From biological question to graph model

A biological question can be compelling long before it is computationally precise. One useful role of modelling is to expose the assumptions hiding between those two states.

The question

My graph cross-correction project starts from a simplified question: if only some nuclei in a multinucleated muscle fibre are genetically corrected, could a locally transported corrective signal accumulate enough to affect neighbouring nuclei?

Turning biology into structure

The model represents nuclei as nodes and local transport as edges. Corrected nuclei act as sources. Diffusion, decay and a rescue threshold turn the qualitative hypothesis into quantities that can be varied and tested.

for t in range(num_steps):
    diffusion = -alpha * (L @ u)
    decay = -beta * u
    u = u + dt * (diffusion + decay + source)
    exposure += u * dt
    rescued = exposure >= rescue_threshold

What the simulation is — and is not

The value of the exercise is not to claim a calibrated biological result. The current model deliberately simplifies fibre geometry, signal chemistry, stochastic expression and tissue-level variation. Its value is in making assumptions explicit and creating a framework for sensitivity testing.

What I am taking forward

The interesting part for me is the translation itself: biological observation → mathematical abstraction → executable model → sensitivity analysis. That reasoning chain is increasingly central to how I want to approach computational genomics.