History-dependent multiple-time-scale dynamics in a single-neuron model

Fractional order memcapacitive neuromorphic elements reproduce and predict neuronal function

There is an increasing need to implement neuromorphic systems that are both energetically and computationally efficient. There is also great interest in using electric elements with memory, memelements, that can implement complex neuronal functions intrinsically. A feature not widely incorporated in neuromorphic systems is history-dependent action potential time adaptation which is widely seen in real cells. Previous theoretical work shows that power-law history dependent spike time adaptation, seen in several brain areas and species, can be modeled with fractional order differential equations. Here, we show that fractional order spiking neurons can be implemented using super-capacitors. The super-capacitors have fractional order derivative and memcapacitive properties. We implemented two circuits, a leaky integrate and fire and a Hodgkin-Huxley. Both circuits show power-law spiking time adaptation and optimal coding properties. The spiking dynamics reproduced previously published computer simulations. However, the fractional order Hodgkin-Huxley circuit showed novel dynamics consistent with criticality. We compared the responses of this circuit to recordings from neurons in the weakly-electric fish that have previously been shown to perform fractional order differentiation of their sensory input. The criticality seen in the circuit was confirmed in spontaneous recordings in the live fish. Furthermore, the circuit also predicted long-lasting stimulation that was also corroborated experimentally. Our work shows that fractional order memcapacitors provide intrinsic memory dependence that could allow implementation of computationally efficient neuromorphic devices. Memcapacitors are static elements that consume less energy than the most widely studied memristors, thus allowing the realization of energetically efficient neuromorphic devices.

Photobiomodulation effects of pulsed and continuous wave near-infrared laser on the proliferation and migration of human gingival fibroblasts: An in vitro study

There are limited data on comparison of pulsed and continuous wave in photobiomodulation therapy (PBM). This study aimed to investigate the effect of PBM with 980 nm laser in pulsed and continuous wave on the proliferation and migration of human gingival fibroblasts (HGF) cells. Cultured HGF were divided into three main groups: (1) irradiated in pulsed mode (frequencies of 50 and 25 KHz; energy densities of 3 and 5 J/cm2 ), (2) irradiated in continuous mode (energy densities of 3.2 and 5.2 J/cm2 ), and (3) no irradiation as control group. HGF proliferation rate was measured by MTT assay at 24, 48, and 72 h post irradiation. In addition, HGF migration rate was measured by scratch test at 24 h post PBM. At 24 h, the group received continuous irradiation at 5.2 J/cm2 showed significantly higher proliferation compared with the control group (p = 0.012). At 48 and 72 h, the groups received continuous, and 50 Hz pulsed irradiation at energy densities of 5.2 and 5 J/cm2 respectively, had significantly higher HGF proliferation rates compared to the control (p < 0.05). Only the continuous irradiations were effective in significant increase of the cell migration. In conclusion, continuous PBM at energy density of 5.2 J/cm2 showed promising effect on HGF proliferation and migration.

Mechanisms of human dynamic object recognition revealed by sequential deep neural networks

Humans can quickly recognize objects in a dynamically changing world. This ability is showcased by the fact that observers succeed at recognizing objects in rapidly changing image sequences, at up to 13 ms/image. To date, the mechanisms that govern dynamic object recognition remain poorly understood. Here, we developed deep learning models for dynamic recognition and compared different computational mechanisms, contrasting feedforward and recurrent, single-image and sequential processing as well as different forms of adaptation. We found that only models that integrate images sequentially via lateral recurrence mirrored human performance (N = 36) and were predictive of trial-by-trial responses across image durations (13-80 ms/image). Importantly, models with sequential lateral-recurrent integration also captured how human performance changes as a function of image presentation durations, with models processing images for a few time steps capturing human object recognition at shorter presentation durations and models processing images for more time steps capturing human object recognition at longer presentation durations. Furthermore, augmenting such a recurrent model with adaptation markedly improved dynamic recognition performance and accelerated its representational dynamics, thereby predicting human trial-by-trial responses using fewer processing resources. Together, these findings provide new insights into the mechanisms rendering object recognition so fast and effective in a dynamic visual world.

The time scales of irreversibility in spontaneous brain activity are altered in obsessive compulsive disorder

We study how obsessive-compulsive disorder (OCD) affects the complexity and time-reversal symmetry-breaking (irreversibility) of the brain resting-state activity as measured by magnetoencephalography (MEG). Comparing MEG recordings from OCD patients and age/sex matched control subjects, we find that irreversibility is more concentrated at faster time scales and more uniformly distributed across different channels of the same hemisphere in OCD patients than in control subjects. Furthermore, the interhemispheric asymmetry between homologous areas of OCD patients and controls is also markedly different. Some of these differences were reduced by 1-year of Kundalini Yoga meditation treatment. Taken together, these results suggest that OCD alters the dynamic attractor of the brain's resting state and hint at a possible novel neurophysiological characterization of this psychiatric disorder and how this therapy can possibly modulate brain function.

Effect of Photobiomodulation Therapy on the Increase of Viability and Proliferation of Human Mesenchymal Stem Cells

BACKGROUND AND OBJECTIVES

We have investigated how low intensity laser irradiation emitted by a multiwave-locked system (MLS M1) affects the viability and proliferation of human bone marrow mesenchymal stem cells (MSCs) depending on the parameters of the irradiation.

STUDY DESIGN/MATERIALS AND METHODS

Cells isolated surgically from the femoral bone during surgery were identified by flow cytometry and cell differentiation assays. For irradiation, two wavelengths (808 and 905 nm) with the following parameters were used: power density 195, 230, and 318 mW/cm ² , doses of energy 3, 10, and 20 J (energy density 0.93-6.27 J/cm ² ), and in continuous (CW) or pulsed emission (PE) (frequencies 1,000 and 2,000 Hz).

RESULTS

There were statistically significant increases of cell viability and proliferation after irradiation at 3 J (CW; 1,000 Hz), 10 J (1,000 Hz), and 20 J (2,000 Hz).

CONCLUSIONS

Irradiation with the MLS M1 system can be used in vitro to modulate MSCs in preparation for therapeutic applications. This will assist in designing further studies to optimize the radiation parameters and elucidate the molecular mechanisms of action of the radiation. Lasers Surg. Med. © 2019 Wiley Periodicals, Inc.

