Abstract
Single-cell responses are shaped by the geometry of signalling kinetic trajectories carved in a multidimensional space spanned by signalling protein abundances. It is, however, challenging to assay a large number (more than 3) of signalling species in live-cell imaging, which makes it difficult to probe single-cell signalling kinetic trajectories in large dimensions. Flow and mass cytometry techniques can measure a large number (4 to more than 40) of signalling species but are unable to track single cells. Thus, cytometry experiments provide detailed time-stamped snapshots of single-cell signalling kinetics. Is it possible to use the time-stamped cytometry data to reconstruct single-cell signalling trajectories? Borrowing concepts of conserved and slow variables from non-equilibrium statistical physics we develop an approach to reconstruct signalling trajectories using snapshot data by creating new variables that remain invariant or vary slowly during the signalling kinetics. We apply this approach to reconstruct trajectories using snapshot data obtained from in silico simulations, live-cell imaging measurements, and, synthetic flow cytometry datasets. The application of invariants and slow variables to reconstruct trajectories provides a radically different way to track objects using snapshot data. The approach is likely to have implications for solving matching problems in a wide range of disciplines.
Highlights
Tracking signalling events in single cells is a key step towards understanding single-cell response mechanisms
The mass action kinetics of the biochemical reactions are described as an autonomous system of linear firstorder ordinary differential equations (ODEs)
We have developed a framework for matching single cells across time using time-stamped data from flow and mass cytometry experiments
Summary
Tracking signalling events in single cells is a key step towards understanding single-cell response mechanisms. Our understanding regarding the link between the geometry of signalling kinetic trajectories and single-cell responses are often limited to few [1,2,3] molecular species. This is because spectral overlap between fluorescent dyes and photo-toxicity induced by excited fluorophores [3] make it challenging to track a large number (more than 3) of molecular species in live-cell imaging experiments. Flow cytometry [4,5] and recently developed mass cytometry experiments [4,5] can assay 4 to more than 40 proteins simultaneously in single cells at multiple times, but it is not possible to track single cells in these experiments. Is it possible to reconstruct single-cell trajectories, even approximately, from such time-stamped snapshot data? An affirmative answer to this question will be valuable for analysing signalling mechanisms or calculation of autocorrelation functions [6] for extracting relevant time scales and inference of signalling networks [7]
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