Bayesian Approach to Model CD137 Signaling in Human M.tuberculosis in vitro Responses

Abstract Immune responses are qualitatively and quantitatively influenced by a complex network of receptor-ligand interactions. Among them, the CD137:CD137L pathway is known to modulate innate and adaptive human responses against Mycobacterium tuberculosis. However, the underlying mechanisms of this regulation remain unclear. In this work, we developed a Bayesian Computational Model (BCM) of in vitro CD137 signaling, devised to fit previously gathered experimental data. The BCM is fed with the data and the prior distribution of the model parameters and it returns theirposterior distribution and the model evidence, which allows comparing alternative signaling mechanisms. The BCM uses a coupled system of non-linear differential equations to describe the dynamics of Antigen Presenting Cells, Natural Killer and T Cells together with the interpheron (IFN)-c and tumor necrosis factor (TNF)-a levels in the media culture. Fast and complete mixing of the media is assumed. The prior distribution of the parameters that describe the dynamics of the immunological response was obtained from the literature and theoretical considerations Our BCM applies successively the Levenberg-Marquardt algorithm to find the maximum a posteriori likelihood (MAP); the Metropolis Markov Chain Monte Carlo method to approximate the posterior distribution of the parameters and Thermodynamic Integration to calculate the evidence of alternative hypothesis. Bayes factors provided decisive evidence favoring direct CD137 signaling on T cells. Moreover, the posterior distribution of the parameters that describe the CD137 signaling showed that the regulation of IFNc levels is based more on T cells survival than on direct induction. Furthermore, the mechanisms that account for the effect of CD137 signaling on TNF-a production were based on a decrease of TNF-a production by APC and, perhaps, on the increase in APC apoptosis. BCM proved to be a useful tool to gain insight on the mechanisms of CD137 signaling during human response against Mycobacterium tuberculosis.Fil: Darío A Fernández Do Porto. UNIV.DE BUENOS AIRES. FAC.DE CS.EXACTAS Y NATURALES. UNIV.DE BUENOS AIRES. FAC.DE CS.EXACTAS Y NATURALES. INST QUIM FISICA D/L/MATERIALES MED AMB Y ENERG.Fil: Jerónimo Auzmendi. UNIV.DE BUENOS AIRES. FAC.DE CS.EXACTAS Y NATURALES. INST QUIM FISICA D/L/MATERIALES MED AMB Y ENERG.Fil: Delfina Peña. UNIV.DE BUENOS AIRES. FAC.DE CS.EXACTAS Y NATURALES. CONSEJO NAC.DE INVEST.CIENTIF.Y TECNICAS. OFICINA DE COORDINACION ADMINISTRATIVA CIUDAD UNIVERSITARIA. INSTITUTO DE QUIMICA BIOLOGICA DE LA FACULTAD DE CS. EXACTAS Y NATURALES. UNIV.DE BUENOS AIRES. FAC.DE CS.EXACTAS Y NATURALES. DTO.DE QUIMICA BIOLOGICA.Fil: Veronica E Garcia. CONSEJO NAC.DE INVEST.CIENTIF.Y TECNICAS. OFICINA DE COORDINACION ADMINISTRATIVA CIUDAD UNIVERSITARIA. INSTITUTO DE QUIMICA BIOLOGICA DE LA FACULTAD DE CS. EXACTAS Y NATURALES.Fil: Luciano Moffatt. UNIV.DE BUENOS AIRES. FAC.DE CS.EXACTAS Y NATURALES. INST QUIM FISICA D/L/MATERIALES MED AMB Y ENERG

Effect of CD137:CD137L pathway on the immune cell cytokine production in tuberculosis.

<p>Different curves represent the best fit of our mathematical model to the data, the median and the 50% of the predictive posterior interval are shown. The mean of the experimental data is shown by triangles. Experimental data were obtained from PBMC of tuberculosis patients stimulated with <i>M.tb</i> Ag in the presence or absence of blocking anti-CD137 mAb. A–B; After 16 and 120 h, the intracellular expression of TNF-α (A) and IFN-γ (B) was determined by flow cytometry, by first gating on monocytes by light scatterand then by gating on CD14⁺ cells. Each represents the mean ± SEM of the percentage of CD14⁺cytokine⁺ cells for each group (11 individuals). C–D; PBMC were stimulated with <i>M.tb</i> Ag for 24 h in the presence or absence of blocking anti-CD137 mAb and intracellular TNF-α (C) and IFN-γ (D) expression on CD56^bright NK cells was determined by flow cytometry by first gating on lymphocytes by light scatter, then by gating on CD3⁻ cells and finally gating on CD56^bright NK cells. Each triangle represents the mean ± SEM (10 individuals). E–F; PBMC were stimulated with <i>M.tb</i> Ag for 4 days in the presence or absence of anti-CD137 blocking mAb. Intracellular TNF-α (E) and IFN-γ (F) expression was determined by flow cytometry in T cells. Each triangles represents the mean ± SEM (16 individuals). Predictions were made according to the following equations (Supporting Information S1): A: R3, B: R2, C: R7, D: R6, E: R12, F: R11.</p

