Information and discriminability as measures of reliability of sensory coding

Response variability is a fundamental issue in neural coding because it limits all information processing. The reliability of neuronal coding is quantified by various approaches in different studies. In most cases it is largely unclear to what extent the conclusions depend on the applied reliability measure, making a comparison across studies almost impossible. We demonstrate that different reliability measures can lead to very different conclusions even if applied to the same set of data: in particular, we applied information theoretical measures (Shannon information capacity and Kullback-Leibler divergence) as well as a discrimination measure derived from signal-detection theory to the responses of blowfly photoreceptors which represent a well established model system for sensory information processing. We stimulated the photoreceptors with white noise modulated light intensity fluctuations of different contrasts. Surprisingly, the signal-detection approach leads to a safe discrimination of the photoreceptor response even when the response signal-to-noise ratio (SNR) is well below unity whereas Shannon information capacity and also Kullback-Leibler divergence indicate a very low performance. Applying different measures, can, therefore, lead to very different interpretations concerning the system's coding performance. As a consequence of the lower sensitivity compared to the signal-detection approach, the information theoretical measures overestimate internal noise sources and underestimate the importance of photon shot noise. We stress that none of the used measures and, most likely no other measure alone, allows for an unbiased estimation of a neuron's coding properties. Therefore the applied measure needs to be selected with respect to the scientific question and the analyzed neuron's functional context.     

Synaptic limitations to contrast coding in the retina of the blowfly Calliphora

We investigate the effects of synaptic transmission on early visual processing by examining the passage of signals from photoreceptors to second order neurons (LMCS). We concentrate on the roles played by three properties of synaptic transmission: (1) the shape of the characteristic curve, relating pre- and postsynaptic signal amplitudes, (2) the dynamics of synaptic transmission and (3) the noise introduced during transmission. The characteristic curve is sigmoidal and follows a simple model of synaptic transmission (Appendix) in which transmitter release rises exponentially with presynaptic potential. According to this model a presynaptic depolarization of 1.50-1.86 mV produces an e-fold increase in postsynaptic conductance. The characteristic curve generates a sigmoidal relation between postsynaptic (LMC) response amplitude and stimulus contrast. The shape and slope of the characteristic curve is unaffected by the state of light adaptation. Retinal antagonism adjusts the characteristic curve to keep it centred on the mean level of receptor response generated by the background. Thus the photoreceptor synapses operate in the mid-region of the curve, where the slope or gain is highest and equals approximately 6. The dynamics of transmission of a signal from photoreceptor to second-order neuron approximates to the sum of two processes with exponential time courses. A momentary receptor depolarization generates a postsynaptic hyperpolarization of time constant 0.5-1.0 ms, followed by a slower and weaker depolarization. Light adaptation increases the relative amplitude of the depolarizing process and reduces its time constant from 80 ms to 1.5 ms. The hyperpolarizing process is too rapid to bandlimit receptor signals. The noise introduced during the passage of the signal from receptor to second-order neuron is measured by comparing signal:noise ratios and noise power spectra in the two cell types. Under daylight conditions from 50 to 70% of the total noise power is generated by events associated with the transmission of photoreceptor signals and the generation of LMC responses. According to the exponential model of transmitter release, the effects of synaptic noise are minimized when synaptic gain is maximized. Moreover, both retinal antagonism and the sigmoidal shape of the characteristic curve promote synaptic gain. We conclude that retinal antagonism and nonlinear synaptic amplification act in concert to protect receptor signals from contamination by synaptic noise. This action may explain the widespread occurrence of these processes in early visual processing.     

Contrast gain, signal-to-noise ratio, and linearity in light-adapted blowfly photoreceptors

Response properties of short-type (R1-6) photoreceptors of the blowfly (Calliphora vicina) were investigated with intracellular recordings using repeated sequences of pseudorandomly modulated light contrast stimuli at adapting backgrounds covering 5 log intensity units. The resulting voltage responses were used to determine the effects of adaptational regulation on signal-to-noise ratios (SNR), signal induced noise, contrast gain, linearity and the dead time in phototransduction. In light adaptation the SNR of the photoreceptors improved more than 100-fold due to (a) increased photoreceptor voltage responses to a contrast stimulus and (b) reduction of voltage noise at high intensity backgrounds. In the frequency domain the SNR was attenuated in low frequencies with an increase in the middle and high frequency ranges. A pseudorandom contrast stimulus by itself did not produce any additional noise. The contrast gain of the photoreceptor frequency responses increased with mean illumination and the gain was best fitted with a model consisting of two second order and one double pole of first order. The coherence function (a normalized measure of linearity and SNR) of the frequency responses demonstrated that the photoreceptors responded linearly (from 1 to 150 Hz) to the contrast stimuli even under fairly dim conditions. The theoretically derived and the recorded phase functions were used to calculate phototransduction dead time, which decreased in light adaptation from approximately 5-2.5 ms. This analysis suggests that the ability of fly photoreceptors to maintain linear performance under dynamic stimulation conditions results from the high early gain followed by delayed compressive feed-back mechanisms.     

