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

Ladder-based resistance training with the progression of training load altered the tibial nerve ultrastructure and muscle fiber area without altering the morphology of the postsynaptic compartment

Scientific evidence regarding the effect of different ladder-based resistance training (LRT) protocols on the morphology of the neuromuscular system is scarce. Therefore, the present study aimed to compare the morphological response induced by different LRT protocols in the ultrastructure of the tibial nerve and morphology of the motor endplate and muscle fibers of the soleus and plantaris muscles of young adult Wistar rats. Rats were divided into groups: sedentary control (control, n = 9), a predetermined number of climbs and progressive submaximal intensity (fixed, n = 9), high-intensity and high-volume pyramidal system with a predetermined number of climbs (Pyramid, n = 9) and lrt with a high-intensity pyramidal system to exhaustion (failure, n = 9). myelinated fibers and myelin sheath thickness were statistically larger in pyramid, fixed, and failure. myelinated axons were statistically larger in pyramid than in control. schwann cell nuclei were statistically larger in pyramid, fixed, and failure. microtubules and neurofilaments were greater in pyramid than in control. morphological analysis of the postsynaptic component of the plantar and soleus muscles did not indicate any significant difference. for plantaris, the type i myofibers were statistically larger in the pyramid and fixed compared to control. the pyramid, fixed, and failure groups for type ii myofibers had larger csa than control. for soleus, the type i myofibers were statistically larger in the pyramid than in control. pyramid and fixed had larger csa for type ii myofibers than control and failure. the pyramid and fixed groups showed greater mass progression delta than the failure. We concluded that the LRT protocols with greater volume and progression of accumulated mass elicit more significant changes in the ultrastructure of the tibial nerve and muscle hypertrophy without endplate changes.

A functional account of stimulation-based aerobic glycolysis and its role in interpreting BOLD signal intensity increases in neuroimaging experiments

In aerobic glycolysis, oxygen is abundant, and yet cells metabolize glucose without using it, decreasing their ATP per glucose yield by 15-fold. During task-based stimulation, aerobic glycolysis occurs in localized brain regions, presenting a puzzle: why produce ATP inefficiently when, all else being equal, evolution should favor the efficient use of metabolic resources? The answer is that all else is not equal. We propose that a tradeoff exists between efficient ATP production and the efficiency with which ATP is spent to transmit information. Aerobic glycolysis, despite yielding little ATP per glucose, may support neuronal signaling in thin (< 0.5 µm), information-efficient axons. We call this the efficiency tradeoff hypothesis. This tradeoff has potential implications for interpretations of task-related BOLD "activation" observed in fMRI. We hypothesize that BOLD "activation" may index local increases in aerobic glycolysis, which support signaling in thin axons carrying "bottom-up" information, or "prediction error"-i.e., the BIAPEM (BOLD increases approximate prediction error metabolism) hypothesis. Finally, we explore implications of our hypotheses for human brain evolution, social behavior, and mental disorders.

