Project Overview
This simulation models the stochastic motion of motor proteins, such as myosin, as they move along intracellular structures. The project uses a biased random walk in a two-level periodic potential landscape to capture the essential features of directional movement, asymmetry, and stochasticity in biological systems.
We implement comprehensive diffusion equations and Boltzmann statistics for protein transport, combining theoretical derivations with numerical simulations to understand the fundamental mechanisms of cellular transport processes.
🔬 Key Biological Concepts
Motor Proteins: Molecular machines that convert chemical energy into mechanical work to transport cargo within cells.
Biased Random Walk: A stochastic process where particles have a preferred direction of movement due to external forces.
Ratchet Potentials: Asymmetric periodic potentials that create directional bias in particle transport.
Boltzmann Statistics: Statistical mechanics principles governing the distribution of particles in energy landscapes.
🔬 Scientific Modeling
- Comprehensive implementation of diffusion equations
- Boltzmann statistics for protein transport
- Two-level periodic potential landscapes
- Asymmetric barriers creating directional bias
� Numerical Analysis
- Monte Carlo simulations with adaptive algorithms
- Analytical comparisons and validation
- Parameter sensitivity analysis
- Statistical error estimation and convergence studies
📊 Data Visualization
- Particle distribution plots over time
- Current flow and transport behavior analysis
- Ratchet potential energy landscapes
- Comparative analysis of different parameters