Quantitative Simulations Predict Treatment Strategies Against Fungal Infections in Virtual Neutropenic Patients

Abstract

The condition of neutropenia, i.e., a reduced absolute neutrophil count in blood, constitutes a major risk factor for severe infections in the affected patients. Candida albicans and Candida glabrata are opportunistic pathogens and the most prevalent fungal species in the human microbiota. In immunocompromised patients, they can become pathogenic and cause infections with high mortality rates. In this study, we use a previously established approach that combines experiments and computational models to investigate the innate immune response during blood stream infections with the two fungal pathogens C. albicans and C. glabrata. First, we determine immune-reaction rates and migration parameters under healthy conditions. Based on these findings, we simulate virtual patients and investigate the impact of neutropenic conditions on the infection outcome with the respective pathogen. Furthermore, we perform in silico treatments of these virtual patients by simulating a medical treatment that enhances neutrophil activity in terms of phagocytosis and migration. We quantify the infection outcome by comparing the response to the two fungal pathogens relative to non-neutropenic individuals. The analysis reveals that these fungal infections in neutropenic patients can be successfully cleared by cytokine treatment of the remaining neutrophils; and that this treatment is more effective for C. glabrata than for C. albicans.

Keywords: bottom-up modeling approach; computer simulations; fungal infections; neutropenia; treatment strategies.

Figure 1

Workflow for studying neutropenia in silico. First, whole-blood infection assays with Candida albicans and Candida glabrata were performed in wet lab. Second, non-spatial immune-reaction rates were fitted using the state-based model. Third, the agent-based model (ABM) was used to estimate migration parameters for neutrophils and monocytes. Based on the fitted non-spatial immune-reaction rates and the fitted migration parameters, virtual neutropenic patients were simulated in the ABM by gradually reducing the neutrophil count. Eventually, a medical treatment of the virtual patients was simulated by increasing the diffusion coefficient and/or the phagocytosis rate of neutrophils.

Figure 2

Experimental data of whole-blood infection assays for Candida albicans (light color) and Candida glabrata (dark color), respectively. After incubation populations of extracellular cells (A), alive cells (B), as well as pathogens phagocytosed by either neutrophils (C) or monocytes (D), were measured by flow cytometry and plating assays.

Figure 3

Transition rates obtained from the calibration of the state-based model (SBM) to experimental data of the whole-blood infection assay for Candida albicans (blue) and Candida glabrata (pink), respectively. The values are compared for the phagocytosis rate for neutrophils (ϕ_N), and by monocytes (ϕ_M), killing rate for neutrophils (κ_N) and monocytes (κ_M), the rate at which the pathogens can evade the immune response with regard to phagocytosis and/or killing (ρ) as well as the rates that define the extracellular killing, i.e., γ and ${\overline{\mathrm{\kappa }}}_{\text{EK}}$. Error bars correspond to SDs.

Figure 4

Result of the agent-based model (ABM) parameter estimation for whole-blood infection assays with Candida albicans (A) and Candida glabrata (B). Adaptive regular grid search was applied to fit the ABM to the experimental data and diffusion coefficients for neutrophils (D_N) and monocytes (D_M) were determined. At each grid point 1 μl blood was simulated, and 30 realizations for each parameter configuration were performed. Three different refinement levels were performed: simulations of the first level are represented as dots, simulations of the second level are represented as squares, and simulations of the third level are represented as triangles. The best fit to the experimental data was found at $\left(D_{\text{N}}^{\text{min}},D_{\text{M}}^{\text{min}}\right)=\left(\text{425\hspace{0.17em}}\mathrm{\mu }{\text{m}}^{\text{2}}∕\text{min},\text{175}\mathrm{\mu }{\text{m}}^{\text{2}}∕\text{min}\right)$ for C. albicans and at $\left(D_{\text{N}}^{\text{min}},D_{\text{M}}^{\text{min}}\right)=(\text{600}\mathrm{\mu }{\text{m}}^{\text{2}}∕\text{min},$ $\text{425}\mathrm{\mu }{\text{m}}^{\text{2}}∕\text{min})$ for C. glabrata.

Figure 5

In silico infections under neutropenic conditions with Candida albicans (A) and Candida glabrata (B) were performed by gradually decreasing the absolute neutrophil count in the agent-based model. Plots show the fraction of killed cells (red), alive and extracellular cells (green), phagocytosed cells by neutrophils (blue), and monocytes (yellow) as well as (alive) cells that are able to evade the immune system (turquoise) at 4 h post infection.

Figure 6

In silico treatment of virtual neutropenic patients (VNP) infected with Candida albicans was simulated using the agent-based model. Stepwise increase of phagocytosis rate and diffusion coefficient of neutrophils was performed for VNP with various severity degrees of neutropenia: VNP1–5: 1,250 (A), 1,000 (B), 750 (C), 500 (D), and 250 (E) neutrophils/μl. Simulated points are classified according to the previously determined patterns: green points show a non-neutropenic infection outcome, yellow points show an infection outcome comparable to a mild neutropenia, orange points show an infection outcome comparable to a moderate neutropenia, and red points show an infection outcome comparable to a severe neutropenia. Solid lines depict the fitted exponential function $f_{{\mathrm{\Phi }}_{\text{N}}}=\text{1}+a\cdot e^{-b\cdot f_{D_{\text{N}}}}$ at the transition to the non-neutropenic infection outcome. For comparison the fitted curves for the five VNP with their severity degrees of neutropenia are shown in panel (F).

Figure 7

In silico treatment of virtual neutropenic patients (VNP) infected with Candida glabrata was simulated using the agent-based model. Stepwise increase of phagocytosis rate and diffusion coefficient of neutrophils was performed for VNP with various severity degrees of neutropenia: VNP1–5: 1,250 (A), 1,000 (B), 750 (C), 500 (D), and 250 (E) neutrophils/μl. Simulated points are classified according to the previously determined patterns: green points show a non-neutropenic infection outcome, yellow points show an infection outcome comparable to a mild neutropenia, orange points show an infection outcome comparable to a moderate neutropenia, and red points show an infection outcome comparable to a severe neutropenia. Solid lines depict the fitted exponential function $f_{{\mathrm{\Phi }}_{\text{N}}}=\text{1}+a\cdot e^{-b\cdot f_{D_{\text{N}}}}$ at the transition to the non-neutropenic infection outcome. For comparison, the fitted curves for the five VNP with their severity degrees of neutropenia are shown in panel (F).

Figure 8

The increase in neutrophil activation required to reach the infection outcome of non-neutropenic patients depends on the severity degree of neutropenia in VNP. (A) Comparison of Candida albicans (blue) and Candida glabrata (pink) infection for various VNP in terms of the factors $f_{D_{\text{N}}}$ and $f_{{\mathrm{\varphi }}_{\text{N}}}$ keeping either $f_{{\mathrm{\varphi }}_{\text{N}}}=\text{1}$ or $f_{D_{\text{N}}}=\text{1}$ fixed. (B) The same as in panel (A) allowing both factors to vary to attain the optimal values $\left(f_{{\mathrm{\varphi }}_{\text{N}}}^{\ast },f_{D_{\text{N}}}^{\ast }\right)$ with minimal distance from $\left(f_{{\mathrm{\varphi }}_{\text{N}}}=\text{1},f_{D_{\text{N}}}=\text{1}\right)$ at which the infection outcome of non-neutropenic patients is reached.