This project is a computational extension of my master's thesis research. It uses simulation and graph-based modelling to test whether a biological hypothesis around molecular cross-correction is plausible under simplified conditions. The central question is: if only a subset of nuclei in a multinucleated muscle fibre are corrected, could locally transported signal accumulate enough to rescue neighbouring nuclei? The model treats this as a structured numerical experiment in signal production, diffusion, decay, and rescue thresholds.
This simulation is conceptually linked to the co-authored publication: Cell-mediated exon skipping normalizes dystrophin expression and muscle function in a new mouse model of Duchenne Muscular Dystrophy . The paper investigates U7 snRNA-mediated exon skipping and cross-correction in multinucleated muscle fibres, providing the biological motivation for this modelling exercise.
| Part | Model change | Purpose |
|---|---|---|
| 1 | Naive line simulation | Turn the biological idea into executable logic |
| 2 | Graph Laplacian diffusion | Replace manual averaging with a formal transport operator |
| 3 | Geometry-based spatial graph | Make connectivity depend on proximity |
| 4 | Parameter sensitivity | Test diffusion, decay, source fraction, and threshold assumptions |
| 5 | Cumulative exposure rescue | Model sustained signal accumulation rather than instant rescue |
# Graph Laplacian diffusion update
# u: signal at each nucleus
# L: graph Laplacian, q: source production
# alpha: diffusion strength, beta: decay, dt: step size
for t in range(num_steps):
diffusion = -alpha * (L @ u)
decay = -beta * u
source = q
u = u + dt * (diffusion + decay + source)
exposure = exposure + u * dt
rescued = exposure >= rescue_threshold
The project shows that rescue depends not only on how many nuclei are corrected, but also where they sit in the spatial network, how strongly signal diffuses, how quickly it decays, and whether rescue requires immediate or cumulative exposure.
This is a proof-of-concept simulator, not a calibrated biological model. It simplifies fibre geometry, signal chemistry, stochastic expression, and tissue-level variation. Its value lies in clarifying assumptions and making the biological hypothesis computationally testable.
This project shows cross-domain reasoning: a thesis-driven biological hypothesis becomes a graph model; the graph model becomes a simulation; and the simulation becomes a structured way to ask what conditions make local rescue plausible before moving toward more experimentally grounded modelling.