Model-based extension of high-throughput to high-content data

Abstract

Background: High-quality quantitative data is a major limitation in systems biology. The experimental data used in systems biology can be assigned to one of the following categories: assays yielding average data of a cell population, high-content single cell measurements and high-throughput techniques generating single cell data for large cell populations. For modeling purposes, a combination of data from different categories is highly desirable in order to increase the number of observable species and processes and thereby maximize the identifiability of parameters.

Results: In this article we present a method that combines the power of high-content single cell measurements with the efficiency of high-throughput techniques. A calibration on the basis of identical cell populations measured by both approaches connects the two techniques. We develop a mathematical model to relate quantities exclusively observable by high-content single cell techniques to those measurable with high-content as well as high-throughput methods. The latter are defined as free variables, while the variables measurable with only one technique are described in dependence of those. It is the combination of data calibration and model into a single method that makes it possible to determine quantities only accessible by single cell assays but using high-throughput techniques. As an example, we apply our approach to the nucleocytoplasmic transport of STAT5B in eukaryotic cells.

Conclusions: The presented procedure can be generally applied to systems that allow for dividing observables into sets of free quantities, which are easily measurable, and variables dependent on those. Hence, it extends the information content of high-throughput methods by incorporating data from high-content measurements.

Figure 1

Workflow for calibrating and linking data from different experiments. The calibration and model are the crucial steps of the procedure described here. Data calibration by a quantile-quantile (QQ) plot allows to translate data from one technique to the units of another measurement. Here, it is necessary to determine quantities with a known relationship from the identical cell population by both methods (blue). Furthermore, a model has to be developed to describe the dependent variables only measurable by one technique in terms of the free variables assessable by both techniques (green). Then, additional cell populations can be measured by the high-throughput technique only and the information content of the data can be increased via the calibration and the model (dashed arrows, red) to be finally combined with cell population data for mathematical modeling by an ordinary differential equation (ODE) model (transparent red). General terms are shown in bold letters, the specific case of the example system is given below. Steps shown in transparent colors are not subject of this study.

Figure 2

Rates and currents of STAT5B nucleocytoplasmic cycling. (A) Summary of all rates α_imp and α_exp. The rates directly correspond to the exponential of the fits to the FRAP data. Gaussian error propagation leads to the error bars for α_imp and α_exp. The relative uncertainty of the fitted parameter a₁ is negligible compared to the relative uncertainty of the denominator. Relative errors of concentrations and volumes can be estimated to be around 10% and lead to the rate uncertainties. In addition, for the currents (panels (B)-(D)) a small constant error has been added to every point to avoid overvaluing small currents. (B) Michaelis-Menten fit for import (left) and export currents (right) not normalized, (C) normalized to nucleus surface area and (D) normalized to the respective originating compartment volume. χ² values of the fit are indicated in the plot.

Figure 3

Pairwise import/export model comparison. Plot of the estimated significance of model difference for pairwise compared import models (upper left triangle) and export models (lower right triangle). Values q < 0.5 indicate superiority of the model on the vertical axis compared to the model on the horizontal axis at a confidence level of 1 - q. Accordingly for values q > 0.5.

Figure 4

Data calibration. (A) Scatter plot of flow cytometry forward scatter versus side scatter. Excluded data points are shown in light grey. Dashed lines indicate chosen cut for data exclusion. (B) X²curves for the quantile-quantile plot versus the cut position for the flow cytometry data for cell volume (dashed line) and fluorescence intensity (solid line). (C) Quantile-quantile plots for cell volumes (left) and fluorescence intensities (right) used for calibration. Cell populations treated with 10 ng/ml and 250 ng/ml doxycycline are both included. Flow cytometry data are raw data, microscopy data have been transformed to represent the same parameters as flow cytometry data. The number of quantiles corresponds to the number of microscopy data points.

Figure 5

Current distribution. Distribution of import (left) and export (right) currents for exemplary cell populations treated with 5 ng/ml doxycycline (dashed lines) or 50 ng/ml doxycycline (solid lines). Transport currents are normalized to the size of the respective originating compartment.