Neurons can increase in size dramatically during growth. In many species neurons 8 must preserve their intrinsic dynamics and physiological function across several length scales. For 9 example, neurons in crustacean central pattern generators generate similar activity patterns 10 despite multiple-fold increases in their size and changes in morphology. This scale invariance hints 11 at regulation mechanisms that compensate for size changes by somehow altering membrane 12 currents. Using conductance-based neuron models, we asked whether simple activity-dependent 13 feedback can maintain intrinsic voltage dynamics in a neuron as its size is varied. Despite relying 14 only on a single sensor that measures time-averaged intracellular calcium as a proxy for activity, we 15 found that this regulation mechanism could regulate conductance densities of ion channels, and 16 was robust to changes in the size of the neuron. By mapping changes in cell size onto 17 perturbations in the space of conductance densities of all channels, we show how robustness to 18 size change coexists with sensitivity to perturbations that alter the ratios of maximum 19 conductances of different ion channel types. Our findings suggest that biological regulation that is 20 optimized for coping with expected perturbations such as size changes will be vulnerable to other 21 kinds of perturbations such as channel deletions. 22 29 three-fold increase in cell size (Bucher and Pflüger, 2000). RPeD1, a neuron in the respiratory 30 central pattern generator in Lymnaea, maintains resting membrane potential, spike amplitude 31 and membrane resistance despite two-fold growth from juvenile to adult (McComb et al., 2003). 32 In crickets, patterns of motor neuron output responsible for song production appear up to four 33 moults before the adult form (Bentley and Hoy, 1970). In lobsters, the co-ordinated bursting activity 34 of pyloric neurons is indistinguishable between juveniles and adults, despite a many-fold increase 35 in their size (Bucher et al., 2005). Even in embryonic stages, when these cells are even smaller, 36 the pyloric circuit central pattern generator (CPG) expresses spontaneous albeit less stereotyped 37 rhythmic activity (Casasnovas and Meyrand, 1995; Richards et al., 1999). 38 Neurons achieve their target behavior by expressing specific combinations of voltage and 39 calcium gated ion channels (Prinz et al., 2003). This leads to the question of how neurons maintain 40 1 of 20 Manuscript to be submitted to eLife a target function by regulating ion channel expression as the size of the cell increases. Can regulatory 41 mechanisms preserve neuron behavior during growth? 42 Homeostatic regulation has been proposed as a mechanism that can tune neuronal parameters 43 like ion channel densities to drive neuronal activity to some desired set point (LeMasson et al.,

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