Did evolution optimize the intrinsic properties of the ion channels in each type of neuron to minimize the energy costs of spiking? The fast-spiking interneurons in the cortex must fire at high frequencies for extended periods without adaptation. We simulated a model of this interneuron and compared the energy needed to produce action potentials singly and in trains for a wide range of channel densities and kinetic parameters and examined which combinations of parameters maximized spiking function while minimizing energetic cost (Hasenstaub, Otte et al. 2010). We found that the kinetic parameters for the fast-spiking interneuron minimized the energy per spike for a train of action potentials, but not for a single action potential, in comparison with pyramidal neurons that had thicker spikes that were less costly than the thin spike of the interneuron, but were not as economical per spike in a spike train. We confirmed these results for sodium channels using a dynamic current clamp in neocortical fast spiking interneurons. We found further evidence supporting the minimum hypothesis in a wide range of other neurons from several species and concluded that the ion channels in these neurons minimize energy expenditure in their normal range of spiking.
Some neurons behave like integrators, compatible with a firing rate code; but others behave like a coincidence detector, which can support spike time coding. Using long depolarizing stimuli and dynamic clamp in slice experiments, we showed that CA1 hippocampal pyramidal cells can switch from integrators to coincidence detectors (Prescott, Ratte et al. 2008). The switch is explained by increased outward current contributed by the M-type potassium current, which shifts the balance of inward and outward currents active at perithreshold potentials and thereby converts the spike-initiating mechanism as predicted by dynamical systems analysis. We also demonstrated how IAHP minimizes perturbation of the interspike interval caused by high frequency noise (Prescott and Sejnowski 2008; Drion, Bonjean et al. 2010). Experiments confirmed that different classes of spinal cord neurons express the subthreshold currents predicted by our simulations class (Prescott, De Koninck et al. 2008). This provides a fundamental link between biophysical properties and qualitative differences in how neurons encode sensory input. The phase response curve is also different for neurons in different classes. We showed that acetylcholine, which is released in the cortex during states of high arousal, can change the type of phase response of a cortical pyramidal neuron, probably by inhibiting IM (Stiefel, Gutkin et al. 2008; Stiefel, Gutkin et al. 2009).
Only 5% of the synapses on the cortical layer 4 spiny stellate cells are from the thalamus. We simulated inputs to a reconstructed multi-compartmental model of a spiny stellate cell based on simultaneously recorded spike trains from thalamic and cortical spiny stellate cells in response to drifting gratings from cats (Kara, Reinagel et al. 2000). Synchronous thalamic spikes were surprisingly effective in driving the spiny stellate cell, consistent with the recorded outputs (Wang, Spencer et al. 2010). Furthermore, the threshold synchrony magnitude could be regulated by adjusting the ratio of background inhibitory to excitatory inputs from the cortex to the spiny stellate cell. Different thalamic inputs carried different spike patterns that sampled from the input distribution, which resulted in highly reliable responses from the spiny stellate cells (Wang submitted). Synchronous firing of spikes has been detected throughout the cortex, which suggests that regulating synchrony may be a flexible and efficient way to regulate the flow of information between cortical areas as well as the input to the cortex (Tiesinga, Fellous et al. 2008).
We explored integration of synaptic inputs in active dendrites in a compartmental model. First, we showed that presynaptic depression combined with slow postsynaptic potassium conductances can produce a balanced output and keep the cell near threshold where it is sensitive to input correlations without the need to fine tune the network inhibition (Volman, Levine et al. 2009). In another study, we showed that when asynchronous release is included along with shunting inhibition, the input-output gain of the neurons can be altered in opposite directions depending on the level of shunting (Volman, Levine et al. 2010). In a third study, we showed that in cortical pyramidal neurons subthreshold oscillations can become phase locked after a strong inhibitory input and influence the response to an excitatory input 1-2 seconds later (Stiefel, Fellous et al. 2010). In contrast, isolated inhibitory interneurons exhibit stochastic fluctuations, which are driven by internal sources of noise (Englitz, Stiefel et al. 2008). Finally, we developed a novel approach to determining the function of dendrites using a genetic algorithm to find a dendritic tree that computes a desired function (Stiefel and Sejnowski 2007).
Oscillations over a wide range of frequencies occur in the cortex and hippocampus and there is increasing interest in studying them. My goal is to understand the biophysical mechanisms underlying these oscillations and their possible functions (Paulsen and Sejnowski 2006; Sejnowski and Paulsen 2006). In the hippocampus, there is a strong theta oscillation during locomotion and when a neuron spikes in a place field, the relative phase of the spike precesses; we showed that a network model of phase precession reproduces the intracellular depolarization (Romani, Sejnowski et al. 2010) that has been measured in vivo (Harvey 2009). We also developed models of the gamma oscillations that occur in the cortex during attention based on negative feedback from fast-spiking inhibitory neurons (Mishra, Fellous et al. 2006; Tiesinga and Sejnowski 2009; Tiesinga and Sejnowski 2010), as well as coupling of the gamma oscillations to lower frequency oscillations (Miller, Hermes et al. 2010). Finally, in collaboration with Ted Bullock at UCSD, we modeled traveling waves in choral nerve networks (Chen, Stiefel et al. 2008).
There is increasing interest in cortical interneurons and the possible role they may have in controlling the timing of spikes in cortical circuits. In particular, recent experimental evidence points to fast-spiking cortical interneurons, which constitute 5% of all cortical neurons, as a key circuit element in regulating the response gain of nearby pyramidal neurons. In this paper we used cortical circuit models to examine the conclusion from optogenetic studies that these interneurons are implicated in generating gamma oscillations (30–80 Hz) in the cortex (Cardin et al., 2009; Sohal et al., 2009). We showed that these optogenetic experiments could not distinguish between two different models that could in principle generate gamma oscillations, either through reciprocal feedback between the pyramidal neurons and the interneurons, or by reciprocal interactions between the interneurons themselves. Furthermore, we proposed new experiments that could be done to tease apart these two mechanisms. This is an important question because the phase relationships between the inhibitory and excitatory neurons in the cortex is different for the two models, with implications for entrainment between different populations of neurons.