Computational modeling and experimentation in a model system for network dynamics reveal how network phase relationships are temperature-compensated in terms of their underlying synaptic and intrinsic membrane currents.

The fast transient potassium or A current (IA) plays an important role in determining the activity of central pattern generator neurons. We have previously shown that the shal K+ channel gene encodes IA in neurons of the pyloric network in the spiny lobster. To further study how IA shapes pyloric neuron and network activity, we microinjected RNA for a shal-GFP fusion protein into four identified pyloric neuron types. Neurons expressing shal-GFP had a constant increase in IA amplitude, regardless of cell type. This increase in IA was paralleled by a concomitant increase in the hyperpolarization-activated cation current Ih in all pyloric neurons. Despite significant increases in these currents, only modest changes in cell firing properties were observed. We used models to test two hypotheses to explain this failure to change firing properties. First, this may reflect the mislocalization of the expressed shal protein solely to the somata and initial neurites of injected neurons, rendering it electrically remote from the integrating region in the neuropil. To test this hypothesis, we generated a multicompartment model where increases in IA could be localized to the soma, initial neurite, or neuropil/axon compartments. Although spike activity was somewhat more sensitive to increases in neuropil/axon versus somatic/primary neurite IA, increases in IA limited to the soma and primary neurite still evoked much more dramatic changes than were seen in the shal-GFP-injected neurons. Second, the effect of the increased IA could be compensated by the endogenous increase in Ih. To test this, we modeled the compensatory increases of IA and Ih with a cycling two-cell model. We found that the increase in Ih was sufficient to compensate the effects of increased IA, provided that they increase in a constant ratio, as we observed experimentally in both shal-injected and noninjected neurons. Thus an activity-independent homeostatic mechanism maintains constant neuronal activity in the face of dramatic increases in IA.

Small central pattern generating circuits found in invertebrates have significant advantages for the study of the circuit mechanisms that generate brain rhythms. Experimental and computational studies of small oscillatory circuits reveal that similar rhythms can arise from disparate mechanisms. Animal-to-animal variation in the properties of single neurons and synapses may underly robust circuit performance, and can be revealed by perturbations. Neuromodulation can produce altered circuit performance but also ensure reliable circuit function.

Central-pattern-generating neural circuits function reliably throughout an animal's life, despite constant molecular turnover and environmental perturbations. Fluctuations in temperature pose a problem to the nervous systems of poikilotherms because their body temperature follows the ambient temperature, thus affecting the temperature-dependent dynamics of various subcellular components that constitute neuronal circuits. In the crustacean stomatogastric nervous system, the pyloric circuit produces a triphasic rhythm comprising the output of the pyloric dilator, lateral pyloric, and pyloric constrictor neurons. In vitro, the phase relationships of these neurons are maintained over a fourfold change in pyloric frequency as temperature increases from 7°C to 23°C. To determine whether these temperature effects are also found in intact crabs, in the presence of sensory feedback and neuromodulator-rich environments, we measured the temperature dependence of the pyloric frequency and phases in vivo by implanting extracellular electrodes into Cancer borealis and Cancer pagurus and shifting tank water temperature from 11°C to 26°C. Pyloric frequency in the intact crab increased significantly with temperature (Q10 = 2-2.5), while pyloric phases were generally conserved. For a subset of the C. borealis experiments, animals were subsequently dissected and the stomatogastric ganglion subjected to a similar temperature ramp in vitro. We found that the maximal frequency attained at high temperatures in vivo is lower than it is under in vitro conditions. Our results demonstrate that, over a wide temperature range, the phases of the pyloric rhythm in vivo are generally preserved, but that the frequency range is more restricted than it is in vitro.

Neuronal physiology depends on a neuron’s ion channel composition and unique morphology. Variable ion channel compositions can produce similar neuronal physiologies across animals. Less is known regarding the morphological precision required to produce reliable neuronal physiology. Theoretical studies suggest that moraphology is tightly tuned to minimize wiring and conduction delay of synaptic events. We utilize high-resolution confocal microscopy and custom computational tools to characterize the morphologies of four neuron types in the stomatogastric ganglion (STG) of the crab Cancer borealis. Macroscopic branching patterns and fine cable properties are variable within and across neuron types. We compare these neuronal structures to synthetic minimal spanning neurite trees constrained by a wiring cost equation and find that STG neurons do not adhere to prevailing hypotheses regarding wiring optimization principles. In this highly modulated and oscillating circuit, neuronal structures appear to be governed by a space-filling mechanism that outweighs the cost of inefficient wiring.DOI: http://dx.doi.org/10.7554/eLife.22352.001