From Plan to Pivot: How Model-Informed Drug Development Shaped the Dose Strategy of the Zibotentan/Dapagliflozin ZENITH Trials.

Getting the dose right is a key challenge in drug development; model-informed drug development (MIDD) provides powerful tools to shape dose strategies and inform decision making. In this tutorial, the case study of the ZENITH trials showcases how a set of clinical pharmacology and MIDD approaches informed an impactful dose strategy. The endothelin A receptor antagonist zibotentan, combined with the sodium-glucose co-transporter-2 inhibitor dapagliflozin, has yielded a robust and significant albuminuria reduction in the Phase IIb trial ZENITH-CKD and is being investigated for reduction of kidney function decline in a high-risk chronic kidney disease population in the Phase III trial ZENITH High Proteinuria. Endothelin antagonist treatment has, until now, been limited by the class effect fluid retention. ZENITH-CKD investigated a wide range of zibotentan doses based on pharmacokinetics in renal impairment, competitor-data exposure-response modeling, and clinical trial simulations. Recruitment delays reduced interim analysis data availability; here, supportive dose-response modeling recovered decision-making confidence. At trial completion, the low-dose arm enabled Phase III dose selection between Phase IIb doses. Dose-response modeling of efficacy and Kaplan-Meier analyses of tolerability identified a kidney-function-based low-dose strategy of 0.25 or 0.75 mg zibotentan (with 10 mg dapagliflozin) to balance benefit/risk in ZENITH High Proteinuria. The applied clinical pharmacology and MIDD principles enabled successful Phase IIb dose finding, rationalized and built confidence in the innovative Phase III dosing strategy and identified a potential therapeutic window for zibotentan/dapagliflozin, providing the opportunity for a significant improvement in the treatment of chronic kidney disease with high proteinuria.

The myeloperoxidase inhibitor mitiperstat (AZD4831) does not prolong the QT interval at expected therapeutic doses.

Mitiperstat is a myeloperoxidase inhibitor in clinical development for treatment of patients with heart failure and preserved or mildly reduced ejection fraction, non-alcoholic steatohepatits and chronic obstructive pulmonary disease. We aimed to assess the risk of QT-interval prolongation with mitiperstat using concentration-QT (C-QT) modeling. Healthy male volunteers were randomized to receive single oral doses of mitiperstat 5, 15, 45, 135, or 405 mg (n = 6 per dose) or matching placebo (n = 10) in a phase 1 study (NCT02712372). Time-matched pharmacokinetic and digital electrocardiogram data were collected at the baseline (pre-dose) and at 11 time-points up to 48 h post-dose. C-QT analysis was prespecified as an exploratory objective. The prespecified linear mixed effects model used baseline-adjusted QT interval corrected for the heart rate by Fridericia's formula (ΔQTcF) as a dependent variable and plasma mitiperstat concentration as an independent variable. Initial exploratory analyses indicated that all model assumptions were met (no effect on heart rate; appropriate use of QTcF; no hysteresis; linear concentration-response relationship). Model-predicted mean baseline-corrected and placebo-adjusted ΔΔQTcF was +0.73 ms (90% confidence interval [CI]: -1.73, +3.19) at the highest anticipated clinical exposure (0.093 µmol/L) during treatment with mitiperstat 5 mg once daily. The upper 90% CI was below the established threshold of regulatory concern. The 16-fold margin to the highest observed exposure was high enough to mean that a positive control was not needed. Mitiperstat is not associated with risk of QT-interval prolongation at expected therapeutic concentrations.

Efficacy and safety of zibotentan and dapagliflozin in patients with chronic kidney disease: study design and baseline characteristics of the ZENITH-CKD trial.

