Rapid-Acting and Human Insulins: Hexamer Dissociation Kinetics upon Dilution of the Pharmaceutical Formulation

Abstract

Purpose: Comparison of the dissociation kinetics of rapid-acting insulins lispro, aspart, glulisine and human insulin under physiologically relevant conditions.

Methods: Dissociation kinetics after dilution were monitored directly in terms of the average molecular mass using combined static and dynamic light scattering. Changes in tertiary structure were detected by near-UV circular dichroism.

Results: Glulisine forms compact hexamers in formulation even in the absence of Zn²⁺. Upon severe dilution, these rapidly dissociate into monomers in less than 10 s. In contrast, in formulations of lispro and aspart, the presence of Zn²⁺ and phenolic compounds is essential for formation of compact R6 hexamers. These slowly dissociate in times ranging from seconds to one hour depending on the concentration of phenolic additives. The disadvantage of the long dissociation times of lispro and aspart can be diminished by a rapid depletion of the concentration of phenolic additives independent of the insulin dilution. This is especially important in conditions similar to those after subcutaneous injection, where only minor dilution of the insulins occurs.

Conclusion: Knowledge of the diverging dissociation mechanisms of lispro and aspart compared to glulisine will be helpful for optimizing formulation conditions of rapid-acting insulins.

Keywords: circular dichroism; dissociation kinetics; insulin analog; light scattering; rapid-acting.

Fig. 1

Association equilibria (M_rel = M_app/M_mon) of lispro, aspart, glulisine and human insulin (a) in 10 mM PBS, pH 7.4 in the absence of Zn²⁺ and phenolic ligands and (b) under formulation conditions with constant concentrations of phenolic ligands as specified in Supplemental Table I. (c) Average relative molecular masses M_rel = M_app/M_mon and (d) Stokes radii R_S of the four insulins in formulation at c = 3.5 mg/ml before dilution (large unframed symbols) and after dilution of formulation with PBS, pH 7.4 (edged symbols), T = 23°C. The ratio of insulin to Zn²⁺ and phenolic ligands is kept constant throughout the dilution series. The arrows depict the 1:20 dilution jump applied during scheme I kinetic experiments. Error bars indicating typical deviations (±10% for M_rel and ±3% for R_S) are omitted in this and subsequent figures for clarity.

Fig. 2

Changes of the relative light scattering intensity after a 1:20 dilution jump of Humalog® with PBS, pH 7.4, T = 23°C (final insulin concentration 0.18 mg/ml). For comparison, we have also shown the scattering intensity of the corresponding solvent (1:20 dilution of placebo with PBS).

Fig. 3

Changes of the average relative molecular masses M_rel after 1:20 dilution jumps of formulations with PBS, pH 7.4, T = 23°C. The large open symbols at t = 0 indicate the initial M_rel in formulation measured in equilibrium experiments. The continuous lines show single-exponential fits to the experimental data (for results see Table I).

Fig. 4

Near-UV CD spectra obtained for (a) Humalog®, (b) NovoRapid®, (c) Apidra®, and (d) Insuman Rapid®. All figures additionally contain the respective spectra after 1:20 dilution of the formulations with PBS, pH 7.4, T = 23°C (light blue) and of the insulin dissolved in PBS, pH 7.4, T = 23°C (dark blue, RAI only). The arrows indicate the expected signal changes at 255 nm (a, b, d) or 275 nm (c) during kinetic experiments.

Fig. 5

Changes of the specific ellipticities after 1:20 dilution jumps of formulations with PBS, pH 7.4, T = 23°C. The symbols at t = 0 indicate the specific ellipticities in formulation measured during equilibrium experiments. The observable kinetic traces for Humalog®, NovoRapid® and Insuman Rapid® could be fitted by single-exponentials within the experimental error (for results see Table I).

Fig. 6

Dependence of the observable dissociation time τ on final concentration of phenolic additives after dilution for lispro and aspart. Humalog® contains 29 mM m-cresol, while NovoRapid® contains 16 mM m-cresol and 16 mM phenol. The methods for variation of final concentration are described in Materials and Methods. For the calculations of τ, we have used the light scattering results and fitted the concentration dependence by an empirical power law τ(c) = τ₀ + a_*c^b .

