Adrienne L. Fairhall

Fractional differentiation by neocortical pyramidal neurons

Neural systems adapt to changes in stimulus statistics. However, it is not known how stimuli with complex temporal dynamics drive the dynamics of adaptation and the resulting firing rate. For single neurons, it has often been assumed that adaptation has a single time scale. We found that single rat neocortical pyramidal neurons adapt with a time scale that depends on the time scale of changes in stimulus statistics. This multiple time scale adaptation is consistent with fractional order differentiation, such that the neurons firing rate is a fractional derivative of slowly varying stimulus parameters. Biophysically, even though neuronal fractional differentiation effectively yields adaptation with many time scales, we found that its implementation required only a few properly balanced known adaptive mechanisms. Fractional differentiation provides single neurons with a fundamental and general computation that can contribute to efficient information processing, stimulus anticipation and frequency-independent phase shifts of oscillatory neuronal firing.

Timescales of Inference in Visual Adaptation

Adaptation is a hallmark of sensory function. Adapting optimally requires matching the dynamics of adaptation to those of changes in the stimulus distribution. Here we show that the dynamics of adaptation in the responses of mouse retinal ganglion cells depend on stimulus history. We hypothesized that the accumulation of evidence for a change in the stimulus distribution controls the dynamics of adaptation, and developed a model for adaptation as an ongoing inference problem. Guided by predictions of this model, we found that the dynamics of adaptation depend on the discriminability of the change in stimulus distribution and that the retina exploits information contained in properties of the stimulus beyond the mean and variance to adapt more quickly when possible.

Two-Dimensional Time Coding in the Auditory Brainstem

Avian nucleus magnocellularis (NM) spikes provide a temporal code representing sound arrival times to downstream neurons that compute sound source location. NM cells act as high-pass filters by responding only to discrete synaptic events while ignoring temporally summed EPSPs. This high degree of input selectivity insures that each output spike from NM unambiguously represents inputs that contain precise temporal information. However, we lack a quantitative description of the computation performed by NM cells. A powerful model for predicting output firing rate given an arbitrary current input is given by a linear/nonlinear cascade: the stimulus is compared with a known relevant feature by linear filtering, and based on that comparison, a nonlinear function predicts the firing response. Spike-triggered covariance analysis allows us to determine a generalization of this model in which firing depends on more than one spike-triggering feature or stimulus dimension. We found two current features relevant for NM spike generation; the most important simply smooths the current on short time scales, whereas the second confers sensitivity to rapid changes. A model based on these two features captured more mutual information between current and spikes than a model based on a single feature. We used this analysis to characterize the changes in the computation brought about by pharmacological manipulation of the biophysical properties of the neurons. Blockage of low-threshold voltage-gated potassium channels selectively eliminated the requirement for the second stimulus feature, generalizing our understanding of input selectivity by NM cells. This study demonstrates the power of covariance analysis for investigating single neuron computation.

Mosquitoes Use Vision to Associate Odor Plumes with Thermal Targets

All moving animals, including flies, sharks, and humans, experience a dynamic sensory landscape that is a function of both their trajectory through space and the distribution of stimuli in the environment. This is particularly apparent for mosquitoes, which use a combination of olfactory, visual, and thermal cues to locate hosts. Mosquitoes are thought to detect suitable hosts by the presence of a sparse CO₂ plume, which they track by surging upwind and casting crosswind. Upon approach, local cues such as heat and skin volatiles help them identify a landing site. Recent evidence suggests that thermal attraction is gated by the presence of CO₂, although this conclusion was based experiments in which the actual flight trajectories of the animals were unknown and visual cues were not studied. Using a three-dimensional tracking system, we show that rather than gating heat sensing, the detection of CO₂ actually activates a strong attraction to visual features. This visual reflex guides the mosquitoes to potential hosts where they are close enough to detect thermal cues. By experimentally decoupling the olfactory, visual, and thermal cues, we show that the motor reactions to these stimuli are independently controlled. Given that humans become visible to mosquitoes at a distance of 5-15 m, visual cues play a critical intermediate role in host localization by coupling long-range plume tracking to behaviors that require short-range cues. Rather than direct neural coupling, the separate sensory-motor reflexes are linked as a result of the interaction between the animals reactions and the spatial structure of the stimuli in the environment.

Multiple Timescale Encoding of Slowly Varying Whisker Stimulus Envelope in Cortical and Thalamic Neurons In Vivo

Adaptive processes over many timescales endow neurons with sensitivity to stimulus changes over a similarly wide range of scales. Although spike timing of single neurons can precisely signal rapid fluctuations in their inputs, the mean firing rate can convey information about slower-varying properties of the stimulus. Here, we investigate the firing rate response to a slowly varying envelope of whisker motion in two processing stages of the rat vibrissa pathway. The whiskers of anesthetized rats were moved through a noise trajectory with an amplitude that was sinusoidally modulated at one of several frequencies. In thalamic neurons, we found that the rate response to the stimulus envelope was also sinusoidal, with an approximately frequency-independent phase advance with respect to the input. Responses in cortex were similar but with a phase shift that was about three times larger, consistent with a larger amount of rate adaptation. These response properties can be described as a linear transformation of the input for which a single parameter quantifies the phase shift as well as the degree of adaptation. These results are reproduced by a model of adapting neurons connected by synapses with short-term plasticity, showing that the observed linear response and phase lead can be built up from a network that includes a sequence of nonlinear adapting elements. Our study elucidates how slowly varying envelope information under passive stimulation is preserved and transformed through the vibrissa processing pathway.

