Information Rate and Spike-Timing Precision of Proprioceptive Afferents

The processing of proprioceptive signals in distributed networks: insights from insect motor control

The integration of sensory information is required to maintain body posture and to generate robust yet flexible locomotion through unpredictable environments. To anticipate required adaptations in limb posture and enable compensation of sudden perturbations, an animal's nervous system assembles external (exteroception) and internal (proprioception) cues. Coherent neuronal representations of the proprioceptive context of the body and the appendages arise from the concerted action of multiple sense organs monitoring body kinetics and kinematics. This multimodal proprioceptive information, together with exteroceptive signals and brain-derived descending motor commands, converges onto premotor networks - i.e. the local neuronal circuitry controlling motor output and movements - within the ventral nerve cord (VNC), the insect equivalent of the vertebrate spinal cord. This Review summarizes existing knowledge and recent advances in understanding how local premotor networks in the VNC use convergent information to generate contextually appropriate activity, focusing on the example of posture control. We compare the role and advantages of distributed sensory processing over dedicated neuronal pathways, and the challenges of multimodal integration in distributed networks. We discuss how the gain of distributed networks may be tuned to enable the behavioral repertoire of these systems, and argue that insect premotor networks might compensate for their limited neuronal population size by, in comparison to vertebrate networks, relying more heavily on the specificity of their connections. At a time in which connectomics and physiological recording techniques enable anatomical and functional circuit dissection at an unprecedented resolution, insect motor systems offer unique opportunities to identify the mechanisms underlying multimodal integration for flexible motor control.

An information theoretic method to resolve millisecond-scale spike timing precision in a comprehensive motor program

Sensory inputs in nervous systems are often encoded at the millisecond scale in a precise spike timing code. There is now growing evidence in behaviors ranging from slow breathing to rapid flight for the prevalence of precise timing encoding in motor systems. Despite this, we largely do not know at what scale timing matters in these circuits due to the difficulty of recording a complete set of spike-resolved motor signals and assessing spike timing precision for encoding continuous motor signals. We also do not know if the precision scale varies depending on the functional role of different motor units. We introduce a method to estimate spike timing precision in motor circuits using continuous MI estimation at increasing levels of added uniform noise. This method can assess spike timing precision at fine scales for encoding rich motor output variation. We demonstrate the advantages of this approach compared to a previously established discrete information theoretic method of assessing spike timing precision. We use this method to analyze the precision in a nearly complete, spike resolved recording of the 10 primary wing muscles control flight in an agile hawk moth, Manduca sexta. Tethered moths visually tracked a robotic flower producing a range of turning (yaw) torques. We know that all 10 muscles in this motor program encode the majority of information about yaw torque in spike timings, but we do not know whether individual muscles encode motor information at different levels of precision. We demonstrate that the scale of temporal precision in all motor units in this insect flight circuit is at the sub-millisecond or millisecond-scale, with variation in precision scale present between muscle types. This method can be applied broadly to estimate spike timing precision in sensory and motor circuits in both invertebrates and vertebrates.

Stimulator compensation and generation of Gaussian noise stimuli with defined amplitude spectra for studying input–output relations of sensory systems

Gaussian noise is an important stimulus for the study of biological systems, especially sensory and neural systems. Since these systems are inherently nonlinear, the properties of the noise strongly influence the outcome of the analysis. Therefore, it is crucial to use a well-defined and controlled noise stimulus. In this paper, we first use the example of an insect filiform sensillum, a simple mechanoreceptor with a single sensory cell, to show that changes in the amplitude and spectral properties of the noise stimulus indeed affect the linear transfer function of the sensillum. We then explain step-by-step how to use the inverse fast Fourier transform to generate a Gaussian noise that has an arbitrary user-defined amplitude spectrum, including a band-limited white noise with a perfectly sharp cutoff edge. Finally, we demonstrate how such a perfect band-limited Gaussian white noise stimulus can also be generated with a non-perfect stimulator using a simple procedure that compensates for the filtering properties of the stimulator. With this approach, one can generate well-defined Gaussian noise stimuli that can be adapted to any application. For example, one can generate visual, sound, or vibrational stimuli for experimental research in visual physiology, auditory physiology, and biotremology, as well as inputs for testing various models in theoretical research.

