Quantitative systems pharmacology models

QSP models join a drug's pharmacokinetics to its pharmacodynamics through the biology of the disease: pathways, cells and feedbacks, down to a clinical endpoint. Each model here was rebuilt from its original publication as an mrgsolve model and runs in your browser; nothing to install. The first load takes about half a minute while R starts up in the page.

Warfarin and the coagulation cascade

54 speciesPT / INRVitamin K

The humoral coagulation network with warfarin PK and the vitamin K cycle. Clotting factors fall at their own turnover rates, and the prothrombin time of a simulated plasma sample gives the INR.

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Wajima T, Isbister GK, Duffull SB. Clin Pharmacol Ther 2009;86:290-298.

Bone and mineral: denosumab and teriparatide

RANKL-OPGCalcium / PTHBMD

Calcium and phosphate homeostasis joined to osteoblast and osteoclast remodelling. Follows CTx, bone-specific ALP and lumbar-spine BMD through treatment and after stopping.

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Peterson MC, Riggs MM. Bone 2010;46:49-63; CPT Pharmacometrics Syst Pharmacol 2012;1:e14 (OpenBoneMin, GPL-3).

MAPK inhibitors in BRAF(V600E) colorectal cancer

Signalling feedbackVirtual patientsRECIST

EGFR-RAS-RAF-MEK-ERK signalling with feedback, tumour growth and four targeted drugs. Simulates a virtual trial for any combination and compares regimens in the same patients.

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Kirouac DC, Schaefer G, Chan J, et al. npj Syst Biol Appl 2017;3:14.

Glucose, insulin and the incretins

GLP-1 / GIPGlucagonLiraglutide

The 4GI model: glucose, insulin, GLP-1, glucagon and GIP with the feedbacks between them, in healthy volunteers and type 2 diabetes, with a GLP-1 receptor agonist.

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Bosch R, Petrone M, Arends R, et al. CPT Pharmacometrics Syst Pharmacol 2022;11:302-317.

mRNA vaccines: from nanoparticle to antibody

220 equationsGerminal centresAffinity maturation

LNP uptake by innate cells, dendritic-cell maturation, helper T cells, B cells in 17 affinity classes and the antibody response to BNT162b2 and mRNA-1273, against trial data. Change dose, interval and boosters.

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Dasti A, et al. CPT Pharmacometrics Syst Pharmacol 2025. COSBI model, non-commercial licence.

PROTAC degraders and the hook effect

Ternary complexCatalytic degradationDmax / DC50

Targeted protein degradation: ternary complex formation with cooperativity, catalytic degradation on top of target turnover, and the hook effect. Predicts Dmax, DC50 and DCmax for a series of BTK degraders from their binding constants.

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A mechanistic pharmacodynamic modeling framework for PROTACs. Pharmaceutics 2023;15:195.

Antibody-drug conjugate: T-DM1 from mouse to patient

ADCTumour dispositionPayload release

Trastuzumab emtansine crosses tumour vessels, binds HER2, is internalised and releases its DM1 payload inside the cell. Eleven mouse tumour models give the killing constants; human PK is scaled from monkeys; weekly and front-loaded regimens are compared with every 3 weeks.

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Singh AP, Shah DK. AAPS J 2017;19:1054-1070; Singh AP, Maass KF, Betts AM, et al. AAPS J 2016;18:861-875.

T-cell engager and cytokine release

Bispecific CD20xCD3IL-6 / CRSStep-up dosing

Mosunetuzumab tethers T cells to B cells across blood, spleen, lymph nodes and marrow. Compares step-up and full first doses: B-cell killing, T-cell activation and margination, and the IL-6 surge that drives cytokine release syndrome.

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Hosseini I, Gadkar K, Stefanich E, et al. npj Syst Biol Appl 2020;6:28.

CAR-T cell kinetics

Cell therapyExpansion / persistenceVirtual patients

Tisagenlecleucel expands thousands-fold, contracts, then persists for years. The population model from the pediatric ALL trials, with its between-patient variability, covariates, and the effect of tocilizumab and steroids on expansion.

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Stein AM, Grupp SA, Levine JE, et al. CPT Pharmacometrics Syst Pharmacol 2019;8:285-295.

How it works

Every model is a single mrgsolve model file. Run locally with mrgsolve installed, the apps simulate through mrgsolve. In the browser the same file is translated to R and solved with a stiff Rosenbrock solver, and the test suite checks the two engines against each other, and each model against its published results, before every deployment. Source: github.com/Wrlog/QSP. For physiologically based pharmacokinetic (PK-only) models, see the PBPK models.