I(θ) quantifies individual cells’ ability to sense their environment as a function of the cell state parameters θ. The distribution pCeeMI (I) of single cell sensing abilities is

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 pCeeMI(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 effectively shuttles it out of the nucleus. D. The estimated distribution of single cell mutual information values for the EGF/EGFR pathway. The inset shows the input distribution corresponding to the maximum of the average of (blue), along with the input distribution corresponding to the channel capacity of ICSA (green). E. Same as D for the IGF/FoxO pathway. We additionally show the experimentally estimated pCeeMI(I) (pink).

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).