Investigations of a compartmental model for leucine kinetics using nonlinear mixed effects models with ordinary and stochastic differential equations

Nonlinear mixed effects models represent a powerful tool to simultaneously analyze 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 analyzed. We find that the interindividual variation of the model parameters is much smaller for the nonlinear mixed effects 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 nonlinear mixed effects 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

<p>Abstract</p> <p>Background</p> <p>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.</p> <p>Results</p> <p>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.</p> <p>Conclusions</p> <p>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.</p

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 epsilon-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.Original Publication:Mikael Sunnaker, Henning Schmidt, Mats Jirstrand and Gunnar Cedersund, Zooming of states and parameters using a lumping approach including back-translation, 2010, BMC SYSTEMS BIOLOGY, (4), 28.http://dx.doi.org/10.1186/1752-0509-4-28Licensee: BioMed Centralhttp://www.biomedcentral.com

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. Contact: [email protected]; [email protected] Supplementary information: Supplementary data are available at Bioinformatics onlin

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). Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics onlin

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: NCT0472483

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.ISSN:1553-734XISSN:1553-735

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.ISSN:1471-210