Analysis of anomalous subdiffusion of single molecules in biomembranes with periodic barriers
Ching-Ya Cheng1*, Chia-Lung Hsieh1
1Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan
* Presenter:Ching-Ya Cheng,
The cell membrane is a crowded and heterogeneous environment, which is composed of different lipids and proteins with great diversity. Increasing evidence suggests that the microscopic molecular diffusion in the biological membrane can deviate from normal diffusion. Anomalous subdiffusion has been observed in various membrane systems where the dynamics are closely connected to the viscoelastic properties of the membrane, molecular crowding, and nanoscopic membrane structures. In the cell plasma membrane at the length scale of 50 to 500 nm, besides anomalous diffusion, it was found that the membranes are compartmentalized by cytoskeletons underneath the membrane which act as semi-permeable barriers to diffusing membrane molecules. Therefore, the microscopic dynamics of membrane molecules are expected to be regulated simultaneously by the anomalous diffusion and the semi-permeable barriers, both of which play important roles in facilitating membrane functions. However, it is not trivial how to measure anomalous diffusion and how to estimate membrane diffusion barriers. First, it is technically challenging to measure molecular dynamics at a small length scale (nanometers) and timescale (microseconds). Moreover, the theoretical model for reconstructing original membrane dynamics and organization from the experimental data is still lacking. The challenge for data analysis is that both the anomalous diffusion and membrane barriers affect the molecular diffusion over similar length scale and timescale, making it very difficult to dissect their individual effects from the experimental data.
In this work, using computational data, we establish a procedure to accurately estimate the anomalous subdiffusion and the diffusion barrier from the diffusion trajectory of a single membrane molecule. We choose to start with simulated 2D fractional Brownian motion (FBM) of a single membrane molecule in the presence of a periodic semi-permeable diffusion barrier. The diffusion trajectory is analyzed by calculating the time-average mean square displacement (MSD). The effects of anomalous diffusion and diffusion barrier to the MSD results are closely inspected. Using regression analysis, we can distinguish the effects of anomalous diffusion and diffusion barrier, by which the anomalous exponent (α) and the properties of diffusion barrier (size and strength) can be estimated accurately. We also explore the possibility of using machine learning to estimate the anomalous diffusion and membrane barriers. Our data analysis makes it possible to study membrane dynamics (anomalous diffusion) and organization (barriers) simultaneously from single-molecule data even when their effects on molecular diffusion occur at a similar length scale and timescale. This work significantly enhances the information one could extract from the single-molecule trajectory data.

Keywords: fractional Brownian motion (FBM) , semi-permeable barriers, time-average mean square displacement (MSD)