ProteinDiffusion.jl (WIP)

Modelling the diffusion of proteins on cell membranes for two fusion modes:

• Full Fusion: The vesicle is fully incorporated into the cellular membrane.
• Kiss-and-Run: The vesicle opens a small pore, delivers proteins, then detaches.

This package simulates both scenarios as a concentration level diffusion on the surface of a sphere (full fusion) or connected spheres (kiss-and-run).

Usage

Installation

This package is not registered, and thus can only be installed through cloning this repository.

Loading

After git cloning, run

using ProteinDiffusion

Running

Define the cell and vesicle

v = Membrane(1.0, 1.0)
c = Membrane(2.0, 0.2)

Run the full fusion model.

f = FullFusion(v, c)

View the diffusion

plot(f, arc)

Run the KNR fusion model.

Rj = 0.4
k = KNRFusion(v, c, Rj)

View the diffusion

plot(k.arc)

The raw output data are stored in f.raw and k.raw, and can also be plotted as above.

Model Details

As detailed in the documentation:

1. The full fusion and kiss-and-run fusion models consist of diffusion on a sphere and on connected spheres respectively.
2. The weak form is derived for each fusion mode.
3. The weak form for each mode is then fed to the same 1-dimensional finite element method implementation.
4. Due to stiffness, a backward Euler method discretizes the resulting ODE system.
5. The solved dynamics are interpolated into a function.

Development Roadmap

[x] Include angular extremeties in grid. [ ] Derive base timestep. (Hard, or non-dimensionalise?) [ ] Develop tests for known analytic solutions. [x] Decrease timestepping (especially for integration, becomes visibly piecewise-linear). [ ] Reduce computation time for integration, i.e. don't integrate, use trapezoidal rule instead. [ ] Parse for valid inputs. [ ] Create comparison structure/function. [ ] Compute fusion spot radius. [ ] Simulate pixellation.

Discussion

• TIRF Microscopy method research.
  • Pixel sizes.
  • TIRF zone.
  • Frequency and incident angle of light source.
• Point spread functions.
• Spot radius is the pre-fusion vesicle radius.
• Ring size "same" as spot radius.
• Family of curves.
• Is diffusion slow because of KNR or because of diffusivity?
• Photo taking bleaches the proteins.
  • Lots of early photos.
  • Photos spread out.

References