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WIREs Syst Biol Med
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Tuneable resolution as a systems biology approach for multi‐scale, multi‐compartment computational models

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The use of multi‐scale mathematical and computational models to study complex biological processes is becoming increasingly productive. Multi‐scale models span a range of spatial and/or temporal scales and can encompass multi‐compartment (e.g., multi‐organ) models. Modeling advances are enabling virtual experiments to explore and answer questions that are problematic to address in the wet‐lab. Wet‐lab experimental technologies now allow scientists to observe, measure, record, and analyze experiments focusing on different system aspects at a variety of biological scales. We need the technical ability to mirror that same flexibility in virtual experiments using multi‐scale models. Here we present a new approach, tuneable resolution, which can begin providing that flexibility. Tuneable resolution involves fine‐ or coarse‐graining existing multi‐scale models at the user's discretion, allowing adjustment of the level of resolution specific to a question, an experiment, or a scale of interest. Tuneable resolution expands options for revising and validating mechanistic multi‐scale models, can extend the longevity of multi‐scale models, and may increase computational efficiency. The tuneable resolution approach can be applied to many model types, including differential equation, agent‐based, and hybrid models. We demonstrate our tuneable resolution ideas with examples relevant to infectious disease modeling, illustrating key principles at work. WIREs Syst Biol Med 2014, 6:225–245. doi: 10.1002/wsbm.1270 This article is categorized under: Analytical and Computational Methods > Computational Methods Analytical and Computational Methods > Dynamical Methods Models of Systems Properties and Processes > Mechanistic Models
Coupled use of wet‐lab and virtual experiments. Left side: Scientific flow of wet‐lab experiments from design through interpretation. Right side: Scientific flow of virtual experiments from design through interpretation. Two cycles intersect to generate hypotheses to pose and address new questions. Iteration is a key component of this process and involves multiple cycles on either or both sides.
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Outcome distributions across different model resolutions describing T cell recruitment. Total bacteria count at day 200 is used as proxy for TB outcome (x‐axis). Each plot displays the outcome from 900 different parameter combinations resulting from the virtual experiments described in the text. Each point is the combination of total bacterial count and Tγ cell fluxes at 200 days post infection. (a) GRANSIM. (b) GRANSIM‐LN. (c) re‐engineered GRANSIM.
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Comparisons of Tγ cell fluxes across different model resolutions. T cells that make the cytokine IFN‐γ (Tγ) are shown on the y‐axis. The x‐axis represents total bacteria count. Each plot displays a total of 900 × 200 points. Each point is the combination of total bacteria count and Tγ cell fluxes at a certain day during a simulated 200‐day infection. Different colors correspond to different time intervals. (a) Results using the fine‐grained version of T cell recruitment (GRANSIM‐LN). (b) The data from (a) with examples of linear and quadratic functions superimposed to fit the data. (c) Results using the improved coarse‐grained model in which the fine‐grained fluxes in (a) are approximated using the linear and quadratic functions illustrated in (b). For days 0–60, we use linear approximations. For days 60–200 we use quadratic functions. We fit simulated Tγ and TC fluxes separately. In order to cross‐validate with fine‐grained LN outcome distributions, we truncated the approximations at a certain level of total bacteria, below which the flux becomes 0. For example after day 30, if bacteria <35, fluxes are set to 0.
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Refinement of GRANSIMTNF. Using uncertainty and sensitivity analyses and knowledge gained from GRANSIMTNF‐NFKB, the intermediate resolution model GRANSIMTNF was improved (top panels). Simulation results are shown for the timing of NF‐κB‐mediated responses, including macrophage activation to efficiently kill bacteria, TNF expression, and chemokine expression, and their effects on (a) bacteria numbers 200 days post‐infection and (b) activated fraction of macrophages 50 days post‐infection. Bottom panels show results from GRANSIMTNF‐NFKB in which the timing of NF‐κB‐mediated responses is regulated by their corresponding mRNA stabilities (half‐lives). Simulations are run varying the stability of mRNA transcripts corresponding to macrophage‐activating molecules, chemokines, and TNF while maintaining the average extent of the responses at containment baseline levels. To maintain the average extent of each response as its corresponding mRNA stability is varied, we simultaneously vary another parameter associated with a process downstream of mRNA translation. Parameters varied to adjust the extent of the three NF‐κB mediated responses are: TNF secretion rate, chemokine secretion rate, ACT concentration threshold for macrophage activation, and macrophage activation rate constant. Four values of mRNA half‐life were tested in fine‐grain simulations: 12 min, 30 min, 1 h, and 3 h. Top panels show results from the modified GRANSIMTNF in which the timing of NF‐κB‐mediated responses is regulated by new parameters kactivation, kchemokine, and kTNF. Four values tested for each of these three parameters in intermediate resolution simulations are: 1.26 × 10−8, 3.97 × 10−8, and 1.26 × 10−7 and 3.97 × 10−7 (#/cell)−1 s−1. All other parameters are kept at their containment (baseline) levels. Simulation results are averaged over 10 repetitions.
