A single spinal motoneuron receives tens of thousands of synapses. The neurotransmitters released by many of these synapses act on iontotropic receptors and alter the driving potential of neighboring synapses. This interaction introduces an intrinsic nonlinearity in motoneuron input-output properties where the response to two simultaneous inputs is less than the linear sum of the responses to each input alone. Our goal was to determine the impact of this nonlinearity on the current delivered to the soma during activation of predetermined numbers and distributions of excitatory and inhibitory synapses. To accomplish this goal we constructed compartmental models constrained by detailed measurements of the geometry of the dendritic trees of three feline motoneurons. The current "lost" as a result of local changes in driving potential was substantial and resulted in a highly nonlinear relationship between the number of active synapses and the current reaching the soma. Background synaptic activity consisting of a balanced activation of excitatory and inhibitory synapses further decreased the current delivered to the soma, but reduced the nonlinearity with respect to the total number of active excitatory synapses. Unexpectedly, simulations that mimicked experimental measures of nonlinear summation, activation of two sets of excitatory synapses, resulted in nearly linear summation. This result suggests that nonlinear summation can be difficult to detect, despite the substantial "loss" of current arising from nonlinear summation. The magnitude of this "loss" appears to limit motoneuron activity, based solely on activation of iontotropic receptors, to levels that are inadequate to generate functionally meaningful muscle forces. 10.1152/jn.00439.2005

To act as computational devices, neurons must perform mathematical operations as they transform synaptic and modulatory input into output firing rate. Experiments and theory indicate that neuronal firing typically represents the sum of synaptic inputs, an additive operation, but multiplication of inputs is essential for many computations. Multiplication by a constant produces a change in the slope, or gain, of the inputoutput relationship, amplifying or scaling down the sensitivity of the neuron to changes in its input. Such gain modulation occurs in vivo, during contrast invariance of orientation tuning, attentional scaling, translation-invariant object recognition, auditory processing and coordinate transformations. Moreover, theoretical studies highlight the necessity of gain modulation in several of these tasks. Although potential cellular mechanisms for gain modulation have been identified, they often rely on membrane noise and require restrictive conditions to work. Because nonlinear components are used to scale signals in electronics, we examined whether synaptic nonlinearities are involved in neuronal gain modulation. We used synaptic stimulation and the dynamic-clamp technique to investigate gain modulation in granule cells in acute slices of rat cerebellum. Here we show that when excitation is mediated by synapses with short-term depression (STD), neuronal gain is controlled by an inhibitory conductance in a noise-independent manner, allowing driving and modulatory inputs to be multiplied together. The nonlinearity introduced by STD transforms inhibition-mediated additive shifts in the inputoutput relationship into multiplicative gain changes. When granule cells were driven with bursts of high-frequency mossy fibre input, as observed in vivo, larger inhibition-mediated gain changes were observed, as expected with greater STD. Simulations of synaptic integration in more complex neocortical neurons suggest that STD-based gain modulation can also operate in neurons with large dendritic trees. Our results establish that neurons receiving depressing excitatory inputs can act as powerful multiplicative devices even when integration of postsynaptic conductances is linear.

At the first synapse in the auditory pathway, the receptor potential of mechanosensory hair cells is converted into a firing pattern in auditory nerve fibers. For the accurate coding of timing and intensity of sound signals, transmitter release at this synapse must occur with the highest precision. To measure directly the transfer characteristics of the hair cell afferent synapse, we implemented simultaneous whole-cell recordings from mammalian inner hair cells (IHCs) and auditory nerve fiber terminals that typically receive input from a single ribbon synapse. During a 1-s IHC depolarization, the synaptic response depressed >90%, representing the main source for adaptation in the auditory nerve. Synaptic depression was slightly affected by alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor desensitization; however, it was mostly caused by reduced vesicular release. When the transfer function between transmitter release and Ca(2+) influx was tested at constant open probability for Ca(2+) channels (potentials >0 mV), a super linear relation was found. This relation is presumed to result from the cooperative binding of three to four Ca(2+) ions at the Ca(2+) sensor. However, in the physiological range for receptor potentials (-50 to -30 mV), the relation between Ca(2+) influx and afferent activity was linear, assuring minimal distortion in the coding of sound intensity. Changes in Ca(2+) influx caused an increase in release probability, but not in the average size of multivesicular synaptic events. By varying Ca(2+) buffering in the IHC, we further investigate how Ca(2+) channel and Ca(2+) sensor at this synapse might relate.

Hearing in mammals relies on the highly synchronous synaptic transfer between cochlear inner hair cells (IHCs) and the auditory nerve. We studied the presynaptic function of single mouse IHCs by monitoring membrane capacitance changes and voltage-gated Ca(2+) currents. Exocytosis initially occurred at a high rate but then slowed down within a few milliseconds, despite nearly constant Ca(2+) influx. We interpret the observed secretory depression as depletion of a readily releasable pool (RRP) of about 280 vesicles. These vesicles are probably docked close to Ca(2+) channels at the ribbon-type active zones of the IHCs. Continued depolarization evoked slower exocytosis occurring at a nearly constant rate for at least 1 s and depending on "long-distance" Ca(2+) signaling. Refilling of the RRP after depletion followed a biphasic time course and was faster than endocytosis. RRP depletion is discussed as a mechanism for fast auditory adaptation.