Na+/ K+-pump activity in photoreceptors of the blowfly Calliphora : a model analysis based on membrane potential measurements

Na⁺/K⁺-pump activity and intracellular Na⁺ and K⁺ concentration changes in blowfly photoreceptors are derived from intracellular potential measurements in␣vivo with a model based on the Goldman-Hodgkin-Katz theory for membrane currents. The relation between the intracellular Na⁺ concentration and the pump activity appears to follow a Hill function with a Hill coefficient of 1 and a maximal possible Na⁺ current due to pump activity of about −4 nA. The developed photoreceptor model incorporates the slow and fast voltage-dependent K⁺ channels of the blowfly photoreceptor of which the properties were taken from the literature. Accepted: 5 August 1996     

Light adaptation in Drosophila photoreceptors: II. Rising temperature increases the bandwidth of reliable signaling

It is known that an increase in both the mean light intensity and temperature can speed up photoreceptor signals, but it is not known whether a simultaneous increase of these physical factors enhances information capacity or leads to coding errors. We studied the voltage responses of light-adapted Drosophila photoreceptors in vivo from 15 to 30 degrees C, and found that an increase in temperature accelerated both the phototransduction cascade and photoreceptor membrane dynamics, broadening the bandwidth of reliable signaling with an effective Q(10) for information capacity of 6.5. The increased fidelity and reliability of the voltage responses was a result of four factors: (1) an increased rate of elementary response, i.e., quantum bump production; (2) a temperature-dependent acceleration of the early phototransduction reactions causing a quicker and narrower dispersion of bump latencies; (3) a relatively temperature-insensitive light-adapted bump waveform; and (4) a decrease in the time constant of the light-adapted photoreceptor membrane, whose filtering matched the dynamic properties of the phototransduction noise. Because faster neural processing allows faster behavioral responses, this improved performance of Drosophila photoreceptors suggests that a suitably high body temperature offers significant advantages in visual performance.     

Light adaptation in Drosophila photoreceptors: I. Response dynamics and signaling efficiency at 25 degrees C

Besides the physical limits imposed on photon absorption, the coprocessing of visual information by the phototransduction cascade and photoreceptor membrane determines the fidelity of photoreceptor signaling. We investigated the response dynamics and signaling efficiency of Drosophila photoreceptors to natural-like fluctuating light contrast stimulation and intracellular current injection when the cells were adapted over a 4-log unit light intensity range at 25 degrees C. This dual stimulation allowed us to characterize how an increase in the mean light intensity causes the phototransduction cascade and photoreceptor membrane to produce larger, faster and increasingly accurate voltage responses to a given contrast. Using signal and noise analysis, this appears to be associated with an increased summation of smaller and faster elementary responses (i.e., bumps), whose latency distribution stays relatively unchanged at different mean light intensity levels. As the phototransduction cascade increases, the size and speed of the signals (light current) at higher adapting backgrounds and, in conjunction with the photoreceptor membrane, reduces the light-induced voltage noise, and the photoreceptor signal-to-noise ratio improves and extends to a higher bandwidth. Because the voltage responses to light contrasts are much slower than those evoked by current injection, the photoreceptor membrane does not limit the speed of the phototransduction cascade, but it does filter the associated high frequency noise. The photoreceptor information capacity increases with light adaptation and starts to saturate at approximately 200 bits/s as the speed of the chemical reactions inside a fixed number of transduction units, possibly microvilli, is approaching its maximum.     

