Single neuron dynamics models linking theory and experiment
this is caused by the fact that ai is not in its steady state after the switch and needs time to approach its new equilibrium value. ultimately, combining biophysical and functional knowledge should yield a coherent picture of adaptation. other examples for multiple input channels are visual stimuli at different locations within the receptive field and odor constituents that lead to different dependences of the neural response on odor concentration. of kuramoto model showing neural synchronization and oscillations in the mean field. for the switch from the high-intensity 10 khz to the low-intensity 4 khz stimulus, the deflection is in the downward direction and, correspondingly, δr is negative. the auditory nerve contains the axons of the receptor neurons. because stimulus intensity s and output firing rate r are usually tightly coupled (for higher intensity, the firing rate is also higher), both processes tend to work in the same direction. this phenomenon is best seen in local field potentials which reflect the synchronous activity of local groups of neurons, but has also been shown in eeg and meg recordings providing increasing evidence for a close relation between synchronous oscillatory activity and a variety of cognitive functions such as perceptual grouping. purely theoretical formulations of the binding-by-synchrony hypothesis were proposed first, but subsequently extensive experimental evidence has been reported supporting the potential role of synchrony as a relational code. neural oscillations could create periodic time windows in which input spikes have larger effect on neurons, thereby providing a mechanism for decoding temporal codes. evoked potentials and event-related potentials are obtained from an electroencephalogram by stimulus-locked averaging, i. for g(x) = x, ao,∞(r) = α·r, and ai,∞(s) = β·r, with proportionality constants α and β, the mathematical solution is given in the appendix. natural stimuli for grasshoppers, such as their courtship songs, usually contain broad carrier-frequency bands (von helversen and von helversen, 1994; stumpner and von helversen, 2001)..Vilin yy, ruben pc (2001) slow inactivation in voltage-gated sodium channels: molecular substrates and contributions to channelopathies. linear oscillators and limit-cycle oscillators qualitatively differ in terms of how they respond to fluctuations in input. since then, numerous studies have replicated these findings and extended them to different modalities such as eeg, providing extensive evidence of the functional role of gamma oscillations in visual perception., 2001) and to allow discrimination between slightly different songs (machens et al. however, for a biophysical interpretation or for understanding the response to dynamical, fluctuating stimuli, such a distinction will be important..French as (1984b) the receptor potential and adaptation in the cockroach tactile spine. however, the experimental assessment of input-driven adaptation that we used in this study is independent of whether the adaptation components act in a subtractive or divisive manner. used various sound frequencies between 1 and 15 khz covering approximately the whole range of sensitivity of the recorded receptor neurons. quantitative models can estimate the strength of neural oscillations in recorded data. have identified some intrinsic neuronal properties that play an important role in generating membrane potential oscillations. models based on these principles have been used to provide mathematical descriptions of neural oscillations and eeg rhythms. dh, smith dv, shick tr (1972) gustatory cross adaptation: sourness and bitterness. in the absence of extrinsic neural and hormonal control, cells in the sa node will rhythmically discharge. a number of nuclei in the brainstem have diffuse projections throughout the brain influencing concentration levels of neurotransmitters such as norepinephrine, acetylcholine and serotonin. sound intensities s1 and s2 were chosen so that the recorded neuron had the same (predefined) firing rate r for both tones in the steady state. the stimulus switch occurred in each case after half the stimulus duration, and the parameter values shown in the plots indicate the sound frequency and intensity of the tones before and after the switch.