Corollary discharge enables proprioception from lateral line sensory feedback

Animals modulate sensory processing in concert with motor actions. Parallel copies of motor signals, called corollary discharge (CD), prepare the nervous system to process the mixture of externally and self-generated (reafferent) feedback that arises during locomotion. Commonly, CD in the peripheral nervous system cancels reafference to protect sensors and the central nervous system from being fatigued and overwhelmed by self-generated feedback. However, cancellation also limits the feedback that contributes to an animal's awareness of its body position and motion within the environment, the sense of proprioception. We propose that, rather than cancellation, CD to the fish lateral line organ restructures reafference to maximize proprioceptive information content. Fishes' undulatory body motions induce reafferent feedback that can encode the body's instantaneous configuration with respect to fluid flows. We combined experimental and computational analyses of swimming biomechanics and hair cell physiology to develop a neuromechanical model of how fish can track peak body curvature, a key signature of axial undulatory locomotion. Without CD, this computation would be challenged by sensory adaptation, typified by decaying sensitivity and phase distortions with respect to an input stimulus. We find that CD interacts synergistically with sensor polarization to sharpen sensitivity along sensors' preferred axes. The sharpening of sensitivity regulates spiking to a narrow interval coinciding with peak reafferent stimulation, which prevents adaptation and homogenizes the otherwise variable sensor output. Our integrative model reveals a vital role of CD for ensuring precise proprioceptive feedback during undulatory locomotion, which we term external proprioception.

Nonlinearization: naturalistic stimulation and nonlinear dynamic behavior in a spider mechanoreceptor

In a previous study, we used linear frequency response analysis to show that naturalistic stimulation of spider primary mechanosensory neurons produced different response dynamics than the commonly used Gaussian random noise. We isolated this difference to the production of action potentials from receptor potential and suggested that the different distribution of frequency components in the naturalistic signal increased the nonlinearity of action potential encoding. Here, we tested the relative contributions of first- and second-order processes to the action potential signal by measuring linear and quadratic coherence functions. Naturalistic stimulation shifted the linear coherence toward lower frequencies, while quadratic coherence was always higher than linear coherence and increased with naturalistic stimulation. In an initial attempt to separate the order of time-dependent and nonlinear processes, we fitted quadratic frequency response functions by two block-structured models consisting of a power-law filter and a static second-order nonlinearity in alternate cascade orders. The same cascade models were then fitted to the original time domain data by conventional numerical analysis algorithms, using a polynomial function as the static nonlinearity. Quadratic models with a linear filter followed by a static nonlinearity were favored over the reverse order, but with weak significance. Polynomial nonlinear functions indicated that rectification is a major nonlinearity. A complete quantitative description of sensory encoding in these primary mechanoreceptors remains elusive but clearly requires quadratic and higher nonlinear operations on the input signal to explain the sensitivity of dynamic behavior to different input signal patterns.

The presynaptic machinery at the synapse of C. elegans

Synapses are specialized contact sites that mediate information flow between neurons and their targets. Important physical interactions across the synapse are mediated by synaptic adhesion molecules. These adhesions regulate formation of synapses during development and play a role during mature synaptic function. Importantly, genes regulating synaptogenesis and axon regeneration are conserved across the animal phyla. Genetic screens in the nematode Caenorhabditis elegans have identified a number of molecules required for synapse patterning and assembly. C. elegans is able to survive even with its neuronal function severely compromised. This is in comparison with Drosophila and mice where increased complexity makes them less tolerant to impaired function. Although this fact may reflect differences in the function of the homologous proteins in the synapses between these organisms, the most likely interpretation is that many of these components are equally important, but not absolutely essential, for synaptic transmission to support the relatively undemanding life style of laboratory maintained C. elegans. Here, we review research on the major group of synaptic proteins, involved in the presynaptic machinery in C. elegans, showing a strong conservation between higher organisms and highlight how C. elegans can be used as an informative tool for dissecting synaptic components, based on a simple nervous system organization.

