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Single cell responses are shaped by the geometry of signaling kinetic trajectories carved in a multidimensional space spanned by signaling protein abundances. It is however challenging to assay large number (>3) of signaling species in live-cell imaging which makes it difficult to probe single cell signaling kinetic trajectories in large dimensions. Flow and mass cytometry techniques can measure a large number (4 - >40) of signaling species but are unable to track single cells. Thus cytometry experiments provide detailed time stamped snapshots of single cell signaling kinetics. Is it possible to use the time stamped cytometry data to reconstruct single cell signaling trajectories? Borrowing concepts of conserved and slow variables from non-equilibrium statistical physics we develop an approach to reconstruct signaling trajectories using snapshot data by creating new variables that remain invariant or vary slowly during the signaling kinetics. We apply this approach to reconstruct trajectories using snapshot data obtained from in silico simulations and live-cell imaging measurements. The use of invariants and slow variables to reconstruct trajectories provides a radically different way to track object using snapshot data. The approach is likely to have implications for solving matching problems in a wide range of disciplines.
The development of single-cell technologies provides the opportunity to identify new cellular states and reconstruct novel cell-to-cell relationships. Applications range from understanding the transcriptional and epigenetic processes involved in meta
Mathematical methods of information theory constitute essential tools to describe how stimuli are encoded in activities of signaling effectors. Exploring the information-theoretic perspective, however, remains conceptually, experimentally and computa
We study the stochastic kinetics of a signaling module consisting of a two-state stochastic point process with negative feedback. In the active state, a product is synthesized which increases the active-to-inactive transition rate of the process. We
Continuous time Hamiltonian Monte Carlo is introduced, as a powerful alternative to Markov chain Monte Carlo methods for continuous target distributions. The method is constructed in two steps: First Hamiltonian dynamics are chosen as the determinist
Electronic Health Records (EHRs) are typically stored as time-stamped encounter records. Observing temporal relationship between medical records is an integral part of interpreting the information. Hence, statistical analysis of EHRs requires that cl