Input-Driven Components of Spike-Frequency Adaptation Can Be
among the most important are harmonic (linear) oscillators, limit cycle oscillators, and delayed-feedback oscillators. ck, schütze h, franz a, kolesnikova o, stemmler mb, ronacher b, herz avm (2003) single auditory neurons rapidly discriminate conspecific communication signals. oscillations have been most widely studied in neural activity generated by large groups of neurons. theses biomarkers are often named "eeg biomarkers" or "neurophysiological biomarkers" and are quantified using quantitative electroencephalography (qeeg). orchestrates protein kinase a and β2-adrenergic receptor signaling critical for synaptic plasticity and memory. it is a set of nonlinear ordinary differential equations that approximates the electrical characteristics of a neuron, in particular the generation and propagation of action potentials. however, if the probability of a large group of neurons is rhythmically modulated at a common frequency, they will generate oscillations in the mean field (see also figure at top of page). an in-depth analysis of the firing-rate transients may then reveal details of the adaptation dynamics.., subtractive or divisive) and regardless of the exact dynamics of ao and ai, as long as ao is determined only by r. here, we systematically test for additional input-driven adaptation components and their effects on the spiking activity of the auditory receptors by analyzing in vivo recordings of spike trains from single fibers in the auditory nerve. spikes were recorded and used to calculate the neural response for each stimulus. they generally arise when a physical system is perturbed by a small degree from a minimum-energy state, and are well-understood mathematically. in particular, we determined for different sound frequencies those intensities that are required to yield a predefined steady-state firing rate of the neuron. because the two switching directions lead to different signs of δr, we analyzed δrlh and δrhl separately. the dynamics of these ion channels have been captured in the well-established hodgkin–huxley model that describes how action potentials are initiated and propagated by means of a set of differential equations. many models are used in the field, each defined at a different level of abstraction and trying to model different aspects of neural systems. if only output-driven adaptation was present, the firing rate should stay at the constant steady-state level; in contrast, input-driven adaptation components will be disequilibrated and therefore transiently affect the firing rate. 3 shows a collection of such data from four different recorded receptor neurons. for example, retinal waves are thought to have properties that define early connectivity of circuits and synapses between cells in the retina. spikes were detected on-line from the recorded voltage trace with the custom-made on-line electrophysiology laboratory software and used for on-line calculations of firing rates and automatic tuning of the sound intensities. the firing rate is initially high and decays during the first few hundred milliseconds. a major area of research in neuroscience involves determining how oscillations are generated and what their roles are. kj, rieke f (2003) slow na+ inactivation and variance adaptation in salamander retinal ganglion cells. the steady-state level of firing is equal for the two tones, and the initial firing-rate transients after stimulus onset are also strikingly similar. size and time constants of the effect vary considerably between cells (note the different scales on the x- and y-axes), but the direction of the firing-rate deflection has a clear relationship with the direction of the switch; switches from lower to higher sound intensity lead to upward deflections and vice versa. if numerous neurons spike in synchrony, they can give rise to oscillations in local field potentials. here, we modify this approach by using stimuli that are tuned to the same output level and therefore should cross-adapt each other according to pure output-driven adaptation. insight about the functional roles of input-driven and output-driven adaptation may result from comparisons with other sensory modalities. neural tissue can generate oscillatory activity in many ways, driven either by mechanisms within individual neurons or by interactions between neurons.
Single Neuron Dynamics — Models Linking Theory and Experiment
neurons can generate multiple action potentials in sequence forming so-called spike trains. by its resonance properties, the tympanic membrane filters the sound wave and is thereby responsible for the different sensitivities at different sound frequencies in single receptor neurons (michelsen, 1971b; schiolten et al. consequently, neural oscillations have been linked to cognitive states, such as awareness and consciousness. these experiments showed that groups of spatially segregated neurons engage in synchronous oscillatory activity when activated by visual stimuli. we tested for correlations between the parameters describing input-driven adaptation (its strength and time constant) and parameters describing the stimulation (intensities, evoked firing rates).: we request your email address only to inform the recipient that it was you who recommended this article, and that it is not junk mail. the kuramoto model is widely used to study oscillatory brain activity and several extensions have been proposed that increase its neurobiological plausibility, for instance by incorporating topological properties of local cortical connectivity. contrast to the model, the time courses of upward and downward deflections are not symmetric. field models are another important tool in studying neural oscillations and are a mathematical framework describing evolution of variables such as mean firing rate in space and time..Chander d, chichilnisky ej (2001) adaptation to temporal contrast in primate and salamander retina. this allows the simulation of a large number of interconnected neurons that form a neural network. from intrinsic properties of neurons, network properties are also an important source of oscillatory activity. the following two simple explanations of this correlation are therefore possible: (1) the strength and time constant of input-driven adaptation within a neuron are directly coupled, or (2) a larger effect of input-driven adaptation leads to a larger contribution of the corresponding time constant to the mixture reflected in the firing-rate transient. single neurons and groups of neurons can generate oscillatory activity spontaneously. for example, when a person looks at a tree, visual cortex neurons representing the tree trunk and those representing the branches of the same tree would oscillate in synchrony to form a single representation of the tree. the first-order dynamics and the subtractive contribution of ao and ai as well as the instantaneous function for r are chosen merely for mathematical simplicity and are not crucial for the conclusions that we will draw from the model. other frequency bands are: delta (1–4 hz), theta (4–8 hz), beta (13–30 hz) and gamma (30–70 hz) frequency band, where faster rhythms such as gamma activity have been linked to cognitive processing. we thank olga kolesnikova and hartmut schütze for assistance with the experiments and jan benda for helpful discussions..Torkkeli ph, sekizawa s, french as (2001) inactivation of voltage-activated na(+) currents contributes to different adaptation properties of paired mechanosensory neurons.., a single neuron or neural ensemble) by its circular phase alone and hence ignores the amplitude of oscillations (amplitude is constant). we found that δrlh and δrhl are not correlated with δrl (fig. upward or downward deflection of the firing rate can be used to characterize the direction, strength, and time constant of the adaptation process ai. dao/dt and dai/dt symbolize the temporal derivatives of ao and ai, respectively, leading to first-order differential equations that capture the build-up and decay of adaptation. for each recorded receptor neuron, we identified stimuli with different sound frequencies that evoke the same steady-state firing rate. we fitted exponential curves to the firing-rate differences after the switch to obtain the initial firing-rate difference, δr, and the decay time constant, τ. the initial firing-rate difference, δr, and the decay time constant, τ, are obtained from exponential fits of the firing-rate transients after the stimulus switch. frequency of ongoing oscillatory activity is increased between t1 and t2. oscillations are commonly studied from a mathematical framework and belong to the field of "neurodynamics", an area of research in the cognitive sciences that places a strong focus upon the dynamic character of neural activity in describing brain function. subsequent stages of the transduction chain obtain only information about the filtered stimulus intensities and thus cannot induce an adaptation mechanism that is triggered by the absolute intensity level.