BACKGROUND: Sodium-glucose co-transporter 2 inhibitors (SGLT2is) are part of the standard of care for patients with chronic kidney disease (CKD), both with and without type 2 diabetes. Endothelin A (ETA) receptor antagonists have also been shown to slow progression of CKD. Differing mechanisms of action of SGLT2 and ETA receptor antagonists may enhance efficacy. We outline a study to evaluate the effect of combination zibotentan/dapagliflozin versus dapagliflozin alone on albuminuria and estimated glomerular filtration rate (eGFR). METHODS: We are conducting a double-blind, active-controlled, Phase 2b study to evaluate the efficacy and safety of ETA receptor antagonist zibotentan and SGLT2i dapagliflozin in a planned 415 adults with CKD (Zibotentan and Dapagliflozin for the Treatment of CKD; ZENITH-CKD). Participants are being randomized (1:2:2) to zibotentan 0.25 mg/dapagliflozin 10 mg once daily (QD), zibotentan 1.5 mg/dapagliflozin 10 mg QD and dapagliflozin 10 mg QD alone, for 12 weeks followed by a 2-week off-treatment wash-out period. The primary endpoint is the change in log-transformed urinary albumin-to-creatinine ratio (UACR) from baseline to Week 12. Other outcomes include change in blood pressure from baseline to Week 12 and change in eGFR the study. The incidence of adverse events will be monitored. Study protocol-defined events of special interest include changes in fluid-related measures (weight gain or B-type natriuretic peptide). RESULTS: A total of 447 patients were randomized and received treatment in placebo/dapagliflozin (n = 177), zibotentan 0.25 mg/dapagliflozin (n = 91) and zibotentan 1.5 mg/dapagliflozin (n =  179). The mean age was 62.8 years, 30.9% were female and 68.2% were white. At baseline, the mean eGFR of the enrolled population was 46.7 mL/min/1.73 m2 and the geometric mean UACR was 538.3 mg/g. CONCLUSION: This study evaluates the UACR-lowering efficacy and safety of zibotentan with dapagliflozin as a potential new treatment for CKD. The study will provide information about an effective and safe zibotentan dose to be further investigated in a Phase 3 clinical outcome trial. CLINICAL TRIAL REGISTRATION NUMBER: NCT04724837.

Pharmacokinetics and Tolerability of Zibotentan in Patients with Concurrent Moderate Renal and Moderate Hepatic Impairment.

BACKGROUND AND OBJECTIVE: Zibotentan, a selective endothelin A receptor antagonist, is in development for chronic liver and kidney disease. The pharmacokinetics (PK) of zibotentan were previously investigated in patients with either renal impairment or hepatic impairment, but the impact of both pathologies on PK was not evaluated. This study evaluated the PK and tolerability of a single oral dose of zibotentan in participants with concurrent moderate renal impairment and moderate hepatic impairment versus control participants. METHODS: Twelve participants with moderate renal and hepatic impairment and 11 healthy matched control participants with no clinically significant liver or kidney disease were enrolled in an open-label, parallel-group study design. After administration of a single oral dose of zibotentan 5 mg, blood and urine sampling was performed. Pharmacokinetic parameters were determined for each of the two cohorts and compared. Comparisons between the cohorts were based on the geometric least squares mean ratio for the primary endpoints, which were area under the plasma concentration-time curve (AUC) from time zero to infinity (AUC∞) and from time zero to the time of the last measurable concentration (AUClast), and maximum plasma drug concentration (Cmax) on Day 1 through 120 h post-dose. Secondary endpoints included apparent total body clearance (CL/F) on Day 1 through 120 h post-dose. Safety endpoints were assessed up to discharge. RESULTS: In total, 11 participants with concurrent moderate renal and hepatic impairment, and 11 controls, completed the study. Zibotentan was generally well tolerated, and no new clinically significant safety findings were observed. Total exposure (AUC∞ and AUClast) was approximately 2.10-fold higher in participants with concurrent moderate renal and hepatic impairment versus controls, while Cmax and total nonrenal body clearance were similar among all groups. A regression-based post hoc analysis, comparing exposure and CL/F in patients with concurrent impairment to patients with either renal or hepatic impairment alone, showed that CL/F with concurrent impairment was approximately half of that in controls and was positively correlated with reduction of renal function. Inclusion of the data on concurrent moderate renal and hepatic impairment in the regression analysis led to a narrower confidence interval for the predicted mean CL/F in participants with moderate hepatic impairment. CONCLUSION: The presented findings advance the understanding of the PK of zibotentan in both renal impairment and hepatic impairment, with and without overlapping pathologies, and will thus increase the confidence of dose selection in future studies, particularly in vulnerable patient populations with concurrent renal and hepatic impairment. TRIAL REGISTRATION: ClinicalTrials.gov identifier: NCT05112419.

