The role of uncertainty and negative feedback loops in the evolution of induced immune defenses

Abstract

Organisms use constitutive or induced defenses against pathogens and other external threats. Constitutive defenses are constantly on, whereas induced defenses are activated when needed. Each of these strategies has costs and benefits, which can affect the type of defense that evolves in response to pathogens. In addition, induced defenses are usually regulated by multiple negative feedback mechanisms that prevent overactivation of the immune response. However, it is unclear how negative feedback affects the costs, benefits, and evolution of induced responses. To address this gap, we developed a mechanistic model of the well-characterized Drosophila melanogaster immune signaling network that includes 3 separate mechanisms of negative feedback as a representative of the widespread phenomenon of multilevel regulation of induced responses. We show that, under stochastic fly-bacteria encounters, an induced defense is favored when bacterial encounters are rare or uncertain, but in ways that depend on the bacterial proliferation rate. Our model also predicts that the specific negative regulators that optimize the induced response depend on the bacterial proliferation rate, linking negative feedback mechanisms to the factors that favor induction.

Keywords: bacterial infection; constitutive defense; immunity; negative regulation.

Fig. 1.

Diagram showing the Imd signaling pathway for induction of antimicrobial peptides. The letters in the diagram correspond to the variables in the system of ordinary differential equations of the induced model (Equations (1)–(9)). Peptidoglycans (G) produced by bacteria (B) bind to cell surface receptors (R), forming a receptor complex (C) that initiates an NF-κB signaling pathway to activate the transcription factor Relish (N). Relish promotes the transcription of AMP genes (A), which leads to the production of AMPs (A). Relish also induces the production of Pirk (P), scavengers of peptidoglycans (L), and at least 1 gene encoding a component of the repressosome complex (S). AMPs destroy bacteria, and Pirk reduces available cell surface receptors. Repressosome (S) competes with Relish (N) for binding to the promoter of AMP genes.

Fig. 2.

Simulated environments with different numbers (density) and patchiness of bacterial colonies. Each dot represents a bacterial colony on a $100\times 100$ lattice.

Fig. 3.

Induced responses tend to outperform constitutive defenses when flies inhabit environments with low densities and heterogeneous distributions of bacteria. The relative fitness of constitutive versus induced strategies is shown as heat maps for environments with different densities (d) and patchiness (p) of bacteria. Patchiness values (p) for each cell are reported in Supplementary Table 2. Red cells indicate that the fitness of the induced response (F_induced) is higher than fitness of the constitutive defense (F_constitutive), and blue cells indicate that F_constitutive > F_induced. Heat maps in the same column show induced responses that were optimized with the same frequency of the sinusoidal input of bacteria (Φ), and heat maps in each row show the results for the same proliferation rate of bacteria ($k_0$). Asterisks show the environment in which the induced defense has the highest relative fitness.

Fig. 4.

Proportion of induced wins (PIW) for different proliferation rates of bacteria and fitness functions. PIW (y-axis) was calculated using either the (A) stochastic or (B) sinusoidal oscillating model. a and b) Equation (10) was used to calculate fitness of the induced defense. c) PIW is plotted when either immunopathology or bacterial load has more impact on the host. A modified version of Equation (11) was used, where either A or B was multiplied by 2 (x-axis) and $k_0=0.1$. For results using the original Equation (11), refer to Supplementary Fig. 8 in File S1. a–c) PIW measures the proportion of environments in which an induced response outperforms constitutive defense. The results are shown for induced response optimized in environments with varying frequencies of encounters with bacteria (Φ). The green and purple lines ($\mathit{\Phi }=0.01$ and $\mathit{\Phi }=0.001$) on panel b overlap.

Fig. 5.

Induction outperforms constitutive defense as the number of different environments a fly inhabits increases. The proportion of times induction outperforms constitutive defense, PIW (x-axis), is plotted against the number of possible environments that are sampled (without replacement). Graphs in a column have the same bacterial proliferation rate ($k_0$), and graphs in a row have the same Φ value used to optimize the induced model. Induction outperforms constitutive defense above the dashed line (PIW > 0.5), and constitutive defense performs better below the dashed line (PIW < 0.5).

Fig. 6.

The concentration of proteins that act via negative feedback to modulate Imd signaling. The box plots show the concentration of proteins involved in negative regulation of the Imd signaling pathway (y-axis) in environments with 2 different densities (d) of bacteria (x-axis) that possess different proliferation rates ($k_0$) across 1,000 simulations. Induced defenses were optimized with different frequencies of bacterial encounters $(\mathrm{\Phi })$. The distribution of bacteria in all analyses is heterogeneous ($p=1$).

Fig. 7.

A higher rate of production of PGRP-LB and Pirk is beneficial against bacteria with a low proliferation rate. The proportion of induced wins (PIW) is shown (y-axis) for different parameter values that control the production rates of PGRP-LB and Pirk. The parameter values are changed by multiplying the optimized values for $\mathit{\Phi }=0.1$ by a constant $(\gamma )$ (x-axis). The analysis is done for low (cyan line) and high (brown line) bacterial proliferation rates (k₀). The dashed lines delineate the γ value for which maximum PIW is achieved for low (cyan) and high (brown) bacterial proliferation rates.

Fig. 8.

A stronger binding of the repressosome complex to the promoter is beneficial against bacteria with a high proliferation rate if PGRP-LB and Pirk have low expression. Number of environments (out of a total of 30) in which induced defense reaches its maximum fitness (y-axis) for 4 repressosome binding energy values (x-axis). The repressosome binding energy is manipulated by multiplying by a constant $(\delta )$ for an induced defense that is optimized with $\mathit{\Phi }=0.1$ and $k_0$ = 0.5. The analysis is done for low (cyan line) and high (brown line) bacterial proliferation rates (k₀). a) High production of PGRP-LB and Pirk $(\gamma =1)$. b) Low production of PGRP-LB and Pirk $(\gamma =0.5)$.

Fig. 9.

Certainty and uncertainty of encountering bacteria in environments with different density and patchiness of bacterial populations. Certainty of exposure is shown with shades of blue, and certainty of no exposure is shown with shades of red. Environments that favor constitutive defenses are specified by “constitutive”, and environments that favor induced defenses by “induced”.