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Congruent behaviors achieved from two model resolutions. The predicted roles of TNF R1 internalization and NF‐κB signaling in determining granuloma outcomes are shown. Simulations with GRANSIMTNF (Example 1) show that reducing TNFR1 internalization enhances bacterial killing and increases the probability of bacterial clearance. However, the increased TNF concentrations that result give rise to excessive macrophage activation and increased tissue inflammation. Simulations with GRANSIMTNF‐NFKB (Example 2) show that containment of bacteria is achieved when a balance exists between the NF‐κB‐mediated bacterial killing activities and the NF‐κB‐mediated inflammation. These levels of model resolution are well‐suited to exploring potential pharmacological interventions of the signaling pathway. Snapshots of granulomas follow the same color mapping for cells as in Figure . The range of behaviors simulated with the two resolutions shows model congruency (see Figure ).
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Schematic representation of the multi‐scale multi‐compartment model of the immune response to Mycobacterium tuberculosis infection. (a) An overview of selected agent‐based model (ABM) rules of interaction between host cells, bacteria and lung environment as implemented in GRANSIM which focuses on cellular and tissue scale dynamics. (b–d) Molecular‐scale tumor necrosis factor (TNF) sub‐model that can be embedded at three levels of resolution [coarse (b), intermediate (c), fine (d)] in GRANSIM. The molecular‐scale model for TNF (c) is described in Ref and when implemented in the granuloma model is termed GRANSIMTNF (Example 1). The molecular‐scale model for NF‐κB (d) is described in Ref and when implemented in the granuloma model is termed GRANSIMTNF‐NFKB (Example 2). (e and f) The lymph node (LN) dynamics are described as in Ref at two levels of resolution [coarse (e), fine (f)] (Example 3). Abbreviations: Mycobacterium tuberculosis (Mtb), macrophage (mac), antigen (Ag), chronically infected macrophage (Mci), activated macrophage (Ma), pro‐inflammatory IFN‐γ producing T cell (Tγ) cytotoxic T cell (Tc), regulatory T cell (Treg), TNF‐α converting enzyme (TACE), TNF receptor types 1 and 2 (TNFR1, TNFR2), membrane and soluble forms of TNF (mTNF, sTNF).
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Nonhuman primate and simulated granulomas. (a) Histopathology of a granuloma in a primate infected with Mycobacterium tuberculosis at ∼30 weeks post‐infection (courtesy of JoAnne Flynn, University of Pittsburgh). This typical caseous granuloma shows central necrosis (N) surrounded by macrophages (M) and an outer cuff of lymphocytes (T cells) (L). (b) Snapshot of a simulated TB granuloma at 200 days post‐infection. Cell types: macrophages (resting‐green, activated‐blue, infected‐orange, and chronically infected‐red), effector lymphocytes pro‐inflammatory interferon‐γ (IFN‐γ) producing T cells‐Tγ in pink, cytotoxic T cell‐Tc in purple, regulatory T cell‐Treg in light blue, extracellular bacteria (olive green), vascular sources‐gray, necrotic spots (x). The granuloma shown in (b) has a total bacterial load of ∼2 × 105 M. tuberculosis, mostly extracellular, proliferating and located in the necrotic core.
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These four spectra inform modeling approaches, characterize how multi‐scale models can be used within the larger biomedical context, and help distinguish our tuneable resolution approach from multi‐resolution modeling. Locations on the top two spectra characterize the current state of knowledge about biological systems and phenomena of interest. For immune responses to tuberculosis (TB) and other diseases, the locations selected typically fall within the aqua box. The pink area characterizes systems for which trusted, fine‐grained explanatory mechanisms are available at the highest level of resolution needed.
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Comparing the behavior of multi‐scale models (determined with virtual experiments) and the behavior of a biological system (determined with wet‐lab experiments). The degree to which a model captures the biological system is represented by overlap between the model and biological system shapes (purple and yellow, or green and yellow). The degree to which the fine‐ and coarse‐grained models predict the same behavior is represented by overlap between the purple and green shapes. In order to toggle between the two models to simulate resolution tuning, acceptable similarities (sufficient congruency) for the same set of phenomena must be observed. After initial sensitivity and uncertainty analyses, phenomena overlap between the sibling models is typically inadequate, indicating that further refinements are needed, possibly in both models, providing a degree of cross‐model validation (panels a–c). Because the two model versions are not the same, we should not expect complete overlap across their full range of realizations. Hayenga et al. provide an instructive demonstration of achieving congruency between an agent‐based and a continuum‐based biomechanical model.
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Tuneable resolution approach. Top: An initial model (shown as 3 puzzle pieces) functions within an environment (A1). Fine‐graining a portion of the initial model to generate A2a, and subsequently a portion of that latter model to generate A3, adds additional scales of relevance. Progression from A3 to A2b demonstrates re‐engineering of the previous scale model (A2a) to reflect knowledge gained at A3. Bottom: An initial model is refined to include additional scales of interest in the environment as model development progresses from B1 through B3. Depending on the question or aspect, the user choses the appropriate level of resolution.
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