A semi-mechanistic exposure-response model to assess the effects of verinurad, a potent URAT1 inhibitor, on serum and urine uric acid in patients with hyperuricemia-associated diseases.

Verinurad, a uric acid transporter 1 (URAT1) inhibitor, lowers serum uric acid by promoting its urinary excretion. Co-administration with a xanthine oxidase inhibitor (XOI) to simultaneously reduce uric acid production rate reduces the potential for renal tubular precipitation of uric acid, which can lead to acute kidney injury. The combination is currently in development for chronic kidney disease and heart failure. The aim of this work was to apply and extend a previously developed semi-mechanistic exposure-response model for uric acid kinetics to include between-subject variability to verinurad and its combinations with XOIs, and to provide predictions to support future treatment strategies. The model was developed using data from 12 clinical studies from a total of 434 individuals, including healthy volunteers, patients with hyperuricemia, and renally impaired subjects. The model described the data well, taking into account the impact of various patient characteristics such as renal function, baseline fractional excretion of uric acid, and race. The potencies (EC50s) of verinurad (reducing uric acid reuptake), febuxostat (reducing uric acid production), and oxypurinol (reducing uric acid production) were: 29, 128, and 13,030 ng/mL, respectively. For verinurad, symptomatic hyperuricemic (gout) subjects showed a higher EC50 compared with healthy volunteers (37 ng/mL versus 29 ng/mL); while no significant difference was found for asymptomatic hyperuricemic patients. Simulations based on the uric acid model were performed to assess dose-response of verinurad in combination with XOI, and to investigate the impact of covariates. The simulations demonstrated application of the model to support dose selection for verinurad.

Lugar de acceso y tipo de anticoagulante en pacientes con síndrome coronario agudo en clase Killip avanzada o con parada cardiaca extrahospitalaria / Choice of access site and type of anticoagulant in acute coronary syndromes with advanced Killip class or out-of-hospital cardiac arrest

INTRODUCCIÓN Y OBJETIVOS: A menudo se excluye de los ensayos clínicos a los pacientes hemodinámica o eléctricamente vulnerables, por lo que escasea la información sobre el acceso vascular y el tratamiento antitrombótico óptimos. En este trabajo se estudia la evolución de los pacientes vulnerables con síndrome coronario agudo tratados invasivamente según el acceso fuera radial o femoral y el tratamiento fuera con bivalirudina o con heparina no fraccionada (HNF). MÉTODOS: El estudio MATRIX aleatorizó a 8.404 pacientes a acceso radial o femoral y a 7.213 pacientes a bivalirudina o a HNF. Se consideró vulnerables a 934 pacientes (11,1%) debido a clase Killip avanzada (808), parada cardiaca (168) o ambas a la vez (42). El objetivo primario compuesto a 30 días fueron los eventos cardiovasculares y cerebrovasculares mayores (MACE: muerte, infarto de miocardio e ictus) y los eventos clínicos adversos netos (NACE: MACE o hemorragia grave). RESULTADOS: El acceso radial, comparado con el femoral, redujo los MACE y NACE de modo similar en pacientes vulnerables y no vulnerables. El acceso radial se asoció con un claro beneficio relativo en la mortalidad total y cardiovascular y las hemorragias BARC 3 o 5, con mayor beneficio absoluto en los pacientes vulnerables. Los efectos de la bivalirudina comparada con la HNF en MACE y NACE concuerdan entre pacientes vulnerables y no vulnerables. La bivalirudina se asoció con menores mortalidad cardiovascular y por todas las causas en pacientes vulnerables, pero no en los no vulnerables, con test de interacción en el límite. La bivalirudina redujo las hemorragias en ambos grupos de pacientes, con un beneficio absoluto mayor en el caso de los pacientes vulnerables. CONCLUSIONES: En pacientes con síndrome coronario agudo sometidos a tratamiento invasivo, los efectos de los tratamientos aleatorizados fueron concordantes entre los pacientes vulnerables y los no vulnerables, pero la reducción del riesgo absoluto del acceso radial y bivalirudina fue mayor en los vulnerables, con una reducción de 5 a 10 veces en el número de pacientes que es necesario tratar

