The transition between acute and chronic infections in light of energy control: a mathematical model of energy flow in response to infection

Figures

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  Figure 1.. Schematic of the energy-flow model. The four compartments of the network comprise brain (B), immune system (I), blood vessel (V) and fat tissue (F). Energy enters the system from the gut (Jg) for use by the brain (Ub), immune system (Ui) and other tissues (Je). Fat tissue acts as an energy buffer and blood vessels as a central connector of these compartments. The amount of usable energy in the brain and immune system undercuts their daily usage even under healthy conditions, indicating that these two organs largely rely on energy flow from fat (Uf) or gut (Jg) to blood (V), and subsequently from blood to the brain (Jb) and to immune system (Ji). Energy flow between compartments is regulated by network variables (symbols linked to signs in the legend; colours depict the regulating compartment). One-sided inhibition operates only when the regulating factor is below its homeostatic level. See text for details. Numbers indicate homeostatic levels of energy in kJ or energy flow in kJ d−1.

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  Figure 2.. Acute versus chronic infections in the energy network. Starting from network equilibrium, pathogen was raised from 0 to P0 = 1 (see electronic supplementary material, equation S3) at day 0. (a) Time until pathogen elimination (1% of inoculation dose) in dependence on the clearance rate (dp). Negative values denote persisting pathogen. A critical clearance rate (Ccrit) for pathogen elimination exists between the red and the blue points. (b) Time until energy homeostasis (healthy or diseased) is re-established to 99% in all compartments. (c) Pathogen dynamics (black, left axis) and fat energy content (green, right axis) with a clearance rate (dp) at the blue point in (a). (d) Assumed biphasic impact of brain activity on the immune response (figure 1; Ub regulates Ui). The healthy homeostatic state assumed to be (1.0, 1.0). Maximum stimulation is at (vb, vi), with v0 the maximum inhibition. The physiological upper limit of the brain energy usage rate is 1.4-fold (see Methods). (e) The critical clearance rate (Ccrit) in dependence on the most sensitive host properties (dp fixed, blue square in a). (f) Pathogen level in response to a therapy raising the clearance rate from dp = 1.12…

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  Figure 3.. Model response to acute (blue) or chronic (red) infections. Starting from network equilibrium, pathogen level was raised from 0 to P0 = 1 (see electronic supplementary material, equation S3), at day 0. dp = 1.16 d−1 (blue, acute infection) and 1.15 d−1 (red, chronic infection), see blue and red points in figure 2a. All quantities are defined in figure 1 and electronic supplementary material, equations S3–S14, and normalized with respect to their healthy homeostatic levels (rel.). Parameters are given in electronic supplementary material, table S1. The broken time axis indicates long-term behaviour.

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  Figure 4.. Lipolysis resistance (LR) impairs acute, but improves chronic immune response. Starting from network equilibrium, pathogen level was raised from 0 to P0 = 1 (see electronic supplementary material, equation S3), at day 0. (a–c) In an otherwise cleared infection (dp = 1.16 d−1; blue point in figure 2a), LR was raised from 0 to 0.05 (magenta) or 0.1 (orange) from day 5 onwards (a). This delayed or prevented pathogen clearance (b). Fat energy was reduced (c). (d–i) In chronic infection (dp = 1.15 d−1; red point in figure 2a), LR was raised from 0 to 1 (magenta) or 2 (orange) from day 200 onwards (d), which reduced or cleared the pathogen (e) and impacted fat (f), brain (g), immune (h) and vessel (i) energy. The cyan curves show the reference Lr = 0. The cusps in the curves before day 500 (g–i) reflect rapid dynamics around pathogen clearance. The left side of the cusp is associated with rapid pathogen clearance (e), the right with increased fat energy (f). The inflection points after day 500 (g,h) are due to the inflection points in the biphasic effects of the stress hormone axes responses onto the immune system (see also figure 2d). (j) Mechanisms involved in LR improved immune…

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  Figure 5.. Dynamic lipolysis resistance (LR) impacts immune response to infections. In silico experiments in figure 2a were repeated using the LR model for different LR growth rates (α). (a) Steady state pathogen level (black dots, left axis) and infection duration (green circles, right axis) in simulations with clearance rate dp = 1.16 d−1 (blue point in figure 2a). The infection duration is the time until the pathogen level dropped below 1% of the inoculation dose. (b) The amount of energy in the fat compartment (black dots, left axis) and the level of LR (green circles, right axis) at the time point of pathogen clearance (green circles in a). The light pink background indicates that the infection was not cleared within the simulated time frame, which is 100 years. Parameters in electronic supplementary material, table S1. rel., relative to homeostatic level; arb., arbitrary.