SUMMARY How do neurons develop, control, and maintain their electrical signaling properties in spite of ongoing protein turnover and perturbations to activity? From generic assumptions about the molecular biology underlying channel expression, we derive a simple model and show how it encodes an “activity set point” in single neurons. The model generates diverse self-regulating cell types and relates correlations in conductance expression observed in vivo to underlying channel expression rates. Synaptic as well as intrinsic conductances can be regulated to make a self-assembling central pattern generator network; thus, network-level homeostasis can emerge from cell-autonomous regulation rules. Finally, we demonstrate that the outcome of homeostatic regulation depends on the complement of ion channels expressed in cells: in some cases, loss of specific ion channels can be compensated; in others, the homeostatic mechanism itself causes pathological loss of function.

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.neuronal excitability | robustness | computational models | control theory T he electrophysiological signature of every neuron is determined by the number and kind of voltage-dependent conductances in its membrane. Most neurons express many voltage-dependent conductances, some of which may have overlapping or degenerate physiological functions (1-6). Furthermore, neurons in the brains of long-lived animals must maintain reliable function over the animal's lifetime while all of their ion channels and receptors are replaced in the membrane over hours, days, or weeks. Consequently, ongoing turnover of ion channels of various types must occur without compromising the essential excitability properties of the neuron (5, 7-10).Both theoretical and experimental studies suggest that maintaining stable intrinsic excitability is accomplished via homeostatic, negative feedback processes that use intracellular Ca 2+ concentrations as a sensor of activity and then alter the synthesis, insertion, and degradation of membrane conductances to achieve a target activity level (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27). Among the modeling studies are several different homeostatic tuning rules that differ in how sensor readout is coupled to the changes in conductance necessary to achieve a target activity (11,13,14,28). Regardless, these models can self-assemble from randomized initial conditions, and they will change their conductance densities in response to perturbation or synaptic drive. In one of these homeostatic self-tuning models (14), similar activity patterns can be associated with different sets of conductance densities.Thus, it is perhaps not surprising that experimental studies also find a considerable range in the conductance densities of voltagedependent channels and in the mRNA expression of their ion channel genes (29-36). The experimental st...

Neuromodulation underlies many behavioral states and has been extensively studied in small circuits. This has allowed the systematic exploration of how neuromodulatory substances and the neurons that release them can influence circuit function. The physiological state of a network and its level of activity can have profound effects on how the modulators act, a phenomenon known as state dependence. We provide insights from experiments and computational work that show how state dependence can arise and the consequences it can have for cellular and circuit function. These observations pose a general unsolved question that is relevant to all nervous systems: How is robust modulation achieved in spite of animal-to-animal variability and degenerate, nonlinear mechanisms for the production of neuronal and network activity?

Glycogen synthase kinase-3 (GSK3) is a critical enzyme in neuronal physiology, however any specific role in presynaptic function is not yet known. We show that GSK3 phosphorylates a key residue on the large GTPase dynamin I (Ser-774) both in vitro and in primary rat neuronal cultures. This is dependent on prior phosphorylation of Ser-778 by cyclin-dependent kinase 5 (cdk5). We found a specific requirement for GSK3 in activity-dependent bulk endocytosis (ADBE), but not clathrin-mediated endocytosis (CME) using both acute inhibition with pharmacological antagonists and silencing of expression using shRNA. Moreover we showed that the specific phosphorylation of Ser-774 on dynamin I by GSK3 is both necessary and sufficient for ADBE. This is the first demonstration of a presynaptic role for GSK3 and reveals that a protein kinase signalling cascade prepares synaptic vesicles (SVs) for retrieval during elevated neuronal activity.

SUMMARY Rhythmic oscillations are common features of nervous systems. One of the fundamental questions posed by these rhythms is how individual neurons or groups of neurons are recruited into different network oscillations. We modeled competing fast and slow oscillators connected to a hub neuron with electrical and inhibitory synapses. We explore the patterns of coordination shown in the network as a function of the electrical coupling and inhibitory synapse strengths with the help of a novel visualization method that we call the “parameterscape.” The hub neuron can be switched between the fast and slow oscillators by multiple network mechanisms, indicating that a given change in network state can be achieved by degenerate cellular mechanisms. These results have importance for interpreting experiments employing optogenetic, genetic, and pharmacological manipulations to understand circuit dynamics.

