A Persistent Random-Walk Model of Molecular Transport in Neuronal Dendritic Trees
Abstract
A two-level analytical framework is presented for modeling random walk transport of messenger ribonucleic acid (mRNA) molecules along neuronal microtubules from soma to synapses. Motivated by empirical observations of mRNA cargo motion, the transport within a dendrite is modeled by a persistent telegraph process with pauses. Theoretical expressions for the probability of traversing the dendrite and the mean time for such travel are derived for different and equal probabilities of persistence. These results are used for the construction of a semi-Markov model of motion of mRNA cargo within the whole neuron. The semi-Markov model provides the probabilities of absorption at a given synapse and corresponding mean first-passage times (MFPTs) from the soma, where mRNA is transcribed. The theoretical expressions, together with experimentally obtained parameter values, are used to calculate MFPTs for neurons with empirically reconstructed morphology. The model predicts that when retrograde persistence is stronger, the MFPT to each synapse is effectively the same. Otherwise, when the persistence is more pronounced in the anterograde direction, the transport in the neuron resembles the motion along a single dendrite -- nearly linear dependence of MFPT on the distance between soma and synapse. These findings are theoretically justified when the lengths of dendrites are considerably longer than the distance traversed during a typical run.
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BibTeX
@misc{basnarkov2026persistent,
title = {{A Persistent Random-Walk Model of Molecular Transport in Neuronal Dendritic Trees}},
author = {Lasko Basnarkov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.00995},
eprint = {2608.00995},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.00995},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Persistent Random-Walk Model of Molecular Transport in Neuronal Dendritic Trees
AU - Lasko Basnarkov
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2608.00995
UR - https://arxiv.org/abs/2608.00995
AB - A two-level analytical framework is presented for modeling random walk transport of messenger ribonucleic acid (mRNA) molecules along neuronal microtubules from soma to synapses. Motivated by empirical observations of mRNA cargo motion, the transport within a dendrite is modeled by a persistent telegraph process with pauses. Theoretical expressions for the probability of traversing the dendrite and the mean time for such travel are derived for different and equal probabilities of persistence. These results are used for the construction of a semi-Markov model of motion of mRNA cargo within the whole neuron. The semi-Markov model provides the probabilities of absorption at a given synapse and corresponding mean first-passage times (MFPTs) from the soma, where mRNA is transcribed. The theoretical expressions, together with experimentally obtained parameter values, are used to calculate MFPTs for neurons with empirically reconstructed morphology. The model predicts that when retrograde persistence is stronger, the MFPT to each synapse is effectively the same. Otherwise, when the persistence is more pronounced in the anterograde direction, the transport in the neuron resembles the motion along a single dendrite -- nearly linear dependence of MFPT on the distance between soma and synapse. These findings are theoretically justified when the lengths of dendrites are considerably longer than the distance traversed during a typical run.
ER -