It is often assumed that cellular and synaptic properties need to be regulated to specific values to allow a neuronal network to function properly. To determine how tightly neuronal properties and synaptic strengths need to be tuned to produce a given network output, we simulated more than 20 million versions of a three-cell model of the pyloric network of the crustacean stomatogastric ganglion using different combinations of synapse strengths and neuron properties. We found that virtually indistinguishable network activity can arise from widely disparate sets of underlying mechanisms, suggesting that there could be considerable animal-to-animal variability in many of the parameters that control network activity, and that many different combinations of synaptic strengths and intrinsic membrane properties can be consistent with appropriate network performance.

Prinz, Astrid A., Cyrus P. Billimoria, and Eve Marder. Alternative to hand-tuning conductance-based models: construction and analysis of databases of model neurons. J Neurophysiol 90: 3998 -4015, 2003. First published August 27, 2003 10.1152/jn.00641.2003. Conventionally, the parameters of neuronal models are hand-tuned using trial-and-error searches to produce a desired behavior. Here, we present an alternative approach. We have generated a database of about 1.7 million single-compartment model neurons by independently varying 8 maximal membrane conductances based on measurements from lobster stomatogastric neurons. We classified the spontaneous electrical activity of each model neuron and its responsiveness to inputs during runtime with an adaptive algorithm and saved a reduced version of each neuron's activity pattern. Our analysis of the distribution of different activity types (silent, spiking, bursting, irregular) in the 8-dimensional conductance space indicates that the coarse grid of conductance values we chose is sufficient to capture the salient features of the distribution. The database can be searched for different combinations of neuron properties such as activity type, spike or burst frequency, resting potential, frequency-current relation, and phaseresponse curve. We demonstrate how the database can be screened for models that reproduce the behavior of a specific biological neuron and show that the contents of the database can give insight into the way a neuron's membrane conductances determine its activity pattern and response properties. Similar databases can be constructed to explore parameter spaces in multicompartmental models or small networks, or to examine the effects of changes in the voltage dependence of currents. In all cases, database searches can provide insight into how neuronal and network properties depend on the values of the parameters in the models. I N T R O D U C T I O NThe spontaneous firing pattern of a neuron and how it responds to inputs from other neurons is crucially determined by the densities and dynamics of the ion channels in the neuron's membrane. These membrane conductances have a nonlinear dependence on the membrane potential, which itself is changed by the currents flowing through the conductances. A neuron with even a small number of membrane conductances is a complex dynamical system, and predicting the behavior of a cell with a physiologically realistic set of currents becomes very difficult.Faced with ongoing channel turnover, neurons must constantly adjust their membrane currents to maintain their electrical identity (Marder and Prinz 2002). Experiments and simulations have shown that even small changes in one or a few currents can dramatically alter the activity of a neuron (De Schutter and Bower 1994;Goldman et al. 2001). On the other hand, similar activity can be achieved with widely varying sets of conductances in biological and model neurons (Bhalla and Bower 1993;De Schutter and Bower 1994;Foster et al. 1993;Goldman et al. 2001;Golowasch et al. 1999a...

Which features of network output are well preserved during growth of the nervous system and across different preparations of the same size? To address this issue, we characterized the pyloric rhythms generated by the stomatogastric nervous systems of 99 adult and 12 juvenile lobsters (Homarus americanus). Anatomical studies of single pyloric network neurons and of the whole stomatogastric ganglion (STG) showed that the STG and its neurons grow considerably from juvenile to adult. Despite these changes in size, intracellularly recorded membrane potential waveforms of pyloric network neurons and the phase relationships in the pyloric rhythm were very similar between juvenile and adult preparations. Across adult preparations, the cycle period and number of spikes per burst were not tightly maintained, but the mean phase relationships were independent of the period of the rhythm and relatively tightly maintained across preparations. We interpret this as evidence for homeostatic regulation of network activity.

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SummaryIndividual neurons display characteristic firing patterns determined by the number and kind of ion channels in their membranes. We describe experimental and computational studies that suggest that neurons use activity sensors to regulate the number and kind of ion channels and receptors in their membrane to maintain a stable pattern of activity and to compensate for ongoing processes of degradation, synthesis and insertion of ion channels and receptors. We show that similar neuronal and network outputs can be produced by a number of different combinations of ion channels and synapse strengths. This suggests that individual neurons of the same class may each have found an acceptable solution to a genetically determined pattern of activity, and that networks of neurons in different animals may produce similar output patterns by somewhat variable underlying mechanisms.

We studied the effect of synaptic inputs of different amplitude and duration on neural oscillators by simulating synaptic conductance pulses in a bursting conductance-based pacemaker model and by injecting artificial synaptic conductance pulses into pyloric pacemaker neurons of the lobster stomatogastric ganglion using the dynamic clamp. In the model and the biological neuron, the change in burst period caused by inhibitory and excitatory inputs of increasing strength saturated, such that synaptic inputs above a certain strength all had the same effect on the firing pattern of the oscillatory neuron. In contrast, increasing the duration of the synaptic conductance pulses always led to changes in the burst period, indicating that neural oscillators are sensitive to changes in the duration of synaptic input but are not sensitive to changes in the strength of synaptic inputs above a certain conductance. This saturation of the response to progressively stronger synaptic inputs occurs not only in bursting neurons but also in tonically spiking neurons. We identified inward currents at hyperpolarized potentials as the cause of the saturation in the model neuron. Our findings imply that activity-dependent or modulator-induced changes in synaptic strength are not necessarily accompanied by changes in the functional impact of a synapse on the timing of postsynaptic spikes or bursts.

To determine why elements of central pattern generators phase lock in a particular pattern under some conditions but not others, we tested a theoretical pattern prediction method. The method is based on the tabulated open loop pulsatile interactions of bursting neurons on a cycle-by-cycle basis and was tested in closed loop hybrid circuits composed of one bursting biological neuron and one bursting model neuron coupled using the dynamic clamp. A total of 164 hybrid networks were formed by varying the synaptic conductances. The prediction of 1:1 phase locking agreed qualitatively with the experimental observations, except in three hybrid circuits in which 1:1 locking was predicted but not observed. Correct predictions sometimes required consideration of the second order phase resetting, which measures the change in the timing of the second burst after the perturbation. The method was robust to offsets between the initiation of bursting in the presynaptic neuron and the activation of the synaptic coupling with the postsynaptic neuron. The quantitative accuracy of the predictions fell within the variability (10%) in the experimentally observed intrinsic period and phase resetting curve (PRC), despite changes in the burst duration of the neurons between open and closed loop conditions.

Neurons, and realistic models of neurons, typically express several different types of voltage-gated conductances. These conductances are subject to continual regulation. Therefore it is essential to understand how changes in the conductances of a neuron affect its intrinsic properties, such as burst period or delay to firing after inhibition of a particular duration and magnitude. Even in model neurons, it can be difficult to visualize how the intrinsic properties vary as a function of their underlying maximal conductances. We used a technique, called clutter-based dimension reordering (CBDR), which enabled us to visualize intrinsic properties in high-dimensional conductance spaces. We applied CBDR to a family of models with eight different types of voltage- and calcium-dependent channels. CBDR yields images that reveal structure in the underlying conductance space. CBDR can also be used to visualize the results of other types of analysis. As examples, we use CBDR to visualize the results of a connected-components analysis, and to visually evaluate the results of a separating-hyperplane (i.e., linear classifier) analysis. We believe that CBDR will be a useful tool for visualizing the conductance spaces of neuronal models in many systems.