Tutorial ADAPT Case study 1. Data sampling / error model. Yared Paalvast Yvonne Rozendaal

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1 Tutorial ADAPT Yared Paalvast Yvonne Rozendaal Case study 1. Data sampling / error model 1.1 Visualize raw data (dataset1a.mat) time data: t concentration data: G 1.2 Linear interpolation: interpolate in time between data points Such that you obtain data at every minute 1.3 Repeat 1.2 using smooth interpolation (cubic smoothing spline) 1.4 Take the standard deviation into account: sample first from data points as if from a normal distributed (use given mean and standard deviation in the data), then interpolate in time as well. 1.5 Now use dataset1b.mat (same as 1 but with less data points) and repeat the questions above. What are the effects of the number of time points/sampling frequencies on the dynamics/kinetics of the obtained curves?

2 Case study 2. Minimal glucose model Minimal glucose model (1) describing plasma glucose concentrations and insulin action upon an Oral Glucose Tolerance Test (OGTT). This model structure is schematically visualized below: The corresponding ODEs are as follows: dg Ra -(p1 + X) * G + p1 * Gb + dt Vg dx dt -p2 * X + p3 * I In which G represents glucose, X insulin action, Gb basal glucose, Ra rate of appearance of exogenous glucose, Vg the distribution volume for glucose and I the measured insulin concentration in the plasma. p1, p2 and p3 are the parameters that govern the dynamics and output of the model. The rate of exogenous glucose appearance in the plasma is defined using an exponential decaying function(2): ( 1) Ra * ( ke ) * t * exp( ( ke* t) ) * D in which k e represents the gastric emptying rate, σ a shape parameter and D the ingested carbohydrate dose. The ODE model is implemented in MATLAB and provided in ODE_min_gluc_model.m. OGTT response data (3) of obese normal glucose tolerant (NGT) and type 2 diabetes (T2D) patients can be loaded through: data = load_data2('ngt'); data = load_data2('t2d'); Data fields can be obtained through: time: data.t mean glucose data: data.g_mean standard deviation of glucose data: data.g_sd mean insulin data: data.i_mean standard deviation of insulin data: data.i_sd

3 2.1 Add insulin as input to the provided m-file. Keep in mind that you need to interpolate the insulin data before it can be used in the model. In the data, only measurements are included at t= 0,15,30,45,60,90,120,180,240 min. 2.2 When we now want to run the model and perform simulations with it, we have to define values for the model parameters. Simulate the model with the following parameter values as initial guess: p1 = 1e-2; p2 = 1e-2; p3 = 1e-2; k_e = 1e-1; σ = 1; Assume that the insulin action (X) is zero at t=0 and use the following values for the model constants: Gb = data.g_mean(1), Vg = 17, D = 40e3. How does the model output correspond to the data? 2.3 Define and implement a (general) objective function. With this function you define how well the model output corresponds to the measured glucose data. Or, in other words, what the difference (error) is between the model and data. 2.4 Optimize the model according to the objective function, i.e. estimate parameter values such that the model resembles the data. 2.5 Add an additional penalty (constraint) to the objective function: assure that the area under the Ra curve (AUC) is equivalent (or at least in the same order of magnitude) to the given carbohydrate dose. 2.6 Compute the insulin sensitivity for both NGT and T2D data. Insulin sensitivity, in this model, is defined as: SI = p3/p2 What are the differences in insulin sensitivity between these two groups? 2.7 What if less time points are included in the data (especially around peak time)? What effect would this have on the optimization procedure?

4 Case study 3. Murine cholesterol model Now moving on to a more complex model describing cholesterol and lipoprotein metabolism in mice upon pharmacological activation of the Liver X receptor. This is the case for which ADAPT was developed initially by Tiemann et al. (4), to unravel which processes were causing the adaptations seen upon LXR activation. 3.1 To initialize the ADAPT package, run setup.m 3.2 To be able to speed up simulations, we make use of compilers to convert ODE models to MEX files (Matlab executables). For this purpose, one needs a software development kit (available at e.g. Open MATLAB and type cd $PARSER$\CVode to go to the directory where the toolbox is extracted. Here you type edit choosecompiler. Set compiler, to the compiler you wish to use (default=1). Depending on which compiler you choose, there are various options to set. Subsequently we need to set various paths, so the toolbox can find all required files. First directory is the parser directory. Set parserdir to the appropriate path $PARSER$. Note that it is important that you end this line with a backslash. (Further instructions can be found at Instructions.pdf in the odemex folder) Otherwise, one can choose to perform simulations and run ADAPT without the MEX compilation through setting: model.options.usemex = 0; in the run files

5 The necessary model files are located in the folder model -> Tiemann Run model using traditional simulation (steady state model): runtiemann.m model.options.numtimesteps = 1; 3.4 Now the model using the ADAPT method through increasing the number of time steps. Why do you think is ADAPT necessary to simulate the data? 3.5 Remove flux data from data set: what effects do this have on the model output? You can do this by removing the specific data components (DATASET.FIELDS) in tiemanndata.m 3.6 Apart from the data that is currently provided in the model, gene expression data is available as well. Hypothesize on how this data could be used to verify the modelling results, e.g. do they confirm the trend in the predicted flux data? Think about the general aspects of this course: how can you integrate multiple types of data (in ADAPT)?

6 References 1. Cobelli C, Dalla Man C, Toffolo G, Basu R, Vella A, Rizza R. The oral minimal model method. Diabetes. 2014;63: Elashoff JD, Reedy TJ, Meyer JH. Analysis of gastric emptying data. Gastroenterology. 1982;83: Jørgensen NB, Jacobsen SH, Dirksen C, Bojsen-Møller KN, Naver L, Hvolris L, Clausen TR, Wulff BS, Worm D, et al. Acute and long-term effects of Roux-en-Y gastric bypass on glucose metabolism in subjects with Type 2 diabetes and normal glucose tolerance. Am J Physiol Endocrinol Metab. 2012;303:E Tiemann CA, Vanlier J, Oosterveer MH, Groen AK, Hilbers PAJ, van Riel NAW. Parameter trajectory analysis to identify treatment effects of pharmacological interventions. PLoS Comput Biol. 2013;9:e