Mathematical modelling is a labour intensive process involving several iterations of testing on real data and manual model modifications. In biology, the domain knowledge guiding model development is in many cases itself incomplete and uncertain. A major problem in this context is that biological systems are open. Missed or unknown external influences as well as erroneous interactions in the model could thus lead to severely misleading results. Here we introduce the dynamic elastic-net, a data driven mathematical method which automatically detects such model errors in ordinary differential equation (ODE) models. We demonstrate for real and simulated data, how the dynamic elastic-net approach can be used to automatically (i) reconstruct the error signal, (ii) identify the target variables of model error, and (iii) reconstruct the true system state even for incomplete or preliminary models. Our work provides a systematic computational method facilitating modelling of open biological systems under uncertain knowledge.
Ordinary differential equations (ODEs) are a popular approach to quantitatively model molecular networks based on biological knowledge. However, such knowledge is typically restricted. Wrongly modelled biological mechanisms as well as relevant external influence factors that are not included into the model are likely to manifest in major discrepancies between model predictions and experimental data. Finding the exact reasons for such observed discrepancies can be quite challenging in practice. In order to address this issue, we suggest a Bayesian approach to estimate hidden influences in ODE-based models. The method can distinguish between exogenous and endogenous hidden influences. Thus, we can detect wrongly specified as well as missed molecular interactions in the model. We demonstrate the performance of our Bayesian dynamic elastic-net with several ordinary differential equation models from the literature, such as human JAK–STAT signalling, information processing at the erythropoietin receptor, isomerization of liquid α-Pinene, G protein cycling in yeast and UV-B triggered signalling in plants. Moreover, we investigate a set of commonly known network motifs and a gene-regulatory network. Altogether our method supports the modeller in an algorithmic manner to identify possible sources of errors in ODE-based models on the basis of experimental data.
Upadacitinib is an oral Janus kinase inhibitor approved for the treatment of rheumatoid arthritis (RA) and recently approved by the European Medicines Agency for the treatment of psoriatic arthritis (PsA). The efficacy and safety profile of upadacitinib in PsA have been established in the SELECT-PsA program in two global phase 3 studies which evaluated upadacitinib 15 and 30mg QD. The analyses described here characterized upadacitinib pharmacokinetics and exposure-response relationships for efficacy and safety endpoints using data from the SELECT-PsA studies. Upadacitinib pharmacokinetics in PsA patients were characterized through a Bayesian population analysis approach and were comparable to pharmacokinetics in RA patients. Exposure-response relationships for key efficacy and safety endpoints were characterized using data from 1,916 PsA patients. The percentage of patients achieving efficacy endpoints at Week 12 (ACR50 and ACR70), 16 and 24 (sIGA0/1) increased with increasing upadacitinib average plasma concentration over a dosing interval, while no clear exposure-response trend was observed for ACR20 at Week 12 or ACR20/50/70 at Week 24 within the range of plasma exposures evaluated in the phase 3 PsA studies. No clear trends for exposure-response relationships were identified for experiencing pneumonia, herpes zoster infection, hemoglobin <8g/dL, lymphopenia (Grade≥3), or neutropenia (Grade≥3) after 24 weeks of treatment. Shallow relationships with plasma exposures were observed for serious infections and hemoglobin decrease >2g/dL from baseline at Week 24. Based on exposure-response analyses, the upadacitinib 15mg QD regimen is predicted to achieve robust efficacy in PsA patients and to be associated with limited incidences of reductions in hemoglobin or occurrence of serious infections.
Budigalimab is a humanized, recombinant, Fc mutated IgG1 monoclonal antibody targeting programmed cell death 1 (PD‐1) receptor, currently in phase I clinical trials. The safety, efficacy, pharmacokinetics (PKs), pharmacodynamics (PDs), and budigalimab dose selection from monotherapy dose escalation and multihistology expansion cohorts were evaluated in patients with previously treated advanced solid tumors who received budigalimab at 1, 3, or 10 mg/kg intravenously every 2 weeks (Q2W) in dose escalation, including Japanese patients that received 3 and 10 mg/kg Q2W. PK modeling and PK/PD assessments informed the dosing regimen in expansion phase using data from body‐weight‐based dosing in the escalation phase, based on which patients in the multihistology expansion cohort received flat doses of 250 mg Q2W or 500 mg every four weeks (Q4W). Immune‐related adverse events (AEs) were reported in 11 of 59 patients (18.6%), of which 1 of 59 (1.7%) was considered grade ≥ 3 and the safety profile of budigalimab was consistent with other PD‐1 targeting agents. No treatment‐related grade 5 AEs were reported. Four responses per Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 were reported in the dose escalation cohort and none in the multihistology expansion cohort. PK of budigalimab was approximately dose proportional and sustained > 99% peripheral PD‐1 receptor saturation was observed by 2 hours postdosing, across doses. PK/PD and safety profiles were comparable between Japanese and Western patients, and exposure‐safety analyses did not indicate any trends. Observed PK and PD‐1 receptor saturation were consistent with model predictions for flat doses and less frequent regimens, validating the early application of PK modeling and PK/PD assessments to inform the recommended dose and regimen, following dose escalation.
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