Schematic overview of scMRA and scCNR. (A) The methods exploit natural heterogeneity of phospho-and total protein abundances between cells to infer the network topology and quantify the interaction strengths between network nodes. (B) The methods take phospho-and total protein abundances from single cells as input, with additional cell population annotations for scCNR. Optionally the methods can be enriched with perturbation data and a prior network topology. The algorithms exploit deviations of total protein from the population mean (R tot ) as 'natural perturbations'. They fit the data to describe single-cell deviations of phosphoprotein from its population mean (R) for a single population (scMRA) or several populations in parallel (scCNR) to derive (cell populationspecific) interaction strengths (r). The algorithms penalize the number of edges in the network. scCNR further penalizes the number of population-specific interaction strengths.

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... cell Modular Response Analysis (scMRA) reconstructs signal transduction networks from the quantification of phosphoand total proteins in single cells. scMRA exploits the stochastic variability of total protein levels between single cells as natural perturbations to the signaling network (Fig. 1A). Stochastic di↵erences in the abundance of total proteins between cells directly a↵ect the abundance of the corresponding phosphoproteins. These changes in phosphoprotein levels then propagate through the network leading to distinct steady states of the network in each individual cell. Each cell is considered as an independent ...

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... levels then propagate through the network leading to distinct steady states of the network in each individual cell. Each cell is considered as an independent measurement of the underlying signaling network. scMRA reconstructs a unique set of interaction strengths for a cell population (yellow and blue boxes representing populations A and B in Fig. 1). To model the variation between cell populations (which may represent for instance di↵erent cell states, cells with and without an oncogenic mutation, cells before and after acquiring resistance to a drug, or cells that are cultured for a long time in the presence or absence of an inhibitor), we developed single cell Comparative ...

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... to the methods are deviations of abundances of total (R tot ) and phosphoprotein (R) of each cell from the cell population mean, for each node in the network (Fig. 1B, 'Input'). The output is the network topology described by interaction strengths between phosphoproteins (r), and sensitivities of phosphoproteins to deviations in its total protein (s) (Fig. 1B, 'Output'). scMRA is formulated as a MIQP problem and fits a model that (i) for each node in each cell aims to explain the deviations of ...

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... methods are deviations of abundances of total (R tot ) and phosphoprotein (R) of each cell from the cell population mean, for each node in the network (Fig. 1B, 'Input'). The output is the network topology described by interaction strengths between phosphoproteins (r), and sensitivities of phosphoproteins to deviations in its total protein (s) (Fig. 1B, 'Output'). scMRA is formulated as a MIQP problem and fits a model that (i) for each node in each cell aims to explain the deviations of phosphoprotein abundance from the population mean and (ii) penalizes the model complexity (number of interactions) to derive a core signaling network. scCNR also derives a core signaling network with a ...

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... mean and (ii) penalizes the model complexity (number of interactions) to derive a core signaling network. scCNR also derives a core signaling network with a small number of interaction strength di↵erences between cell populations, while still producing a good model fit by (iii) penalizing the number of population-specific interaction strengths (Fig. 1B, ...

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... e.g. by small molecular inhibitors, can be included in the experimental design and model to facilitate network reconstruction. Furthermore, the formulation of the algorithm allows for easy integration of prior network information for cases where the topology might be established and the main interest lies in quantifying the interactions (Fig. 1B, ...