Cytokine-receptor model.

<p>The cytokine receptor consists of two subunits, the α-chain (IL-4Rα) and the common γ-chain (CD132). IL-4Rα subunits are internalized and recycled, while common γ-chain, antibody and cytokine are degraded after internalization.</p

The agonistic effect in the IL-4/T cell model.

<p>Blue lines are for the γ-chain blocking antibody, red lines are for the α-chain blocking antibody. (a) Reproduction of the sIL-4Rα agonistic effect from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0149154#pone.0149154.ref005" target="_blank">5</a>]. IL-4 bioactivity measurements (red squares) were normalized to baseline (incubation with 250 pM IL-4, without sIL-4Rα). For sIL-4Rα /IL-4 binding, a K_D of 600 pM was used [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0149154#pone.0149154.ref029" target="_blank">29</a>]; the initial number of T cells (2e+05 per ml) was estimated from the experimental description. (b,c,d) Dependencies of the agonistic effect upon parameter values in the IL-4/T cell model (sensitivity analysis), (b) Effect of varying IL-4/mAb binding affinities (solid, dashed and dashed-dotted lines are for K_d values of, respectively, 20, 100 and 500 pM); (c) Effect of varying EC₅₀ values in the proliferation rate Emax function (solid, dashed, and dashed-&-dotted lines are for, respectively, 20, 50 and 100 signaling complexes per cell); (d) effect of varying incubation times (solid, dashed and dashed-dotted lines are for, respectively, cell counts measured after 2, 3, and 5 days). In all simulations, reference parameters were set as follows: initial IL-4 concentration was 250 pM and the initial number of T cells was 1e+06 per ml, other parameter values: IL-4/mAb binding K_D = 20 pM; EC₅₀ = 20 signaling complexes per cell; incubation time = 3 days. 100% of the effect corresponds to the calculated number of cells for model parameters (K_D, incubation time, EC₅₀) set in the absence of any mAb. With an antibody that blocks the binding to the α-chain (red lines), the agonistic effect may occur. With an antibody that blocks the binding to the γ-chain, a monotonic decrease in the cytokine effect is observed (blue lines).</p

Kinetics of free interleukin, signaling, proliferation rate and cell count.

<p>In the model, T cells were incubated with IL-4 250 pM and different concentrations of mAb (5 pM—red lines, 250 pM–blue lines, 10000 pM–green lines; mAb K_D set at 20 pM) during 6 days. (a, e) Time course of free IL-4 (100% represents the initial IL-4 concentration of 250 pM); (b, f) Time course of number of the signaling complexes per cell; (c, g) Proliferation rates, expressed as an Emax function of the number of signaling complexes, with EC₅₀ = 20 signaling complexes per cell; (d, h) Time course of cellular proliferation, expressed as T-cell count. The initial number of T cells is 1 x 10⁶ per ml.</p

A Generic Mechanism for Enhanced Cytokine Signaling <i>via</i> Cytokine-Neutralizing Antibodies

<div><p>Enhancement or inhibition of cytokine signaling and corresponding immune cells responses are critical factors in various disease treatments. Cytokine signaling may be inhibited by cytokine-neutralizing antibodies (CNAs), which prevents further activation of cytokine receptors. However, CNAs may result in enhanced—instead of inhibitory—cytokine signaling (an “agonistic effect”) in various <i>in vitro</i> and <i>in vivo</i> experiments. This may lead to lack of efficacy or adverse events for cytokine-inhibiting based medicines. Alternatively, cytokine-antibody complexes may produce stronger signaling <i>vs</i>. cytokine alone, thereby increasing the efficacy of stimulating cytokine-based drugs, at equal or lower cytokine doses. In this paper, the effect of cytokine signaling enhancement by a CNA was studied in a generic mathematical model of interleukin-4 (IL-4) driven T-cell proliferation. The occurrence of the agonistic effect depends upon the antibody-to-cytokine binding affinity and initial concentrations of antibody and cytokine. Model predictions were in agreement with experimental studies. When the cytokine receptor consists of multiple subunits with substantially differing affinities (<i>e</i>.<i>g</i>., IL-4 case), the choice of the receptor chain to be blocked by the antibody is critical, for the agonistic effect to appear. We propose a generic mechanism for the effect: initially, binding of the CNA to the cytokine reduces free cytokine concentration; yet, cytokine molecules bound within the cytokine-CNA complex—and released later and over time—are “rescued” from earlier clearance <i>via</i> cellular internalization. Hence, although free cytokine-dependent signalling may be less potent initially, it will also be more sustained over time; and given non-linear dynamics, it will lead ultimately to larger cellular effector responses, <i>vs</i>. the same amount of free cytokine in the absence of CNA. We suggest that the proposed mechanism is a generic property of {cytokine, CNA, receptor} triads, both <i>in vitro</i> and <i>in vivo</i>, and can occur in a predictable fashion for a variety of cytokines of the immune system.</p></div

Agonistic effect of an IL-4 neutralizing mAb: model simulations for an <i>in vivo</i> case <i>vs</i>. an <i>in vitro</i> case.

