Think like an experimentalist 10/11/10

Melissa, you’re a modeler! And I do “systems biology”. So model this data for me!!

Useful dataUnuseful data No indication of treatment times given in figure legend Multiple time points, multiple variables, independent loading control, Pixel density quantification

Aspects to consider for experimental design that complements modeling (from Kreutz & Timmer) In comparison to classical biochemical studies, establishment of mechanistic mathematical models requires a relative large amount of data Measurements obtained by experimental repetitions have to be comparable on a quantitative not only on a qualitative level A measure of confidence is required for each data point The number of measured conditions should clearly exceed the number of all unknown model parameters Validation of dynamic models requires measurements of the time dependency after external perturbations Perturbations of a single player (e.g. by knockout, over-expression and similar techniques) provide valuable information for the establishment of a mechanistic model

Aspects to consider for experimental design that complements modeling (cont.) The biochemical mechanisms between the observables should be reasonably known The predictive power of mathematical models increases with the level of available knowledge. It could therefore be preferable to concentrate experimental efforts on well understood subsystems If the modeled proteins could not be observed directly, measurements of other proteins that interact with the players of interest, can be informative. The amount of information from such additional observables depends on the required enlargement of the model The velocity of the underlying dynamics indicates meaningful sampling intervals  t. The measurements should seem relatively smooth. If the considered hypothesis are characterized by a different dynamics, this difference determines proper sampling times

Aspects to consider for experimental design that complements modeling (cont.) Steady-state concentrations provide useful information The number of molecules per cell or the total concentration is a very useful information. The order of magnitude of the number of molecules (i.e. tens or thousands) per cellular compartment has to be known Thresholds for a qualitative change of the system behavior, i.e. the switching conditions, are insightful information Calibration measurements with known protein concentrations are advantageous because the number of scaling parameters is reduced The specificity of the experimental technique is crucial for quantitative interpretation of the measurements For the applied measurement techniques, the relationship between the output (e.g. intensities) and the underlying truth (e.g. concentrations) has to be known. Usually, a linear dependency is preferable

Optimal Sampling Experiments cost time and $$ Often, a minimal set of measurements are made for time-dependent data Limited by reagents Space on plate # of cells/quantity of tissue Replicates often limited to n=3

Modeling was performed based upon existing data. If experiments were to be redone, would there be a better set of time points to select??

This is an optimization problem Several approaches, such as: – Compute the determinant of the Fisher information matrix (inverse of the covariance matrix of the estimated parameters) – Use an initial guess of [T 0, T 1 ] N and initial guess of parameter values – Re-estimate parameter values – Re-calculate det(F) – Iterate to maximize F for new sampling time vector Kutalik et al, Biosystems, 2004

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Question: is any experimentalist going to go through this exercise prior to collecting data? Reality: “heuristic” approach usually taken

Features: Measurements of the time dependency after external perturbation Perturbations of a single player to provide information for the establishment of a mechanistic model Measurements obtained by experimental repetitions have to be comparable on a quantitative not only on a qualitative level A measure of confidence is required for each data point For the applied measurement technique, the relationship between the intensity and the underlying truth has to be known. Usually, a linear dependency is preferable Note how sampling interval changes over timecourse

What data would be useful for determining unknown parameters? What are the units here?

P = pro-inflammatory cytokines Salva et al, Ped Pulmonol, 1996 McAllister et al, J Immunol, 2005.