Naturalistic stimulation changes the dynamic response of action potential encoding in a mechanoreceptor

Naturalistic signals were created from vibrations made by locusts walking on a Sansevieria plant. Both naturalistic and Gaussian noise signals were used to mechanically stimulate VS-3 slit-sense mechanoreceptor neurons of the spider, Cupiennius salei, with stimulus amplitudes adjusted to give similar firing rates for either stimulus. Intracellular microelectrodes recorded action potentials, receptor potential, and receptor current, using current clamp and voltage clamp. Frequency response analysis showed that naturalistic stimulation contained relatively more power at low frequencies, and caused increased neuronal sensitivity to higher frequencies. In contrast, varying the amplitude of Gaussian stimulation did not change neuronal dynamics. Naturalistic stimulation contained less entropy than Gaussian, but signal entropy was higher than stimulus in the resultant receptor current, indicating addition of uncorrelated noise during transduction. The presence of added noise was supported by measuring linear information capacity in the receptor current. Total entropy and information capacity in action potentials produced by either stimulus were much lower than in earlier stages, and limited to the maximum entropy of binary signals. We conclude that the dynamics of action potential encoding in VS-3 neurons are sensitive to the form of stimulation, but entropy and information capacity of action potentials are limited by firing rate.

Proprioceptive feedback modulates coordinating information in a system of segmentally distributed microcircuits

The system of modular neural circuits that controls crustacean swimmerets drives a metachronal sequence of power-stroke (PS, retraction) and return-stroke (RS, protraction) movements that propels the animal forward efficiently. These neural modules are synchronized by an intersegmental coordinating circuit that imposes characteristic phase differences between these modules. Using a semi-intact preparation that left one swimmeret attached to an otherwise isolated central nervous system (CNS) of the crayfish, Pacifastacus leniusculus, we investigated how the rhythmic activity of this system responded to imposed movements. We recorded extracellularly from the PS and RS nerves that innervated the attached limb and from coordinating axons that encode efference copies of the periodic bursts in PS and RS axons. Simultaneously, we recorded from homologous nerves in more anterior and posterior segments. Maintained retractions did not affect cycle period but promptly weakened PS bursts, strengthened RS bursts, and caused corresponding changes in the strength and timing of efference copies in the module's coordinating axons. Changes in these efference copies then caused changes in the phase and duration, but not the strength, of PS bursts in modules controlling neighboring swimmerets. These changes were promptly reversed when the limb was released. Each swimmeret is innervated by two nonspiking stretch receptors (NSSRs) that depolarize when the limb is retracted. Voltage clamp of an NSSR changed the durations and strengths of bursts in PS and RS axons innervating the same limb and caused corresponding changes in the efference copies of this motor output.

Mechanisms of coordination in distributed neural circuits: encoding coordinating information

We describe synaptic connections through which information essential for encoding efference copies reaches two coordinating neurons in each of the microcircuits that controls limbs on abdominal segments of the crayfish, Pacifastacus leniusculus. In each microcircuit, these coordinating neurons fire bursts of spikes simultaneously with motor neurons. These bursts encode timing, duration, and strength of each motor burst. Using paired microelectrode recordings, we demonstrate that one class of nonspiking neurons in each microcircuit's pattern-generating kernel--IPS--directly inhibits the ASCE coordinating neuron that copies each burst in power-stroke (PS) motor neurons. This inhibitory synapse parallels IPS's inhibition of the same PS motor neurons. Using a disynaptic pathway to control its membrane potential, we demonstrate that a second type of nonspiking interneuron in the pattern-generating kernel--IRSh--inhibits the DSC coordinating neuron that copies each burst in return-stroke (RS) motor neurons. This inhibitory synapse parallels IRS's inhibition of the microcircuit's RS motor neurons. Experimental changes in the membrane potential of one IPS or one IRSh neuron simultaneously changed the strengths of motor bursts, durations, numbers of spikes, and spike frequency in the simultaneous ASCE and DSC bursts. ASCE and DSC coordinating neurons link the segmentally distributed microcircuits into a coordinated system that oscillates with the same period and with stable phase differences. The inhibitory synapses from different pattern-generating neurons that parallel their inhibition of different sets of motor neurons enable ASCE and DSC to encode details of each oscillation that are necessary for stable, adaptive synchronization of the system.

