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Related Concept Videos

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Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
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Related Experiment Video

Updated: Feb 10, 2026

Visualizing Diffusional Dynamics of Gold Nanorods on Cell Membrane using Single Nanoparticle Darkfield Microscopy
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Pseudotime graph diffusion for post hoc visualization of inferred single-cell trajectories.

Brandon Lukas1, Jingbo Pang2, Timothy J Koh2

  • 1Department of Biomedical Engineering, University of Illinois Chicago, Chicago, USA.

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|February 9, 2026
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Pseudotime Graph Diffusion (PGD) smooths cell features along trajectories, improving visualization and interpretation of single-cell data dynamics. This method enhances understanding of complex cellular processes like wound healing.

Keywords:
Markov processesRNAbiological processesgraph theoryinformation diffusionsmoothing methods

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Area of Science:

  • Computational biology
  • Single-cell analysis
  • Bioinformatics

Background:

  • Visualizations are crucial for interpreting single-cell trajectories but often fail to accurately represent trajectory structure.
  • Inaccurate trajectory representations compromise the interpretation of cellular dynamics and downstream analyses.

Purpose of the Study:

  • To introduce Pseudotime Graph Diffusion (PGD), a novel post hoc framework for enhancing the interpretation of single-cell trajectory data.
  • To improve the fidelity of visual representations of inferred cellular trajectories.

Main Methods:

  • PGD employs random-walk diffusion on a pseudotime graph to smooth cell-level features.
  • The framework propagates information along inferred trajectory paths to enhance continuity and structure.
  • PGD was applied to visualize monocyte and macrophage trajectories during wound healing.

Main Results:

  • PGD-smoothed embeddings significantly improved the visualization of complex inferred trajectories.
  • The method demonstrated effectiveness in smoothing monocyte and macrophage dynamics during wound healing.
  • PGD was extended to enable trajectory-aware gene expression smoothing.

Conclusions:

  • PGD offers a lightweight and interpretable solution for improving single-cell trajectory analysis.
  • By enhancing the agreement between visualizations and inferred trajectories, PGD facilitates more accurate interpretation of dynamic cellular processes.
  • The framework provides a valuable tool for researchers studying cellular dynamics and differentiation pathways.