INTRODUCTION AND OBJECTIVES: Patients who are vulnerable to hemodynamic or electrical disorders (VP) are often excluded from clinical trials and data on the optimal access-site or antithrombotic treatment are limited. We assessed outcomes of transradial vs transfemoral access and bivalirudin vs unfractionated heparin (UFH) in VP with acute coronary syndrome undergoing invasive management. METHODS: The MATRIX trial randomized 8404 patients to radial or femoral access and 7213 patients to bivalirudin or UFH. Among them, 934 (11.1%) were deemed VP due to advanced Killip class (n = 808), cardiac arrest (n = 168), or both (n = 42). The 30-day coprimary outcomes were major adverse cardiovascular and cerebrovascular events (MACE: death, myocardial infarction, or stroke) and net adverse clinical events (NACE: MACE or major bleeding). RESULTS: MACE and NACE were similarly reduced with radial vs femoral access in VP and non-VP. Transradial access was also associated with consistent relative benefits in all-cause and cardiovascular mortality or Bleeding Academic Research Consortium (BARC) 3 or 5 bleeding with greater absolute benefits in VP. The effects of bivalirudin vs UFH on MACE and NACE were consistent in VP and non-VP. Bivalirudin was associated with lower all-cause and cardiovascular mortality in VP but not in non-VP, with borderline interaction testing. Bivalirudin reduced bleeding in both VP and non-VP with a larger absolute benefit in VP. CONCLUSIONS: In acute coronary syndrome patients undergoing invasive management, the effects of randomized treatments were consistent in VP and non-VP, but absolute risk reduction with radial access and bivalirudin were greater in VP, with a 5- to 10-fold lower number needed to treat for benefits

Choice of access site and type of anticoagulant in acute coronary syndromes with advanced Killip class or out-of-hospital cardiac arrest.

INTRODUCTION AND OBJECTIVES: Patients who are vulnerable to hemodynamic or electrical disorders (VP) are often excluded from clinical trials and data on the optimal access-site or antithrombotic treatment are limited. We assessed outcomes of transradial vs transfemoral access and bivalirudin vs unfractionated heparin (UFH) in VP with acute coronary syndrome undergoing invasive management. METHODS: The MATRIX trial randomized 8404 patients to radial or femoral access and 7213 patients to bivalirudin or UFH. Among them, 934 (11.1%) were deemed VP due to advanced Killip class (n = 808), cardiac arrest (n = 168), or both (n = 42). The 30-day coprimary outcomes were major adverse cardiovascular and cerebrovascular events (MACE: death, myocardial infarction, or stroke) and net adverse clinical events (NACE: MACE or major bleeding). RESULTS: MACE and NACE were similarly reduced with radial vs femoral access in VP and non-VP. Transradial access was also associated with consistent relative benefits in all-cause and cardiovascular mortality or Bleeding Academic Research Consortium (BARC) 3 or 5 bleeding with greater absolute benefits in VP. The effects of bivalirudin vs UFH on MACE and NACE were consistent in VP and non-VP. Bivalirudin was associated with lower all-cause and cardiovascular mortality in VP but not in non-VP, with borderline interaction testing. Bivalirudin reduced bleeding in both VP and non-VP with a larger absolute benefit in VP. CONCLUSIONS: In acute coronary syndrome patients undergoing invasive management, the effects of randomized treatments were consistent in VP and non-VP, but absolute risk reduction with radial access and bivalirudin were greater in VP, with a 5- to 10-fold lower number needed to treat for benefits. Trial registry number: NCT01433627.

TopoFilter: a MATLAB package for mechanistic model identification in systems biology.

BACKGROUND: To develop mechanistic dynamic models in systems biology, one often needs to identify all (or minimal) representations of the biological processes that are consistent with experimental data, out of a potentially large set of hypothetical mechanisms. However, a simple enumeration of all alternatives becomes quickly intractable when the number of model parameters grows. Selecting appropriate dynamic models out of a large ensemble of models, taking the uncertainty in our biological knowledge and in the experimental data into account, is therefore a key current problem in systems biology. RESULTS: The TopoFilter package addresses this problem in a heuristic and automated fashion by implementing the previously described topological filtering method for Bayesian model selection. It includes a core heuristic for searching the space of submodels of a parametrized model, coupled with a sampling-based exploration of the parameter space. Recent developments of the method allow to balance exhaustiveness and speed of the model space search, to efficiently re-sample parameters, to parallelize the search, and to use custom scoring functions. We use a theoretical example to motivate these features and then demonstrate TopoFilter's applicability for a yeast signaling network with more than 250'000 possible model structures. CONCLUSIONS: TopoFilter is a flexible software framework that makes Bayesian model selection and reduction efficient and scalable to network models of a complexity that represents contemporary problems in, for example, cell signaling. TopoFilter is open-source, available under the GPL-3.0 license at https://gitlab.com/csb.ethz/TopoFilter. It includes installation instructions, a quickstart guide, a description of all package options, and multiple examples.

