A pair of motion-sensitive neurons in the locust encode approaches of a looming object

1. We reexamine the possibilities for analyzing and interpreting the time course of correlation in spike trains simultaneously and separably recorded from two neurons. 2. We develop procedures to quantify and properly normalize the classical joint peristimulus time scatter diagram. These allow separation of the "raw" correlation into components caused by direct stimulus modulations of the single-neuron firing rates and those caused by various types of interaction between the two neurons. 3. A newly developed significance test ("surprise") is applied to evaluate such inferences. 4. Application of the new procedures to simulated spike trains allowed the recovery of the known circuitry. In particular, it proved possible to recover fast stimulus-locked modulations of "effective connectivity," even if they were masked by strong direct stimulus modulations of individual firing rates. These procedures thus present a clearly superior alternative to the commonly used "shift predictor." 5. Adopting a model-based approach, we generalize the classical measures for quantifying a direct interneuronal connection ("efficacy" and "contribution") to include possible stimulus-locked time variations. 6. Application of the new procedures to real spike trains from several different preparations showed that fast stimulus-locked modulations of "effective connectivity" also occur for real neurons.

Multiplicative operations are important in sensory processing, but their biophysical implementation remains largely unknown. We investigated an identified neuron (the lobula giant movement detector, LGMD, of locusts) whose output firing rate in response to looming visual stimuli has been described by two models, one of which involves a multiplication. In this model, the LGMD multiplies postsynaptically two inputs (one excitatory, one inhibitory) that converge onto its dendritic tree; in the other model, inhibition is presynaptic to the LGMD. By using selective activation and inactivation of pre- and postsynaptic inhibition, we show that postsynaptic inhibition has a predominant role, suggesting that multiplication is implemented within the neuron itself. Our pharmacological experiments and measurements of firing rate versus membrane potential also reveal that sodium channels act both to advance the response of the LGMD in time and to map membrane potential to firing rate in a nearly exponential manner. These results are consistent with an implementation of multiplication based on dendritic subtraction of two converging inputs encoded logarithmically, followed by exponentiation through active membrane conductances.

Functional interactions between neurons in vivo are often quantified by cross-correlation functions (CCFs) between their spike trains. It is therefore essential to understand quantitatively how CCFs are shaped by different factors, such as connectivity, synaptic parameters, and background activity. Here, we study the CCF between two neurons using analytical calculations and numerical simulations. We quantify the role of synaptic parameters, such as peak conductance, decay time, and reversal potential, and analyze how various patterns of connectivity influence CCF shapes. In particular, we find that the symmetry of the CCF distinguishes in general, but not always, the case of shared inputs between two neurons from the case in which they are directly synaptically connected. We systematically examine the influence of background synaptic inputs from the surrounding network that set the baseline firing statistics of the neurons and modulate their response properties. We find that variations in the background noise modify the amplitude of the cross-correlation function as strongly as variations of synaptic strength. In particular, we show that the postsynaptic neuron spiking regularity has a pronounced influence on CCF amplitude. This suggests an efficient and flexible mechanism for modulating functional interactions.