Multiplicative computation in the vestibulo-ocular reflex (VOR).

Multiplicative computation is a basic operation that is crucial for neural information processing, but examples of multiplication by neural pathways that perform well-defined sensorimotor transformations are scarce. Here in behaving monkeys, we identified a multiplication of vestibular and eye position signals in the vestibulo-ocular reflex (VOR). Monkeys were trained to maintain fixation on visual targets at different horizontal locations and received brief unilateral acoustic clicks (1 ms, rarefaction, 85 approximately 110 db NHL) that were delivered into one of their external ear canals. We found that both the click-evoked horizontal eye movement responses and the click-evoked neuronal responses of the abducens neurons exhibited linear dependencies on horizontal conjugate eye position, indicating that the interaction of vestibular and horizontal conjugate eye position was multiplicative. Latency analysis further indicated that the site of the multiplication was within the direct VOR pathways. Based on these results, we propose a novel neural mechanism that implements the VOR gain modulation by fixation distance and gaze eccentricity. In this mechanism, the vestibular signal from a single labyrinth interacts multiplicatively with the position signals of each eye (Principle of Multiplication). These effects, however, interact additively with the other labyrinth (Principle of Addition). Our analysis suggests that the new mechanism can implement the VOR gain modulation by fixation distance and gaze eccentricity within the direct VOR pathways.

Effect of stochastic synaptic and dendritic dynamics on synaptic plasticity in visual cortex and hippocampus.

Various forms of synaptic plasticity, including spike timing-dependent plasticity, can be accounted for by calcium-dependent models of synaptic plasticity. However, recent results in which synaptic plasticity is induced by multi-spike protocols cannot simply be accounted for by linear superposition of plasticity due to spike pairs or by existing calcium-dependent models. In this paper, we show that multi-spike protocols can be accounted for if, in addition to the dynamics of back-propagating action potentials, stochastic synaptic dynamics are taken into account. We show that a stochastic implementation can account for the data better than a deterministic implementation and is also more robust. Our results demonstrate that differences between experimental results obtained in hippocampus and visual cortex can be accounted for by the different synaptic and dendritic dynamics in these two systems.

A biophysical basis for the inter-spike interaction of spike-timing-dependent plasticity.

Although spike-timing-dependent plasticity (STDP) is well characterized when pre- and postsynaptic spikes are paired with a given time lag, how this generalizes for more complex spike-trains is unclear. Recent experiments demonstrate that contributions to synaptic plasticity from different spike pairs within a spike train do not add linearly. In the visual cortex conditioning with spike triplets shows that the effect of the first spike pair dominates over the second. Using a previously proposed calcium-dependent plasticity model, we show that short-term synaptic dynamics and interaction between successive back-propagating action potentials (BPAP) may jointly account for the nonlinearities observed. Paired-pulse depression and attenuation of BPAPs are incorporated into the model through the use-dependent depletion of pre- and postsynaptic resources, respectively. Simulations suggest that these processes may play critical roles in determining how STDP operates in the context of natural spike-trains.

Role of A-type K+ channels in spike broadening observed in soma and axon of Hermissenda type-B photoreceptors: a simulation study.

In Hermissenda type-B photoreceptors, the spike is generated in the axon and back-propagated to the soma, resulting in smaller somatic spikes. Experimentally, blocking the A-type K+ current (IK,A) results in broadening of somatic spikes. Similarly, in a compartmental model of the photoreceptor, reducing the maximum A-type K+ conductance (gK,Amax) results in broadening of somatic spikes. However, simulations predict that little or no broadening of axonal spikes occurs when gK,Amax is reduced. The results can be explained by the voltage-dependent properties of IK,A and the different potential ranges that the somatic and axonal spike traverse. Because of the steeper I-V curve and faster activation of the K+ channels at higher potentials, the recruitment of additional K+ channels in the axon is able to compensate for the decrease in K+ conductance, yielding less spike broadening. These results also support the idea that spike duration in the axon may not be reliably inferred based upon recordings collected from the soma.

Computational model of touch sensory cells (T Cells) of the leech: role of the afterhyperpolarization (AHP) in activity-dependent conduction failure.

Bursts of spikes in T cells produce an AHP, which results from activation of a Na+/K+ pump and a Ca2+-dependent K+ current. Activity-dependent increases in the AHP are believed to induce conduction block of spikes in several regions of the neuron, which in turn, may decrease presynaptic invasion of spikes and thereby decrease transmitter release. To explore this possibility, we used the neurosimulator SNNAP to develop a multi-compartmental model of the T cell. The model incorporated empirical data that describe the geometry of the cell and activity-dependent changes of the AHP. Simulations indicated that at some branching points, activity-dependent increases of the AHP reduced the number of spikes transmitted from the minor receptive fields to the soma and beyond. More importantly, simulations also suggest that the AHP could modulate, under some circumstances, transmission from the soma to the synaptic terminals, suggesting that the AHP can regulate spike conduction within the presynaptic arborizations of the cell and could in principle contribute to the synaptic depression that is correlated with increases in the AHP.

Voltage-clamp analysis and computational model of dopaminergic neurons from mouse retina.

