Quantifying scaling exponents for neurite morphology of in vitro-cultured human iPSC-derived neurons using discrete Loewner evolution: A statistical−physical approach to the neuropathology in Alzheimer's disease

Defining the morphological disorders causing neurodegenerative diseases is an unresolved problem. In this study, we propose a statistical−physical approach to quantify neurite morphology and evaluate the pathological states induced by Alzheimer's disease (AD). We analyzed the two-dimensional morphologies of neurites of in vitro-cultured human induced-pluripotent stem cell-derived neurons, reprogrammed from both a healthy person and a patient with AD, using discrete chordal Loewner evolution. For the numerically calculated Loewner driving forces, detrended fluctuation analysis was performed, and the morphological characteristics of the neurites were quantified using short-range and long-range scaling exponents. The day in vitro (DIV)-dependent behaviors of the scaling exponents and the associated neurite-type categorizations suggested that differences between healthy and AD neurites can be observed from the early stage (DIV3) of their development. Notably, AD neurites have less long-range autocorrelations than healthy neurites, particularly in the earlier stages (DIV3–10). Immunofluorescence-staining results suggested that these differences precede significant expressions of β-amyloid and phosphorylated tau, which are known as biological factors causing AD. We expect that these results will lead to a theoretical interpretation of the neurogenerative disease, providing the physical properties of individual neurites with different morphologies.