Translating slow-binding inhibition kinetics into cellular and in vivo effects

Abstract

Many drug candidates fail in clinical trials owing to a lack of efficacy from limited target engagement or an insufficient therapeutic index. Minimizing off-target effects while retaining the desired pharmacodynamic (PD) response can be achieved by reduced exposure for drugs that display kinetic selectivity in which the drug-target complex has a longer half-life than off-target-drug complexes. However, though slow-binding inhibition kinetics are a key feature of many marketed drugs, prospective tools that integrate drug-target residence time into predictions of drug efficacy are lacking, hindering the integration of drug-target kinetics into the drug discovery cascade. Here we describe a mechanistic PD model that includes drug-target kinetic parameters, including the on- and off-rates for the formation and breakdown of the drug-target complex. We demonstrate the utility of this model by using it to predict dose response curves for inhibitors of the LpxC enzyme from Pseudomonas aeruginosa in an animal model of infection.

Figure 1

Structures of P. aeruginosa LpxC Inhibitors (CHIR-090, compounds 1–6)

Figure 2. Rapid-dilution progress curves for P. aeruginosa LpxC inhibitors establish residence time

Progress curve data for P. aeruginosa LpxC inhibitors at 37 °C. Legend indicates compound 1–6. Reactions were conducted under conditions where compound rebinding after disassociation is minimized and the observed time constant for reactivation is indicative of the residence time.

Figure 3. P. aeruginosa PAO1 post antibiotic effect data for representative LpxC inhibitors

Legends on plots indicate the fold-excess of compound above MIC for the first hour of incubation. Post antibiotic effect data and mechanistic pharmacodynamic model fit for a, Compound 1, b, Compound 4 and c, Compound 6. Data points (symbols) represent mean values from triplicate, independent test occasions. Error bars represent 1 standard deviation of the log₁₀CFU mean. Lines represent model fits to the data using parameters as described in Supplemental Tables 3, 6 and 8. Red asterisks indicate data that were below the limit of detection and omitted from fits (2 and 3 hours 8× MIC panel b and 1–3 hours 16× MIC panel c). d, Correlation of calculated PAE determined at 4×MIC with measured residence time (Table 1). Fitting these data to a linear regression model resulted in a correlation coefficient of 0.87; Compound 4 was excluded from this analysis since the residence time measurements may have been confounded by target rebinding and/or additional slow-binding kinetic effects for this analog (Table 1).

Figure 4. Derivation of a pharmacodynamic model incorporating time-dependent target inhibition parameters

A two-step, competitive binding kinetic mechanism was used to describe the time-dependent inhibition parameters, where the enzyme states E, ES and EI are in rapid equilibrium governed by the catalytic and dissociation constants K_m and K_i with substrate (S) and free inhibitor (I) respectively. The time-dependent conversion of EI to EI* is described by the (on) rate constant k₅, and the slower (off)-rate constant, k₆. The general antibacterial PD model for drug effects on logarithmically growing cells (N), is a mass balance relationship of the intrinsic growth rate, k_growth, and intrinsic maximal drug-induced kill rate (k_{kill_max}) as function of the drug concentration (C) governed by the Hill equation logistic. To link these two models, growth was modeled as being dependent on the amount of ES, and that all other enzyme species contribute to cellular growth inhibition. Solving for the mathematical relationship corresponding to all enzyme states except ES, substitution of this manifold for the Hill logistic, and integration led to a closed, analytical solution. For this new PD model, definitions of the terms M and β are also shown. We added an additional parameter, p_m, to all instances of the ratio [I]/K_i to account for permeation effects that reduce the level of free I at the target site from that in bulk media.

Figure 5. In vivo efficacy curves for Compound 6 with mechanistic pharmacodynamic model fit

In vivo single dose bacterial P. aeruginosa PAO1 CFU thigh tissue burden after administration of Compound 6 at 10 mg/kg (blue square), 50 mg/kg (red square) and 250 mg/kg (black square). Error bars represent the S.E.M. (n=6 mice/timepoint). Open circles represent the vehicle, untreated control group. Lines represent mechanistic PD model simulations. Solid lines utilized PK parameters from Supplementary Table 11 and biochemical parameters from Supplementary Table 8, but with k_growth = 0.45 (10 mg/kg dose) or 0.60 (50 and 250mg/kg doses) log₁₀CFU/h and k_{kill_max} = 1.9 log₁₀CFU/h. Dashed lines represent the identical simulation but with k₅ and k₆ each increased 2000-fold to 120 and 40 min⁻¹ respectively to simulate fast reversible target binding behavior while maintaining the full potency ascribed to the K_i* state.