A New Method for Optimizing Sepsis Therapy by Nivolumab and Meropenem Combination: Importance of Early Intervention and CTL Reinvigoration Rate as a Response Marker

Abstract

Background: Recently, there has been a growing interest in applying immune checkpoint blockers (ICBs), so far used to treat cancer, to patients with bacterial sepsis. We aimed to develop a method for predicting the personal benefit of potential treatments for sepsis, and to apply it to therapy by meropenem, an antibiotic drug, and nivolumab, a programmed cell death-1 (PD-1) pathway inhibitor. Methods: We defined an optimization problem as a concise framework of treatment aims and formulated a fitness function for grading sepsis treatments according to their success in accomplishing the pre-defined aims. We developed a mathematical model for the interactions between the pathogen, the cellular immune system and the drugs, whose simulations under diverse combined meropenem and nivolumab schedules, and calculation of the fitness function for each schedule served to plot the fitness landscapes for each set of treatments and personal patient parameters. Results: Results show that treatment by meropenem and nivolumab has maximum benefit if the interval between the onset of the two drugs does not exceed a dose-dependent threshold, beyond which the benefit drops sharply. However, a second nivolumab application, within 7-10 days after the first, can extinguish a pathogen which the first nivolumab application failed to remove. The utility of increasing nivolumab total dose above 6 mg/kg is contingent on the patient's personal immune attributes, notably, the reinvigoration rate of exhausted CTLs and the overall suppression rates of functional CTLs. A baseline pathogen load, higher than 5,000 CFU/μL, precludes successful nivolumab and meropenem combination therapy, whereas when the initial load is lower than 3,000 CFU/μL, meropenem monotherapy suffices for removing the pathogen. Discussion: Our study shows that early administration of nivolumab, 6 mg/kg, in combination with antibiotics, can alleviate bacterial sepsis in cases where antibiotics alone are insufficient and the initial pathogen load is not too high. The study pinpoints the role of precision medicine in sepsis, suggesting that personalized therapy by ICBs can improve pathogen elimination and dampen immunosuppression. Our results highlight the importance in using reliable markers for classifying patients according to their predicted response and provides a valuable tool in personalizing the drug regimens for patients with sepsis.

Keywords: PD-1; fitness landscape; immunosuppression; inflammation; intensive care; mathematical model; nivolumab; simulation.

Figure 1

A graphical display of the drug-disease-host model. The model is based on seven major assumptions: (1) HSCs (H) continually differentiate into myeloid cells (M; neutrophils, macrophages) and lymphoid cells (L, CTLs); (2) the presence of pathogen (P) biases HSC differentiation toward the myeloid lineage; (3) CTLs encounter APCs (such as macrophages) that have phagocytized antigen, and expand their population in response; (4) neutrophils and CTLs inhibit pathogen growth; (5) pathogen causes healthy CTLs (L) to differentiate into exhausted CTLs (L_X) (via activation of the programmed cell death-1 receptor; PD-1); (6) exhausted CTLs hinder proliferation of healthy CTLs; (7) nivolumab (N) induces the reinvigoration of exhausted CTLs back into the functional CTL compartment by blocking the PD-1 pathway. Straight arrows, activation; dashed arrows, differentiation; blunted arrows, inhibition.

Figure 2

Effects of meropenem application on the pathogen load and neutrophil and CD8⁺ CTL counts. Model simulations of the three populations of interest: neutrophils (dashed lines), CD8⁺ CTLs (dash-dot) and pathogen (continuous), under continuous treatment with meropenem (antibiotics), 70 mg/L i.v., administered at t = 0. Initial neutrophil level M(t = 0) = 4.5·10³Cells/μL; initial CTL level L(t = 0) = 1.5·10³Cells/μL. Initial pathogen load P(t = 0) = 4·10³ CFU/μL. For equations see Methods section. For parameter values see Table 1.

