Single-cell variability in multicellular organisms

Abstract

Noisy gene expression is of fundamental importance to single cells, and is therefore widely studied in single-celled organisms. Extending these studies to multicellular organisms is challenging since their cells are generally not isolated, but individuals in a tissue. Cell-cell coupling via signalling, active transport or pure diffusion, ensures that tissue-bound cells are neither fully independent of each other, nor an entirely homogeneous population. In this article, we show that increasing the strength of coupling between cells can either increase or decrease the single-cell variability (and, therefore, the heterogeneity of the tissue), depending on the statistical properties of the underlying genetic network. We confirm these predictions using spatial stochastic simulations of simple genetic networks, and experimental data from animal and plant tissues. The results suggest that cell-cell coupling may be one of several noise-control strategies employed by multicellular organisms, and highlight the need for a deeper understanding of multicellular behaviour.

Fig. 1

Differences between a population of isolated cells and a tissue of cells. a A population of isolated cells: each cell contains an identical genetic network. b A tissue of cells: each cell contains an identical genetic network and some molecules can be transported between neighbouring cells (dotted lines). c Typical single-cell protein trajectories of system (1) in isolated cells. d Typical single-cell protein trajectories of system (1) in a tissue of connected cells: noise is clearly reduced compared to c. e Typical single-cell protein trajectories of system (3) in isolated cells. f Typical single-cell protein trajectories of system (3) in a tissue of connected cells: noise is clearly increased compared to e. Parameter values are v₀ = 4, d₀ = 1, v₁ = 10, d₁ = 1, t = 10, N² = 100, V_C = 1 for system (1) and k₁ = 32, k₂ = 0.01, t = 10, N² = 100, V_C = 1 for system (3)

Fig. 2

L as a function of protein transport rate for the two-stage gene expression system (1). Theoretical values for the fast transport limit (red), and slow transport limit (green) are shown as solid lines. Simulation data is shown for the average single-cell variability (blue squares) for a variety of protein transport rates. Parameter values are v₀ = 3, d₀ = 1, v₁ = 10; d₁ = 1, V_C = 1, V_T = 100. Inset: schematic diagram of system (1)

Fig. 3

L as a function of protein transport rate for the dimerisation system (3). Theoretical values for the fast transport limit (red) and slow transport limit (green) are shown as solid lines. Simulation data is shown for the average single-cell variability L (blue squares) for a variety of protein transport rates. Parameter values are k₁ = 32, k₂ = 0.01, V_C = 1, V_T = 100. Inset: schematic diagram of system (3)

Fig. 4

L as a function of protein transport rate for the three-stage gene expression system (8). Theoretical values for the fast transport limit (red), and slow transport limit (green) are shown as solid lines. Simulation data is shown for the average single-cell variability (blue squares) for a variety of protein transport rates. Parameter values are k_on = 0.1, k_off = 0.1, $v_0^{\mathrm{on}}=3,v_0^{\mathrm{off}}=1$, d₀ = 1, v₁ = 1, d₁ = 1, V_C = 1, V_T = 25. Inset: schematic diagram of system (8)

Fig. 5

Comparison of fast (red) and slow (green) transport limits with single-cell data (blue squares: mean; blue bars: 1 standard deviation above mean) for a a tissue of 117 E18.5 rat pituitary cells, b a tissue of 114 P1.5 rat pituitary cells. Insets: typical single-cell trajectories from the raw data. Data are taken from ref.

Fig. 6

Comparison of fast (red) and slow (green) transport limits with single-pixel data (blue squares: mean; blue bars: 1 standard deviation above mean) for a a single leaf of Arabidopsis thaliana, b a population of 30 mouse fibroblast cells. Insets: typical single-cell trajectories from the raw data. Data is taken from a ref. , available at ref. , b ref.