Estimation of diffusion constants from single molecular measurement without explicit tracking

Shunsuke Teraguchi, Yutaro Kumagai

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Background: Time course measurement of single molecules on a cell surface provides detailed information about the dynamics of the molecules that would otherwise be inaccessible. To extract the quantitative information, single particle tracking (SPT) is typically performed. However, trajectories extracted by SPT inevitably have linking errors when the diffusion speed of single molecules is high compared to the scale of the particle density. Methods: To circumvent this problem, we develop an algorithm to estimate diffusion constants without relying on SPT. The proposed algorithm is based on a probabilistic model of the distance to the nearest point in subsequent frames. This probabilistic model generalizes the model of single particle Brownian motion under an isolated environment into the one surrounded by indistinguishable multiple particles, with a mean field approximation. Results: We demonstrate that the proposed algorithm provides reasonable estimation of diffusion constants, even when other methods suffer due to high particle density or inhomogeneous particle distribution. In addition, our algorithm can be used for visualization of time course data from single molecular measurements. Conclusions: The proposed algorithm based on the probabilistic model of indistinguishable Brownian particles provide accurate estimation of diffusion constants even in the regime where the traditional SPT methods underestimate them due to linking errors.

Original languageEnglish
Article number15
JournalBMC Systems Biology
Publication statusPublished - 2018 Apr 11
Externally publishedYes


  • Brownian motion
  • Diffusion constants
  • Expectation maximization algorithm
  • Probabilistic model
  • Single molecular measurement

ASJC Scopus subject areas

  • Structural Biology
  • Modelling and Simulation
  • Molecular Biology
  • Computer Science Applications
  • Applied Mathematics


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