Role of time scales and topology on the dynamics of complex networks

The interplay between time scales and structural properties of complex networks of nonlinear oscillators can generate many interesting phenomena, like amplitude death, cluster synchronization, frequency synchronization, etc. We study the emergence of such phenomena and their transitions by considering a complex network of dynamical systems in which a fraction of systems evolves on a slower time scale on the network. We report the transition to amplitude death for the whole network and the scaling near the transitions as the connectivity pattern changes. We also discuss the suppression and recovery of oscillations and the crossover behavior as the number of slow systems increases. By considering a scale free network of systems with multiple time scales, we study the role of heterogeneity in link structure on dynamical properties and the consequent critical behaviors. In this case with hubs made slow, our main results are the escape time statistics for loss of complete synchrony as the slowness spreads on the network and the self-organization of the whole network to a new frequency synchronized state. Our results have potential applications in biological, physical, and engineering networks consisting of heterogeneous oscillators.

Long-Term Activity Dynamics of Single Neurons and Networks

The firing rate of neuronal spiking in vitro and in vivo significantly varies over extended timescales, characterized by long-memory processes and complex statistics, and appears in spontaneous as well as evoked activity upon repeated stimulus presentation. These variations in response features and their statistics, in face of repeated instances of a given physical input, are ubiquitous in all levels of brain-behavior organization. They are expressed in single neuron and network response variability but even appear in variations of subjective percepts or psychophysical choices and have been described as stemming from history-dependent, stochastic, or rate-determined processes.But what are the sources underlying these temporally rich variations in firing rate? Are they determined by interactions of the nervous system as a whole, or do isolated, single neurons or neuronal networks already express these fluctuations independent of higher levels? These questions motivated the application of a method that allows for controlled and specific long-term activation of a single neuron or neuronal network, isolated from higher levels of cortical organization.This chapter highlights the research done in cultured cortical networks to study (1) the inherent non-stationarity of neuronal network activity, (2) single neuron response fluctuations and underlying processes, and (3) the interface layer between network and single cell, the non-stationary efficacy of the ensemble of synapses impinging onto the observed neuron.

Traits of criticality in membrane potential fluctuations of pyramidal neurons in the CA1 region of rat hippocampus

Evidence that neural circuits are operating near criticality has been provided at various levels of brain organisation with a presumed role in maximising information processing and multiscale activity association. Criticality has been linked to excitation at both the single-cell and network levels, as action potential generation marks an obvious phase transition from a resting to an excitable state. Using in vitro intracellular recordings, we examine irregular, small amplitude membrane potential fluctuations from CA1 pyramidal neurons of Wistar male rats. We show that these fluctuations, confounded with noise, carry information relevant to the neuronal state. The underlying dynamics exhibit intermittent characteristics shown to describe the temporal fluctuations of the order parameter of a macroscopic system at its critical point even in the absence of firing. An externally applied stimulus serves as the control parameter, driving the system in and out of its critical state. Based on our experimental observations we calculate the equivalent of the isothermal critical exponent δ_h finding a value which depends on the applied stimulus. For each neuron there is a stimulus amplitude for which the critical behaviour becomes most pronounced. The corresponding mean value of δ_h in the considered ensemble of neurons is δ_h  ≈ 1.89, close to theoretical predictions for critical networks. Finally, we show that the firing rate of a neuron decreases exponentially with δ_h .

Pulse frequency dependency of photobiomodulation on the bioenergetic functions of human dental pulp stem cells

Photobiomodulation (PBM) therapy contributes to pain relief, wound healing, and tissue regeneration. The pulsed wave (PW) mode has been reported to be more effective than the continuous wave (CW) mode when applying PBM to many biological systems. However, the reason for the higher effectiveness of PW-PBM is poorly understood. Herein, we suggest using delayed luminescence (DL) as a reporter of mitochondrial activity after PBM treatment. DL originates mainly from mitochondrial electron transport chain systems, which produce reactive oxygen species (ROS) and adenosine triphosphate (ATP). The decay time of DL depends on the pulse frequencies of applied light, which correlate with the biological responses of human dental pulp stem cells (hDPSCs). Using a low-power light whose wavelength is 810 nm and energy density is 38 mJ/cm², we find that a 300-Hz pulse frequency prolonged the DL pattern and enhanced alkaline phosphatase activity. In addition, we analyze mitochondrial morphological changes and their volume density and find evidence supporting mitochondrial physiological changes from PBM treatment. Our data suggest a new methodology for determining the effectiveness of PBM and the specific pulse frequency dependency of PBM in the differentiation of hDPSCs.

Fractional-order leaky integrate-and-fire model with long-term memory and power law dynamics

Pyramidal neurons produce different spiking patterns to process information, communicate with each other and transform information. These spiking patterns have complex and multiple time scale dynamics that have been described with the fractional-order leaky integrate-and-Fire (FLIF) model. Models with fractional (non-integer) order differentiation that generalize power law dynamics can be used to describe complex temporal voltage dynamics. The main characteristic of FLIF model is that it depends on all past values of the voltage that causes long-term memory. The model produces spikes with high interspike interval variability and displays several spiking properties such as upward spike-frequency adaptation and long spike latency in response to a constant stimulus. We show that the subthreshold voltage and the firing rate of the fractional-order model make transitions from exponential to power law dynamics when the fractional order α decreases from 1 to smaller values. The firing rate displays different types of spike timing adaptation caused by changes on initial values. We also show that the voltage-memory trace and fractional coefficient are the causes of these different types of spiking properties. The voltage-memory trace that represents the long-term memory has a feedback regulatory mechanism and affects spiking activity. The results suggest that fractional-order models might be appropriate for understanding multiple time scale neuronal dynamics. Overall, a neuron with fractional dynamics displays history dependent activities that might be very useful and powerful for effective information processing.