Navigating sensory conflict in dynamic environments using adaptive state estimation

Most conventional robots rely on controlling the location of the center of pressure to maintain balance, relying mainly on foot pressure sensors for information. By contrast, humans rely on sensory data from multiple sources, including proprioceptive, visual, and vestibular sources. Several models have been developed to explain how humans reconcile information from disparate sources to form a stable sense of balance. These models may be useful for developing robots that are able to maintain dynamic balance more readily using multiple sensory sources. Since these information sources may conflict, reliance by the nervous system on any one channel can lead to ambiguity in the system state. In humans, experiments that create conflicts between different sensory channels by moving the visual field or the support surface indicate that sensory information is adaptively reweighted. Unreliable information is rapidly down-weighted, then gradually up-weighted when it becomes valid again. Human balance can also be studied by building robots that model features of human bodies and testing them under similar experimental conditions. We implement a sensory reweighting model based on an adaptive Kalman filter in a bipedal robot, and subject it to sensory tests similar to those used on human subjects. Unlike other implementations of sensory reweighting in robots, our implementation includes vision, by using optic flow to calculate forward rotation using a camera (visual modality), as well as a three-axis gyro to represent the vestibular system (non-visual modality), and foot pressure sensors (proprioceptive modality). Our model estimates measurement noise in real time, which is then used to recompute the Kalman gain on each iteration, improving the ability of the robot to dynamically balance. We observe that we can duplicate many important features of postural sway in humans, including automatic sensory reweighting, effects, constant phase with respect to amplitude, and a temporal asymmetry in the reweighting gains.     

Phototransduction in primate cones and blowfly photoreceptors: different mechanisms, different algorithms, similar response

Phototransduction in primate cones is compared with phototransduction in blowfly photoreceptor cells. Phototransduction in the two cell types utilizes not only different molecular mechanisms, but also different signal processing steps, producing range compression, contrast constancy, and an intensity-dependent integration time. The dominant processing step in the primate cone is a strongly compressive nonlinearity due to cGMP hydrolysis by phosphodiesterase. In the blowfly photoreceptor a considerable part of the range compression is performed by the nonlinear membrane of the cell. Despite these differences, both photoreceptor cell types are similarly effective in compressing the wide range of naturally occurring intensities, and in converting intensity variations into contrast variations. A direct comparison of the responses to a natural time series of intensities, simulated in the cone and measured in the blowfly photoreceptor, shows that the responses are quite similar.     

Saccadic flight strategy facilitates collision avoidance: closed-loop performance of a cyberfly

Behavioural and electrophysiological experiments suggest that blowflies employ an active saccadic strategy of flight and gaze control to separate the rotational from the translational optic flow components. As a consequence, this allows motion sensitive neurons to encode during translatory intersaccadic phases of locomotion information about the spatial layout of the environment. So far, it has not been clear whether and how a motor controller could decode the responses of these neurons to prevent a blowfly from colliding with obstacles. Here we propose a simple model of the blowfly visual course control system, named cyberfly, and investigate its performance and limitations. The sensory input module of the cyberfly emulates a pair of output neurons subserving the two eyes of the blowfly visual motion pathway. We analyse two sensory–motor interfaces (SMI). An SMI coupling the differential signal of the sensory neurons proportionally to the yaw rotation fails to avoid obstacles. A more plausible SMI is based on a saccadic controller. Even with sideward drift after saccades as is characteristic of real blowflies, the cyberfly is able to successfully avoid collisions with obstacles. The relative distance information contained in the optic flow during translatory movements between saccades is provided to the SMI by the responses of the visual output neurons. An obvious limitation of this simple mechanism is its strong dependence on the textural properties of the environment.     

Shaker K(+)-channels are predicted to reduce the metabolic cost of neural information in Drosophila photoreceptors

Shaker K(+)-channels are one of several voltage-activated K(+)-channels expressed in Drosophila photoreceptors. We have shown recently that Shaker channels act as selective amplifiers, attenuating some signals while boosting others. Loss of these channels reduces the photoreceptor information capacity (bits s(-1)) and induces compensatory changes in photoreceptors enabling them to minimize the impact of this loss upon coding natural-like stimuli. Energy as well as coding is also an important consideration in understanding the role of ion channels in neural processing. Here, we use a simple circuit model that incorporates the major ion channels, pumps and exchangers of the photoreceptors to derive experimentally based estimates of the metabolic cost of neural information in wild-type (WT) and Shaker mutant photoreceptors. We show that in WT photoreceptors, which contain Shaker K(+)-channels, each bit of information costs approximately half the number of ATP molecules than each bit in Shaker photoreceptors, in which lack of the Shaker K(+)-channels is compensated by increased leak conductance. Additionally, using a Hodgkin-Huxley-type model coupled to the circuit model we show that the amount of leak present in both WT and Shaker photoreceptors is optimized to both maximize the available voltage range and minimize the metabolic cost.     