The computational power of the human brain

At the end of the 20th century, analog systems in computer science have been widely replaced by digital systems due to their higher computing power. Nevertheless, the question keeps being intriguing until now: is the brain analog or digital? Initially, the latter has been favored, considering it as a Turing machine that works like a digital computer. However, more recently, digital and analog processes have been combined to implant human behavior in robots, endowing them with artificial intelligence (AI). Therefore, we think it is timely to compare mathematical models with the biology of computation in the brain. To this end, digital and analog processes clearly identified in cellular and molecular interactions in the Central Nervous System are highlighted. But above that, we try to pinpoint reasons distinguishing in silico computation from salient features of biological computation. First, genuinely analog information processing has been observed in electrical synapses and through gap junctions, the latter both in neurons and astrocytes. Apparently opposed to that, neuronal action potentials (APs) or spikes represent clearly digital events, like the yes/no or 1/0 of a Turing machine. However, spikes are rarely uniform, but can vary in amplitude and widths, which has significant, differential effects on transmitter release at the presynaptic terminal, where notwithstanding the quantal (vesicular) release itself is digital. Conversely, at the dendritic site of the postsynaptic neuron, there are numerous analog events of computation. Moreover, synaptic transmission of information is not only neuronal, but heavily influenced by astrocytes tightly ensheathing the majority of synapses in brain (tripartite synapse). At least at this point, LTP and LTD modifying synaptic plasticity and believed to induce short and long-term memory processes including consolidation (equivalent to RAM and ROM in electronic devices) have to be discussed. The present knowledge of how the brain stores and retrieves memories includes a variety of options (e.g., neuronal network oscillations, engram cells, astrocytic syncytium). Also epigenetic features play crucial roles in memory formation and its consolidation, which necessarily guides to molecular events like gene transcription and translation. In conclusion, brain computation is not only digital or analog, or a combination of both, but encompasses features in parallel, and of higher orders of complexity.

Revisiting neural information, computing and linking capacity

Neural information theory represents a fundamental method to model dynamic relations in biological systems. However, the notion of information, its representation, its content and how it is processed are the subject of fierce debates. Since the limiting capacity of neuronal links strongly depends on how neurons are hypothesized to work, their operating modes are revisited by analyzing the differences between the results of the communication models published during the past seven decades and those of the recently developed generalization of the classical information theory. It is pointed out that the operating mode of neurons is in resemblance with an appropriate combination of the formerly hypothesized analog and digital working modes; furthermore that not only the notion of neural information and its processing must be reinterpreted. Given that the transmission channel is passive in Shannon's model, the active role of the transfer channels (the axons) may introduce further transmission limits in addition to the limits concluded from the information theory. The time-aware operating model enables us to explain why (depending on the researcher's point of view) the operation can be considered either purely analog or purely digital.

Targeting the Pancreatic α-Cell to Prevent Hypoglycemia in Type 1 Diabetes

Life-threatening hypoglycemia is a limiting factor in the management of type 1 diabetes. People with diabetes are prone to develop hypoglycemia because they lose physiological mechanisms that prevent plasma glucose levels from falling. Among these so-called counterregulatory responses, secretion of glucagon from pancreatic α-cells is preeminent. Glucagon, a hormone secreted in response to a lowering in glucose concentration, counteracts a further drop in glycemia by promoting gluconeogenesis and glycogenolysis in target tissues. In diabetes, however, α-cells do not respond appropriately to changes in glycemia and, thus, cannot mount a counterregulatory response. If the α-cell could be targeted therapeutically to restore its ability to prevent hypoglycemia, type 1 diabetes could be managed more efficiently and safely. Unfortunately, the mechanisms that allow the α-cell to respond to hypoglycemia have not been fully elucidated. We know even less about the pathophysiological mechanisms that cause α-cell dysfunction in diabetes. Based on published findings and unpublished observations, and taking into account its electrophysiological properties, we propose here a model of α-cell function that could explain its impairment in diabetes. Within this frame, we emphasize those elements that could be targeted pharmacologically with repurposed U.S. Food and Drug Administration-approved drugs to rescue α-cell function and restore glucose counterregulation in people with diabetes.

Ladder-based resistance training elicited similar ultrastructural adjustments in forelimb and hindlimb peripheral nerves of young adult Wistar rats