Neural oscillation - Wikipedia these seizures are transient signs and/or symptoms of abnormal, excessive or hypersynchronous neuronal activity in the brain. in particular, some forms of bci allow users to control a device by measuring the amplitude of oscillatory activity in specific frequency bands, including mu and beta rhythms. neurons in a neural ensemble rarely all fire at exactly the same moment, i. as such, the frequency of large-scale oscillations does not need to match the firing pattern of individual neurons. in individual neurons, oscillations can appear either as oscillations in membrane potential or as rhythmic patterns of action potentials, which then produce oscillatory activation of post-synaptic neurons. we model the response of a sensory neuron to external input (e. "resting gaba concentration predicts peak gamma frequency and fmri amplitude in response to visual stimulation in humans". between build-up and decay of adaptation also have been observed in other systems (smirnakis et al.., a stimulus with sound frequency and intensity that were constant and equaled those in the second half of the switch stimulus) (fig. the sound stimulus is successively transformed, the sound pressure waves cause oscillations of the tympanic membrane, the animal's ear drum, which in turn leads to the opening of mechanosensory ion channels in the attached receptor neurons, and finally the induced transduction currents may trigger action potentials (gray, 1960; michelsen, 1971a; hill, 1983a,b). clarify the idea of input-driven and output-driven adaptation, we investigate a minimal model that contains both of these mechanisms.. resonance behavior that does not result in action potentials, may also contribute to oscillatory activity by facilitating synchronous activity of neighboring neurons. hence, these cells generate the normal sinus rhythm and are called pacemaker cells as they directly control the heart rate. laurent and colleagues showed that oscillatory synchronization has an important functional role in odor perception..Madison dv, nicoll ra (1984) control of the repetitive discharge of rat ca1 pyramidal neurones in vitro. "the intrinsic electrophysiological properties of mammalian neurons: a new insight into cns function". "a mechanism for cognitive dynamics: neuronal communication through neuronal coherence". these oscillations are also observed in motor output of physiological tremor and when performing slow finger movements. 2c shows schematic drawings of the sounds used to investigate this neuron. the somata of the receptor neurons are contained in the auditory ganglion on the inner side of the tympanum. we analyzed spike-train responses recorded in vivo from auditory receptor neurons in locusts. noise-driven harmonic oscillators realistically simulate alpha rhythm in the waking eeg as well as slow waves and spindles in the sleep eeg. addition to fast direct synaptic interactions between neurons forming a network, oscillatory activity is modulated by neurotransmitters on a much slower time scale. therefore, when both a bottom and a top bound for the required intensity were found, additional measurements for five intensities in the determined range in steps of 1 db were repeated four to six times. "breaking the silence: brain-computer interfaces (bci) for communication and motor control". gollischfind this author on google scholarfind this author on pubmedsearch for this author on this siteandreas v.., the model neuron is more sensitive to some stimuli than to others). these oscillations can be disrupted by gaba blocker picrotoxin, and the disruption of the oscillatory synchronization leads to impairment of behavioral discrimination of chemically similar odorants in bees and to more similar responses across odors in downstream β-lobe neurons. for instance, the amplitude and phase of alpha activity at the moment of visual stimulation predicts whether a weak stimulus will be perceived by the subject.
