Dendrite Control Theory: A Unifying Framework Bridging Neuronal Morphology And Dendritic Voltage Behavior

Control theory and dendritic computation have revolutionized their respective fields, yet they rarely converge. Here, we use control theory as a framework to reveal how dendritic morphology and synaptic input organization constrain structural resilience and energy cost. Treating diverse dendritic trees as connected network nodes, we demonstrate that the degree of structural symmetry dictates easy- versus hard-to-access control states. Notably, control inputs restricted solely to peripheral terminal branches are mathematically sufficient to govern the voltage states of the entire dendrite and soma, granting striking resilience against input loss elsewhere. Conversely, limiting input dimensionality amplifies voltage fluctuations and metabolic costs. These findings expose fundamental biophysical trade-offs between wiring cost, functional flexibility, robustness, and energy efficiency, suggesting interneurons generally exhibit higher resilience while excitatory neurons feature superior controllability. We introduce 'Dendrite Control Theory' as a rigorous engineering framework linking neuronal morphology directly to computation and robustness, offering a new neuroscience research paradigm.