<p>Red lines are for the α-chain blocking mAb, blue lines are for the γ-chain blocking mAb. (a) simulations for the <i>in vitro</i> case, (b) simulations for the <i>in vivo</i> case. The following experimental conditions were used in the model simulations: incubation time = 3 days; initial concentration of IL-4 = 250 pM; initial cells density = 4e+06 cells/ml; mAb/IL-4 binding K_D = 20 pM; EC₅₀ = 20 signaling complexes per cell. For simulations of the <i>in vivo</i> conditions, systemic elimination rates of 1.26 1/h and 0.004 1/h were added, respectively, for IL-4 and the mAb.</p

Schematics of main biochemical reactions in a cytokine-receptor model.

<p>1 –binding of cytokine with antibody, 2 –binding of cytokine with receptor on the cell membrane, 3 –internalization of cytokine/receptor complex (relatively fast), 4 –degradation of cytokine in endosome (lysosome), 5 –recycling of receptor from endosome to the cell surface and internalization (relatively slow) of free receptor.</p

Additional file 1 of PeTTSy: a computational tool for perturbation analysis of complex systems biology models

This PDF includes the derivation of period derivatives, phase derivatives, phase infinitesimal response curves and describes the projection of the solution derivative onto rotational and amplitude variations (for the Amplitude/Phase Derivatives Scatterplot)

Table1_Optimization of the MACE endpoint composition to increase power in studies of lipid-lowering therapies—a model-based meta-analysis.docx

AimsTo develop a model-informed methodology for the optimization of the Major Adverse Cardiac Events (MACE) composite endpoint, based on a model-based meta-analysis across anti-hypercholesterolemia trials of statin and anti-PCSK9 drugs.Methods and resultsMixed-effects meta-regression modeling of stand-alone MACE outcomes was performed, with therapy type, population demographics, baseline and change over time in lipid biomarkers as predictors. Randomized clinical trials up to June 28, 2022, of either statins or anti-PCSK9 therapies were identified through a systematic review process in PubMed and ClinicalTrials.gov databases. In total, 54 studies (270,471 patients) were collected, reporting 15 different single cardiovascular events. Treatment-mediated decrease in low density lipoprotein cholesterol, baseline levels of remnant and high-density lipoprotein cholesterol as well as non-lipid population characteristics and type of therapy were identified as significant covariates for 10 of the 15 outcomes. The required sample size per composite 3- and 4-point MACE endpoint was calculated based on the estimated treatment effects in a population and frequencies of the incorporated events in the control group, trial duration, and uncertainty in model parameters.ConclusionA quantitative tool was developed and used to benchmark different compositions of 3- and 4-point MACE for statins and anti-PCSK9 therapies, based on the minimum population size required to achieve statistical significance in relative risk reduction, following meta-regression modeling of the single MACE components. The approach we developed may be applied towards the optimization of the design of future trials in dyslipidemia disorders as well as in other therapeutic areas.</p

Table1_Optimization of the MACE endpoint composition to increase power in studies of lipid-lowering therapies—a model-based meta-analysis.docx

AimsTo develop a model-informed methodology for the optimization of the Major Adverse Cardiac Events (MACE) composite endpoint, based on a model-based meta-analysis across anti-hypercholesterolemia trials of statin and anti-PCSK9 drugs.Methods and resultsMixed-effects meta-regression modeling of stand-alone MACE outcomes was performed, with therapy type, population demographics, baseline and change over time in lipid biomarkers as predictors. Randomized clinical trials up to June 28, 2022, of either statins or anti-PCSK9 therapies were identified through a systematic review process in PubMed and ClinicalTrials.gov databases. In total, 54 studies (270,471 patients) were collected, reporting 15 different single cardiovascular events. Treatment-mediated decrease in low density lipoprotein cholesterol, baseline levels of remnant and high-density lipoprotein cholesterol as well as non-lipid population characteristics and type of therapy were identified as significant covariates for 10 of the 15 outcomes. The required sample size per composite 3- and 4-point MACE endpoint was calculated based on the estimated treatment effects in a population and frequencies of the incorporated events in the control group, trial duration, and uncertainty in model parameters.ConclusionA quantitative tool was developed and used to benchmark different compositions of 3- and 4-point MACE for statins and anti-PCSK9 therapies, based on the minimum population size required to achieve statistical significance in relative risk reduction, following meta-regression modeling of the single MACE components. The approach we developed may be applied towards the optimization of the design of future trials in dyslipidemia disorders as well as in other therapeutic areas.</p