Forecasting and Dynamics of Huntington's disease: A Machine Learning approach for Fractional-Order Mathematical Model

Huntington's disease (HD) is an autosomal dominant neurodegenerative disorder caused by expansion of CAG repeats in the HTT gene, leading to accumulation of mutant huntingtin and progressive neuronal dysfunction, particularly in vulnerable brain regions such as the striatum. Although length of CAG repeats is a major determinant of the risk of disease, it does not account for all the variance in age of onset, rate of progression or region of neurodegeneration. The aim of this work was to construct a fractional-order mathematical model to investigate the potential role of pure, interrupted and mosaic HTT repeat states in mutation instability and toxic-burden accumulation.

A fractional-order P-I-M model with the Caputo operator was designed to describe biologic memory in long-term progression of HD. The compartments describe phenomenological mutation-state burdens of pure uninterrupted repeats, interrupted repeats and age-dependent somatic mosaicism. Positivity, boundedness, equilibrium behavior, local stability, reproductive number and parameter sensitivity was studied. The outputs from AlphaFold were only used as additional computational parameters for disorder prediction and not as direct inputs.

Numerical simulations indicated a trend toward mosaic dominance, suggesting that the cumulative toxic burden may be largely due to somatic mosaicism. The variations in fractional order suggested the effect of memory depth on the timing and rate of instability accumulation. The sensitivity analysis found the parameters for repeat instability and mosaic self-amplification to be the key drivers of model behavior. The regional extension reproduced a plausible gradient of vulnerability with the highest modelled burden in striatum followed by cortex, hippocampus and cerebellum.

The proposed framework connects HTT repeat structure, somatic mosaicism, fractional temporal memory and regional neurotoxicity in an exploratory mechanistic model of HD progression. Future calibration with clinical and experimental data sets is needed.