Design and rationale of the Management of High Bleeding Risk Patients Post Bioresorbable Polymer Coated Stent Implantation With an Abbreviated Versus Standard DAPT Regimen (MASTER DAPT) Study.

BACKGROUND: The optimal duration of antiplatelet therapy in high-bleeding risk (HBR) patients with coronary artery disease treated with newer-generation drug-eluting bioresorbable polymer-coated stents remains unclear. DESIGN: MASTER DAPT (clinicaltrial.govNCT03023020) is an investigator-initiated, open-label, multicenter, randomized controlled trial comparing an abbreviated versus a standard duration of antiplatelet therapy after bioresorbable polymer-coated Ultimaster (TANSEI) sirolimus-eluting stent implantation in approximately 4,300 HBR patients recruited from ≥100 interventional cardiology centers globally. After a mandatory 30-day dual-antiplatelet therapy (DAPT) run-in phase, patients are randomized to (a) a single antiplatelet regimen until study completion or up to 5 months in patients with clinically indicated oral anticoagulation (experimental 1-month DAPT group) or (b) continue DAPT for at least 5 months in patients without or 2 in patients with concomitant indication to oral anticoagulation, followed by a single antiplatelet regimen (standard antiplatelet regimen). With a final sample size of 4,300 patients, this study is powered to assess the noninferiority of the abbreviated antiplatelet regimen with respect to the net adverse clinical and major adverse cardiac and cerebral events composite end points and if satisfied for the superiority of abbreviated as compared to standard antiplatelet therapy duration in terms of major or clinically relevant nonmajor bleeding. Study end points will be adjudicated by a blinded Clinical Events Committee. CONCLUSIONS: The MASTER DAPT study is the first randomized controlled trial aiming at ascertaining the optimal duration of antiplatelet therapy in HBR patients treated with sirolimus-eluting bioresorbable polymer-coated stent implantation.

Shoulder pain in the Swiss spinal cord injury community: prevalence and associated factors.

PURPOSE: To determine the prevalence of shoulder pain and to identify factors associated with shoulder pain in a nationwide survey of individuals living with spinal cord injury (SCI) in Switzerland. METHODS: Data was collected through the 2012 community survey of the Swiss SCI Cohort Study (SwiSCI) (N = 1549; age 52.3 ± 14.8; 29% female). Sociodemographic and socioeconomic circumstances, SCI characteristics, health conditions as well as mobility independence and sporting activities were evaluated as predictor variables. Analyses were adjusted for item non-response (using multiple imputation) and unit-nonresponse (using inverse probability weighting). RESULTS: The adjusted prevalence of shoulder pain was 35.8% (95% CI: 33.4-38.3). Multivariable regression analysis revealed higher odds of shoulder pain in females as compared to males (odds ratio: 1.89; 95% CI: 1.44-2.47), and when spasticity (1.36; 1.00-1.85) and contractures (2.47; 1.91-3.19) were apparent. Individuals with complete paraplegia (1.62; 1.13-2.32) or any tetraplegia (complete: 1.63; 1.01-2.62; incomplete: 1.82; 1.30-2.56) showed higher odds of shoulder pain compared to those with incomplete paraplegia. CONCLUSIONS: This survey revealed a high prevalence of shoulder pain. Sex, SCI severity, and specific health conditions were associated with having shoulder pain. Implications for rehabilitation Individuals with spinal cord injury have a high prevalence of shoulder pain. Females, individuals with complete paraplegia or any tetraplegia and individuals with contractures and spasticity should receive considerable attention in rehabilitation programmes due to their increased odds of having shoulder pain.

Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks.