Firing rate is an important means of encoding information in the nervous system. To reliably encode a wide range of signals, neurons need to achieve a broad range of firing frequencies and to move smoothly between low and high firing rates. This can be achieved with specific ionic currents, such as A-type potassium currents, which can linearize the frequency-input current curve. By applying recently developed mathematical tools to a number of biophysical neuron models, we show how currents that are classically thought to permit low firing rates can paradoxically cause a jump to a high minimum firing rate when expressed at higher levels. Consequently, achieving and maintaining a low firing rate is surprisingly difficult and fragile in a biological context. This difficulty can be overcome via interactions between multiple currents, implying a need for ion channel degeneracy in the tuning of neuronal properties.FI curve | bifurcation | Type I excitability | Type II excitability | reduced neuron model F iring rates encode the intensities of many signals in the nervous system, whether these are inputs from sensory organs, internal representations of percepts, or muscle contraction commands in motor nerves. For a neuron to represent continuously varying signals in its firing rate, it must be able to fire at low, high, and all intermediate frequencies. Experimentally, this means the frequency-input current (or FI) curve has a specific shape, called Type I, such that firing frequency smoothly approaches zero at current threshold (1-6). By contrast, so-called Type II neurons have a lower bound in their firing frequency and move abruptly from quiescence to fast spiking, with this transition visible as a sharp jump in the FI curve at threshold (1,3,5).Type I behavior is physiologically unlikely with a minimal set of membrane currents such as the voltage-gated sodium and delayed-rectifier potassium currents in the standard squid giant axon Hodgkin-Huxley model, which is Type II. Classic experimental (1, 7) and theoretical studies (3-5, 8, 9) revealed that a Type II membrane (such as a squid giant axon) can be turned into a Type I membrane by adding an inactivating (A-type) potassium conductance, I A . As the density of I A channels increases from zero, the membrane is able to support progressively lower firing frequencies at spiking threshold. The resulting linearization of the FI curve from Type II to Type I has clear consequences for encoding information in firing rate as well as other computational properties such as thresholding and gain scaling, all of which are subjects of intense research (10-17).We now show that this picture is incomplete. Using rigorous but intuitive methods (18) and building on previous technical results (19-21), we show that introducing I A to a Type II neuron progressively linearizes but then delinearizes the FI curve as I A density increases further. Consequently, I A density must be tuned in a strict range to achieve Type I behavior. However, we show that other, unrelated currents including v...

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In order to maintain stable functionality in the face of continually changing input, neurones in the CNS must dynamically modulate their electrical characteristics. It has been hypothesized that in order to retain stable network function, neurones possess homeostatic mechanisms which integrate activity levels and alter network and cellular properties in such a way as to counter long-term perturbations. Here we describe a simple model system where we investigate the effects of sustained neuronal depolarization, lasting up to several days, by exposing cultures of primary hippocampal pyramidal neurones to elevated concentrations (10-30 mm) of KCl. Following exposure to KCl, neurones exhibit lower input resistances and resting potentials, and require more current to be injected to evoke action potentials. This results in a rightward shift in the frequency-input current (FI) curve which is explained by a simple linear model of the subthreshold I-V relationship. No changes are observed in action potential profiles, nor in the membrane potential at which action potentials are evoked. Furthermore, following depolarization, an increase in subthreshold potassium conductance is observed which is accounted for within a biophysical model of the subthreshold I-V characteristics of neuronal membranes. The FI curve shift was blocked by the presence of the L-type Ca 2+ channel blocker nifedipine, whilst antagonism of NMDA receptors did not interfere with the effect. Finally, changes in the intrinsic properties of neurones are reversible following removal of the depolarizing stimulus. We suggest that this experimental system provides a convenient model of homeostatic regulation of intrinsic excitability, and permits the study of temporal characteristics of homeostasis and its dependence on stimulus magnitude.