Many parameter sets in a multicompartment model oscillator are robust to temperature perturbations.

Neurons in cold-blooded animals remarkably maintain their function over a wide range of temperatures, even though the rates of many cellular processes increase twofold, threefold, or many-fold for each 10°C increase in temperature. Moreover, the kinetics of ion channels, maximal conductances, and Ca(2+) buffering each have independent temperature sensitivities, suggesting that the balance of biological parameters can be disturbed by even modest temperature changes. In stomatogastric ganglia of the crab Cancer borealis, the duty cycle of the bursting pacemaker kernel is highly robust between 7 and 23°C (Rinberg et al., 2013). We examined how this might be achieved in a detailed conductance-based model in which exponential temperature sensitivities were given by Q10 parameters. We assessed the temperature robustness of this model across 125,000 random sets of Q10 parameters. To examine how robustness might be achieved across a variable population of animals, we repeated this analysis across six sets of maximal conductance parameters that produced similar activity at 11°C. Many permissible combinations of maximal conductance and Q10 parameters were found over broad regions of parameter space and relatively few correlations among Q10s were observed across successful parameter sets. A significant portion of Q10 sets worked for at least 3 of the 6 maximal conductance sets (∼11.1%). Nonetheless, no Q10 set produced robust function across all six maximal conductance sets, suggesting that maximal conductance parameters critically contribute to temperature robustness. Overall, these results provide insight into principles of temperature robustness in neuronal oscillators.

Correlations in ion channel expression emerge from homeostatic tuning rules.

Experimental observations reveal that the expression levels of different ion channels vary across neurons of a defined type, even when these neurons exhibit stereotyped electrical properties. However, there are robust correlations between different ion channel expression levels, although the mechanisms that determine these correlations are unknown. Using generic model neurons, we show that correlated conductance expression can emerge from simple homeostatic control mechanisms that couple expression rates of individual conductances to cellular readouts of activity. The correlations depend on the relative rates of expression of different conductances. Thus, variability is consistent with homeostatic regulation and the structure of this variability reveals quantitative relations between regulation dynamics of different conductances. Furthermore, we show that homeostatic regulation is remarkably insensitive to the details that couple the regulation of a given conductance to overall neuronal activity because of degeneracy in the function of multiple conductances and can be robust to "antihomeostatic" regulation of a subset of conductances expressed in a cell.

Increase in sodium conductance decreases firing rate and gain in model neurons.

We studied the effects of increased sodium conductance on firing rate and gain in two populations of conductance-based, single-compartment model neurons. The first population consisted of 1000 model neurons with differing values of seven voltage-dependent conductances. In many of these models, increasing the sodium conductance threefold unexpectedly reduced the firing rate and divisively scaled the gain at high input current. In the second population, consisting of 1000 simplified model neurons, we found that enhanced sodium conductance changed the frequency-current (FI) curve in two computationally distinct ways, depending on the firing rate. In these models, increased sodium conductance produced a subtractive shift in the FI curve at low firing rates because the additional sodium conductance allowed the neuron to respond more strongly to equivalent input current. In contrast, at high input current, the increase in sodium conductance resulted in a divisive change in the gain because the increased conductance produced a proportionally larger activation of the delayed rectifier potassium conductance. The control and sodium-enhanced FI curves intersect at a point that delimits two regions in which the same biophysical manipulation produces two fundamentally different changes to the model neuron's computational properties. This suggests a potentially difficult problem for homeostatic regulation of intrinsic excitability.

Precise temperature compensation of phase in a rhythmic motor pattern.

Most animal species are cold-blooded, and their neuronal circuits must maintain function despite environmental temperature fluctuations. The central pattern generating circuits that produce rhythmic motor patterns depend on the orderly activation of circuit neurons. We describe the effects of temperature on the pyloric rhythm of the stomatogastric ganglion of the crab, Cancer borealis. The pyloric rhythm is a triphasic motor pattern in which the Pyloric Dilator (PD), Lateral Pyloric (LP), and Pyloric (PY) neurons fire in a repeating sequence. While the frequency of the pyloric rhythm increased about 4-fold (Q(10) approximately 2.3) as the temperature was shifted from 7 degrees C to 23 degrees C, the phase relationships of the PD, LP, and PY neurons showed almost perfect temperature compensation. The Q(10)'s of the input conductance, synaptic currents, transient outward current (I(A)), and the hyperpolarization-activated inward current (I(h)), all of which help determine the phase of LP neuron activity, ranged from 1.8 to 4. We studied the effects of temperature in >1,000 computational models (with different sets of maximal conductances) of a bursting neuron and the LP neuron. Many bursting models failed to monotonically increase in frequency as temperature increased. Temperature compensation of LP neuron phase was facilitated when model neurons' currents had Q(10)'s close to 2. Together, these data indicate that although diverse sets of maximal conductances may be found in identified neurons across animals, there may be strong evolutionary pressure to restrict the Q(10)'s of the processes that contribute to temperature compensation of neuronal circuits.

Serotonin regulates electrical coupling via modulation of extrajunctional conductance: H-current.

Synaptic strength can be highly variable from animal to animal within a species or over time within an individual. The process of synaptic plasticity induced by neuromodulatory agents might be unpredictable when the underlying circuits subject to modulation are themselves inherently variable. Serotonin (5-hydroxytryptomine; 5HT) and serotonergic signaling pathways are important regulators of animal behavior and are pharmacological targets in a wide range of neurological disorders. We have examined the effect of 5HT on electrical synapses possessing variable coupling strengths. While 5HT decreased electrical coupling at synapses with weak electrical connectivity, synapses with strong electrical coupling were less affected by 5HT treatment, as follows from the equations used for calculating coupling coefficients. The fact that the modulatory effect of 5HT on electrical connections was negatively correlated with the strength of electrical coupling suggests that the degree of electrical coupling within a neural network impacts subsequent neuromodulation of those synapses. Biophysical studies indicated that these effects were primarily due to 5HT-induced modulation of membrane currents that indirectly affect junctional coupling at synaptic contacts. In support of these experimental analyses, we created a simple model of coupled neurons to demonstrate that modulation of electrical coupling could be due solely to 5HT effects on H-channel conductance. Therefore, variability in the strength of electrical coupling in neural circuits can determine the pharmacological effect of this neuromodulatory agent.