Parametric uncertainty is a particularly challenging and relevant aspect of systems analysis in domains such as systems biology where, both for inference and for assessing prediction uncertainties, it is essential to characterize the system behavior globally in the parameter space. However, current methods based on local approximations or on Monte-Carlo sampling cope only insufficiently with high-dimensional parameter spaces associated with complex network models. Here, we propose an alternative deterministic methodology that relies on sparse polynomial approximations. We propose a deterministic computational interpolation scheme which identifies most significant expansion coefficients adaptively. We present its performance in kinetic model equations from computational systems biology with several hundred parameters and state variables, leading to numerical approximations of the parametric solution on the entire parameter space. The scheme is based on adaptive Smolyak interpolation of the parametric solution at judiciously and adaptively chosen points in parameter space. As Monte-Carlo sampling, it is "non-intrusive" and well-suited for massively parallel implementation, but affords higher convergence rates. This opens up new avenues for large-scale dynamic network analysis by enabling scaling for many applications, including parameter estimation, uncertainty quantification, and systems design.

Topological augmentation to infer hidden processes in biological systems.

MOTIVATION: A common problem in understanding a biochemical system is to infer its correct structure or topology. This topology consists of all relevant state variables-usually molecules and their interactions. Here we present a method called topological augmentation to infer this structure in a statistically rigorous and systematic way from prior knowledge and experimental data. RESULTS: Topological augmentation starts from a simple model that is unable to explain the experimental data and augments its topology by adding new terms that capture the experimental behavior. This process is guided by representing the uncertainty in the model topology through stochastic differential equations whose trajectories contain information about missing model parts. We first apply this semiautomatic procedure to a pharmacokinetic model. This example illustrates that a global sampling of the parameter space is critical for inferring a correct model structure. We also use our method to improve our understanding of glutamine transport in yeast. This analysis shows that transport dynamics is determined by glutamine permeases with two different kinds of kinetics. Topological augmentation can not only be applied to biochemical systems, but also to any system that can be described by ordinary differential equations. AVAILABILITY AND IMPLEMENTATION: Matlab code and examples are available at: http://www.csb.ethz.ch/tools/index

Near-optimal experimental design for model selection in systems biology.

MOTIVATION: Biological systems are understood through iterations of modeling and experimentation. Not all experiments, however, are equally valuable for predictive modeling. This study introduces an efficient method for experimental design aimed at selecting dynamical models from data. Motivated by biological applications, the method enables the design of crucial experiments: it determines a highly informative selection of measurement readouts and time points. RESULTS: We demonstrate formal guarantees of design efficiency on the basis of previous results. By reducing our task to the setting of graphical models, we prove that the method finds a near-optimal design selection with a polynomial number of evaluations. Moreover, the method exhibits the best polynomial-complexity constant approximation factor, unless P = NP. We measure the performance of the method in comparison with established alternatives, such as ensemble non-centrality, on example models of different complexity. Efficient design accelerates the loop between modeling and experimentation: it enables the inference of complex mechanisms, such as those controlling central metabolic operation. AVAILABILITY: Toolbox 'NearOED' available with source code under GPL on the Machine Learning Open Source Software Web site (mloss.org).

Automatic generation of predictive dynamic models reveals nuclear phosphorylation as the key Msn2 control mechanism.

Predictive dynamical models are critical for the analysis of complex biological systems. However, methods to systematically develop and discriminate among systems biology models are still lacking. We describe a computational method that incorporates all hypothetical mechanisms about the architecture of a biological system into a single model and automatically generates a set of simpler models compatible with observational data. As a proof of principle, we analyzed the dynamic control of the transcription factor Msn2 in Saccharomyces cerevisiae, specifically the short-term mechanisms mediating the cells' recovery after release from starvation stress. Our method determined that 12 of 192 possible models were compatible with available Msn2 localization data. Iterations between model predictions and rationally designed phosphoproteomics and imaging experiments identified a single-circuit topology with a relative probability of 99% among the 192 models. Model analysis revealed that the coupling of dynamic phenomena in Msn2 phosphorylation and transport could lead to efficient stress response signaling by establishing a rate-of-change sensor. Similar principles could apply to mammalian stress response pathways. Systematic construction of dynamic models may yield detailed insight into nonobvious molecular mechanisms.

Approximate Bayesian computation.

Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology).

Investigations of a compartmental model for leucine kinetics using non-linear mixed effects models with ordinary and stochastic differential equations.

Non-linear mixed effects (NLME) models represent a powerful tool to simultaneously analyse data from several individuals. In this study, a compartmental model of leucine kinetics is examined and extended with a stochastic differential equation to model non-steady-state concentrations of free leucine in the plasma. Data obtained from tracer/tracee experiments for a group of healthy control individuals and a group of individuals suffering from diabetes mellitus type 2 are analysed. We find that the interindividual variation of the model parameters is much smaller for the NLME models, compared to traditional estimates obtained from each individual separately. Using the mixed effects approach, the population parameters are estimated well also when only half of the data are used for each individual. For a typical individual, the amount of free leucine is predicted to vary with a standard deviation of 8.9% around a mean value during the experiment. Moreover, leucine degradation and protein uptake of leucine is smaller, proteolysis larger and the amount of free leucine in the body is much larger for the diabetic individuals than the control individuals. In conclusion, NLME models offers improved estimates for model parameters in complex models based on tracer/tracee data and may be a suitable tool to reduce data sampling in clinical studies.

A method for zooming of nonlinear models of biochemical systems.

BACKGROUND: Models of biochemical systems are typically complex, which may complicate the discovery of cardinal biochemical principles. It is therefore important to single out the parts of a model that are essential for the function of the system, so that the remaining non-essential parts can be eliminated. However, each component of a mechanistic model has a clear biochemical interpretation, and it is desirable to conserve as much of this interpretability as possible in the reduction process. Furthermore, it is of great advantage if we can translate predictions from the reduced model to the original model. RESULTS: In this paper we present a novel method for model reduction that generates reduced models with a clear biochemical interpretation. Unlike conventional methods for model reduction our method enables the mapping of predictions by the reduced model to the corresponding detailed predictions by the original model. The method is based on proper lumping of state variables interacting on short time scales and on the computation of fraction parameters, which serve as the link between the reduced model and the original model. We illustrate the advantages of the proposed method by applying it to two biochemical models. The first model is of modest size and is commonly occurring as a part of larger models. The second model describes glucose transport across the cell membrane in baker's yeast. Both models can be significantly reduced with the proposed method, at the same time as the interpretability is conserved. CONCLUSIONS: We introduce a novel method for reduction of biochemical models that is compatible with the concept of zooming. Zooming allows the modeler to work on different levels of model granularity, and enables a direct interpretation of how modifications to the model on one level affect the model on other levels in the hierarchy. The method extends the applicability of the method that was previously developed for zooming of linear biochemical models to nonlinear models.

Zooming of states and parameters using a lumping approach including back-translation.

BACKGROUND: Systems biology models tend to become large since biological systems often consist of complex networks of interacting components, and since the models usually are developed to reflect various mechanistic assumptions of those networks. Nevertheless, not all aspects of the model are equally interesting in a given setting, and normally there are parts that can be reduced without affecting the relevant model performance. There are many methods for model reduction, but few or none of them allow for a restoration of the details of the original model after the simplified model has been simulated. RESULTS: We present a reduction method that allows for such a back-translation from the reduced to the original model. The method is based on lumping of states, and includes a general and formal algorithm for both determining appropriate lumps, and for calculating the analytical back-translation formulas. The lumping makes use of efficient methods from graph-theory and -decomposition and is derived and exemplified on two published models for fluorescence emission in photosynthesis. The bigger of these models is reduced from 26 to 6 states, with a negligible deviation from the reduced model simulations, both when comparing simulations in the states of the reduced model and when comparing back-translated simulations in the states of the original model. The method is developed in a linear setting, but we exemplify how the same concepts and approaches can be applied to non-linear problems. Importantly, the method automatically provides a reduced model with back-translations. Also, the method is implemented as a part of the systems biology toolbox for matlab, and the matlab scripts for the examples in this paper are available in the supplementary material. CONCLUSIONS: Our novel lumping methodology allows for both automatic reduction of states using lumping, and for analytical retrieval of the original states and parameters without performing a new simulation. The two models can thus be considered as two degrees of zooming of the same model. This is a conceptually new development of model reduction approaches, which we think will stimulate much further research and will prove to be very useful in future modelling projects.