Single Neuron Dynamics — Models Linking Theory and Experiment
frequency changes are also commonly observed in central pattern generators and directly relate to the speed of motor activities, such as step frequency in walking. of the temporary change of the firing rate, the adaptation component ao also shows a small transient deflection and then resumes its original steady-state value.. we performed intracellular recordings from axons of receptor neurons in the auditory nerve of adult locusta migratoria. note that in this model, r is not given by a differential equation but by an instantaneous function of s, ao, and ai. b, firing rate r and the two adaptation components ao and ai for a stimulation where the stimulus is switched from x to y at time t = 1 sec. in contrast, other components of adaptation may be caused by, in a feedforward way, the sensory or synaptic input, which the neuron receives. oscillatory activity in single neurons can also be observed in sub-threshold fluctuations in membrane potential. neurons can generate rhythmic patterns of action potentials or spikes. "a dendritic mechanism for decoding traveling waves: principles and applications to motor cortex". the measured firing-rate transients thus correspond to the decay and the build-up of input-driven adaptation, respectively. this may be caused by a slow component present in the decay of input-driven adaptation, but its origin and possible function remain to be elucidated. neural oscillations and synchronization have been linked to many cognitive functions such as information transfer, perception, motor control and memory. the predefined firing rates for all recordings lay between 50 and 150 hz, and experiments were performed for stimulus lengths t of 800, 1200, or 1500 msec. only the initial and final 2 msec of each part are displayed to show the half-millisecond linear increase or decrease used for stimulus onset, offset, and the switch. in the model, the output activity (firing rate r) is a function of s and an input-driven adaptation component, ai, as well as an output-driven component, ao:The function g(x) captures the stimulus-response function of the neuron and may typically include rectification and saturation. here, we demonstrate how an input-driven component of adaptation can be uncovered in vivo from recordings of spike trains in an insect auditory receptor neuron, even if the total adaptation is dominated by output-driven components. the frequency of these oscillations was in the range of 40 hz and differed from the periodic activation induced by the grating, suggesting that the oscillations and their synchronization were due to internal neuronal interactions. it is very common in single neurons where spike timing is adjusted to neuronal input (a neuron may spike at a fixed delay in response to periodic input, which is referred to as phase locking) and may also occur in neuronal ensembles when the phases of their neurons are adjusted simultaneously. the observed phenomenon might be a consequence of the mechanical constraints and nonlinear properties that come with the specific way of stimulus coupling. the first discovered and best-known frequency band is alpha activity (7. neurons are locally connected, forming small clusters that are called neural ensembles. using bifurcation analysis, different oscillatory varieties of these neuronal models can be determined, allowing for the classification of types of neuronal responses. models adopt a variety of abstractions in order to describe complex oscillatory dynamics observed in brain activity. for example, the activity of an auditory neuron does not depend only on the sound intensity but also on the sensitivity of the neuron to the sound frequency of the stimulus, and a visual neuron may respond to light intensity but with an additional dependence on how well the stimulus overlaps with the spatial receptive field or spectral sensitivity of the neuron. and characterization of a sleep-active cell group in the rostral medullary brainstem. upper panel shows spiking of individual neurons (with each dot representing an individual action potential within the population of neurons), and the lower panel the local field potential reflecting their summed activity. "oscillatory properties of guinea-pig inferior olivary neurones and their pharmacological modulation: an in vitro study". these tuning effects are captured by the factor kn, where the index n stands for the different applied types of stimuli; if the neuron is more sensitive to a particular stimulus, kn will be larger..Breckow j, sippel m (1985) mechanics of the transduction of sound in the tympanal organ of adults and larvae of locusts.
Single neuron dynamics and computation
a-f, the panels display the relationships between δr,τ, the sound intensities s1 and s2, and the total level of adaptation after stimulus onset, δrl for the lower intensity and δrh for the higher intensity. has recently been proposed that even if phases are not aligned across trials, induced activity may still cause event-related potentials because ongoing brain oscillations may not be symmetric and thus amplitude modulations may result in a baseline shift that does not average out. in particular, it aims to relate dynamic patterns of brain activity to cognitive functions such as perception and memory. examples include viscoelasticity of mechanoreceptors, transducer adaptation in hair cells, and short-term synaptic depression. resetting occurs when input to a neuron or neuronal ensemble resets the phase of ongoing oscillations. depending on the properties of the connection, such as the coupling strength, time delay and whether coupling is excitatory or inhibitory, the spike trains of the interacting neurons may become synchronized..Stephen ro, bennet-clark hc (1982) the anatomical and mechanical basis of stimulation and frequency analysis in the locust ear. after the switch, the input-driven adaptation slowly builds up to its new level and, consequently, the firing rate decays back to the steady-state level. 