Deriving allometric scaling rules and providing Insights into the dynamics of LNP based mRNA therapeutics with an exactly solvable mathematical model

Objective: To derive allometric scaling relationships for mRNA clearance, half-life, and volume of distribution. To apply a lower dimensional mathematical model to analyze human clinical PK data for an mRNA encoded monoclonal antibody (mAb) against chikungunya virus. To use the analytic expression for protein PK to establish allometric scaling relationships for the AUC, Cmax, and tmax of the encoded protein and derive the equation for the dose of mRNA required for anti-viral efficacy. Methods: Noncompartmental analysis of the published mRNA PK data for mouse, Rat, NHP, and human was performed and allometric scaling rules for mRNA clearance, elimination half-life, and volume of distribution were determined. To analyze human clinical data, a lower dimensional differential equation was used to relate systemic mRNA level to systemic protein exposure. Model was calibrated to human mRNA and mAb PK data (August A. et al.) to estimate the effective translation rate. An approximate analytic solution for protein concentration over time was derived and was shown to fit the data well. Analytic expression for the protein concentration was then used to construct equations for AUC, Cmax, and tmax and establish allometric scaling rules. Results: The allometric exponents for mRNA clearance, elimination half-life, and volume of distribution were 0.7, 0.3, and 1 respectively. The model based estimate of the effective translation rate for the production of the mRNA encoded mAb in human was ~0.3-0.55 /hr. The mAb exposure over time was well described by a formula relating protein concentration to the dose of mRNA, translation rate, and elimination half-lives of the protein and mRNA. The protein AUC was linearly related to the mRNA translation rate, and the elimination half-lives of mRNA and protein. The derived expression provided the allometric scaling for protein AUC with exponent of 0.3. The approximate relationship for protein tmax and the estimated allometric scaling are then provided. The approximate relationship for Cmax of the protein was then derived and shown to be independent of the mRNA clearance. It was shown that under certain conditions, the protein Cmax was independent of the body weight. Conclusions: Allometric scaling rules were established for mRNA PK using the published data for LNP based mRNA therapeutics. A lower dimensional mathematical model of mRNA and encoded protein was then used to derive explicit analytic expressions for protein AUC, Cmax, and tmax and determine allometric scaling rules for these exposure metrics. Results demonstrated that the mathematical model was able to describe the human mRNA and protein PK data and construct allometric scaling laws that could aid in human dose projection from preclinical species. The analytic expression demonstrated the explicit dependence of protein AUC on parameters related to the mRNA design such as the translation rate and mRNA plasma half-life. Overall, analytic models could be powerful tools in interrogating the dynamics of LNP based mRNA therapeutics and help establish allometric scaling relationships to support better design of mRNA therapeutics.