Dynamical Timescale Explains Marginal Stability in Excitability Dynamics

Action potentials, taking place over milliseconds, are the basis of neural computation. However, the dynamics of excitability over longer, behaviorally relevant timescales remain underexplored. A recent experiment used long-term recordings from single neurons to reveal multiple timescale fluctuations in response to constant stimuli, along with more reliable responses to variable stimuli. Here, we demonstrate that this apparent paradox is resolved if neurons operate in a marginally stable dynamic regime, which we reveal using a novel inference method. Excitability in this regime is characterized by large fluctuations while retaining high sensitivity to external varying stimuli. A new model with a dynamic recovery timescale that interacts with excitability captures this dynamic regime and predicts the neurons' response with high accuracy. The model explains most experimental observations under several stimulus statistics. The compact structure of our model permits further exploration on the network level.SIGNIFICANCE STATEMENT Excitability is the basis for all neural computations and its long-term dynamics reveal a complex combination of many timescales. We discovered that neural excitability operates under a marginally stable regime in which the system is dominated by internal fluctuation while retaining high sensitivity to externally varying stimuli. We offer a novel approach to modeling excitability dynamics by assuming that the recovery timescale is itself a dynamic variable. Our model is able to capture a wide range of experimental phenomena using few parameters with significantly higher predictive power than previous models.

Neural oscillations as a signature of efficient coding in the presence of synaptic delays

Cortical networks exhibit 'global oscillations', in which neural spike times are entrained to an underlying oscillatory rhythm, but where individual neurons fire irregularly, on only a fraction of cycles. While the network dynamics underlying global oscillations have been well characterised, their function is debated. Here, we show that such global oscillations are a direct consequence of optimal efficient coding in spiking networks with synaptic delays and noise. To avoid firing unnecessary spikes, neurons need to share information about the network state. Ideally, membrane potentials should be strongly correlated and reflect a 'prediction error' while the spikes themselves are uncorrelated and occur rarely. We show that the most efficient representation is when: (i) spike times are entrained to a global Gamma rhythm (implying a consistent representation of the error); but (ii) few neurons fire on each cycle (implying high efficiency), while (iii) excitation and inhibition are tightly balanced. This suggests that cortical networks exhibiting such dynamics are tuned to achieve a maximally efficient population code.

DOI:http://dx.doi.org/10.7554/eLife.13824.001

How can we study reasoning in the brain?

The brain did not develop a dedicated device for reasoning. This fact bears dramatic consequences. While for perceptuo-motor functions neural activity is shaped by the input's statistical properties, and processing is carried out at high speed in hardwired spatially segregated modules, in reasoning, neural activity is driven by internal dynamics and processing times, stages, and functional brain geometry are largely unconstrained a priori. Here, it is shown that the complex properties of spontaneous activity, which can be ignored in a short-lived event-related world, become prominent at the long time scales of certain forms of reasoning. It is argued that the neural correlates of reasoning should in fact be defined in terms of non-trivial generic properties of spontaneous brain activity, and that this implies resorting to concepts, analytical tools, and ways of designing experiments that are as yet non-standard in cognitive neuroscience. The implications in terms of models of brain activity, shape of the neural correlates, methods of data analysis, observability of the phenomenon, and experimental designs are discussed.

Neuronal spike timing adaptation described with a fractional leaky integrate-and-fire model

The voltage trace of neuronal activities can follow multiple timescale dynamics that arise from correlated membrane conductances. Such processes can result in power-law behavior in which the membrane voltage cannot be characterized with a single time constant. The emergent effect of these membrane correlations is a non-Markovian process that can be modeled with a fractional derivative. A fractional derivative is a non-local process in which the value of the variable is determined by integrating a temporal weighted voltage trace, also called the memory trace. Here we developed and analyzed a fractional leaky integrate-and-fire model in which the exponent of the fractional derivative can vary from 0 to 1, with 1 representing the normal derivative. As the exponent of the fractional derivative decreases, the weights of the voltage trace increase. Thus, the value of the voltage is increasingly correlated with the trajectory of the voltage in the past. By varying only the fractional exponent, our model can reproduce upward and downward spike adaptations found experimentally in neocortical pyramidal cells and tectal neurons in vitro. The model also produces spikes with longer first-spike latency and high inter-spike variability with power-law distribution. We further analyze spike adaptation and the responses to noisy and oscillatory input. The fractional model generates reliable spike patterns in response to noisy input. Overall, the spiking activity of the fractional leaky integrate-and-fire model deviates from the spiking activity of the Markovian model and reflects the temporal accumulated intrinsic membrane dynamics that affect the response of the neuron to external stimulation.

Spike adaptation is a property of most neurons. When spike time adaptation occurs over multiple time scales, the dynamics can be described by a power-law. We study the computational properties of a leaky integrate-and-fire model with power-law adaptation. Instead of explicitly modeling the adaptation process by the contribution of slowly changing conductances, we use a fractional temporal derivative framework. The exponent of the fractional derivative represents the degree of adaptation of the membrane voltage, where 1 is the normal leaky integrator while values less than 1 produce increasing correlations in the voltage trace. The temporal correlation is interpreted as a memory trace that depends on the value of the fractional derivative. We identify the memory trace in the fractional model as the sum of the instantaneous differentiation weighted by a function that depends on the fractional exponent, and it provides non-local information to the incoming stimulus. The spiking dynamics of the fractional leaky integrate-and-fire model show memory dependence that can result in downward or upward spike adaptation. Our model provides a framework for understanding how long-range membrane voltage correlations affect spiking dynamics and information integration in neurons.

Self-organized criticality in single-neuron excitability

We present experimental and theoretical arguments, at the single-neuron level, suggesting that neuronal response fluctuations reflect a process that positions the neuron near a transition point that separates excitable and unexcitable phases. This view is supported by the dynamical properties of the system as observed in experiments on isolated cultured cortical neurons, as well as by a theoretical mapping between the constructs of self-organized criticality and membrane excitability biophysics.

Is the brain's inertia for motor movements different for acceleration and deceleration?