Effects of channel blocking on information transmission and energy efficiency in squid giant axons

Action potentials are the information carriers of neural systems. The generation of action potentials involves the cooperative opening and closing of sodium and potassium channels. This process is metabolically expensive because the ions flowing through open channels need to be restored to maintain concentration gradients of these ions. Toxins like tetraethylammonium can block working ion channels, thus affecting the function and energy cost of neurons. In this paper, by computer simulation of the Hodgkin-Huxley neuron model, we studied the effects of channel blocking with toxins on the information transmission and energy efficiency in squid giant axons. We found that gradually blocking sodium channels will sequentially maximize the information transmission and energy efficiency of the axons, whereas moderate blocking of potassium channels will have little impact on the information transmission and will decrease the energy efficiency. Heavy blocking of potassium channels will cause self-sustained oscillation of membrane potentials. Simultaneously blocking sodium and potassium channels with the same ratio increases both information transmission and energy efficiency. Our results are in line with previous studies suggesting that information processing capacity and energy efficiency can be maximized by regulating the number of active ion channels, and this indicates a viable avenue for future experimentation.     

A theoretical account of cue averaging in the rodent head direction system

Head direction (HD) cell responses are thought to be derived from a combination of internal (or idiothetic) and external (or allothetic) sources of information. Recent work from the Jeffery laboratory shows that the relative influence of visual versus vestibular inputs upon the HD cell response depends on the disparity between these sources. In this paper, we present simulation results from a model designed to explain these observations. The model accurately replicates the Knight et al. data. We suggest that cue conflict resolution is critically dependent on plastic remapping of visual information onto the HD cell layer. This remap results in a shift in preferred directions of a subset of HD cells, which is then inherited by the rest of the cells during path integration. Thus, we demonstrate how, over a period of several minutes, a visual landmark may gain cue control. Furthermore, simulation results show that weaker visual landmarks fail to gain cue control as readily. We therefore suggest a second longer term plasticity in visual projections onto HD cell areas, through which landmarks with an inconsistent relationship to idiothetic information are made less salient, significantly hindering their ability to gain cue control. Our results provide a mechanism for reliability-weighted cue averaging that may pertain to other neural systems in addition to the HD system.     

Equilibrating errors: reliable estimation of information transmission rates in biological systems with spectral analysis-based methods

Shannon’s seminal approach to estimating information capacity is widely used to quantify information processing by biological systems. However, the Shannon information theory, which is based on power spectrum estimation, necessarily contains two sources of error: time delay bias error and random error. These errors are particularly important for systems with relatively large time delay values and for responses of limited duration, as is often the case in experimental work. The window function type and size chosen, as well as the values of inherent delays cause changes in both the delay bias and random errors, with possibly strong effect on the estimates of system properties. Here, we investigated the properties of these errors using white-noise simulations and analysis of experimental photoreceptor responses to naturalistic and white-noise light contrasts. Photoreceptors were used from several insect species, each characterized by different visual performance, behavior, and ecology. We show that the effect of random error on the spectral estimates of photoreceptor performance (gain, coherence, signal-to-noise ratio, Shannon information rate) is opposite to that of the time delay bias error: the former overestimates information rate, while the latter underestimates it. We propose a new algorithm for reducing the impact of time delay bias error and random error, based on discovering, and then using that size of window, at which the absolute values of these errors are equal and opposite, thus cancelling each other, allowing minimally biased measurement of neural coding.     

Erbliche Ionenkanalerkrankungen der Netzhaut

Retinal channelopathies are clinically and genetically heterogeneous, and are caused by mutations in genes for a variety of ion channels such as cyclic nucleotide-gated channels, voltage-gated potassium and calcium channels, an inwardly rectifying potassium channel, a calcium-dependent chloride channel and the TRPM1 channel. This broad spectrum of disease-associated ion channels is also reflected in the diversity of pathophysiological consequences. Mutations in retinal ion channels may affect phototransduction, thereby impairing the detection of light or interfere with the transmission of the stimulus from the photoreceptor to second-order neurons. Ion channels located in the retinal pigment epithelium, which supports normal retina function, can also be affected in some diseases.     

