Drug-target residence time: critical information for lead optimization

Abstract

Failure due to poor in vivo efficacy is a primary contributor to attrition during the development of new chemotherapeutics. Lead optimization programs that in their quest for efficacy focus solely on improving the affinity of drug-target binding are flawed, since this approach ignores the fluctuations in drug concentration that occur in vivo. Instead the lifetime of the drug-target complex must also be considered, since drugs only act when they are bound to their targets. Consequently, to improve the correlation between the in vitro and in vivo activity of drugs, measurements of drug-target residence time must be incorporated into the drug discovery process.

Figure 1. Residence time, pharmacokinetics and pharmacodynamics

An analysis that demonstrates how residence time affects the amount of drug-target complex (pharmacodynamics) as a function of time. The drug is assumed to reach a maximum concentration (C_max) of 500 nM at the target site 1 h after dosing, and to have an elimination half-life of 1 h (pharmacokinetics) so that the drug concentration at time t is given by D(t) = C_max * 2^(−t/1) (●). The fractional occupancy of the target by the drug, given as a percentage, is shown for three drugs all of which have equilibrium dissociation constants of 14 nM for the final drug-target complex (DT for a rapid reversible inhibitor, DT* for a slow-onset inhibitor) so that at C_max (500 nM), the target in each case is 97 % occupied by drug (500/(500+14)). This assumes that the concentration of target is ≪ 500 nM and that no substrate is present to compete for binding to the target. For the histone deacetylase inhibitor pimelic diphenylamide 106 [–7], the percent target occupancy has been plotted as a function of time using a drug-target complex half-life (t_1/2) of 8 h (the k_off value for this inhibitor is 0.086 h⁻¹ and t_R = 11.6 h) (▲). The percent target occupancy at time t is then given by %occupancy = 97 * 2^(−t/8) assuming that the drug does not rebind to the target (i.e independent of the free drug concentration). A similar analysis has been performed for a hypothetical drug with t_1/2 = 72 h (t_R = 104 h) (◆). Also shown is the percent target occupancy for a rapid reversible (RR) drug calculated directly from the K_d value of 14 nM where %occupancy = 97 * (D(t)/(D(t)+K_d) and D(t) is the drug concentration at time t as calculated previously (◾).

Figure 2. Free energy profiles for drug-target interactions

T and D refer to target and drug respectively. A) One-step binding mechanism, in which k₁ and k₂ are the forward and reverse rate constants, respectively, and K_d is the dissociation constant. B) Two-step induced fit binding mechanism. k₁ and k₂ are the rate constants for formation of the initial TD complex, while k₃ and k₄ are the rate constants for the isomerization step leading to the final TD* complex. In the example shown k₃ and k₄ are small so that formation and breakdown of TD* is slow. K_d is the dissociation constant of TD, while K_d* is the dissociation constant of TD* and determines the true affinity of the drug for its target.

Figure 3. In vitro and in vivo data for the F. tularensis FabI inhibitors

A) Structures of the diphenyl ether inhibitors. B) Linear correlation between t_R and in vivo efficacy [18]. C) Ground state (GS) and transition state (TS) contributions to the residence time of each compound. Changes in the free energy of the ground state have been calculated at 298K relative to compound 1 which has the shortest residence time. The change in ground state free energy of compound x relative to the compound 1 is given by ΔG_GS = −RTln(K_i(x)/K_i(1)), where K_i(1) and K_i(x) are the equilibrium dissociation constants for the two compounds from ftuFabI, and R=1.986 calK⁻¹mol⁻¹. In order to determine how the change in transition state free energy contributes to the change in residence time, the change in transition state free energy between the two compounds is given by △G_TS = −RT(ln(K_i(1)/K_i(x))−ln(k_off(1)/k_off(x))), where k_off(1) and k_off(x) are the dissociation rate constants of the two compounds from ftuFabI. Ground state (GS) contributions are shown in blue, where a positive value indicates the ground state has been stabilized relative to the standard state while a negative value reflects a relative destabilization of the ground state. Transition state (TS) contributions are shown in red, where positive values indicate transition state destabilization and negative values indicate transition state stabilization relative to the standard state.

Figure 4. Ground state and transition state contributions to changes in residence time for the compounds in Table 1

Changes in the free energy of the ground state (GS) and transition state (TS) for each compounds in Table 1 has been calculated relative to a transient-binding drug with a thermodynamic affinity of 1 μM for its target and a drug-target residence time (t_R) of 0.01s (k_off = 100 s⁻¹). △G_GS and △G_TS have been calculated as described in the legend to Figure 2: △G_GS = −RTln(K_i(x)/1×10⁻⁶), and △G_TS = −RT(ln(1×10⁻⁶/K_i(x))−ln(100/k_off(x))). Ground state (GS) and transition state (TS) contributions are shown in blue and red, respectively, as defined for Figure 2.