Single molecule simulations in complex geometries with embedded dynamic one-dimensional structures.

Area of Science:

• Biochemistry
• Computational Biology
• Cell Biology

Background:

• Stochastic reaction-diffusion models are crucial for biochemical networks with low molecule counts or diffusion limitations.
• Biological systems often involve reactions and transport on 1D structures (e.g., DNA, microtubules) within cells.
• The dynamic nature of cytoskeletal structures necessitates advanced simulation capabilities.

Purpose of the Study:

• To develop a versatile simulation algorithm for reaction-diffusion systems.
• To integrate single-molecule simulations in 3D space with those on 1D structures of arbitrary shape.
• To model complex molecular interactions including diffusion, reaction, association/dissociation, and transport on dynamic 1D structures.

Main Methods:

• Developed a simulation algorithm combining 3D and 1D single-molecule simulations.
• Approximated arbitrary 1D curves with piecewise linear segments for computational efficiency and accuracy.
• Incorporated molecular diffusion, reactions in space and on 1D structures, and active transport.

Main Results:

• The algorithm successfully simulates molecules diffusing and reacting in 3D space and on 1D structures.
• It models molecule association/dissociation with 1D structures.
• The simulation accurately captures dynamic 1D structures (movement, growth, shrinkage) and molecular transport.

Conclusions:

• The presented algorithm offers high flexibility and accuracy for simulating complex biochemical processes in cellular environments.
• It provides a powerful tool for studying reaction-diffusion systems involving 1D cellular structures.
• The method is validated through five numerical examples demonstrating its capabilities.