Tracking the Morphological Evolution of Neuronal Dendrites by First-Passage Analysis

A high degree of structural complexity arises in dynamic neuronal dendrites due to extensive branching patterns and diverse spine morphologies, which enable the nervous system to adjust function, construct complex input pathways and thereby enhance the computational power of the system. Owing to the determinant role of dendrite morphology in the functionality of the nervous system, recognition of pathological changes due to neurodegenerative disorders is of crucial importance. We show that the statistical analysis of a temporary signal generated by cargos that have diffusively passed through the complex dendritic structure yields vital information about dendrite morphology. As a feasible scenario, we propose engineering mRNA-carrying multilamellar liposomes to diffusively reach the soma and release mRNAs, which are translated into a specific protein upon encountering ribosomes. The concentration of this protein over a large population of neurons can be externally measured, as a detectable temporary signal. Using a stochastic coarse-grained approach for first-passage through dendrites, we connect the key morphological properties affected by neurodegenerative diseases – including the density and size of spines, the extent of the tree, and the segmental increase of dendrite diameter towards soma – to the characteristics of the evolving signal. Thus, we establish a direct link between the dendrite morphology and the statistical characteristics of the detectable signal. Our approach provides a fast noninvasive measurement technique to indirectly extract vital information about the morphological evolution of dendrites in the course of neurodegenerative disease progression.

💡 Research Summary

The authors present a novel, non‑invasive method for monitoring the structural evolution of neuronal dendrites, particularly the changes that occur during neurodegenerative diseases. The core idea is to use multilamellar liposomes loaded with messenger RNA (mRNA) as diffusively moving cargo. After the liposomes travel through the complex dendritic arbor and reach the soma, the mRNA is translated into a specific protein. The concentration of this protein, summed over a large population of neurons, can be measured externally (e.g., by MRI or PET) as a transient signal I(t).

To relate this measurable signal to dendritic morphology, the authors construct a coarse‑grained stochastic model of a dendritic tree. The tree is represented as a binary branching structure of depth n with an average branch length L. A particle at each discrete time step either hops to a neighboring node with probability q or remains at its current node with probability 1‑q. The hopping probability q captures the trapping effect of dendritic spines; it depends on spine head and neck volumes, spine density ρ, and the effective diffusion constant D. Directional bias p models the systematic increase in dendrite diameter toward the soma. Using an allometric relation between parent and child branch cross‑sectional areas (parameterized by exponent κ), the authors derive p = 1 /