Abstract
The clustering of membrane-bound proteins facilitates their transport by cortical actin flow in early Caenorhabditis elegans embryo cell polarity. PAR-3 clustering is critical for this process, yet the biophysical processes that couple protein clusters to cortical flow remain unknown. We develop a discrete, stochastic agent-based model of protein clustering and test four hypothetical models for how clusters may interact with the flow. Results show that the canonical way to assess transport characteristics from single-particle tracking data used thus far in this area, the Péclet number, is insufficient to distinguish these hypotheses and that all models can account for transport characteristics quantified by this measure. However, using this model, we demonstrate that these different cluster–cortex interactions may be distinguished using a different metric, namely the scalar projection of cluster displacement on to the flow displacement vector. Our results thus provide a testable way to use existing single-particle tracking data to test how endogenous protein clusters may interact with the cortical flow to localize during polarity establishment. To facilitate this investigation, we also develop both improved simulation and semi-analytic methodologies to quantify motion summary statistics (e.g., Péclet number and scalar projection) for these stochastic models as a function of biophysical parameters.
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Code availability
We used Python 3.8.7 (Python Software Foundation, https://www.python.org/), Matplotlib (Hunter 2007), Pandas (McKinney 2010), NumPy (Harris et al. 2020), SciPy (Virtanen et al. 2020), Numba (Lam et al. 2015), seaborn (Waskom 2021), Joblib (https://joblib.readthedocs.io), and Jupyter (Pérez and Granger 2007) for our simulations and analysis. The code used to make the figures is available as a GitHub repository at https://github.com/zmurchok/par-protein-transport-model.
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Acknowledgements
We acknowledge John J. Vastola for helpful discussions. This work was supported by a National Science Foundation, United States, Grant DMS1562078 (to WRH) and a Natural Sciences and Engineering Research Council of Canada (NSERC) Postdoctoral Fellowship Award (to CZ).
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Zmurchok, C., Holmes, W.R. Biophysical Models of PAR Cluster Transport by Cortical Flow in C. elegans Early Embryogenesis. Bull Math Biol 84, 40 (2022). https://doi.org/10.1007/s11538-022-00997-6
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DOI: https://doi.org/10.1007/s11538-022-00997-6