To analyze the morphological response induced by high-volume, high-intensity ladder-based resistance training (LRT) on the ultrastructure of the radial (forelimb) and sciatic (hindlimb) nerves of adults Wistar rats. Twenty rats were equally distributed into groups: sedentary (SED) and LRT. After the rodents were subjected to the maximum load (ML) carrying test, the LRT group performed 6-8 progressive climbs (2 × 50% ML, 2 × 75% ML, 2 × 100% ML, and 2 × 100% ML + 30 g) three times per week. After 8 weeks, the radial and sciatic nerves were removed and prepared for transmission electron microscopy. In the radial nerve, myelinated axons cross-sectional area (CSA), unmyelinated axons CSA, myelin sheath thickness, and Schwann cells nuclei area were statistically larger in the LRT group than SED (p < 0.05). Also, the number of microtubules and neurofilaments per field were statistically higher in the LRT group than in SED (p < 0.01). For sciatic nerve, myelinated fibers CSA, unmyelinated axons CSA, myelin sheath thickness, Schwann cells nuclei area, and the number of neurofilaments per field were statistically larger in the LRT group compared to the SED group (p < 0.05). LRT with high-volume and high-intensity effectively induce similar changes in adult Wistar rats' radial and sciatic nerves' ultrastructure.

The Relationship between Sparseness and Energy Consumption of Neural Networks

About 50-80% of total energy is consumed by signaling in neural networks. A neural network consumes much energy if there are many active neurons in the network. If there are few active neurons in a neural network, the network consumes very little energy. The ratio of active neurons to all neurons of a neural network, that is, the sparseness, affects the energy consumption of a neural network. Laughlin's studies show that the sparseness of an energy-efficient code depends on the balance between signaling and fixed costs. Laughlin did not give an exact ratio of signaling to fixed costs, nor did they give the ratio of active neurons to all neurons in most energy-efficient neural networks. In this paper, we calculated the ratio of signaling costs to fixed costs by the data from physiology experiments. The ratio of signaling costs to fixed costs is between 1.3 and 2.1. We calculated the ratio of active neurons to all neurons in most energy-efficient neural networks. The ratio of active neurons to all neurons in neural networks is between 0.3 and 0.4. Our results are consistent with the data from many relevant physiological experiments, indicating that the model used in this paper may meet neural coding under real conditions. The calculation results of this paper may be helpful to the study of neural coding.

High-Frequency Synchronization Improves Firing Rate Contrast and Information Transmission Efficiency in E/I Neuronal Networks

High-frequency synchronization has been found in many real neural systems and is confirmed by excitatory/inhibitory (E/I) network models. However, the functional role played by it remains elusive. In this paper, it is found that high-frequency synchronization in E/I neuronal networks could improve the firing rate contrast of the whole network, no matter if the network is fully connected or randomly connected, with noise or without noise. It is also found that the global firing rate contrast enhancement can prevent the number of spikes of the neurons measured within the limited time window from being confused by noise, thereby enhancing the information encoding efficiency (quantified by entropy theory here) of the neuronal system. The mechanism of firing rate contrast enhancement is also investigated. Our work implies a possible functional role in information transmission of high-frequency synchronization in neuronal systems.

Upper Limit on the Thermodynamic Information Content of an Action Potential

In computational neuroscience, spiking neurons are often analyzed as computing devices that register bits of information, with each action potential carrying at most one bit of Shannon entropy. Here, I question this interpretation by using Landauer's principle to estimate an upper limit for the quantity of thermodynamic information that can be processed within a single action potential in a typical mammalian neuron. A straightforward calculation shows that an action potential in a typical mammalian cortical pyramidal cell can process up to approximately 3.4 · 1011 bits of thermodynamic information, or about 4.9 · 1011 bits of Shannon entropy. This result suggests that an action potential can, in principle, carry much more than a single bit of Shannon entropy.

A biohybrid fly-robot interface system that performs active collision avoidance

We have designed a bio-hybrid fly-robot interface (FRI) to study sensorimotor control in insects. The FRI consists of a miniaturized recording platform mounted on a two-wheeled robot and is controlled by the neuronal spiking activity of an identified visual interneuron, the blowfly H1-cell. For a given turning radius of the robot, we found a proportional relationship between the spike rate of the H1-cell and the relative distance of the FRI from the patterned wall of an experimental arena. Under closed-loop conditions during oscillatory forward movements biased towards the wall, collision avoidance manoeuvres were triggered whenever the H1-cell spike rate exceeded a certain threshold value. We also investigated the FRI behaviour in corners of the arena. The ultimate goal is to enable autonomous and energy-efficient manoeuvrings of the FRI within arbitrary visual environments.