The brain's ability to synchronize movements with external cues is used daily, yet neuroscience is far from a full understanding of the brain mechanisms that facilitate and set behavioral limits on these sequential performances. This functional magnetic resonance imaging (fMRI) study was designed to help understand the neural basis of behavioral performance differences on a synchronizing movement task during increasing (acceleration) and decreasing (deceleration) metronome rates. In the MRI scanner, subjects were instructed to tap their right index finger on a response box in synchrony to visual cues presented on a display screen. The tapping rate varied either continuously or in discrete steps ranging from 0.5 Hz to 3 Hz. Subjects were able to synchronize better during continuously accelerating rhythms than in continuously or discretely decelerating rhythms. The fMRI data revealed that the precuneus was activated more during continuous deceleration than during acceleration with the hysteresis effect significant at rhythm rates above 1 Hz. From the behavioral data, two performance measures, tapping rate and synchrony index, were derived to further analyze the relative brain activity during acceleration and deceleration of rhythms. Tapping rate was associated with a greater brain activity during deceleration in the cerebellum, superior temporal gyrus and parahippocampal gyrus. Synchrony index was associated with a greater activity during the continuous acceleration phase than during the continuous deceleration or discrete acceleration phases in a distributed network of regions including the prefrontal cortex and precuneus. These results indicate that the brain's inertia for movement is different for acceleration and deceleration, which may have implications in understanding the origin of our perceptual and behavioral limits.

Temporal whitening by power-law adaptation in neocortical neurons

Spike-frequency adaptation (SFA) is widespread in the CNS, but its function remains unclear. In neocortical pyramidal neurons, adaptation manifests itself by an increase in the firing threshold and by adaptation currents triggered after each spike. Combining electrophysiological recordings in mice with modeling, we found that these adaptation processes lasted for more than 20 s and decayed over multiple timescales according to a power law. The power-law decay associated with adaptation mirrored and canceled the temporal correlations of input current received in vivo at the somata of layer 2/3 somatosensory pyramidal neurons. These findings suggest that, in the cortex, SFA causes temporal decorrelation of output spikes (temporal whitening), an energy-efficient coding procedure that, at high signal-to-noise ratio, improves the information transfer.

Conserved N-terminal negative charges support optimally efficient N-type inactivation of Kv1 channels

N-type inactivation is produced by the binding of a potassium channel's N-terminus within the open pore, blocking conductance. Previous studies have found that introduction of negative charges into N-terminal inactivation domains disrupts inactivation; however, the Aplysia AKv1 N-type inactivation domain contains two negatively charged residues, E2 and E9. Rather than being unusual, sequence analysis shows that this N-terminal motif is highly conserved among Kv1 sequences across many phyla. Conservation analysis shows some tolerance at position 9 for other charged residues, like D9 and K9, whereas position 2 is highly conserved as E2. To examine the functional importance of these residues, site directed mutagenesis was performed and effects on inactivation were recorded by two electrode voltage clamp in Xenopus oocytes. We find that inclusion of charged residues at positions 2 and 9 prevents interactions with non-polar sites along the inactivation pathway increasing the efficiency of pore block. In addition, E2 appears to have additional specific electrostatic interactions that stabilize the inactivated state likely explaining its high level of conservation. One possible explanation for E2's unique importance, consistent with our data, is that E2 interacts electrostatically with a positive charge on the N-terminal amino group to stabilize the inactivation domain at the block site deep within the pore. Simple electrostatic modeling suggests that due to the non-polar environment in the pore in the blocked state, even a 1 Å larger separation between these charges, produced by the E2D substitution, would be sufficient to explain the 65× reduced affinity of the E2D N-terminus for the pore. Finally, our studies support a multi-step, multi-site N-type inactivation model where the N-terminus interacts deep within the pore in an extended like structure placing the most N-terminal residues 35% of the way across the electric field in the pore blocked state.

Time scales in cognitive neuroscience

Cognitive neuroscience boils down to describing the ways in which cognitive function results from brain activity. In turn, brain activity shows complex fluctuations, with structure at many spatio-temporal scales. Exactly how cognitive function inherits the physical dimensions of neural activity, though, is highly non-trivial, and so are generally the corresponding dimensions of cognitive phenomena. As for any physical phenomenon, when studying cognitive function, the first conceptual step should be that of establishing its dimensions. Here, we provide a systematic presentation of the temporal aspects of task-related brain activity, from the smallest scale of the brain imaging technique's resolution, to the observation time of a given experiment, through the characteristic time scales of the process under study. We first review some standard assumptions on the temporal scales of cognitive function. In spite of their general use, these assumptions hold true to a high degree of approximation for many cognitive (viz. fast perceptual) processes, but have their limitations for other ones (e.g., thinking or reasoning). We define in a rigorous way the temporal quantifiers of cognition at all scales, and illustrate how they qualitatively vary as a function of the properties of the cognitive process under study. We propose that each phenomenon should be approached with its own set of theoretical, methodological and analytical tools. In particular, we show that when treating cognitive processes such as thinking or reasoning, complex properties of ongoing brain activity, which can be drastically simplified when considering fast (e.g., perceptual) processes, start playing a major role, and not only characterize the temporal properties of task-related brain activity, but also determine the conditions for proper observation of the phenomena. Finally, some implications on the design of experiments, data analyses, and the choice of recording parameters are discussed.

Distinct effects of brief and prolonged adaptation on orientation tuning in primary visual cortex

Recent stimulus history-adaptation-alters neuronal responses and perception. Previous electrophysiological and perceptual studies suggest that prolonged adaptation strengthens and makes more persistent the effects seen after briefer exposures. However, no systematic comparison has been made between the effects of adaptation lasting hundreds of milliseconds, which might arise during a single fixation, and the more prolonged adaptation typically used in imaging and perceptual studies. Here we determine how 0.4, 4, and 40 s of adaptation alters orientation tuning in primary visual cortex of anesthetized macaque monkeys, and how quickly responses recover after adapter offset. We measured responses to small (1.3°) and large (7.4°) gratings because previous work has shown that adaptation effects can depend on stimulus size. Adaptation with small gratings reduced responsivity and caused tuning to shift away from the adapter. These effects strengthened with more prolonged adaptation. For responses to large gratings, brief and prolonged adaptation produced indistinguishable effects on responsivity but caused opposite shifts in tuning preference. Recovery from adaptation was notably slower after prolonged adaptation, even when this did not induce stronger effects. We show that our results can be explained by an adaptation-induced weakening of surround suppression, the dynamics of this suppression, and differential effects of brief and prolonged adaptation across response epochs. Our findings show that effects do not simply scale with adaptation duration and suggest that distinct strategies exist for adjusting to moment-to-moment fluctuations in input and to more persistent visual stimuli.