Consequences of converting graded to action potentials upon neural information coding and energy efficiency

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na(+) and K(+) channels, with generator potential and graded potential models lacking voltage-gated Na(+) channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na(+) channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a 'footprint' in the generator potential that obscures incoming signals. These three processes reduce information rates by ∼50% in generator potentials, to ∼3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation.

Functional analysis of ultra high information rates conveyed by rat vibrissal primary afferents

Sensory receptors determine the type and the quantity of information available for perception. Here, we quantified and characterized the information transferred by primary afferents in the rat whisker system using neural system identification. Quantification of "how much" information is conveyed by primary afferents, using the direct method (DM), a classical information theoretic tool, revealed that primary afferents transfer huge amounts of information (up to 529 bits/s). Information theoretic analysis of instantaneous spike-triggered kinematic stimulus features was used to gain functional insight on "what" is coded by primary afferents. Amongst the kinematic variables tested--position, velocity, and acceleration--primary afferent spikes encoded velocity best. The other two variables contributed to information transfer, but only if combined with velocity. We further revealed three additional characteristics that play a role in information transfer by primary afferents. Firstly, primary afferent spikes show preference for well separated multiple stimuli (i.e., well separated sets of combinations of the three instantaneous kinematic variables). Secondly, neurons are sensitive to short strips of the stimulus trajectory (up to 10 ms pre-spike time), and thirdly, they show spike patterns (precise doublet and triplet spiking). In order to deal with these complexities, we used a flexible probabilistic neuron model fitting mixtures of Gaussians to the spike triggered stimulus distributions, which quantitatively captured the contribution of the mentioned features and allowed us to achieve a full functional analysis of the total information rate indicated by the DM. We found that instantaneous position, velocity, and acceleration explained about 50% of the total information rate. Adding a 10 ms pre-spike interval of stimulus trajectory achieved 80-90%. The final 10-20% were found to be due to non-linear coding by spike bursts.

Modifying spiking precision in conductance-based neuronal models

The temporal precision of a neuron's spiking can be characterized by calculating its "jitter," defined as the standard deviation of the timing of individual spikes in response to repeated presentations of a stimulus. Sub-millisecond jitters have been measured for neurons in a variety of experimental systems and appear to be functionally important in some instances. We have investigated how modifying a neuron's maximal conductances affects jitter using the leaky integrate-and-fire (LIF) model and an eight-conductance Hodgkin-Huxley type (HH8) model. We observed that jitter can be largely understood in the LIF model in terms of the neuron's filtering properties. In the HH8 model we found the role of individual conductances in determining jitter to be complicated and dependent on the model's spiking properties. Distinct behaviors were observed for populations with slow (<11.5 Hz) and fast (>11.5 Hz) spike rates and appear to be related to differences in a particular channel's activity at times just before spiking occurs.

The effect of neural noise on spike time precision in a detailed CA3 neuron model

Experimental and computational studies emphasize the role of the millisecond precision of neuronal spike times as an important coding mechanism for transmitting and representing information in the central nervous system. We investigate the spike time precision of a multicompartmental pyramidal neuron model of the CA3 region of the hippocampus under the influence of various sources of neuronal noise. We describe differences in the contribution to noise originating from voltage-gated ion channels, synaptic vesicle release, and vesicle quantal size. We analyze the effect of interspike intervals and the voltage course preceding the firing of spikes on the spike-timing jitter. The main finding of this study is the ranking of different noise sources according to their contribution to spike time precision. The most influential is synaptic vesicle release noise, causing the spike jitter to vary from 1 ms to 7 ms of a mean value 2.5 ms. Of second importance was the noise incurred by vesicle quantal size variation causing the spike time jitter to vary from 0.03 ms to 0.6 ms. Least influential was the voltage-gated channel noise generating spike jitter from 0.02 ms to 0.15 ms.

