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Highlights d Efferents in neuromasts of the lateral line convey a close copy of the motor signal d Efferents suppress hair cell glutamate release within 50 ms of first motor spike d Efferent modulation is biased toward hair cells activated during forward motion d Motor activity blocks ''push-pull'' signaling of stimulus direction

Hair cells transmit mechanical information by converting deflection of the hair bundle into synaptic release of glutamate. We have investigated this process in the lateral line of larval zebrafish (male and female) to understand how stimuli are encoded within a neuromast. Using multiphoton microscopy in vivo, we imaged synaptic release of glutamate using the reporter iGluSnFR as well as deflections of the cupula. We found that the neuromast is composed of a functionally diverse population of hair cells. Half the hair cells signaled cupula motion in both directions from rest, either by increasing glutamate release in response to a deflection in the positive direction or by reducing release in the negative direction. The relationship between cupula deflection and glutamate release demonstrated maximum sensitivity at displacements of just ∼40 nm in the positive direction. The remaining hair cells only signaled motion in one direction and were less sensitive, extending the operating range of the neuromast beyond 1 μm. Adaptation of the synaptic output was also heterogeneous, with some hair cells generating sustained glutamate release in response to a steady deflection of the cupula and others generating transient outputs. Finally, a distinct signal encoded a return of the cupula to rest: a large and transient burst of glutamate release from hair cells unresponsive to the initial stimulus. A population of hair cells with these different sensitivities, operating ranges, and adaptive properties will allow the neuromast to encode weak stimuli while maintaining the dynamic range to signal the amplitude and duration of stronger deflections.SIGNIFICANCE STATEMENT Hair cells transmit information about mechanical stimuli by converting very small deflections of their hair bundle into changes in the release of the neurotransmitter glutamate. We have measured this input/output relation in the live fish using a fluorescent protein and find that different hair cells vary in their mechanical sensitivity and the time course of their response. These variations will allow the fish to sense the timing and duration of both very weak stimuli (∼40 nm deflections) and strong stimuli (∼1 μm), underlying the ability of the fish to avoid predators and maintain its body position in flowing water.

a b s t r a c tWe compare the performance of perturbation, projection, and stochastic simulation algorithms for solving the multi-country RBC model described in Den Haan et al.(this issue). The main challenge of solving this model comes from its large number of continuous-valued state variables, ranging between four and 20 in the specifications we consider. The algorithms differ substantially in terms of speed and accuracy, and a clear trade-off exists between the two. Perturbation methods are very fast but invoke large approximation errors except at points close to the steady state; the projection methods considered are accurate on a large area of the state space but are very slow for specifications with many state variables; stochastic simulation methods have lower accuracy than projection methods, but their computational cost increases only moderately with the state-space dimension. Simulated series generated by different methods can differ noticeably, but only small differences are found in unconditional moments of simulated variables. On the basis of our comparison, we identify the factors that account for differences in accuracy and speed across methods, and we suggest directions for further improvement of some approaches.

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