Lecture 13: Athena Chen (Margaret Johnson Lab)

Spatial Cell Modeling Methods 

Due to the complexity of cells, it is useful to use computational tools to understand and predict mechanisms of biological processes. Ordinary differential equations (ODEs) and partial differential equations (PDEs) have proven to be successful at modeling various large systems. However, to understand certain biological processes such as bacterial cell division, high spatial resolution is necessary to discern the underlying mechanisms and interactions. ODEs and PDEs, along with the Gillespie algorithm for stochastic modeling, do not provide spatial resolution at a single-particle level; they are all concentration-based methods. MCell, the Free Propagator Reweighting Algorithm (FPR), and Smoldyn are algorithms that provide single-particle resolution, but may be computationally expensive and may not necessarily yield accurate protein dynamics.

Change in concentration of molecule A in an irreversible 3D reaction A+A -> 0. In this parameter set, the initial distances between molecules causes an increased initial reaction rate.

In her recent work, Athena Chen and her mentors Dr. Margaret Johnson and Dr. Osman Yogurtcu in the Johns Hopkins Biophysics department, analyzed the strengths and limitations of ODEs, PDEs, Gillespie, MCell, Smoldyn, and FPR through establishing and performing a set of benchmark tests. Though all modeling methods extracted the correct equilibrium concentrations for most of the tested reactions, the resulting protein dynamics were not necessarily correct. Simulations at high rates and large densities showed that despite providing single-particle resolution, Smoldyn and MCell do not pick up single-particle effects where the distance between two molecules affects the probability of binding. Furthermore, the dynamics given by Smoldyn and MCell are dependent on the time step selected. On the other hand, FPR correctly identified single-particle effects and yielded dynamics independent of the selected timestep.

As an example of the effects of molecular geometry, diffusion, and stochasticity of protein dynamics, we examined a model for bacterial cell division. From oscillations in protein concentrations, the cell can identify the center of the cell to ensure identical offspring and division of genetic information. 

Written by Athena Chen

Relevant Articles:

1-Yogurtcu, Osman N., and Margaret E. Johnson. "Theory of bi-molecular association dynamics in 2D for accurate model and experimental parameterization of binding rates." The Journal of chemical physics 143.8 (2015): 084117.

2-Andrews, Steven S., et al. "Detailed simulations of cell biology with Smoldyn 2.1." PLoS Comput Biol 6.3 (2010): e1000705.

3-Johnson, Margaret E., and Gerhard Hummer. "Free-Propagator Reweighting Integrator for Single-Particle Dynamics in Reaction-Diffusion Models of Heterogeneous Protein-Protein Interaction Systems." Physical Review X 4.3 (2014): 031037.

4-Kerr, Rex A., et al. "Fast Monte Carlo simulation methods for biological reaction-diffusion systems in solution and on surfaces." SIAM journal on scientific computing 30.6 (2008): 3126-3149.

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Athena Chen is currently working on her Bachelors of Arts in Biophysics and Bachelors of Science in Applied Mathematics and Statistics from Johns Hopkins University. As part of Dr. Margaret Johnson’s lab in the department of Biophysics, she analyzes the accuracy of methods for modeling the dynamics of protein interactions. In her free time, she enjoys yoga and figure skating.