Fig. 7

Compactness of insulin hexamers in Humalog®, NovoRapid®, Apidra® and as reference HI, c = 4.0 mg/ml, in PBS, 0.45 mM ZnCl₂, pH 7.4, T = 23°C (filled symbols). Empty symbols display structural consequences of the removal of Zn²⁺ from the formulations Humalog® and NovoRapid® by adding 0.6 mM EDTA. The simultaneous changes in average molecular mass and average Stokes radius R_S can be conveniently displayed in a diagram R_S versus M in logarithmic scales. Addition of EDTA to Humalog® and NovoRapid® results in a shift to smaller masses while R_S are essentially unchanged. The average compactness according to the scaling laws for compactly folded globular proteins and proteins (without disulphide bonds) unfolded by guanidinium chloride are shown for comparison.

Fig. 8

Influence of Zn²⁺ on the tertiary and quaternary structures of insulin glulisine and HI. (a) Removal of Zn²⁺ from formulation Insuman Rapid® by adding 0.6 mM EDTA diminishes the strong negative CD amplitude characteristic of the R₆ structure. (b) Conversely, addition of 0.25 mM ZnCl₂ to formulation Apidra® converts the shape of the CD spectrum to that observed in the case of the R₆ configuration. For comparison, we have also shown the CD spectrum of NovoRapid® having a shape typical of the R₆ state.

Fig. 9

Influence of Zn²⁺ on the dissociation kinetics of insulin glulisine and HI. (a) Removal of Zn²⁺ from Insuman Rapid® by adding 0.6 mM EDTA makes the dissociation as fast as in the case of Apidra®. However, the large initial mass hints at an association behavior that differs from that of Apidra® (see also Fig. 10). (b) On addition of 0.25 mM ZnCl₂, Apidra® totally loses its fast dissociation properties directly into monomers. Moreover, an initial association state comprising assemblies larger than hexamers is observed. The first step of the kinetics is a fast dissociation towards hexamers, which is followed by slow dissociation into oligomers with an average mass corresponding to four monomers.

Fig. 10

Influence of Zn²⁺ on the association behavior of glulisine in placebo to Apidra®. The association equilibrium is strongly shifted towards hexamers at low concentrations. Second, formation of assemblies larger than hexamers becomes evident at concentrations above 2 mg/ml. This behavior is totally different from that of HI in the presence of Zn²⁺. For comparison, we have also shown the association equilibria of HI in PBS with and without Zn²⁺.

Fig. 11

Visualization of experimental scheme II for investigations imitating the processes after subcutaneous injection. U50 concentrations (B1 and B2) with defined m-cresol concentrations were obtained starting from two initial formulations A1 and A2 via dilution or dialysis using media with varying m-cresol concentration, respectively. The concentrations of all other solution components were kept constant and correspond to a twofold dilution of the respective formulation with PBS.

Fig. 12

Plots of (a) M_rel and (b) [θ]₂₅₅ of lispro versus m-cresol concentration after processing of samples according to experimental scheme II. M_rel was determined at lispro concentrations of U50 (circles) and U5 (crosses). Values at 0 mM and 29 mM m-cresol represent insulin dissolved in PBS and formulation, respectively. The dashed lines separate data obtained by dialysis and dilution.

Fig. 13

Proposed diagram of states and processes appearing during disassembly of the insulins after 1:20 dilution of formulations with PBS. Triangular symbols depict monomeric subunits assembled into well-coordinated oligomers in the presence of particular ligands (black: exclusively R₆; gray: R₆, R₃T₃ and/or T₆; not filled: T₆ or smaller). Open circles represent monomers either isolated or associated to 'oligomeric assemblies'. Upon addition of Zn²⁺, the structure of insulin glulisine in Apidra® (T₆*) can be converted into R₆ showing a dissociation behavior like HI. Concerning the classification of the insulins, see main text.