Modelling the internalisation process of prostate cancer cells for PSMA-specific ligands

Abstract

Introduction: In prostate-specific membrane antigen (PSMA)-targeting radioligand therapy, small molecules are regularly internalised by the tumour cells. To determine the effectiveness of these ligands, the internalised fraction over time is derived from cell studies. Parameters, such as the ligand concentration and the number of cells, are experiment-specific and therefore a comparison between ligands is difficult. A more objective approach that allows better comparison is desirable. Therefore, the aim of this work was to develop a compartmental model that fully describes all relevant pharmacokinetic interactions of PSMA-specific ligands with prostate cancer cells.

Methods: Internalisation studies were performed using the lymph node carcinoma of the prostate cell line LNCaP C4-2 and the prostatic carcinoma cell line PC-3. A new protocol was established for the determination of the PSMA-binding specificity by surface plasmon resonance (SPR). The experimental data in combination with parameters from literature were used for the modelling approach.

Results: A compartmental model which includes the relevant physiological mechanisms was developed. The basic model structure and some parameters originate from the literature. The PSMA-specific association and dissociation rates of Ga-PSMA-11 were measured using surface plasmon resonance technology. The ligand-induced internalisation and PSMA synthesis rates were estimated by fitting the developed model to experimental data obtained using LNCaP C4-2 cells. For all [⁶⁸Ga]Ga-PSMA-11 concentrations and including four various incubation times, the ligand-induced internalisation was determined to be (3.6 ± 0.1) % min^-1.

Conclusions: The presented approach is a prerequisite for better estimation and thus comparison of important ligand-cell interaction parameters, by combining SPR measurements, cell experiments and mathematical modelling.

Advances in knowledge and implications for patient: A compartmental model was developed for evaluation and comparison of PSMA-binding small molecules. A SPR protocol was established for the determination of PSMA-binding specificity.

Keywords: Compartmental modelling; Internalisation rate; PSMA; Surface plasmon resonance.