Graph Cross-Correction Simulation

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.

Core idea: represent nuclei as graph nodes, corrected nuclei as source nodes, local exchange as graph diffusion, and rescue as a threshold or cumulative-exposure outcome.

Biological motivation

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.

The modelling idea

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.

Reasoning chain: biological observation → source nodes → graph structure → Laplacian diffusion → rescue threshold → sensitivity testing.

How the project evolves

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

💻 Tech Stack:

📊 Code Snippets & Visualisations:

# 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
Corrected source nodes → graph diffusion → rescue threshold Green: corrected/source · Gold: rescued/exposed · Grey: below threshold
Conceptual visualisation: Corrected nuclei produce signal; neighbouring nuclei receive transported signal through graph connectivity.

Key result

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.

Limitations

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.

What this demonstrates

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.

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