Axonal Noise as a Source of Synaptic Variability

Post-synaptic potential (PSP) variability is typically attributed to mechanisms inside synapses, yet recent advances in experimental methods and biophysical understanding have led us to reconsider the role of axons as highly reliable transmission channels. We show that in many thin axons of our brain, the action potential (AP) waveform and thus the Ca⁺⁺ signal controlling vesicle release at synapses will be significantly affected by the inherent variability of ion channel gating. We investigate how and to what extent fluctuations in the AP waveform explain observed PSP variability. Using both biophysical theory and stochastic simulations of central and peripheral nervous system axons from vertebrates and invertebrates, we show that channel noise in thin axons (<1 µm diameter) causes random fluctuations in AP waveforms. AP height and width, both experimentally characterised parameters of post-synaptic response amplitude, vary e.g. by up to 20 mV and 0.5 ms while a single AP propagates in C-fibre axons. We show how AP height and width variabilities increase with a ¾ power-law as diameter decreases and translate these fluctuations into post-synaptic response variability using biophysical data and models of synaptic transmission. We find for example that for mammalian unmyelinated axons with 0.2 µm diameter (matching cerebellar parallel fibres) axonal noise alone can explain half of the PSP variability in cerebellar synapses. We conclude that axonal variability may have considerable impact on synaptic response variability. Thus, in many experimental frameworks investigating synaptic transmission through paired-cell recordings or extracellular stimulation of presynaptic neurons, causes of variability may have been confounded. We thereby show how bottom-up aggregation of molecular noise sources contributes to our understanding of variability observed at higher levels of biological organisation.     

Visual information processing using bacteriorhodopsin-based complex LB films

Image extraction and visual information processing using bacteriorhodopsin (bR)-based bioelectronic devices is presented. Image extraction was achieved using a photoreceptor consisting of bR and spiropyran films. The undesired signals from the photoreceptor were automatically eliminated from the whole signal by spiropyran films acting as an optical noise filter that increases the target signal to an undesired signal ratio. For the information processing, the photoreceptor consisting of bR and lipid films deposited with different configurations was used and the target signals were processed to achieve the pattern recognition. The pattern recognition was based on not only the response variability of bacteriorhodopsin, induced by different film configurations, but also on the initial learning process. The input patterns were predicted by simple calculation with the known signals through the initial learning process.     

Spatial information capacity of eyes: Roles of Na+ channels and photon noise in photoreceptor

The spatial information capacity of the human eye for photopic vision has been determined taking into account the intensity response function of the photoreceptor. It has been found that spatial information capacity increases with the mean luminance upto a certain value of mean luminance and after that it starts decreasing. The decrement occurs below the damage threshold. These results are in agreement with the reported experimental observations. It has been concluded that the limited number of Na⁺ channels in the photoreceptor outer segment and the photon noise are responsible for the fall in the information capacity below the damage threshold.Associated with the Biochemistry Cell     

Information processing in the adaptation of Saccharomyces cerevisiae to osmotic stress: an analysis of the phosphorelay system

Cellular signaling is key for organisms to survive immediate stresses from fluctuating environments as well as relaying important information about external stimuli. Effective mechanisms have evolved to ensure appropriate responses for an optimal adaptation process. For them to be functional despite the noise that occurs in biochemical transmission, the cell needs to be able to infer reliably what was sensed in the first place. For example Saccharomyces cerevisiae are able to adjust their response to osmotic shock depending on the severity of the shock and initiate responses that lead to near perfect adaptation of the cell. We investigate the Sln1–Ypd1–Ssk1-phosphorelay as a module in the high-osmolarity glycerol pathway by incorporating a stochastic model. Within this framework, we can imitate the noisy perception of the cell and interpret the phosphorelay as an information transmitting channel in the sense of C.E. Shannon’s “Information Theory”. We refer to the channel capacity as a measure to quantify and investigate the transmission properties of this system, enabling us to draw conclusions on viable parameter sets for modeling the system.     

A model for photoreceptor-based magnetoreception in birds

A large variety of animals has the ability to sense the geomagnetic field and utilize it as a source of directional (compass) information. It is not known by which biophysical mechanism this magnetoreception is achieved. We investigate the possibility that magnetoreception involves radical-pair processes that are governed by anisotropic hyperfine coupling between (unpaired) electron and nuclear spins. We will show theoretically that fields of geomagnetic field strength and weaker can produce significantly different reaction yields for different alignments of the radical pairs with the magnetic field. As a model for a magnetic sensory organ we propose a system of radical pairs being 1) orientationally ordered in a molecular substrate and 2) exhibiting changes in the reaction yields that affect the visual transduction pathway. We evaluate three-dimensional visual modulation patterns that can arise from the influence of the geomagnetic field on radical-pair systems. The variations of these patterns with orientation and field strength can furnish the magnetic compass ability of birds with the same characteristics as observed in behavioral experiments. We propose that the recently discovered photoreceptor cryptochrome is part of the magnetoreception system and suggest further studies to prove or disprove this hypothesis.