. Results: We present the circular colocalization affinity with network structures test (CIRCOAST), a novel statistical hypothesis test to probe for enriched network colocalization in 2D z-projected multichannel images by using agent-based Monte Carlo modeling and image processing to generate the pseudo-null distribution of random cell placement unique to each image. This hypothesis test was validated by confirming that adipose-derived stem cells (ASCs) exhibit enriched colocalization with endothelial cells forming arborized networks in culture and then applied to show that locally delivered ASCs have enriched colocalization with murine retinal microvasculature in a model of diabetic retinopathy. We demonstrate that the CIRCOAST test provides superior power and type I error rates in characterizing intercellular colocalization compared to generic approaches that are confounded by changes in cell or vessel density. Availability and implementation: CIRCOAST source code available at: https://github.com/uva-peirce-cottler-lab/ARCAS. Supplementary information: Supplementary data are available at Bioinformatics online.

Bioinformatics (2019) https://doi.org/10.1093/bioinformatics/bty638, 35(3): 506–514. The publisher wishes to inform the reader that Figures 2, 5 and 6 appeared incorrectly in the above manuscript. Network area fraction dilated by cell radius determines the random cell colocation fraction. The mean ICF was calculated with the MCMRP over 10 000 trials with randomly selected parameters and displayed as a function of (A) cell diameter, (B) cell number, (C) network radius, (D) network fraction, (E) network length density and (F) cell-dilated network fraction (CDNF, N=2 500 images). Pearson correlation coefficient and associated 95% confidence interval and P-values are provided at the top of each scatterplot ASCs exhibit enriched colocalization with HUVECS network, while fluorescent microspheres (μSpheres) do not. (A) ASCs (red) co-cultured with HUVECS (green). (B) Distribution of simulated mean CIRCOAST P-values (blue) of random colocalization of ASC group compared to observed mean CIRCOAST P-value (red). (C) Fluorescent μSpheres seeded on a culture of HUVECs (scale bar 250 um). (D) Distribution of simulated mean CIRCOAST P-values (blue) of random colocalization from fluorescent μSpheres compared to actual mean P-value (red). (E) Circular cell density and (F) endothelial network density between groups. (G) Distribution of P-values (blue) derived from permuting CIRCOAST P-values in a Wilcox sum rank test between ASCs and μSpheres, with observed P-value (red) (N=6 wells, 3 images/well) Injected live and dead ASCs both exhibit enriched intercellular colocalization affinity with the vasculature. (A) Confocal image of retinal vasculature (green, preprocessed and thresholded) and injected with live DiI-labeled circular ASCs (red). (B) Distribution of simulated mean CIRCOAST P-values (blue) of random colocalization of ASC group compared to observed mean binomial P-value (red). (C) Dead DiI-labeled circular ASCs in the retinal vasculature (scale bars 150 um). (D) Distribution of simulated mean CIRCOAST P-values (blue) of random colocalization from dead cell group, compared to actual mean P-value (red). (E) Injected circular cell and (F) endothelial network density between study groups. (G) Distribution of permuted P-vales of Wilcox sum rank test of CIRCOAST P-values between study groups, with observed P-value (red) (N=6 mice, 3 images/mouse) The paper has been corrected online.

Intravenous delivery of human adipose-derived stromal cells (hASCs) is a promising option for the treatment of ischemia. After delivery, hASCs that reside and persist in the injured extravascular space have been shown to aid recovery of tissue perfusion and function, although low rates of incorporation currently limit the safety and efficacy of these therapies. We submit that a better understanding of the trafficking of therapeutic hASCs through the microcirculation is needed to address this and that selective control over their homing (organ- and injury-specific) may be possible by targeting bottlenecks in the homing process. This process, however, is incredibly complex, which merited the use of computational techniques to speed the rate of discovery. We developed a multicell agent-based model (ABM) of hASC trafficking during acute skeletal muscle ischemia, based on over 150 literature-based rules instituted in Netlogo and MatLab software programs. In silico, trafficking phenomena within cell populations emerged as a result of the dynamic interactions between adhesion molecule expression, chemokine secretion, integrin affinity states, hemodynamics and microvascular network architectures. As verification, the model reasonably reproduced key aspects of ischemia and trafficking behavior including increases in wall shear stress, upregulation of key cellular adhesion molecules expressed on injured endothelium, increased secretion of inflammatory chemokines and cytokines, quantified levels of monocyte extravasation in selectin knockouts, and circulating monocyte rolling distances. Successful ABM verification prompted us to conduct a series of systematic knockouts in silico aimed at identifying the most critical parameters mediating hASC trafficking. Simulations predicted the necessity of an unknown selectin-binding molecule to achieve hASC extravasation, in addition to any rolling behavior mediated by hASC surface expression of CD15s, CD34, CD62e, CD62p, or CD65. In vitro experiments confirmed this prediction; a subpopulation of hASCs slowly rolled on immobilized P-selectin at speeds as low as 2 microm/s. Thus, our work led to a fundamentally new understanding of hASC biology, which may have important therapeutic implications.

Agent-based modeling (ABM), also termed 'Individual-based modeling (IBM)', is a computational approach that simulates the interactions of autonomous entities (agents, or individual cells) with each other and their local environment to predict higher level emergent patterns. A literature-derived rule set governs the actions of each individual agent. While this technique has been widely used in the ecological and social sciences, it has only recently been applied in biomedical research. The purpose of this review is to provide an introduction to ABM as it has been used to study complex multi-cell biological phenomena, underscore the importance of coupling models with experimental work, and outline future challenges for the ABM field and its application to biomedical research. We highlight a number of published examples of ABM, focusing on work that has combined experimental with ABM analyses and how this pairing produces new understanding. We conclude with suggestions for moving forward with this parallel approach.