Dopamine modulation of Ih improves temporal fidelity of spike propagation in an unmyelinated axon

We studied how conduction delays of action potentials in an unmyelinated axon depended on the history of activity and how this dependence was changed by the neuromodulator dopamine (DA). The pyloric dilator axons of the stomatogastric nervous system in the lobster, Homarus americanus, exhibited substantial activity-dependent hyperpolarization and changes in spike shape during repetitive activation. The conduction delays varied by several milliseconds per centimeter, and, during activation with realistic burst patterns or Poisson-like patterns, changes in delay occurred over multiple timescales. The mean delay increased, whereas the resting membrane potential hyperpolarized with a time constant of several minutes. Concomitantly with the mean delay, the variability of delay also increased. The variability of delay was not a linear or monotonic function of instantaneous spike frequency or spike shape parameters, and the relationship between these parameters changed with the increase in mean delay. Hyperpolarization was counteracted by a hyperpolarization-activated inward current (I(h)), and the magnitude of I(h) critically determined the temporal fidelity of spike propagation. Pharmacological block of I(h) increased the change in delay and the variability of delay, and increasing I(h) by application of DA diminished both. Consequently, the temporal fidelity of pattern propagation was substantially improved in DA. Standard measurements of changes in excitability or delay with paired stimuli or tonic stimulation failed to capture the dynamics of spike conduction. These results indicate that spike conduction can be extremely sensitive to the history of axonal activity and to the presence of neuromodulators, with potentially important consequences for temporal coding.

Exploring the fundamental dynamics of error-based motor learning using a stationary predictive-saccade task

The maintenance of movement accuracy uses prior performance errors to correct future motor plans; this motor-learning process ensures that movements remain quick and accurate. The control of predictive saccades, in which anticipatory movements are made to future targets before visual stimulus information becomes available, serves as an ideal paradigm to analyze how the motor system utilizes prior errors to drive movements to a desired goal. Predictive saccades constitute a stationary process (the mean and to a rough approximation the variability of the data do not vary over time, unlike a typical motor adaptation paradigm). This enables us to study inter-trial correlations, both on a trial-by-trial basis and across long blocks of trials. Saccade errors are found to be corrected on a trial-by-trial basis in a direction-specific manner (the next saccade made in the same direction will reflect a correction for errors made on the current saccade). Additionally, there is evidence for a second, modulating process that exhibits long memory. That is, performance information, as measured via inter-trial correlations, is strongly retained across a large number of saccades (about 100 trials). Together, this evidence indicates that the dynamics of motor learning exhibit complexities that must be carefully considered, as they cannot be fully described with current state-space (ARMA) modeling efforts.

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.

Stochastic phase transition operator

In this study a Markov operator is introduced that represents the density evolution of an impulse-driven stochastic biological oscillator. The operator's stochastic kernel is constructed using the asymptotic expansion of stochastic processes instead of solving the Fokker-Planck equation. The Markov operator is shown to successfully approximate the density evolution of the biological oscillator considered. The response of the oscillator to both periodic and time-varying impulses can be analyzed using the operator's transient and stationary properties. Furthermore, an unreported stochastic dynamic bifurcation for the biological oscillator is obtained by using the eigenvalues of the product of the Markov operators.

Estimating Neuronal Information: Logarithmic Binning of Neuronal Inter-Spike Intervals

Neurons communicate via the relative timing of all-or-none biophysical signals called spikes. For statistical analysis, the time between spikes can be accumulated into inter-spike interval histograms. Information theoretic measures have been estimated from these histograms to assess how information varies across organisms, neural systems, and disease conditions. Because neurons are computational units that, to the extent they process time, work not by discrete clock ticks but by the exponential decays of numerous intrinsic variables, we propose that neuronal information measures scale more naturally with the logarithm of time. For the types of inter-spike interval distributions that best describe neuronal activity, the logarithm of time enables fewer bins to capture the salient features of the distributions. Thus, discretizing the logarithm of inter-spike intervals, as compared to the inter-spike intervals themselves, yields histograms that enable more accurate entropy and information estimates for fewer bins and less data. Additionally, as distribution parameters vary, the entropy and information calculated from the logarithm of the inter-spike intervals are substantially better behaved, e.g., entropy is independent of mean rate, and information is equally affected by rate gains and divisions. Thus, when compiling neuronal data for subsequent information analysis, the logarithm of the inter-spike intervals is preferred, over the untransformed inter-spike intervals, because it yields better information estimates and is likely more similar to the construction used by nature herself.

Dynamics of excitability over extended timescales in cultured cortical neurons

Although neuronal excitability is well understood and accurately modeled over timescales of up to hundreds of milliseconds, it is currently unclear whether extrapolating from this limited duration to longer behaviorally relevant timescales is appropriate. Here we used an extracellular recording and stimulation paradigm that extends the duration of single-neuron electrophysiological experiments, exposing the dynamics of excitability in individual cultured cortical neurons over timescales hitherto inaccessible. We show that the long-term neuronal excitability dynamics is unstable and dominated by critical fluctuations, intermittency, scale-invariant rate statistics, and long memory. These intrinsic dynamics bound the firing rate over extended timescales, contrasting observed short-term neuronal response to stimulation onset. Furthermore, the activity of a neuron over extended timescales shows transitions between quasi-stable modes, each characterized by a typical response pattern. Like in the case of rate statistics, the short-term onset response pattern that often serves to functionally define a given neuron is not indicative of its long-term ongoing response. These observations question the validity of describing neuronal excitability based on temporally restricted electrophysiological data, calling for in-depth exploration of activity over wider temporal scales. Such extended experiments will probably entail a different kind of neuronal models, accounting for the unbounded range, from milliseconds up.

