Figures and data
A schematic of our computational approach.
(top) single cell data across different input conditions and time points are integrated with a stochastic model of a signaling network using a previous developed maximum entropy approach leading to a distribution over signaling network parameters p(θ) (middle). (bottom) In silico cells are generated using the inferred parameter distribution and cell-state specific mutual information I(θ) and population distribution of cell performances pCeeMl(I) is estimated. The model also evaluates the correlation between cells’ performance and biochemical parameters.
A. The distribution of single cell sensing abilities (horizontal blue histograms) and its averag plotted as a function of the coefficient of variation of the distribution of one cell state variable, the cell surface receptor number The dashed blue lines show the traditional cell state averaged mutual information (Eq. 1). The inset shows the dependence between cell state specific mutual information and cell state variable The input distribution is assumed to be a gamma distribution. B. A schematic showing the effect of heterogeneity in cell states on population level response. Even when individual cells have little overlap in their responses to extracellular signal (bottom), the population level responses could have significant overlap (top), leading to a low mutual information between cell state averaged response and the input. C. A combined schematic of the two growth factor pathways. Extracellular growth factor ligand (red circle) binds to cell surface receptors which are shuttled to and from the plasma membrane continuously. Ligand bound receptors are phosphorylated and activate Akt. Phosphorylated Akt leads to phosphorylation of FoxO which bars it from entering the nucleus. EGF/EGFR model is limited to the reactions on the plasma membrane. The corresponding cell state variables are given by: θ= {kprod, kbind, kunbind, kp, kdp, kdeg,
Dependence on cell state dependent mutual information on biochemical parameters.
(left) The joint distribution pCeeMI (I, χ) of cell state specific mutual information and biochemical parameter χ chosen to be the single cell response range of nuclear FoxO levels (x-axis, see inset for a cartoon). The shaded blue regions are model predictions, and the green line is the model average. The darker shades represent higher probabilities. The red dots represent experimental cells. The cyan line represents experimental averages. (right) same as (left) with biochemical parameter χ chosen to be steady state nuclear Foxo levels in the absence of stimulation. The contours represent 1% to 10%, 10% to 50%, and 50% to 100% of the total probability mass (from faint to dark shading).
Cell state dynamics governs cell state conditioned mutual information.
A. In a simple stochastic model, receptor mRNA is produced at a constant rate from the DNA and the translated into ligand-free receptors. The number of ligand-bound receptors after a short exposure to ligands is considered the output. B. A schematic showing dynamics of receptor numbers when mRNA dynamics are slower compared to signaling time scales. C. Conditioning on receptor numbers leads to differing abilities in sensing the environment when the time scale of mRNA dynamics is slow. In contrast, when the mRNA dynamics are fast (large τ-1), conditioning on cell state variables does not lead to difference in sensing abilities.
