Improved compensation in flow cytometry by multivariable optimization

Abstract

Conventional compensation of flow cytometry (FMC) data of an N-stained sample requires additional data sets, of N single-stained control samples, to estimate the spillover coefficients. Single-stained controls however are the least rigorous controls because any of the multi-stained controls are closer to the N-stained sample. In this paper a new, optimization based, compensation method has been developed that is able to use not only single- but also multi-stained controls to improve estimates of the spillover coefficients. The method is demonstrated on a data set from 5-stained dentritic cells (DCs) with 5 single-stained and 8 multi-stained controls. This approach is practical and leads to significant improvements in FCM compensation.

Authors response to correspondence about an improved compensation method

“…Recently we proposed an optimization based method for compensating flow cytometry data that is able to use any combination of single or multiple stained controls (1). We demonstrate that our method is superior to the standard approach to compensation supported by commercial flow cytometry software which uses only single stained control samples.…”

“…This approximation is formally similar to the linear model used by conventional compensation but the elements of the transformation matrix ( $\overline{\overline{S}}$ in ref. 1) will be different from the spillover coefficients (elements of $\overline{\stackrel{true¯}{S^0}}$ matrix in ref. 1).…”

“…If there is significant deviation from homogeneously stained cells the averages are not adequate for compensation. In our original article (1), homogeneously stained controls have been defined as follows: “For example in a triple-stained control every cell is stained by 3 fluorochromes and the number of double-stained, single-stained and unstained cells is zero or negligibly small”. Deviation from uniform (homogenous) staining will not alter the estimate of compensation parameters as long as the averages are not significantly shifted.…”

“…Figure 1a is equivalent to the figure in our original article (Figure 1b in ref. 1). It shows the goodness of conventional compensations of full size single stained controls and multiple stained controls, i.e.…”

“…On the other hand our optimization based compensation method decreased |Δ| from 42.0 to 23.9, a significant 43% decrease (see Figure 1b, c in our original article, ref. 1). …”