History-dependent excitability as a single-cell substrate of transient memory for information discrimination

Neurons react differently to incoming stimuli depending upon their previous history of stimulation. This property can be considered as a single-cell substrate for transient memory, or context-dependent information processing: depending upon the current context that the neuron "sees" through the subset of the network impinging on it in the immediate past, the same synaptic event can evoke a postsynaptic spike or just a subthreshold depolarization. We propose a formal definition of History-Dependent Excitability (HDE) as a measure of the propensity to firing in any moment in time, linking the subthreshold history-dependent dynamics with spike generation. This definition allows the quantitative assessment of the intrinsic memory for different single-neuron dynamics and input statistics. We illustrate the concept of HDE by considering two general dynamical mechanisms: the passive behavior of an Integrate and Fire (IF) neuron, and the inductive behavior of a Generalized Integrate and Fire (GIF) neuron with subthreshold damped oscillations. This framework allows us to characterize the sensitivity of different model neurons to the detailed temporal structure of incoming stimuli. While a neuron with intrinsic oscillations discriminates equally well between input trains with the same or different frequency, a passive neuron discriminates better between inputs with different frequencies. This suggests that passive neurons are better suited to rate-based computation, while neurons with subthreshold oscillations are advantageous in a temporal coding scheme. We also address the influence of intrinsic properties in single-cell processing as a function of input statistics, and show that intrinsic oscillations enhance discrimination sensitivity at high input rates. Finally, we discuss how the recognition of these cell-specific discrimination properties might further our understanding of neuronal network computations and their relationships to the distribution and functional connectivity of different neuronal types.

Effect of pulsing in low-level light therapy

BACKGROUND AND OBJECTIVE

Low level light (or laser) therapy (LLLT) is a rapidly growing modality used in physical therapy, chiropractic, sports medicine and increasingly in mainstream medicine. LLLT is used to increase wound healing and tissue regeneration, to relieve pain and inflammation, to prevent tissue death, to mitigate degeneration in many neurological indications. While some agreement has emerged on the best wavelengths of light and a range of acceptable dosages to be used (irradiance and fluence), there is no agreement on whether continuous wave or pulsed light is best and on what factors govern the pulse parameters to be chosen.

STUDY DESIGN/MATERIALS AND METHODS

The published peer-reviewed literature was reviewed between 1970 and 2010.

RESULTS

The basic molecular and cellular mechanisms of LLLT are discussed. The type of pulsed light sources available and the parameters that govern their pulse structure are outlined. Studies that have compared continuous wave and pulsed light in both animals and patients are reviewed. Frequencies used in other pulsed modalities used in physical therapy and biomedicine are compared to those used in LLLT.

CONCLUSION

There is some evidence that pulsed light does have effects that are different from those of continuous wave light. However further work is needed to define these effects for different disease conditions and pulse structures.

Near scale-free dynamics in neural population activity of waking/sleeping rats revealed by multiscale analysis

A neuron embedded in an intact brain, unlike an isolated neuron, participates in network activity at various spatial resolutions. Such multiple scale spatial dynamics is potentially reflected in multiple time scales of temporal dynamics. We identify such multiple dynamical time scales of the inter-spike interval (ISI) fluctuations of neurons of waking/sleeping rats by means of multiscale analysis. The time scale of large non-Gaussianity in the ISI fluctuations, measured with the Castaing method, ranges up to several minutes, markedly escaping the low-pass filtering characteristics of neurons. A comparison between neural activity during waking and sleeping reveals that non-Gaussianity is stronger during waking than sleeping throughout the entire range of scales observed. We find a remarkable property of near scale independence of the magnitude correlations as the primary cause of persistent non-Gaussianity. Such scale-invariance of correlations is characteristic of multiplicative cascade processes and raises the possibility of the existence of a scale independent memory preserving mechanism.

Effect of pulsing in low-level light therapy

BACKGROUND AND OBJECTIVE

Low level light (or laser) therapy (LLLT) is a rapidly growing modality used in physical therapy, chiropractic, sports medicine and increasingly in mainstream medicine. LLLT is used to increase wound healing and tissue regeneration, to relieve pain and inflammation, to prevent tissue death, to mitigate degeneration in many neurological indications. While some agreement has emerged on the best wavelengths of light and a range of acceptable dosages to be used (irradiance and fluence), there is no agreement on whether continuous wave or pulsed light is best and on what factors govern the pulse parameters to be chosen.

STUDY DESIGN/MATERIALS AND METHODS

The published peer-reviewed literature was reviewed between 1970 and 2010.

RESULTS

The basic molecular and cellular mechanisms of LLLT are discussed. The type of pulsed light sources available and the parameters that govern their pulse structure are outlined. Studies that have compared continuous wave and pulsed light in both animals and patients are reviewed. Frequencies used in other pulsed modalities used in physical therapy and biomedicine are compared to those used in LLLT.

CONCLUSION

There is some evidence that pulsed light does have effects that are different from those of continuous wave light. However further work is needed to define these effects for different disease conditions and pulse structures.

Fractals in the nervous system: conceptual implications for theoretical neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power-law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review.

History-dependent Dynamics in a Generic Model of Ion Channels - an Analytic Study

Recent experiments have demonstrated that the timescale of adaptation of single neurons and ion channel populations to stimuli slows down as the length of stimulation increases; in fact, no upper bound on temporal timescales seems to exist in such systems. Furthermore, patch clamp experiments on single ion channels have hinted at the existence of large, mostly unobservable, inactivation state spaces within a single ion channel. This raises the question of the relation between this multitude of inactivation states and the observed behavior. In this work we propose a minimal model for ion channel dynamics which does not assume any specific structure of the inactivation state space. The model is simple enough to render an analytical study possible. This leads to a clear and concise explanation of the experimentally observed exponential history-dependent relaxation in sodium channels in a voltage clamp setting, and shows that their recovery rate from slow inactivation must be voltage dependent. Furthermore, we predict that history-dependent relaxation cannot be created by overly sparse spiking activity. While the model was created with ion channel populations in mind, its simplicity and genericalness render it a good starting point for modeling similar effects in other systems, and for scaling up to higher levels such as single neurons which are also known to exhibit multiple time scales.