Isolated dopaminergic amacrine (DA) cells in mouse retina fire rhythmic, spontaneous action potentials and respond to depolarizing current with trains of low-frequency action potentials. To investigate the roles of voltage-gated ion channels in these processes, the transient A-type K+ current (I(K,A)) and Ca2+ current (I(Ca)) in isolated mouse DA cells were analyzed by voltage clamp. The I(K,A) activated at -60 mV and inactivated rapidly. I(Ca) activated at around -30 mV and reached a peak at 10 mV without apparent inactivation. We also extended our previous computational model of the mouse DA cell to include the new electrophysiological data. The model consisted of a membrane capacitance in parallel with eight currents: Na+ transient (I(Na,T)), Na+ persistent (I(Na,P)), delayed rectifier potassium (I(Kdr)), I(K,A), calcium-dependent potassium (I(K,Ca)), L-type Ca2+ I(Ca), hyperpolarization-activated cation current (I(h)), and a leak current (I(L)). Hodgkin-Huxley type equations were used to define the voltage- and time-dependent activation and inactivation. The simulations were implemented using the neurosimulator SNNAP. The model DA cell was spontaneously active from a wide range of initial membrane potentials. The spontaneous action potentials reached 35 mV at the peak and hyperpolarized to -76 mV between spikes. The spontaneous firing frequency in the model was 6 Hz. The model DA cell responded to prolonged depolarizing current injection by increasing its spiking frequency and eventually reaching a depolarization block at membrane potentials greater than -10 mV. The most important current for determining the firing rate was I(K,A). When the amplitude of I(K,A) was decreased, the firing rate increased. I(Ca) and I(K,Ca) also affected the width of action potentials but had only minor effects on the firing rate. Ih affected the firing rate slightly but did not change the waveform of the action potentials.

Spontaneous activity of dopaminergic retinal neurons.

Dopaminergic local circuit neurons in the retina (DA cells) show robust, spontaneous, tetrodotoxin-sensitive pacemaking. To investigate the mechanism underlying this behavior, we characterized the sodium current and a subset of the potassium currents in the cells in voltage-clamp experiments. We found that there is a persistent component of the sodium current in DA cells which activates at more depolarized potentials than the transient component of the current. The transient component was completely inactivated at -50 mV, but DA cells remained able to fire spontaneous action potentials when potassium channels were partially blocked and the membrane potential remained above -40 mV. Based on these electrophysiological data, we developed a reduced computer model that reproduced the major features of DA cells. In simulations at the physiological resting potential, the persistent component of the sodium current was both necessary and sufficient to account for spontaneous activity, and the major contribution of the transient component of the sodium current was to initiate the depolarization of the model cell during the interspike interval. When tonic inhibition was simulated by lowering the input impedance of the model cell, the transient component played a larger role.

A computational study of the role of spike broadening in synaptic facilitation of Hermissenda.

Pavlovian conditioning in Hermissenda produces a decrease in voltage-dependent (I(K,A) and I(Ca)) and Ca2+-dependent (I(K,Ca)) currents, and an increase in the action potential (AP) duration in type B-photoreceptors. In addition, synaptic connections between B and A photoreceptors and B photoreceptor and type I interneurons are facilitated. The increase in AP duration, produced by decreasing one or more K+ currents, may account for synaptic facilitation. The present study examined this issue by using a mathematical model of the B-photoreceptor and the neurosimulator SNNAP. In the model, decreasing g(K,A) by 70% increased the duration of the AP in the terminal by 41% and Ca2+ influx by 30%. However, if the decrease in g(K,A) was combined with a decrease in g(Ca), similar to what has been reported experimentally, the Ca2+ influx decreased by 54%. Therefore, the concomitant change in I(Ca) counter-acted the broadening-induced increase in Ca2+ influx in the synaptic terminal. This result suggests that a spike-duration independent process must contribute to the synaptic facilitation observed following Pavlovian conditioning.

Computational study of enhanced excitability in Hermissenda: membrane conductances modulated by 5-HT.

Serotonin (5-HT) applied to the exposed but otherwise intact nervous system results in enhanced excitability of Hermissenda type-B photoreceptors. Several ion currents in the type-B photoreceptors are modulated by 5-HT, including the A-type K+ current (I(K,A)), sustained Ca2+ current (I(Ca,S)), Ca-dependent K+ current (I(K,Ca)), and a hyperpolarization-activated inward rectifier current (I(h)). In this study, we developed a computational model that reproduces physiological characteristics of type B photoreceptors, e.g. resting membrane potential, dark-adapted spike activity, spike width, and the amplitude difference between somatic and axonal spikes. We then used the model to investigate the contribution of different ion currents modulated by 5-HT to the magnitudes of enhanced excitability produced by 5-HT. Ion currents were systematically varied within limits observed experimentally, both individually and in combinations. A reduction of I(K,A) or I(K,Ca), or an increase in I(h) enhanced excitability by 20-50%. Decreasing I(Ca,S) produced a dramatic decrease in excitability. Reductions of I(K,V) produced only minimal increases in excitability, suggesting that I(K,V) probably plays a minor role in 5-HT induced enhanced excitability. Combinations of changes in I(K,A), I(K,Ca), I(h) and I(Ca,S) produced increases in excitability comparable to experimental observations. After 5-HT application, the cell's depolarization force is shifted from the I(h)-I(Ca,S) combination to predominantly I(h).