Homeostatic plasticity rules that compensate for cell size are susceptible to channel deletion

Neurons can increase in size dramatically during growth. In many species neurons must preserve their intrinsic dynamics and physiological function across several length scales. For example, neurons in crustacean central pattern generators generate similar activity patterns despite multiple-fold increases in their size and changes in morphology. This scale invariance hints at regulation mechanisms that compensate for size changes by somehow altering membrane currents. Using conductance-based neuron models, we asked whether simple activity-dependent feedback can maintain intrinsic voltage dynamics in a neuron as its size is varied. Despite relying only on a single sensor that measures time-averaged intracellular calcium as a proxy for activity, we found that this regulation mechanism could regulate conductance densities of ion channels, and was robust to changes in the size of the neuron. By mapping changes in cell size onto perturbations in the space of conductance densities of all channels, we show how robustness to size change coexists with sensitivity to perturbations that alter the ratios of maximum conductances of different ion channel types. Our findings suggest that biological regulation that is optimized for coping with expected perturbations such as size changes will be vulnerable to other kinds of perturbations such as channel deletions.