The volumes and transcript counts of single cells reveal concentration homeostasis and capture biological noise

Abstract

Transcriptional stochasticity can be measured by counting the number of mRNA molecules per cell. Cell-to-cell variability is best captured in terms of concentration rather than molecule counts, because reaction rates depend on concentrations. We combined single-molecule mRNA counting with single-cell volume measurements to quantify the statistics of both transcript numbers and concentrations in human cells. We compared three cell clones that differ only in the genomic integration site of an identical constitutively expressed reporter gene. The transcript number per cell varied proportionally with cell volume in all three clones, indicating concentration homeostasis. We found that the cell-to-cell variability in the mRNA concentration is almost exclusively due to cell-to-cell variation in gene expression activity, whereas the cell-to-cell variation in mRNA number is larger, due to a significant contribution of cell volume variability. We concluded that the precise relationship between transcript number and cell volume sets the biological stochasticity of living cells. This study highlights the importance of the quantitative measurement of transcript concentrations in studies of cell-to-cell variability in biology.

FIGURE 1:

Statistics of single-cell mRNA numbers. (A) Schematic overview of the smFISH method applied to our reporter gene mRNA. Colocalization of the mRNA molecules with the DAPI counter staining identified spots as nuclear mRNA (m_N); others are cytoplasmic mRNA (m_c). (B) Statistics of the mRNA molecules in the cell (m), nucleus (m_N), and cytoplasm (m_c) for the three different clones (color coded: Clone I is shown in red, Clone II is shown in blue, and Clone III is shown in green). Notation: μ = mean; σ = SD; cv = coefficient of variation; Δ^σ = the fraction of samples between μ - σ and μ + σ; ρ = correlation between m_c and m_N; and *p < 0.001 The 95% confidence intervals of the statistics are given in Supplemental Figure S15. (C) For a specific cell volume (V), the mean mRNA number is calculated from the data. This conditional mean displays linear scaling with respect to volume, indicating homeostasis in mRNA concentration. The gray histogram in the background shows the total number of cells per volume bin for all three clones (bin size = 100 〈m|V〉). Higher counts indicate higher reliability of the corresponding determination of σ. A least-squares linear fit is shown for all three clones. The explained fraction of the variance in 〈m|V〉 with this fit is 0.80, 0.77, and 0.84 for clones I, II, and III, respectively. Supplemental Figure S9 shows the single-cell relation between cell volume and mRNA number. The conditional variances of the data are given in Supplemental Figure S10. (D) Representative confocal images of a cell, with Z1 to Z12 corresponding to subsequent optical sections (z-slices) of the cell. The mRNA molecules are shown in red; the DAPI-stained nucleus is shown in blue. Additional images are given in Supplemental Figure S2. (E–G) Scatter plots of m_c and m_N for the three different clones. Marginal histograms show the distribution of m_c (top) and m_N (right). The measured number of cells is given by n.

FIGURE 2:

Statistics of single-cell volumes. (A) Overview of the determination of the cell volumes. The background intensity was used to track the contour of the cell, and the DAPI signal provides the nuclear contour. The three-dimensional cell image was reconstructed by combining the contours of subsequent z-slices. (B) Statistics of the volumes of the cell (V), nucleus (V_N), and cytoplasm (V_c) for the three different clones (color coded). Notation: μ = mean; σ = SD; cv = coefficient of variation; Δ^σ = the fraction of samples between μ – σ and μ + σ; ρ = correlation between m_c and m_N; and *p < 0.001 (H0: ρ = 0).The 95% confidence intervals of the statistics are given in Supplemental Figure S15. (C–E) Scatter plots of V_c and V_N for the three different clones. Marginal histograms show the distribution of V_c (top) and V_N (right). Supplemental Figure S5 gives the distributions of V. The measured number of cells is given by n.

FIGURE 3:

Statistics of single-cell mRNA concentrations. (A) The previously obtained mRNA number (Figure 1) and volume data (Figure 2) were used to determine the concentration of mRNA in single cells (c), in their nuclei (c_N), and in their cytoplasm (c_c). (B) Statistics of the different mRNA concentrations for the three different clones (color coded). Notation: μ = mean; σ = SD; cv = coefficient of variation; Δ^σ = the fraction of samples between μ – σ and μ + σ; ρ = correlation between m_c and m_N; and *p < 0.001 (H0: ρ = 0). The 95% confidence intervals of the statistics are given in Supplemental Figure S15. (C) For a specific cell volume (V), the mean mRNA concentration (〈c|V〉) is calculated. This conditional mean is constant with respect to volume. The gray histogram in the background shows the number of cells considered per volume bin (bin size = 100 μm³). Higher counts indicate higher reliability of the corresponding determination of A least-squares linear fit is shown for all three clones, indicating mRNA concentration homeostasis. The conditional variances of the data set are shown in Supplemental Figure S10. (D–F) Scatter plots of (c_N) and (c_c) for the three different clones. Marginal histograms show the distribution of (c_c) (top) and (c_N) (right). The given concentration (number per cubic micrometer) can be converted to picomoles (pM) by multiplying with a conversion factor of 1660. The sample size is given by n. The bin size for the marginal histograms is 0.001 #/μm³.

FIGURE 4:

The theoretical and experimental relations between mRNA concentration and mRNA number noise and their dependency on volume. (A) Overview of theoretical relation used to analyze the data. The mRNA number noise and mRNA concentration noise can be decomposed into two terms; the volume-dependent noise and gene-expression noise (see Eq. 1). When there is homeostasis of mRNA concentration, the relation between and depends on the scaling of the variance in the conditional mRNA numbers. Under these conditions, the volume-dependent noise in mRNA numbers equals the noise in the volume distribution . (B) Experimental data of the relation shown in the theoretical section (A). The different colors give the corresponding measures for the three different clones. The circle graphs show how the total mRNA number and mRNA concentration noise are decomposed. mRNA number noise is higher than concentration noise, mainly due to its volume contribution. The scaling of var(m|V) with volume for clone III is shown. The observed scaling is linear or quadratic, resulting in a deviation of ± 4% between and . The scaling of var(m|V) with volume for clones I and II can be found in Supplemental Figure S10.