Contrast sensitivity and behavioural evidence for lateral inhibition in octopus

Behavioural contrast sensitivity in Octopus tetricus was measured in the range of 0.05-12 cycles per degree (cpd) using a fixation reflex. We show that the contrast sensitivity reaches its maximum (between 1 and 4%) at 0.3 cpd, and decreases to approximately half of the maximum value at the lowest spatial frequency. Reduction of sensitivity at low spatial frequency is a signature of lateral inhibition in visual systems. In vertebrates and insects, lateral inhibition helps to overcome the bottleneck of encoding information into spikes. In octopus, photoreceptors generate spikes themselves and are directly connected to the brain through their axons. Therefore, the neural processing occurring in the octopus brain cannot help overcome the bottleneck of encoding information into spikes. We conclude that, in octopus, either the lateral inhibition occurs in the brain after information has been encoded into spikes, or photoreceptors inhibit each other. This is the first time behavioural contrast sensitivity has been measured in a cephalopod.

Cost of auditory sharpness: Model-Based estimate of energy use by auditory brainstem "octopus" neurons

Octopus cells (OCs) of the mammalian auditory brainstem precisely encode timing of fast transient sounds and tone onsets. Sharp temporal fidelity of OCs relies on low resting membrane resistance, which suggests high energy expenditure on maintaining ion gradients across plasma membrane. We provide a model-based estimate of energy consumption in resting and spiking OCs. Our results predict that a resting OC consumes up to 2.6 × 10⁹ ATP molecules (ATPs) per second which remarkably exceeds energy consumption of other CNS neurons. Glucose usage by all OCs in the rat is nevertheless low due to their low number. Major part of the OCs energy use results from the ion mechanisms providing for the low membrane resistance: hyperpolarization-activated mixed cation conductance and low-voltage activated K⁺-conductance. Spatially ordered synapses-a feature of the OCs allowing them to compensate for asynchrony of the synaptic input-brings only a 12% energy saving to OCs excitability cost. Only 13% of total OC energy used for an AP generation (1.5 × 10⁷ ATPs) is associated with the AP generation in the axon initial segment, 64%-with synaptic currents processing and 23%-with keeping resting potential.

Unsupervised identification of states from voltage recordings of neural networks

BACKGROUND

Modern techniques for multi-neuronal recording produce large amounts of data. There is no automatic procedure for the identification of states in recurrent voltage patterns.

NEW METHOD

We propose NetSAP (Network States And Pathways), a data-driven analysis method that is able to recognize multi-neuron voltage patterns (states). To capture the subtle differences between snapshots in voltage recordings, NetSAP infers the underlying functional neural network in a time-resolved manner with a sliding window approach. Then NetSAP identifies states from a reordering of the time series of inferred networks according to a user-defined metric. The procedure for unsupervised identification of states was developed originally for the analysis of molecular dynamics simulations of proteins.

RESULTS

We tested NetSAP on neural network simulations of GABAergic inhibitory interneurons. Most simulation parameters are chosen to reproduce literature observations, and we keep noise terms as control parameters to regulate the coherence of the simulated signals. NetSAP is able to identify multiple states even in the case of high internal noise and low signal coherence. We provide evidence that NetSAP is robust for networks with up to about 50% of the neurons spiking randomly. NetSAP is scalable and its code is open source.

COMPARISON WITH EXISTING METHODS

NetSAP outperforms common analysis techniques, such as PCA and k-means clustering, on a simulated recording of voltage traces of 50 neurons.

CONCLUSIONS

NetSAP analysis is an efficient tool to identify voltage patterns from neuronal recordings.