Cellular mechanisms for integral feedback in visually guided behavior

Significance Visually driven behaviors of Drosophila have become a model system to study how neural circuits process sensory information. Here, we show that one of the computations performed by this system is temporal integration of visual motion. We provide evidence of how this computation might be performed by measuring the activity of identified visual interneurons during tethered flight that are thought to control the described behavior: Presynaptic calcium accumulation in these neurons mimics a leaky temporal integration of the visual motion signal as does the behavior. In the future, the genetic tools available in Drosophila will enable studying the precise mechanism of temporal integration in this model system, which could provide insights into general mechanisms of neuronal information processing. Sensory feedback is a ubiquitous feature of guidance systems in both animals and engineered vehicles. For example, a common strategy for moving along a straight path is to turn such that the measured rate of rotation is zero. This task can be accomplished by using a feedback signal that is proportional to the instantaneous value of the measured sensory signal. In such a system, the addition of an integral term depending on past values of the sensory input is needed to eliminate steady-state error [proportional-integral (PI) control]. However, the means by which nervous systems implement such a computation are poorly understood. Here, we show that the optomotor responses of flying Drosophila follow a time course consistent with temporal integration of horizontal motion input. To investigate the cellular basis of this effect, we performed whole-cell patch-clamp recordings from the set of identified visual interneurons [horizontal system (HS) cells] thought to control this reflex during tethered flight. At high stimulus speeds, HS cells exhibit steady-state responses during flight that are absent during quiescence, a state-dependent difference in physiology that is explained by changes in their presynaptic inputs. However, even during flight, the membrane potential of the large-field interneurons exhibits no evidence for integration that could explain the behavioral responses. However, using a genetically encoded indicator, we found that calcium accumulates in the terminals of the interneurons along a time course consistent with the behavior and propose that this accumulation provides a mechanism for temporal integration of sensory feedback consistent with PI control.

Encoding properties of haltere neurons enable motion feature detection in a biological gyroscope

The halteres of dipteran insects are essential sensory organs for flight control. They are believed to detect Coriolis and other inertial forces associated with body rotation during flight. Flies use this information for rapid flight control. We show that the primary afferent neurons of the haltere’s mechanoreceptors respond selectively with high temporal precision to multiple stimulus features. Although we are able to identify many stimulus features contributing to the response using principal component analysis, predictive models using only two features, common across the cell population, capture most of the cells’ encoding activity. However, different sensitivity to these two features permits each cell to respond to sinusoidal stimuli with a different preferred phase. This feature similarity, combined with diverse phase encoding, allows the haltere to transmit information at a high rate about numerous inertial forces, including Coriolis forces.

Single neuron computation: From dynamical system to feature detector

White noise methods are a powerful tool for characterizing the computation performed by neural systems. These methods allow one to identify the feature or features that a neural system extracts from a complex input and to determine how these features are combined to drive the systems spiking response. These methods have also been applied to characterize the input-output relations of single neurons driven by synaptic inputs, simulated by direct current injection. To interpret the results of white noise analysis of single neurons, we would like to understand how the obtained feature space of a single neuron maps onto the biophysical properties of the membrane, in particular, the dynamics of ion channels. Here, through analysis of a simple dynamical model neuron, we draw explicit connections between the output of a white noise analysis and the underlying dynamical system. We find that under certain assumptions, the form of the relevant features is well defined by the parameters of the dynamical system. Further, we show that under some conditions, the feature space is spanned by the spike-triggered average and its successive order time derivatives.

Sensitivity of firing rate to input fluctuations depends on time scale separation between fast and slow variables in single neurons

Neuronal responses are often characterized by the firing rate as a function of the stimulus mean, or the f–I curve. We introduce a novel classification of neurons into Types A, B−, and B+ according to how f–I curves are modulated by input fluctuations. In Type A neurons, the f–I curves display little sensitivity to input fluctuations when the mean current is large. In contrast, Type B neurons display sensitivity to fluctuations throughout the entire range of input means. Type B− neurons do not fire repetitively for any constant input, whereas Type B+ neurons do. We show that Type B+ behavior results from a separation of time scales between a slow and fast variable. A voltage-dependent time constant for the recovery variable can facilitate sensitivity to input fluctuations. Type B+ firing rates can be approximated using a simple “energy barrier” model.

Decoding Stimulus Variance from a Distributional Neural Code of Interspike Intervals

The spiking output of an individual neuron can represent information about the stimulus via mean rate, absolute spike time, and the time intervals between spikes. Here we discuss a distinct form of information representation, the local distribution of spike intervals, and show that the time-varying distribution of interspike intervals (ISIs) can represent parameters of the statistical context of stimuli. For many sensory neural systems the mapping between the stimulus input and spiking output is not fixed but, rather, depends on the statistical properties of the stimulus, potentially leading to ambiguity. We have shown previously that for the adaptive neural code of the fly H1, a motion-sensitive neuron in the fly visual system, information about the overall variance of the signal is obtainable from the ISI distribution. We now demonstrate the decoding of information about variance and show that a distributional code of ISIs can resolve ambiguities introduced by slow spike frequency adaptation. We examine the precision of this distributional code for the representation of stimulus variance in the H1 neuron as well as in the Hodgkin–Huxley model neuron. We find that the accuracy of the decoding depends on the shapes of the ISI distributions and the speed with which they adapt to new stimulus variances.