3a-c), presumably because the dynamics are governed strongly by output-driven adaptation. the functional characterization of how adaptation depends on the input and output of the neuron is of particular relevance for investigating the neurons from a signal-processing perspective. examples are the generation of rhythmic activity such as a heartbeat and the neural binding of sensory features in perception, such as the shape and color of an object. functional role of synchronized oscillatory activity in the brain was mainly established in experiments performed on awake kittens with multiple electrodes implanted in the visual cortex.., switches from lower to higher sound intensity) generally cause upward deflections of the firing rate (δrlh > 0) and vice versa (fig. in general, however, the correspondence between the biophysical mechanisms and the functional dependence is not always straightforward. bursting neurons have the potential to serve as pacemakers for synchronous network oscillations, and bursts of spikes may underlie or enhance neuronal resonance. however, the auditory ganglion, which contains the receptor-cell somata and is attached to the tympanum, also vibrates during sound stimulation (stephen and bennet-clark, 1982) and thus contributes to the mechanical deformations that induce transduction. note that there is no synapse between the site of mechanosensory transduction and the fibers in the auditory nerve, in contrast to the mammalian inner ear. in particular, inhibitory interneurons play an important role in producing neural ensemble synchrony by generating a narrow window for effective excitation and rhythmically modulating the firing rate of excitatory neurons. the sound intensity in the first half of the switch stimulus is denoted by s1 and in the second half by s2. in the pacinian corpuscle, the viscoelasticity of the capsule leads to a characteristic rapid adaptation (hubbard, 1958; loewenstein and mendelson, 1965), and mammalian hearing systems are influenced by adaptation of the transducer currents (ricci et al. "driving fast-spiking cells induces gamma rhythm and controls sensory responses". output-driven adaptation will consequently be higher during presentation of tone x, and after the switch to tone y, the firing rate will be transiently reduced while this adaptation component decays to the steady-state level of tone y. in the present case, the most striking difference between upward and downward deflections of the firing rate is that in some cells, the firing rate fails to reach the original level after a switch to lower intensity. many neurons, a major contribution to spike-frequency adaptation stems from output-driven components triggered by the spiking activity of the neuron itself. the possible roles of neural oscillations include feature binding, information transfer mechanisms and the generation of rhythmic motor output. for a functional characterization of adaptation, we therefore need to identify the causal relationships between sensory input, neural activity, and the level of adaptation (cf. the two traces show spike trains measured in an auditory nerve fiber during 750 msec stimulation (black bar) with pure tones of 3 and 7 khz and intensities of 78 and 83 db spl, respectively. in modeling the activity of large numbers of neurons, the central idea is to take the density of neurons to the continuum limit, resulting in spatially continuous neural networks. the firing rates and adaptation components are calculated according to the equations introduced in this paper (solutions can be found in appendix).
The Origin of Adaptation in the Auditory Pathway of Locusts Is
"prestimulus oscillatory activity in the alpha band predicts visual discrimination ability". during the experiments, the animals were kept at a constant temperature of 30°c by heating the peltier element. this is especially advantageous when intracellular recordings from the soma or dendrites are not available, and the application of biomedical agents, such as channel blockers, is difficult or impossible. the interaction between neurons can give rise to oscillations at a different frequency than the firing frequency of individual neurons. perceiving different odors leads to different subsets of neurons firing on different sets of oscillatory cycles. oscillatory activity may respond by increases or decreases in frequency and amplitude or show a temporary interruption, which is referred to as phase resetting. at the switch, the response transient is determined primarily by the dynamics of ai, because ao stays near its equilibrium point all the time. it is the most common of all involuntary movements and can affect the hands, arms, eyes, face, head, vocal cords, trunk, and legs. "distinct mechanisms for synchronization and temporal patterning of odor-encoding neural assemblies". some types of neurons will fire rhythmically in the absence of any synaptic input..Heinrich ts, bach m (2002) contrast adaptation: paradoxical effects when the temporal frequencies of adaptation and test differ. indications that spike-frequency adaptation in locust auditory receptor neurons is primarily output driven come from the dependence of the adaptation time constants on the firing rate of the receptors (benda et al. extended experiments could test these hypotheses by repeating the measurements with different sets of stimulus intensities for the same cell. the time constant of ao is rescaled by the factor 1/(α + 1) leading to faster dynamics as a result of the feedback between r and ao. performing the same experiment with more than just two tones could help answer this question, because the resulting set of firing-rate differences may suggest a certain functional dependence of the level of input-driven adaptation on the sound intensity..Sah p, davies p (2000) calcium-activated potassium currents in mammalian neurons. for each recording, two different sound frequencies were chosen, and all of the four resulting combinations for the first and second stimulus sections were presented alternately and repeated 20-150 times, depending on the length of the recording. detailed experimental setup has been described previously (gollisch et al. in the sensory periphery, several mechanosensitive receptor neurons are influenced by adaptation components that are driven by the sensory input. this can be viewed as a quasistatic approximation, which is valid if the time constants of adaptation, τo and τi, are considerably longer than those governing the dynamics of r (e. our method is based on the identification of different inputs that yield the same output and sudden switches between these inputs. tremor is an involuntary, somewhat rhythmic, muscle contraction and relaxation involving to-and-fro movements of one or more body parts. "the oscillation score: an efficient method for estimating oscillation strength in neuronal activity". oscillations are sensitive to several drugs influencing brain activity; accordingly, biomarkers based on neural oscillations are emerging as secondary endpoints in clinical trials and in quantifying effects in pre-clinical studies. model of a biological neuron is a mathematical description of the properties of nerve cells, or neurons, that is designed to accurately describe and predict its biological processes. because the neurons have different sensitivity for different sound frequencies, these intensities will generally be different. interactions amongst these oscillators are introduced by a simple algebraic form (such as a sine function) and collectively generate a dynamical pattern at the global scale. to distinguish between the two directions of the switch, the parameters are labeled δrlh, τlh for switches from lower to higher intensity, and δrhl, τhl for switches from higher to lower intensity, and the data are plotted as open circles and filled squares, respectively. important aspect of the model is that the dynamics of ao and ai depend on only the firing rate r, output of the neuron, stimulus intensity s, and input of the neuron, respectively, and that ao and ai take on steady-state values ao,∞(r) and ai,∞(s), which are only functions of r and s, respectively.