Diagram of APC dynamics in the in vitro culture.

<p>Five different APC subpopulations are described: resting (A₀); activated (A_a); activated and signaling through CD137 (A_s); activated and bound to anti-CD137 blocking mAb (A_bl); and activated, signaling through CD137L and bound to anti-CD137 blocking mAb (A_{s_Ab}). Rows indicate possible mechanisms for each subpopulation. Loss of A₀ is modeled with A₀ uptake of the Ag (in the presence or absence of proinflammatory cytokines (macrophages and DC, respectively)) and death at a rate of µ_A0. A small A₀ ratio expresses receptor and ligand and produces basal levels of cytokines. A_a dynamics show the balance between APC uptake of Ag, natural death (µ_Aa) and TNF-α-induced apoptosis (µα_A). Once A_a interacts with other APC, NK or TL expressing CD137, signaling is initiated (A_s). A_s dynamics includes proliferation, natural death and TNF-α induced apoptosis. A_Ab come from A_a receptor binding to blocking mAb. Although they have the receptor blocked, these cells can be reverse signalized by the antigen (A_{s_Ab}). A_{s_Ab} also comes from A_s that bind the antigen. As we focus on CD137 signaling, parameters (cytokine production, proliferation and apoptosis rates) define two types of activated cells, determined by signaling through CD137 (A_s,A_{s_Ab}) or not (A_a, A_Ab). We assume that all activated APC express ligands and receptors and produce TNF-α, but only a fraction produces IFN-γ. The initial estimation for the induction of apoptosis, proliferation and cytokine secretion by CD137 can be either positive or negative.</p

Fitting of the model (CD137/CD137L expression) to the data.

<p>A, Expression of CD137/CD137L in APC. B, Expression of CD137/CD137L on NK. C, Expression of CD137 on TL. Curves represent the best fit of our mathematical model to the data. The median and the 50% of the predictive posterior interval are shown. Means of experimental data are shown by triangles, error bars indicate the SEM from each group (7 individuals). Experimental data were obtained from PBMC of tuberculosis patients stimulated with <i>M.tb</i> Ag for 0, 16 and 120 h (A), 0, 24 and 120 h (B) or 0, 16, 24 and 120 h (C). CD137 expression was determined by flow cytometry. The cytometric analysis was performed by first gating on monocytes by light scatter and then gating on CD14⁺ cells (A), or by first gating on lymphocytes by light scatter and then on CD3⁻CD56^bright for NK cells (B) or on CD3⁺ for T lymphocytes (C). Predictions were made according to the following equations (Supporting Information S1): A: R4, B: R8, C: R10.</p

Predictions of the alternative model with indirect regulation over TL.

<p>A, CD137 expression on T cells; B, IFN-γ levels in media; C, TL intracelulIar IFN-γ expression. Curves represent the best fit of our mathematical model to the data. The median and the 50% of the predictive posterior interval are shown. Means of experimental data are shown by triangles ± SEM for each group (A, 7 individuals; B, 15 individuals; C, 16 individuals).</p

Diagram of TL dynamics in the in vitro culture.

<p>Four different TL subpopulations are described: non-specific-antigen-T cells (T_ns), specific-antigen naïve T cells (T₀), activated and CD137 co-stimulated cells (T_s); and activated T cells with blocked CD137 (T_b). Rows indicate possible mechanisms for each subpopulation. T_n population only proliferates and dies. T₀ dynamics also includes proliferation and natural death at the same rate as T_n, and can undergo activation/differentiation (and became T_s or T_b) dependent on the presence of activated APC (A_a, A_s, A_{s_Ab} and A_Ab). During activation, T cells express the receptor and, depending on the concentration of anti-CD137 mAb in the media, a portion of them can become blocked. Prior estimates indicate that CD137 signals delivered by agonistic antibodies or by overexpressed ligands can augment T-cell activation or survival. CD137 is not expressed on resting T cells, but rather is induced with antigen (Ag)-receptor signaling. T_s dynamics account for the differentiation of naïve LT₀, proliferation, natural death and TNF-α induced apoptosis. T_bl dynamics incorporates apoptosis induced by CD137 blockage, inhibition and proliferation of IFN-γ and TNF-α production. The model assumes that all activated TL express the receptor.</p

Diagram of CD56^bright NK cell dynamics in the in vitro culture.