Figure 3

Effects of a combined meropenem and nivolumab regimen on the pathogen load and the neutrophil and lymphocyte cell levels. (A,B) Model simulations of the three populations of interest: neutrophils (dashed lines), lymphocytes (dash-dot) and pathogen (continuous), under continuous treatment with meropenem (antibiotics), 70 mg/L i.v. application, administered at t = 0, and nivolumab, single dose, 6 mg/kg, 12 mg/kg (left column, right column, respectively) administered at 24 h, 48 h, 96 h (top, middle, bottom row, respectively; vertical gray lines). Parameters for (A) are CTL exhaustion rate μ_X = 0.01h⁻¹; CTL suppression by exhausted CTLs $s_X^{*}=45·10^3$Cells/μL. Parameters for (B) are CTL exhaustion rate μ_X = 0.07h⁻¹; CTL suppression by exhausted CTLs $s_X^{*}=5·10^3$Cells/μL. Initial neutrophil level M(t = 0) = 4.5·10³Cells/μL; initial CTL level L(t = 0) = 1.5·10³Cells/μL. Initial pathogen load P(t = 0) = 4·10³ CFU/μL. For equations see methods section. For parameter values see Table 1.

Figure 4

Fitness of varying nivolumab regimens and the effect of personal parameters. (A) Fitness values, F, for nivolumab administration times ranging from 0 to 100 h (abscissa) and nivolumab doses ranging from 0 to 12 mg/kg (ordinate). CTL exhaustion rate μ_X = 0.01 h⁻¹; CTL suppression by exhausted CTLs $s_X^{*}=45·10^3$CFU/μL. (B) Fitness values, F, for nivolumab administration times ranging from 0 to 100 h (abscissa) and nivolumab doses ranging from 0 to 12 mg/kg (ordinate).; CTL suppression by exhausted CTLs $s_X^{*}=5·10^3$CFU/μL. (C) Fitness values, F, for CTL exhaustion rate, μ_X, ranging from 0 to 0.1 h⁻¹ (abscissa), and CTL suppression by exhausted CTLs, $s_X^{*}$, ranging from 0 to 50·10³Cells/μL (ordinate). Nivolumab administration time is 48 h; nivolumab dose is 6 mg/kg (ordinate). Initial pathogen load $P_0=4·10^3$CFU/μL (all plates). For equations see methods section. For other parameter values see Table 1. Note that $s_X^{*}=50\times 10^{3}Cells/\mu l-s_X$, where s_X is the suppression parameter in Eq. 6 (the motivation for using this transformation is to make the graph more understandable, since s_X itself has an inverse relationship with the suppression rate).

Figure 5

Effect of the reinvigoration rate on the fitness of varying nivolumab regimens. (A) Fitness values, F, for reinvigoration rates q_X, ranging from 0 to 0.6 h⁻¹ (abscissa) and nivolumab administration times ranging from 0 to 100 h (ordinate), nivolumab dose D = 6 mg/kg. (B) Fitness values, F, for reinvigoration rates q_X, ranging from 0 to 0.6 h⁻¹ (abscissa) and nivolumab doses ranging from 0 to 12 mg/kg (ordinate); nivolumab administration time t_N = 48 h. Initial pathogen load $P_0=4·10^3$ CFU/μL (both plates). For equations see Methods section. For other parameter values see Table 1.

Figure 6

Effect of initial pathogen load on the fitness of nivolumab regimens. (A) Fitness values, F, for initial pathogen loads ranging from 0 to 10·10³ CFU/μL (ordinate) and reinvigoration rates, q_X, ranging from 0 to 0.6 h⁻¹ (abscissa). nivolumab administration time t_N = 48 h; dose D = 6 mg/kg. (B) Fitness values, F, for initial pathogen loads ranging from 0 to 10·10³ CFU/μL (ordinate), and nivolumab dose, D, ranging from 0 to 12 mg/kg. For equations see methods section. For other parameter values see Table 1.

Figure 7

Effect of multiple dosing. (A) Fitness values, F, for treatment regimens comprising a first dosing at 48h with a dose, D₁, ranging between 1 and 11 mg/kg, and a second dosing at time ranging between 96 and 504h, with a dose of 12 mg/kg - D₁. (B) Model simulations of the three populations of interest: neutrophils (dashed lines), lymphocytes (dash-dot) and pathogen(continuous), under continuous treatment with meropenem (antibiotics), 70 mg/L, i.v. application, administered at t=0, and nivolumab, 12 mg/kg, administered in two doses of 6 mg/kg, with administration times as follows: 24h and 168h (top), 48h and 240h (middle), 24h and 336h (bottom). For equations see Methods section. For parameter values, see legend to Figure 3A and Table 1.