The Dynamic Brain: From Spiking Neurons to Neural Masses and
Spike-Train Variability of Auditory Neurons In Vivo: Dynamic
the spikes result in activation of calcium-dependent (madison and nicoll, 1984; vergara et al. class i neurons can generate action potentials with arbitrarily low frequency depending on the input strength, whereas class ii neurons generate action potentials in a certain frequency band, which is relatively insensitive to changes in input strength. for higher-order neurons, it may be applied to disentangle adaptation contributions that are caused by the activity of the investigated neuron itself and those that are inherited from previous processing steps such as short-term synaptic plasticity. basic requirements of the approach are that the investigated neuron (1) receives two or more input channels that can be independently controlled, (2) combines the signals from these input channels so that they converge to the same output channel, and (3) adopts a steady-state activity that can be tuned to be equal for the different input channels. activity is brain activity in the absence of an explicit task, such as sensory input or motor output, and hence also referred to as resting-state activity. 1) and suggests an extension where the time constant τi differs for build-up and decay or explicitly depends on the intensity level, s. these models aim to describe how the dynamics of neural circuitry arise from interactions between individual neurons. neural ensembles can generate oscillatory activity endogenously through local interactions between excitatory and inhibitory neurons.. figure 1 shows examples of firing rates obtained for the model with time constants τo = 50 msec, τi = 150 msec, and parameters α = 0. neurons communicate with one another via synapses and affect the timing of spike trains in the post-synaptic neurons. these mechanisms of output-driven and input-driven adaptation may have different biophysical origins compared with auditory receptor cells but could constitute analogous functional operations. in our experimental data, the following two facts indicate that the output is not affected by such strong nonlinearities, at least in the range of the observed firing-rate deflections, usually several tens of hertz: (1) the simple exponential shape of the transients, and (2) the approximate symmetry between the initial firing-rate differences for upward and downward deflections (fig. 1), we used a linear relationship between the stimulus intensity and the firing rate. for higher-order neurons, a similar analysis may be used to reveal contributions from adaptation in the afferent pathways in contrast to cell-intrinsic adaptation mechanisms. 4f shows that the time constants of the firing-rate deflections are distributed over a wide range between 10 and 300 msec. "collective frequencies and metastability in networks of limit-cycle oscillators with time delay". 4e) as seen in the correlation between δrhl and δrlh (p = -0. as a start, we distinguished between input-driven and output-driven components in the present study. for example, a non-invasive bci interface can be created by placing electrodes on the scalp and then measuring the weak electric signals. the term ongoing brain activity is used in electroencephalography and magnetoencephalography for those signal components that are not associated with the processing of a stimulus or the occurrence of specific other events, such as moving a body part, i.., wakefulness or arousal, and have a pronounced effect on amplitude of different brain waves, such as alpha activity. on the insight gained from this minimal model, we thus proceed as follows to experimentally detect and analyze input-driven adaptation. they can result from postsynaptic potentials from synchronous inputs or from intrinsic properties of neurons. in all experiments, both directions of switching were used, from the low-intensity to the high-intensity tone (left column) and vice versa (right column). if the time constants τo and τi are also similar, the two types of adaptation will be hard to distinguish. for example, one of the best known types is the spike and wave oscillation, which is typical of generalized or absence epileptic seizures, and which resembles normal sleep spindle oscillations. likewise, short-term synaptic plasticity can contribute to adaptation in a feedforward way (best and wilson, 2004). the electric potentials generated by single neurons are far too small to be picked up outside the scalp, and eeg or meg activity always reflects the summation of the synchronous activity of thousands or millions of neurons that have similar spatial orientation. "exploring mechanisms of spontaneous functional connectivity in meg: how delayed network interactions lead to structured amplitude envelopes of band-pass filtered oscillations".
