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Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
Published on: September 5, 2019
Fractional brownian motion versus the continuous-time random walk: a simple test for subdiffusive dynamics.
Marcin Magdziarz1, Aleksander Weron, Krzysztof Burnecki
1Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland. marcin.magdziarz@pwr.wroc.pl
Physical Review Letters
|November 13, 2009
Summary
This study introduces a new test to differentiate between fractional Brownian motion and continuous-time random walks in complex systems. The test suggests that mRNA molecule motion in E. coli cells likely follows fractional Brownian motion.
Area of Science:
- Physics
- Biophysics
- Statistical Mechanics
Background:
- Subdiffusive behavior is common in complex systems.
- Fractional Brownian motion (fBm) and continuous-time random walks (CTRW) with heavy tails are two models explaining subdiffusion.
- Distinguishing between these models is crucial for understanding complex system dynamics.
Purpose of the Study:
- To develop a simple test to distinguish between fBm and heavy-tailed CTRW models.
- To apply this test to experimental data of intracellular transport.
- To determine the underlying stochastic process governing mRNA motion in E. coli.
Main Methods:
- Analysis of "p variations" from a single trajectory.
- Comparison of experimental data with theoretical predictions of fBm and CTRW.
- Application of the test to previously published data on mRNA dynamics in E. coli.
Main Results:
- The proposed test effectively distinguishes between fBm and heavy-tailed CTRW.
- Analysis of Golding and Cox's data indicates that mRNA motion in E. coli does not follow a heavy-tailed CTRW.
- The data strongly suggests that fractional Brownian motion underlies the observed mRNA dynamics.
Conclusions:
- The "p variations" test provides a powerful tool for model selection in subdiffusive processes.
- Intracellular mRNA transport in E. coli is more accurately described by fractional Brownian motion than by a continuous-time random walk.
- This finding has implications for understanding molecular mechanisms within living cells.
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