Modulation of voltage-dependent K+ conductances in photoreceptors trades off investment in contrast gain for bandwidth

Modulation is essential for adjusting neurons to prevailing conditions and differing demands. Yet understanding how modulators adjust neuronal properties to alter information processing remains unclear, as is the impact of neuromodulation on energy consumption. Here we combine two computational models, one Hodgkin-Huxley type and the other analytic, to investigate the effects of neuromodulation upon Drosophila melanogaster photoreceptors. Voltage-dependent K⁺ conductances in these photoreceptors: (i) activate upon depolarisation to reduce membrane resistance and adjust bandwidth to functional requirements; (ii) produce negative feedback to increase bandwidth in an energy efficient way; (iii) produce shunt-peaking thereby increasing the membrane gain bandwidth product; and (iv) inactivate to amplify low frequencies. Through their effects on the voltage-dependent K⁺ conductances, three modulators, serotonin, calmodulin and PIP2, trade-off contrast gain against membrane bandwidth. Serotonin shifts the photoreceptor performance towards higher contrast gains and lower membrane bandwidths, whereas PIP2 and calmodulin shift performance towards lower contrast gains and higher membrane bandwidths. These neuromodulators have little effect upon the overall energy consumed by photoreceptors, instead they redistribute the energy invested in gain versus bandwidth. This demonstrates how modulators can shift neuronal information processing within the limitations of biophysics and energy consumption.

The properties of neurons and neural circuits can be adjusted by neuromodulators, molecules that alter their ability to respond to future activity. Many neuromodulators target voltage-dependent ion channels, molecular components of cell membranes that influence the electrical activity of neurons. Because of their importance, the action of neuromodulators upon voltage-dependent ion channels and the subsequent changes in neural activity has been studied extensively. However, the properties of voltage-dependent ion channels also influence the energy that neural signalling consumes. Here we assess the impact of neuromodulators upon neuronal energy consumption. We use analytical and computational models to determine the impact of different neuromodulators upon the signalling properties and energy consumption of fly photoreceptors. Our models uncover previously unknown properties of voltage-dependent ion channels in fly photoreceptors, showing how they adjust the membrane properties, gain and bandwidth, to prevailing light levels. Neuromodulators alter voltage-dependent ion channel properties, adjusting the gain and bandwidth. Although neuromodulators do not substantially alter the overall energy consumption of photoreceptors, they redistribute energy investment in gain and bandwidth. Hence, our models provide novel insights into the functions that neuromodulators play in neurons and neural circuits.

Non-linear amplification of graded voltage signals in the first-order visual interneurons of the butterfly Papilio xuthus

Lamina monopolar cells (LMCs) are the first-order visual interneurons of insects and crustacea, primarily involved in achromatic vision. Here, we investigated morphological and electrophysiological properties of LMCs in the butterfly Papilio xuthus Using intracellular recording coupled with dye injection, we found two types of LMCs. Cells with roundish terminals near the distal surface of the medulla demonstrating no or small depolarizing spikes were classified as L1/2. Cells with elongated terminals deep in the medulla that showed prominent spiking were classified as L3/4. The majority of LMCs of both types had broad spectral sensitivities, peaking between 480 and 570 nm. Depending on the experimental conditions, spikes varied from small to action potential-like events, with their amplitudes and rates decreasing as stimulus brightness increased. When the eye was stimulated with naturalistic contrast-modulated time series, spikes were reliably triggered by high-contrast components of the stimulus. Spike-triggered average functions showed that spikes emphasize rapid membrane depolarizations. Our results suggest that spikes are mediated by voltage-activated Na⁺ channels, which are mainly inactivated at rest. Strong local minima in the coherence functions of spiking LMCs indicate that the depolarizing conductance contributes to the amplification of graded responses even when detectable spikes are not evoked. We propose that the information transfer strategies of spiking LMCs change with light intensity. In dim light, both graded voltage signals and large spikes are used together without mutual interference, as a result of separate transmission bandwidths. In bright light, signals are non-linearly amplified by the depolarizing conductance in the absence of detectable spikes.