some types of neurons have the tendency to fire at particular frequencies, so-called resonators. "oscillatory activity in sensorimotor cortex of awake monkeys: synchronization of local field potentials and relation to behavior". the most successful and widely used model of neurons, the hodgkin–huxley model, is based on data from the squid giant axon. total level of adaptation after the initial stimulus onset is denoted by δrl for the lower intensity tone and by δrh for the higher intensity tone. the latter is true regardless of the exact dependence of r on ao and ai (e. weakly coupled oscillators can generate a range of dynamics including oscillatory activity. because induced responses may have different phases across measurements and therefore would cancel out during averaging, they can only be obtained using time-frequency analysis. "in vitro neurons in mammalian cortical layer 4 exhibit intrinsic oscillatory activity in the 10- to 50-hz frequency range". each neuron is attached to the tympanum via a short dendrite, a cilium, which protrudes from the distal tip of the dendrite, and an attachment cell, which forms the connection between the tympanum and the cilium (gray, 1960). oscillations are also thought be involved in the sense of time and in somatosensory perception. if the adaptation components would follow more complicated dynamics, the stimulus switches should also result in firing-rate transients only if input-driven adaptation is present. "coherent oscillations in monkey motor cortex and hand muscle emg show task-dependent modulation". recordings were obtained with standard glass microelectrodes (borosilicate, gc100f-10; harvard apparatus, edenbridge, uk) filled with 1 mol/1 kcl, and acoustic stimuli were delivered by loudspeakers (esotec d-260; dynaudio, skanderborg, denmark) on a stereo power amplifier (dca-450; denon electronic gmbh, ratingen, germany) ipsilateral to the recorded auditory nerve. in short, the animal was waxed to a peltier element; the head, legs, wings, and intestines were removed, and the auditory nerves were exposed. we compared the responses from sound presentations for which f1 and f2 as well as s1 and s2 differed (switch stimuli) to responses from presentations for which f1 = f2 and s1 = s2 (pure stimuli). shown by our data, the induced firing-rate deflections can be used to characterize prominent features of this adaptation component such as its strength, time constants, and correlation with different stimulus and activity parameters. these large-scale oscillations can also be measured outside the scalp using electroencephalography (eeg) and magnetoencephalography (meg). class ii neurons are also more prone to display sub-threshold oscillations in membrane potential. the neural activity in these cells shows strong adaptation to prolonged acoustic stimulation and eventually settles to a steady-state firing rate under stationary stimulus conditions. they range from models of the short-term behaviour of individual neurons, through models of how the dynamics of neural circuitry arise from interactions between individual neurons, to models of how behaviour can arise from abstract neural modules that represent complete subsystems. from the firing rate rswitch(t) obtained with the switch stimulus that first contained frequency f1 and then f2, we subtracted the firing rate rpure(t) of the pure stimulus containing f2 in both sections. the fact that equal firing rates lead to approximately equal time courses of adaptation thus indicates that the dynamics of adaptation are governed primarily by the firing rate (i..Brown da, adams pr (1980) muscarinic suppression of a novel voltage-sensitive k+ current in a vertebrate neurone. for example, as originally suggested by matthews (1931, 1933), muscle stress relaxation contributes to adaptation in vertebrate muscle spindles and tendon organs. the oscillatory dynamics of neuronal spiking as identified in the hodgkin–huxley model closely agree with empirical findings. this shows that input-driven adaptation is a general phenomenon in these neurons. correlation coefficients ρ and corresponding p values were calculated with the matlab statistical toolbox (version 6. adaptation terms ao and ai have similar effects for constant stimuli. this work, we aimed to uncover and analyze putative input-driven components in locust auditory receptor neurons, a model system for the mechanosensitive auditory transduction process.