Information transmission in cercal giant interneurons is unaffected by axonal conduction noise

What are the fundamental constraints on the precision and accuracy with which nervous systems can process information? One constraint must reflect the intrinsic “noisiness” of the mechanisms that transmit information between nerve cells. Most neurons transmit information through the probabilistic generation and propagation of spikes along axons, and recent modeling studies suggest that noise from spike propagation might pose a significant constraint on the rate at which information could be transmitted between neurons. However, the magnitude and functional significance of this noise source in actual cells remains poorly understood. We measured variability in conduction time along the axons of identified neurons in the cercal sensory system of the cricket Acheta domesticus, and used information theory to calculate the effects of this variability on sensory coding. We found that the variability in spike propagation speed is not large enough to constrain the accuracy of neural encoding in this system.

Impact of neural noise on a sensory-motor pathway signaling impending collision

Noise is a major concern in circuits processing electrical signals, including neural circuits. There are many factors that influence how noise propagates through neural circuits, and there are few systems in which noise levels have been studied throughout a processing pathway. We recorded intracellularly from multiple stages of a sensory-motor pathway in the locust that detects approaching objects. We found that responses are more variable and that signal-to-noise ratios (SNRs) are lower further from the sensory periphery. SNRs remain low even with the use of stimuli for which the pathway is most selective and for which the neuron representing its final sensory level must integrate many synaptic inputs. Modeling of this neuron shows that variability in the strength of individual synaptic inputs within a large population has little effect on the variability of the spiking output. In contrast, jitter in the timing of individual inputs and spontaneous variability is important for shaping the responses to preferred stimuli. These results suggest that neural noise is inherent to the processing of visual stimuli signaling impending collision and contributes to shaping neural responses along this sensory-motor pathway.

Beyond faithful conduction: short-term dynamics, neuromodulation, and long-term regulation of spike propagation in the axon

Most spiking neurons are divided into functional compartments: a dendritic input region, a soma, a site of action potential initiation, an axon trunk and its collaterals for propagation of action potentials, and distal arborizations and terminals carrying the output synapses. The axon trunk and lower order branches are probably the most neglected and are often assumed to do nothing more than faithfully conducting action potentials. Nevertheless, there are numerous reports of complex membrane properties in non-synaptic axonal regions, owing to the presence of a multitude of different ion channels. Many different types of sodium and potassium channels have been described in axons, as well as calcium transients and hyperpolarization-activated inward currents. The complex time- and voltage-dependence resulting from the properties of ion channels can lead to activity-dependent changes in spike shape and resting potential, affecting the temporal fidelity of spike conduction. Neural coding can be altered by activity-dependent changes in conduction velocity, spike failures, and ectopic spike initiation. This is true under normal physiological conditions, and relevant for a number of neuropathies that lead to abnormal excitability. In addition, a growing number of studies show that the axon trunk can express receptors to glutamate, GABA, acetylcholine or biogenic amines, changing the relative contribution of some channels to axonal excitability and therefore rendering the contribution of this compartment to neural coding conditional on the presence of neuromodulators. Long-term regulatory processes, both during development and in the context of activity-dependent plasticity may also affect axonal properties to an underappreciated extent.

Coding efficiency of fly motion processing is set by firing rate, not firing precision

To comprehend the principles underlying sensory information processing, it is important to understand how the nervous system deals with various sources of perturbation. Here, we analyze how the representation of motion information in the fly's nervous system changes with temperature and luminance. Although these two environmental variables have a considerable impact on the fly's nervous system, they do not impede the fly to behave suitably over a wide range of conditions. We recorded responses from a motion-sensitive neuron, the H1-cell, to a time-varying stimulus at many different combinations of temperature and luminance. We found that the mean firing rate, but not firing precision, changes with temperature, while both were affected by mean luminance. Because we also found that information rate and coding efficiency are mainly set by the mean firing rate, our results suggest that, in the face of environmental perturbations, the coding efficiency is improved by an increase in the mean firing rate, rather than by an increased firing precision.