Fig 1.
Measuring lymphocyte responses using a range of fluorescent probes.
Panels show flow cytometry results for a time point from different representative B or T cell activation experiments. A: CTV can be used to estimate number of cells that divided 4 times since activation (“generation 4” gate). B: Blimp1-GFP reporter and IgG1-APC antibody enable estimation of non-differentiated cells (purple gate). IgG1-APC is a fluorescent probe-conjugated antibody against IgG. C: FUCCI reporter system allows one to estimate cells in different cell cycle stages (labeled quadrants). In each case, estimates are obtained using semi-manual gates. Such gates can be initially set using an automated routine, but it is a common practice to manually validate and adjust the gates.
Fig 2.
Measurement process encapsulates biological variability and experimental error.
Since it is difficult to formalize experimental error, a common strategy is to consider a stochastic measurement generating process as a whole. Measurements can then be described using a measurement distribution. Internally, this distribution is a result of stochastic lymphocyte response and experimental error (including data pre-processing, such as gating).
Table 1.
Assumptions involved in previous measurement models (used either for model fitting or model selection).
Table 2.
Summary of experimental data used in this work.
Fig 3.
Empirical power-law relation between the mean and variance of measurements.
Each point represents a single component of a sample of repeated measurements (replicates). For example, a point can represent repeated estimates of the number of cells falling in the GFP+ gate, or the number of cells in generation two for a particular time point. Each plot corresponds to all measured groups and time points for a particular dataset. The combined plot is composed of a collection of 20 random points sampled uniformly from each dataset. Red lines show fitted power law relations (variance) = α(mean)β, and the fitted power exponent is indicated for each dataset. Green lines show function (variance) = (mean)2/9. Most of the points are located below the green line, indicating that sample means tend to be larger than 3 standard deviations. If one assumes a Gaussian shape for the distribution of the measurements, this tendency indicates that most of the distribution mass is located in the positive Euclidean subspace.
Fig 4.
The problem of assuming zero mean for experimental error.
Consider two fits to the same data extracted from t–il2 dataset for 316 U/mL condition. In this experiment, a data sample comprises repeated estimates of number of cells in a particular generation. The green fit goes through all generation means, except for the first sample pointed by the arrow. The blue fit predicts an arbitrary value everywhere. Intuitively, the green fit is more feasible, but the blue fit is more likely. This happens because for the first sample variance is close to zero which makes the whole green fit nearly impossible. In practice, mismatch at the first sample can be attributed to a non-zero mean of modeling or experimental noise.
Fig 5.
Model fitting using different measurement models.
The Cyton model was fitted to t–n4 data using different measurement models. Resulting AICc scores are 2050.7 (3F), 3633.8 (SSR), 4001.7 (LogNrm), and 109231.8 (LVS). For the fit obtained using LogNrm model, AICc was computed using the SSR measurement model.
Fig 6.
SSR is not suitable for multiconcentration fitting.
ADMBP and Cyton models are fitted to a low and high stimulation condition selected from t–il2 dataset. When a low concentration data is fitted independently, SSR can be used to fit models. However, when both concentrations are fitted simultaneously, SSR tends to ignore low concentration data because the range of these data is comparable to measurement noise for the high concentration measurements. At the same time, 3F tends to produce more balanced fits, because it scales measurement variance in accordance to the mean.