Model Description:

A 3-D agent based model (ABM) (where the agents are dendritic cells (DCs)) is presented that simulates the stochastic response of DCs to viral infection up to 15 hours post infection. Simulation results are in good agreement with the experimentally measured DDX58 transcript and IFN-β transcript distributions at 6 and 11 hours post infection.

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Figure 1: Spatial distribution of the fraction of receptors bound on the DCs. Displayed is the distribution at 8 hours post infection. The colors indicate the range of the fraction of bound receptors on each DC: green denotes an fraction of bound less than 0.2, purple a fraction between 0.2 and 0.3, and orange a fraction between 0.3 and 0.4. It is clear that at 8 hours post infection the spatial distribution of bound receptors is very heterogeneous, which is resulting in noisy induction of the ISGs. The X- , Y-, and Z-axes are in units of single cell length (~30 μm).

The results show that both the spatially random distribution of infected DCs (only infected DCs can express IFNB1) and the broad distribution of times the infected DCs begin to secrete IFN-β lead to an initially heterogeneous distribution in IFN-β in the extracellular medium. During the first 6 hours post infection, the spatial heterogeneity of the IFN-β distribution is amplified in the spatial distribution of the bound IFNAR receptors across the DC population by extracellular communication (via autocrine signaling), see Figure 1. By 11 hours post infection the spatial distribution of IFNAR receptors begins to homogenize due to paracrine signaling between DCs. Bound IFNAR receptors activate the JAK/STAT pathway that induces the interferon stimulated genes (ISGs) such as DDX58 (by modulating the rate DDX58 transitions from a state that results in a basal rate of transcript production to a state that results in an enhanced rate of transcript production). The results show that the spatial heterogeneity of the bound IFNAR distribution leads to a broad distribution of DDX58 transcripts from 7 to 15 hours post infection. The ABM predicts the other ISGs’ transcript distributions will also be broad during these times, which may result in the functional consequence of a broad range of antiviral activity throughout these times. [1]

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Figure 2: Each dendritic cell has intracellular reactions that are depicted diagrammatically above. The intracellular reactions are simulated by means of the Gillespie algorithm.

The stochastic intracellular processes of both infected and uninfected DCs are simulated using the standard Gillespie algorithm [2]. The reactions are depicted diagrammatically in Figure 2 (see the supplementary section of [1] for detailed tables of reactions, rate constants and parameters, and the initial conditions). The method used to simulate the extracellular diffusion of IFN-β is described in detail in [3]. The code is written in C++ and requires the user to download the GSL library in order to compile it. An annotated version of the source code for the 3-D ABM can be downloaded below. See Figure 1 for an example of the spatial distributions that can be produced using this program. For a more comprehensive description of the model see the methods section of [1].

References:

  1. Tabbaa OP, et al.: Noise propagation through extracellular signaling leads to fluctuations in gene expression. BMC Systems Biology 2013 7:94
  2. Gillespie DT: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 1976, 22: 403-434.
  3. Shimoni Y, Nudelman G, Hayot F, and Sealfon SC: Multi-scale stochastic simulation of diffusion-coupled agents and its application to cell culture simulation. PLoS One 2011, 6:e29298-e29298
Source code