A Population Representation of Absolute Light Intensity in the Mammalian Retina

Environmental illumination spans many log units of intensity and is tracked for essential functions that include regulation of the circadian clock, arousal state, and hormone levels. Little is known about the neural representation of light intensity and how it covers the necessary range. This question became accessible with the discovery of mammalian photoreceptors that are required for intensity-driven functions, the M1 ipRGCs. The spike outputs of M1s are thought to uniformly track intensity over a wide range. We provide a different understanding: individual cells operate over a narrow range, but the population covers irradiances from moonlight to full daylight. The range of most M1s is limited by depolarization block, which is generally considered pathological but is produced intrinsically by these cells. The dynamics of block allow the population to code stimulus intensity with flexibility and efficiency. Moreover, although spikes are distorted by block, they are regularized during axonal propagation.

Dendritic Properties Control Energy Efficiency of Action Potentials in Cortical Pyramidal Cells

Neural computation is performed by transforming input signals into sequences of action potentials (APs), which is metabolically expensive and limited by the energy available to the brain. The metabolic efficiency of single AP has important consequences for the computational power of the cell, which is determined by its biophysical properties and morphologies. Here we adopt biophysically-based two-compartment models to investigate how dendrites affect energy efficiency of APs in cortical pyramidal neurons. We measure the Na⁺ entry during the spike and examine how it is efficiently used for generating AP depolarization. We show that increasing the proportion of dendritic area or coupling conductance between two chambers decreases Na⁺ entry efficiency of somatic AP. Activating inward Ca²⁺ current in dendrites results in dendritic spike, which increases AP efficiency. Activating Ca²⁺-activated outward K⁺ current in dendrites, however, decreases Na⁺ entry efficiency. We demonstrate that the active and passive dendrites take effects by altering the overlap between Na⁺ influx and internal current flowing from soma to dendrite. We explain a fundamental link between dendritic properties and AP efficiency, which is essential to interpret how neural computation consumes metabolic energy and how biophysics and morphologies contribute to such consumption.

A consensus layer V pyramidal neuron can sustain interpulse-interval coding

In terms of a single neuron's long-distance communication, interpulse intervals (IPIs) are an attractive alternative to rate and binary codes. As a proxy for an IPI, a neuron's time-to-spike can be found in the biophysical and experimental intracellular literature. Using the current, consensus layer V pyramidal neuron, the present study examines the feasibility of IPI-coding and examines the noise sources that limit the information rate of such an encoding. In descending order of importance, the noise sources are (i) synaptic variability, (ii) sodium channel shot-noise, followed by (iii) thermal noise. The biophysical simulations allow the calculation of mutual information, which is about 3.0 bits/spike. More importantly, while, by any conventional definition, the biophysical model is highly nonlinear, the underlying function that relates input intensity to the defined output variable is linear. When one assumes the perspective of a neuron coding via first hitting-time, this result justifies a pervasive and simplifying assumption of computational modelers-that a class of cortical neurons can be treated as linearly additive, computational devices.

Determine Neuronal Tuning Curves by Exploring Optimum Firing Rate Distribution for Information Efficiency

This paper proposed a new method to determine the neuronal tuning curves for maximum information efficiency by computing the optimum firing rate distribution. Firstly, we proposed a general definition for the information efficiency, which is relevant to mutual information and neuronal energy consumption. The energy consumption is composed of two parts: neuronal basic energy consumption and neuronal spike emission energy consumption. A parameter to model the relative importance of energy consumption is introduced in the definition of the information efficiency. Then, we designed a combination of exponential functions to describe the optimum firing rate distribution based on the analysis of the dependency of the mutual information and the energy consumption on the shape of the functions of the firing rate distributions. Furthermore, we developed a rapid algorithm to search the parameter values of the optimum firing rate distribution function. Finally, we found with the rapid algorithm that a combination of two different exponential functions with two free parameters can describe the optimum firing rate distribution accurately. We also found that if the energy consumption is relatively unimportant (important) compared to the mutual information or the neuronal basic energy consumption is relatively large (small), the curve of the optimum firing rate distribution will be relatively flat (steep), and the corresponding optimum tuning curve exhibits a form of sigmoid if the stimuli distribution is normal.