Adaptive response by state-dependent inactivation

Many membrane channels and receptors exhibit adaptive, or desensitized, response to a strong sustained input stimulus. A key mechanism that underlies this response is the slow, activity-dependent removal of responding molecules to a pool which is unavailable to respond immediately to the input. This mechanism is implemented in different ways in various biological systems and has traditionally been studied separately for each. Here we highlight the common aspects of this principle, shared by many biological systems, and suggest a unifying theoretical framework. We study theoretically a class of models which describes the general mechanism and allows us to distinguish its universal from system-specific features. We show that under general conditions, regardless of the details of kinetics, molecule availability encodes an averaging over past activity and feeds back multiplicatively on the system output. The kinetics of recovery from unavailability determines the effective memory kernel inside the feedback branch, giving rise to a variety of system-specific forms of adaptive response-precise or input-dependent, exponential or power-law-as special cases of the same model.

Predicting not to predict too much: how the cellular machinery of memory anticipates the uncertain future

Although the faculty of memory holds information about the past, it is mostly about the present and the future, because it permits adaptive responses to ongoing events as well as to events yet to come. Since many elements in the future are uncertain, the plasticity machinery that encodes memories in the brain has to operate under the assumption that stored information is likely to require fast and recurrent updating. This assumption is reflected at multiple levels of the brain, including the synaptic and the cellular level. Recent findings cast new light on how combinations of plasticity and metaplasticity mechanisms could permit the brain to balance over time between stability and plasticity of the information stored.

Multiple intermediate states precede pore block during N-type inactivation of a voltage-gated potassium channel

N-type inactivation of voltage-gated potassium channels is an autoinhibitory process that occurs when the N terminus binds within the channel pore and blocks conduction. N-type inactivation and recovery occur with single-exponential kinetics, consistent with a single-step reaction where binding and block occur simultaneously. However, recent structure-function studies have suggested the presence of a preinactivated state whose formation and loss regulate inactivation and recovery kinetics. Our studies on N-type inactivation of the Shaker-type AKv1 channel support a multiple-step inactivation process involving a series of conformational changes in distinct regions of the N terminus that we have named the polar, flex, and latch regions. The highly charged polar region forms interactions with the surface of the channel leading up to the side window openings between the T1 domain and the channel transmembrane domains, before the rate-limiting step occurs. This binding culminates with a specific electrostatic interaction between R18 and EDE161-163 located at the entrance to the side windows. The latch region appears to work together with the flex region to block the pore after polar region binding occurs. Analysis of tail currents for a latch region mutant shows that both blocked and unblocked states exist after the rate-limiting transition is passed. Our results suggest that at least two intermediate states exist for N-type inactivation: a polar region-bound state that is formed before the rate-limiting step, and a pre-block state that is formed by the flex and latch regions during the rate-limiting step.

Timescales of inference in visual adaptation

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

Adaptive transition rates in excitable membranes

Adaptation of activity in excitable membranes occurs over a wide range of timescales. Standard computational approaches handle this wide temporal range in terms of multiple states and related reaction rates emanating from the complexity of ionic channels. The study described here takes a different (perhaps complementary) approach, by interpreting ion channel kinetics in terms of population dynamics. I show that adaptation in excitable membranes is reducible to a simple Logistic-like equation in which the essential non-linearity is replaced by a feedback loop between the history of activation and an adaptive transition rate that is sensitive to a single dimension of the space of inactive states. This physiologically measurable dimension contributes to the stability of the system and serves as a powerful modulator of input–output relations that depends on the patterns of prior activity; an intrinsic scale free mechanism for cellular adaptation that emerges from the microscopic biophysical properties of ion channels of excitable membranes.

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

The response of a population of neurons to time-varying synaptic inputs can show a rich phenomenology, hardly predictable from the dynamical properties of the membrane's inherent time constants. For example, a network of neurons in a state of spontaneous activity can respond significantly more rapidly than each single neuron taken individually. Under the assumption that the statistics of the synaptic input is the same for a population of similarly behaving neurons (mean field approximation), it is possible to greatly simplify the study of neural circuits, both in the case in which the statistics of the input are stationary (reviewed in La Camera et al. in Biol Cybern, 2008) and in the case in which they are time varying and unevenly distributed over the dendritic tree. Here, we review theoretical and experimental results on the single-neuron properties that are relevant for the dynamical collective behavior of a population of neurons. We focus on the response of integrate-and-fire neurons and real cortical neurons to long-lasting, noisy, in vivo-like stationary inputs and show how the theory can predict the observed rhythmic activity of cultures of neurons. We then show how cortical neurons adapt on multiple time scales in response to input with stationary statistics in vitro. Next, we review how it is possible to study the general response properties of a neural circuit to time-varying inputs by estimating the response of single neurons to noisy sinusoidal currents. Finally, we address the dendrite-soma interactions in cortical neurons leading to gain modulation and spike bursts, and show how these effects can be captured by a two-compartment integrate-and-fire neuron. Most of the experimental results reviewed in this article have been successfully reproduced by simple integrate-and-fire model neurons.

Fractional differentiation by neocortical pyramidal neurons

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

Interpreting neurodynamics: concepts and facts

The dynamics of neuronal systems, briefly neurodynamics, has developed into an attractive and influential research branch within neuroscience. In this paper, we discuss a number of conceptual issues in neurodynamics that are important for an appropriate interpretation and evaluation of its results. We demonstrate their relevance for selected topics of theoretical and empirical work. In particular, we refer to the notions of determinacy and stochasticity in neurodynamics across levels of microscopic, mesoscopic and macroscopic descriptions. The issue of correlations between neural, mental and behavioral states is also addressed in some detail. We propose an informed discussion of conceptual foundations with respect to neurobiological results as a viable step to a fruitful future philosophy of neuroscience.

Probability distributions of the logarithm of inter-spike intervals yield accurate entropy estimates from small datasets

The maximal information that the spike train of any neuron can pass on to subsequent neurons can be quantified as the neuronal firing pattern entropy. Difficulties associated with estimating entropy from small datasets have proven an obstacle to the widespread reporting of firing pattern entropies and more generally, the use of information theory within the neuroscience community. In the most accessible class of entropy estimation techniques, spike trains are partitioned linearly in time and entropy is estimated from the probability distribution of firing patterns within a partition. Ample previous work has focused on various techniques to minimize the finite dataset bias and standard deviation of entropy estimates from under-sampled probability distributions on spike timing events partitioned linearly in time. In this manuscript we present evidence that all distribution-based techniques would benefit from inter-spike intervals being partitioned in logarithmic time. We show that with logarithmic partitioning, firing rate changes become independent of firing pattern entropy. We delineate the entire entropy estimation process with two example neuronal models, demonstrating the robust improvements in bias and standard deviation that the logarithmic time method yields over two widely used linearly partitioned time approaches.

