Microcanonical insights into the physicochemical stability of the coformulation of insulin with amylin analogues

Abstract

Injections of insulin are the main treatment for diabetes, but in the long run this therapy can induce serious drawbacks. This has inspired new drugs able to decrease insulin requirements. For instance, human amylin (hIAPP) is a small hormone cosecreted by pancreatic β-cells with insulin to which is a synergistic partner. However, the high amyloidogenicity of hIAPP precluded it as a therapeutics and led to the design of pramlintide (sIAPP), a chimeric analogue with substitutions (A25P, S28P, and S29P) inherited from the aggregation-resistant rat isoform (rIAPP). Despite sIAPP advantages, it still shares with hIAPP a poorly soluble profile at physiological pH that hampers its mixture with insulin. Recent improvements, as charge-enhanced mutants, have been proposed. For instance, sIAPP⁺ was screened in silico by purely microcanonical thermostatistical methods and adds to sIAPP an S20R mutation to uplift its solubility. This suggests that such physically inspired computational approach may also be auspicious on devising effective coformulations of insulin with amylin analogues. In this seminal attempt, we make comparative multicanonical simulations of regular acting human insulin coformulated with hIAPP, sIAPP, or sIAPP⁺. To assess the respective physicochemical stabilities against aggregation, we characterize the structural-phase transitions through the microcanonical thermodynamic formalism and evaluate their time lags using the classical nucleation theory. These results are then correlated with estimates of solvation free energies, modeled by the Poisson-Boltzmann equation, and structural propensities. Experimental essays are compared to our simulations and support our methodology.

Appendix

Trustworthy estimating the multicanonical parameters $\left \{ {\upbeta }_{k},\alpha _{k}\right \}$ for complex oligomeric systems is well-known to be a cumbersome task in serial simulations. We overcome this numerical hindrance by performing massive parallel simulations with the MUCA algorithm devised in [31, 36]. Thus, it would be interesting to provide an illustrative example of how fast the convergence may be established. Figure 5 presents, for a system composed by insulin in a coformulation with sIAPP⁺, the microcanonical entropy $S\left (\varepsilon \right )$ defined by Eq. 3 as a function of the number of sweeps. Multicanonical parameters are updated every 120k Monte Carlo sweeps, sampled in parallel with 1200 CPUs. The simulation clearly converged for the whole energetic range of interest (i.e., − 5.0 ≤ ε ≤− 4.0) after nearly 5M sweeps, since then $S\left (\varepsilon \right )$ gets stabilized. To further ensure the convergence and collect configurations, we accomplished 15M sweeps. Moreover, once the entropy is established the whole microcanonical thermodynamics is derived by the PHAST package [29].

Fig. 5

The numerical convergence of the microcanonical entropy $S\left (\varepsilon \right )$ of the system composed by insulin coformulated with sIAPP⁺as a function of the multicanonical iterations