<p>Five different NK subpopulations are described: resting (N₀), activated (N_a), activated and signaling through CD137 (N_s), activated, signaling and blocked by anti-CD137 mAb (N_{s_Ab}) and activated and blocked (N_Ab). Rows indicate possible mechanisms for each subpopulation. The loss of N₀ is modeled as NK activation (rate k_(N0,Na)A) and death (µN₀). N₀ activation (N_a) requires IL12 (indirectly modeled as activated APC), activated APC and <i>M.tb</i>. The model includes activation and signaling in two steps. Therefore, N_a dynamics includes CD137 signaling by APC or NK cells, natural death, TNF-α induced-apoptosis and proliferation. N_s dynamics includes IFN-γ/TNFα induction by CD137 (IγN, IαN). N_Ab is defined by equations similar to N_a, but with the receptor bound to anti-CD137 blocking mAb. N_{s_Ab} behaves as N_s, but the receptor is also blocked. We assume that all activated NK cells produce IFN-γ, but only a fraction produce TNF-α and expresse ligand/receptor pair.</p

Role of CD137:CD137L pathway in the cytokine microenvironment during human tuberculosis.

<p>A,B; Fitting of the data model (cytokines in media). Curves represent the best fit of our mathematical model to the data. The median and the 50% of the predictive posterior interval are shown. Means of experimental data are shown by triangles ± SEM from each group (7 individuals). Experimental data were obtained from PBMC of tuberculosis patients stimulated with or without <i>M.tb</i> Ag in the presence or absence of CD137 blocking mAb. After 16 h (ON), 2 days or 5 days, cell-free supernatants were collected and assayed for TNF-α (A) and IFN-γ (B) production by ELISA. The mean ± SEM (15 individuals) of IFN-γ and TNF-α secretion levels is shown for each time. C, Predicted kinetic profile of instantaneous TNF-α production rate by total APC according to the BCM; the median and the 50% of the predictive posterior interval are shown. D, Simulation kinetics profile of instantaneous IFN-γ production rate by total NK and total TL; the median and the 50% of the predictive posterior interval are shown. Predictions were made according to the following equations (Supporting Information S1): A: S16 in Supporting Information S1, B: S15 in Supporting Information S1, C: S15′ in Supporting Information S1, D: S16′′ in Supporting Information S1 and S16′′′ in Supporting Information S1. New experimental data was included to validate the model. Levels of TNF-α and IFN-γ produced by PBMC stimulated with <i>M.tb</i> ± α-CD137 for 16 and 24 hours <a href="http://were%20measured%20by%20ELISA.%20IFN-%20and%20TNF-%CE%B1%20levels%20of%20the%20new%20data%20was%20normalized%20as%20following:%20Normalized%20data=new%20data%20old%20mean%20of%20M.tb%20treatment%20at%2016%20h/new%20mean%20of%20M.%20tb%20treatment%20at%2016%20h.%20Normalized%20data%20is%20shown%20by%20bold%20triangles" target="_blank">were measured by ELISA. IFN- and TNF-α levels of the new data was normalized as following: Normalized data=new data old mean of M.tb treatment at 16 h/new mean of M. tb treatment at 16 h. Normalized data is shown by bold triangles</a>.</p

Reduction in the uncertainty of model parameters that describe the CD137 induction on cytokine production, proliferation and apoptosis rates.

<p>Bayesian analysis on the experimental data reduced the uncertainty of the BCM parameter values. Light gray areas represent the prior parameter distribution. Black areas represent the posterior parameter distribution. γIA (Induction factor of IFN-γ production by CD137::CD137L of APC), αIA (Induction factor of TNF-α production by CD137::CD137L of APC), µIA (Induction of death by CD137::CD137L of APC), γIN (Induction factor of IFN-γ production by CD137::CD137L of NK), αIN (Induction factor of TNF-α production by CD137::CD137L of NK), γIT (Induction of IFN-γ production by CD137), αIT (Induction of TNF-α production by CD137), µIT (Induction of apoptosis rate by CD137), κIT (Induction of proliferation rate by CD137).</p