Metabolic Energy of Action Potentials Modulated by Spike Frequency Adaptation

Spike frequency adaptation (SFA) exists in many types of neurons, which has been demonstrated to improve their abilities to process incoming information by synapses. The major carrier used by a neuron to convey synaptic signals is the sequences of action potentials (APs), which have to consume substantial metabolic energies to initiate and propagate. Here we use conductance-based models to investigate how SFA modulates the AP-related energy of neurons. The SFA is attributed to either calcium-activated K⁺ (I_AHP) or voltage-activated K⁺ (I_M) current. We observe that the activation of I_AHP or I_M increases the Na⁺ load used for depolarizing membrane, while produces few effects on the falling phase of AP. Then, the metabolic energy involved in Na⁺ current significantly increases from one AP to the next, while for K⁺ current it is less affected. As a consequence, the total energy cost by each AP gets larger as firing rate decays down. It is also shown that the minimum Na⁺ charge needed for the depolarization of each AP is unaffected during the course of SFA. This indicates that the activation of either adaptation current makes APs become less efficient to use Na⁺ influx for their depolarization. Further, our simulations demonstrate that the different biophysical properties of I_M and I_AHP result in distinct modulations of metabolic energy usage for APs. These investigations provide a fundamental link between adaptation currents and neuronal energetics, which could facilitate to interpret how SFA participates in neuronal information processing.

A Model for an Angular Velocity-Tuned Motion Detector Accounting for Deviations in the Corridor-Centering Response of the Bee

We present a novel neurally based model for estimating angular velocity (AV) in the bee brain, capable of quantitatively reproducing experimental observations of visual odometry and corridor-centering in free-flying honeybees, including previously unaccounted for manipulations of behaviour. The model is fitted using electrophysiological data, and tested using behavioural data. Based on our model we suggest that the AV response can be considered as an evolutionary extension to the optomotor response. The detector is tested behaviourally in silico with the corridor-centering paradigm, where bees navigate down a corridor with gratings (square wave or sinusoidal) on the walls. When combined with an existing flight control algorithm the detector reproduces the invariance of the average flight path to the spatial frequency and contrast of the gratings, including deviations from perfect centering behaviour as found in the real bee's behaviour. In addition, the summed response of the detector to a unit distance movement along the corridor is constant for a large range of grating spatial frequencies, demonstrating that the detector can be used as a visual odometer.

Neural Evolution: Marginal Gains through Soma Location

Unlike in most vertebrate neurons, the soma of many arthropod and mollusc neurons is placed at the end of a thin neurite. Multi-compartment computational modelling suggests this strategy may reduce the attenuation of signals from the dendrites, reducing the energy costs of signalling.

Motor Learning and the Cerebellum

Although our ability to store semantic declarative information can nowadays be readily surpassed by that of simple personal computers, our ability to learn and express procedural memories still outperforms that of supercomputers controlling the most advanced robots. To a large extent, our procedural memories are formed in the cerebellum, which embodies more than two-thirds of all neurons in our brain. In this review, we will focus on the emerging view that different modules of the cerebellum use different encoding schemes to form and express their respective memories. More specifically, zebrin-positive zones in the cerebellum, such as those controlling adaptation of the vestibulo-ocular reflex, appear to predominantly form their memories by potentiation mechanisms and express their memories via rate coding, whereas zebrin-negative zones, such as those controlling eyeblink conditioning, appear to predominantly form their memories by suppression mechanisms and express their memories in part by temporal coding using rebound bursting. Together, the different types of modules offer a rich repertoire to acquire and control sensorimotor processes with specific challenges in the spatiotemporal domain.

