This project is a staged numerical modelling study that explores molecular cross-correction in multinucleated muscle fibres. It asks whether a small number of corrected nuclei can produce enough local signal to rescue neighbouring nuclei through spatial transport.
The project is inspired by U7 snRNA-mediated cross-correction in Duchenne muscular dystrophy. It does not claim to reproduce experimental data. It builds a simplified computational model to test whether local signal transport could plausibly amplify rescue beyond corrected nuclei.
Nuclei are represented as graph nodes. Corrected nuclei act as signal sources. Local exchange is approximated using graph diffusion. Rescue is treated as a threshold response to transported signal.
| 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 biological idea becomes a graph model; the graph model becomes a simulation; the simulation becomes a structured way to ask what conditions make local rescue plausible.