Multi-timescale perceptual history resolves visual ambiguity

When visual input is inconclusive, does previous experience aid the visual system in attaining an accurate perceptual interpretation? Prolonged viewing of a visually ambiguous stimulus causes perception to alternate between conflicting interpretations. When viewed intermittently, however, ambiguous stimuli tend to evoke the same percept on many consecutive presentations. This perceptual stabilization has been suggested to reflect persistence of the most recent percept throughout the blank that separates two presentations. Here we show that the memory trace that causes stabilization reflects not just the latest percept, but perception during a much longer period. That is, the choice between competing percepts at stimulus reappearance is determined by an elaborate history of prior perception. Specifically, we demonstrate a seconds-long influence of the latest percept, as well as a more persistent influence based on the relative proportion of dominance during a preceding period of at least one minute. In case short-term perceptual history and long-term perceptual history are opposed (because perception has recently switched after prolonged stabilization), the long-term influence recovers after the effect of the latest percept has worn off, indicating independence between time scales. We accommodate these results by adding two positive adaptation terms, one with a short time constant and one with a long time constant, to a standard model of perceptual switching.

The power law of sensory adaptation: simulation by a model of excitability in spider mechanoreceptor neurons

The power law of sensory adaptation was introduced more than 50 years ago. It is characterized by action potential adaptation that follows fractional powers of time or frequency, rather than exponential decays and corresponding frequency responses. Power law adaptation describes the responses of a range of vertebrate and invertebrate sensory receptors to deterministic stimuli, such as steps or sinusoids, and to random (white noise) stimulation. Hypotheses about the physical basis of power law adaptation have existed since its discovery. Its cause remains enigmatic, but the site of power law adaptation has been located in the conversion of receptor potentials into action potentials in some preparations. Here, we used pseudorandom noise stimulation and direct spectral estimation to show that simulations containing only two voltage activated currents can reproduce the power law adaptation in two types of spider mechanoreceptors. Identical simulations were previously used to explain the different responses of these two types of sensory neurons to step inputs. We conclude that power law adaptation results during action potential encoding by nonlinear combination of a small number of activation and inactivation processes with different exponential time constants.

Sodium pumps adapt spike bursting to stimulus statistics

Pump activity is a homeostatic mechanism that maintains ionic gradients. Here we examined whether the slow reduction in excitability induced by sodium-pump activity that has been seen in many neuronal types is also involved in neuronal coding. We took intracellular recordings from a spike-bursting sensory neuron in the leech Hirudo medicinalis in response to naturalistic tactile stimuli with different statistical distributions. We show that regulation of excitability by sodium pumps is necessary for the neuron to make different responses depending on the statistical context of the stimuli. In particular, sodium-pump activity allowed spike-burst sizes and rates to code not for stimulus values per se, but for their ratio with the standard deviation of the stimulus distribution. Modeling further showed that sodium pumps can be a general mechanism of adaptation to statistics on the time scale of 1 min. These results implicate the ubiquitous pump activity in the adaptation of neural codes to statistics.

Sensory adaptation

Adaptation occurs in a variety of forms in all sensory systems, motivating the question: what is its purpose? A productive approach has been to hypothesize that adaptation helps neural systems to efficiently encode stimuli whose statistics vary in time. To encode efficiently, a neural system must change its coding strategy, or computation, as the distribution of stimuli changes. Information theoretic methods allow this efficient coding hypothesis to be tested quantitatively. Empirically, adaptive processes occur over a wide range of timescales. On short timescales, underlying mechanisms include the contribution of intrinsic nonlinearities. Over longer timescales, adaptation is often power-law-like, implying the coexistence of multiple timescales in a single adaptive process. Models demonstrate that this can result from mechanisms within a single neuron.

Models and Properties of Power-Law Adaptation in Neural Systems

Many biological systems exhibit complex temporal behavior that cannot be adequately characterized by a single time constant. This dynamics, observed from single channels up to the level of human psychophysics, is often better described by power-law rather than exponential dependences on time. We develop and study the properties of neural models with scale-invariant, power-law adaptation and contrast them with the more commonly studied exponential case. Responses of an adapting firing-rate model to constant, pulsed, and oscillating inputs in both the power-law and exponential cases are considered. We construct a spiking model with power-law adaptation based on a nested cascade of processes and show that it can be “programmed” to produce a wide range of time delays. Finally, within a network model, we use power-law adaptation to reproduce long-term features of the tilt aftereffect.

Multiple time scales of temporal response in pyramidal and fast spiking cortical neurons

Neural dynamic processes correlated over several time scales are found in vivo, in stimulus-evoked as well as spontaneous activity, and are thought to affect the way sensory stimulation is processed. Despite their potential computational consequences, a systematic description of the presence of multiple time scales in single cortical neurons is lacking. In this study, we injected fast spiking and pyramidal (PYR) neurons in vitro with long-lasting episodes of step-like and noisy, in-vivo-like current. Several processes shaped the time course of the instantaneous spike frequency, which could be reduced to a small number (1-4) of phenomenological mechanisms, either reducing (adapting) or increasing (facilitating) the neuron's firing rate over time. The different adaptation/facilitation processes cover a wide range of time scales, ranging from initial adaptation (<10 ms, PYR neurons only), to fast adaptation (<300 ms), early facilitation (0.5-1 s, PYR only), and slow (or late) adaptation (order of seconds). These processes are characterized by broad distributions of their magnitudes and time constants across cells, showing that multiple time scales are at play in cortical neurons, even in response to stationary stimuli and in the presence of input fluctuations. These processes might be part of a cascade of processes responsible for the power-law behavior of adaptation observed in several preparations, and may have far-reaching computational consequences that have been recently described.

Two-dimensional time coding in the auditory brainstem

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