Optimum neural tuning curves for information efficiency with rate coding and finite-time window

An important question for neural encoding is what kind of neural systems can convey more information with less energy within a finite time coding window. This paper first proposes a finite-time neural encoding system, where the neurons in the system respond to a stimulus by a sequence of spikes that is assumed to be Poisson process and the external stimuli obey normal distribution. A method for calculating the mutual information of the finite-time neural encoding system is proposed and the definition of information efficiency is introduced. The values of the mutual information and the information efficiency obtained by using Logistic function are compared with those obtained by using other functions and it is found that Logistic function is the best one. It is further found that the parameter representing the steepness of the Logistic function has close relationship with full entropy, and that the parameter representing the translation of the function associates with the energy consumption and noise entropy tightly. The optimum parameter combinations for Logistic function to maximize the information efficiency are calculated when the stimuli and the properties of the encoding system are varied respectively. Some explanations for the results are given. The model and the method we proposed could be useful to study neural encoding system, and the optimum neural tuning curves obtained in this paper might exhibit some characteristics of a real neural system.

Input-output relation and energy efficiency in the neuron with different spike threshold dynamics

Neuron encodes and transmits information through generating sequences of output spikes, which is a high energy-consuming process. The spike is initiated when membrane depolarization reaches a threshold voltage. In many neurons, threshold is dynamic and depends on the rate of membrane depolarization (dV/dt) preceding a spike. Identifying the metabolic energy involved in neural coding and their relationship to threshold dynamic is critical to understanding neuronal function and evolution. Here, we use a modified Morris-Lecar model to investigate neuronal input-output property and energy efficiency associated with different spike threshold dynamics. We find that the neurons with dynamic threshold sensitive to dV/dt generate discontinuous frequency-current curve and type II phase response curve (PRC) through Hopf bifurcation, and weak noise could prohibit spiking when bifurcation just occurs. The threshold that is insensitive to dV/dt, instead, results in a continuous frequency-current curve, a type I PRC and a saddle-node on invariant circle bifurcation, and simultaneously weak noise cannot inhibit spiking. It is also shown that the bifurcation, frequency-current curve and PRC type associated with different threshold dynamics arise from the distinct subthreshold interactions of membrane currents. Further, we observe that the energy consumption of the neuron is related to its firing characteristics. The depolarization of spike threshold improves neuronal energy efficiency by reducing the overlap of Na(+) and K(+) currents during an action potential. The high energy efficiency is achieved at more depolarized spike threshold and high stimulus current. These results provide a fundamental biophysical connection that links spike threshold dynamics, input-output relation, energetics and spike initiation, which could contribute to uncover neural encoding mechanism.

Dendritic nonlinearities are tuned for efficient spike-based computations in cortical circuits

Cortical neurons integrate thousands of synaptic inputs in their dendrites in highly nonlinear ways. It is unknown how these dendritic nonlinearities in individual cells contribute to computations at the level of neural circuits. Here, we show that dendritic nonlinearities are critical for the efficient integration of synaptic inputs in circuits performing analog computations with spiking neurons. We developed a theory that formalizes how a neuron's dendritic nonlinearity that is optimal for integrating synaptic inputs depends on the statistics of its presynaptic activity patterns. Based on their in vivo preynaptic population statistics (firing rates, membrane potential fluctuations, and correlations due to ensemble dynamics), our theory accurately predicted the responses of two different types of cortical pyramidal cells to patterned stimulation by two-photon glutamate uncaging. These results reveal a new computational principle underlying dendritic integration in cortical neurons by suggesting a functional link between cellular and systems--level properties of cortical circuits.