. a high- and low-amplitude mode, and hence shows that resting-state activity does not just reflect a noise process. 1), but in experiments, such a tuning relies on noisy data and is never perfect. consequently, we observed a strong correlation between s2 - s1 and the complete set of values for δr (ρ = 0. analogously, we calculated the difference between the firing rates for the switch stimulus containing first f2 and then f1 and the pure stimulus containing only f1. aj, wu y-c, fettiplace r (1998) the endogenous calcium buffer and the time course of transducer adaptation in auditory hair cells..Shriki o, hansel d, sompolinsky h (2003) rate models for conductance-based cortical neuronal networks. for each sound frequency, stimuli of length t/2 were presented, and the firing rate was calculated from the spike count in the last 100 msec of the presentation. approach, which we have used to reveal input-driven adaptation components, experimentally depends on measurements of the neuronal firing rate. the context of the present study, we need the solution for stimulus onset and after the switch. in contrast, the relevant output signals of sensory neurons are usually considerably smaller in dimension; for stationary signals, the firing rate may suffice to describe the activity of a single neuron. these spike trains are the basis for neural coding and information transfer in the brain. an example of such a feedback loop is the connections between the thalamus and cortex. this model implies that slow event-related responses, such as asymmetric alpha activity, could result from asymmetric brain oscillation amplitude modulations, such as an asymmetry of the intracellular currents that propagate forward and backward down the dendrites. although individual neuron activities cannot be recovered through non-invasive bci because the skull damps and blurs the electromagnetic signals, oscillatory activity can still be reliably detected. an initially high firing rate decreases over time, even though the stimulus stays constant, and eventually levels off to a steady state after a certain period, which may range from tens of milliseconds to several seconds. at the beginning and end of each stimulus section, the intensity was linearly ramped up or down, respectively, within 0. the time-resolved firing rate at time t after stimulus onset, r(t), was calculated by taking the inverse of the interspike interval (isi) between the last spike before t and the next spike after t and then averaging over trials:Where isin(t) denotes the length of the interspike interval that contains the time point t in the nth trial, and n is the total number of trials. the limited recording time, however, currently precludes such an experiment for locust auditory receptors. "who reads temporal information contained across synchronized and oscillatory spike trains? induced activity generally reflects the activity of numerous neurons: amplitude changes in oscillatory activity are thought to arise from the synchronization of neural activity, for instance by synchronization of spike timing or membrane potential fluctuations of individual neurons. characterizations of the strength and the time constants of adaptation indicate that adaptation primarily depends on the output level of neural activity, the firing rate (benda et al. mathematics of the hodgkin–huxley model are quite complicated and several simplifications have been proposed, such as the fitzhugh–nagumo model and the hindmarsh–rose model. for the main part of the experiments, we used stimuli that contained a switch from one constant-intensity tone to another. more than 50 years later, intrinsic oscillatory behavior was encountered in vertebrate neurons, but its functional role is still not fully understood.), nonlinear dynamics and chaos: where do we go from here? these rhythmic changes in membrane potential do not reach the critical threshold and therefore do not result in an action potential. shown are the two pure stimuli (top row) and the two switch stimuli (bottom row) consisting of two parts with either 4 or 10 khz sound frequency. amplitude of ongoing oscillatory activity is increased between t1 and t2. according to this idea, synchronous oscillations in neuronal ensembles bind neurons representing different features of an object.
Single neuron dynamics models linking theory and experiment
spike trains can form all kinds of patterns, such as rhythmic spiking and bursting, and often display oscillatory activity. "is gamma-band activity in the local field potential of v1 cortex a "clock" or filtered noise? we analyzed the data for both switches from higher to lower intensity and vice versa. ck, stemmler mb, prinz p, krahe r, ronacher b, herz avm (2001) representation of acoustic communication signals by insect auditory receptor neurons..Stumpner a, von helversen d (2001) evolution and function of auditory systems in insects. these firing-rate deflections are evidence of input-driven adaptation and can be used to quantify how this adaptation component affects the neural activity. losing its essential features, the above model can be solved analytically by assuming that the stimulus-response relationship, g(x), and the dependences of the adaptation components on r and s are all linear. here, we investigate this question in more detail by use of a new experimental technique that allows us to measure input-driven adaptation independently of output-driven components. if the two time constants τo and τi are very similar in value, the first exponential contribution, containing the term exp(-t/τi), becomes very small resulting from the (1 - τo/τi) term..Benda j, bethge m, hennig m, pawelzik k, herz avm (2001) spike-frequency adaptation: phenomenological model and experimental tests. oscillatory activity in the brain is widely observed at different levels of observation and is thought to play a key role in processing neural information. central pattern generators are neuronal circuits that—when activated—can produce rhythmic motor patterns in the absence of sensory or descending inputs that carry specific timing information. the excitability of neurons can be subdivided in class i and ii. long-range connections between different brain structures, such as the thalamus and the cortex (see thalamocortical oscillation), involve time-delays due to the finite conduction velocity of axons. resetting also permits the study of evoked activity, a term used in electroencephalography and magnetoencephalography for responses in brain activity that are directly related to stimulus-related activity. a group of neurons engages in synchronized oscillatory activity, the neural ensemble can be mathematically represented as a single oscillator. measuring the firing-rate deflections, we were able to demonstrate the existence of input-driven adaptation in locust auditory receptors and to characterize the relative strength of this adaptation component and its time scales of build-up and decay in individual cells. the model could easily be extended to incorporate this observation by allowing for different time constants in the build-up and decay of input-driven adaptation or by applying an explicit dependence of the time constant on the stimulus intensity. often, a neuron's firing rate depends on the summed activity it receives. different types of coding schemes have been proposed, such as rate coding and temporal coding. kuramoto model of coupled phase oscillators is one of the most abstract and fundamental model used to investigate neural oscillations and synchronization..Smirnakis sm, berry mj, warland dk, bialek w, meister m (1997) adaptation of retinal processing to image contrast and spatial scale. cell-intrinsic currents that contribute to spike-frequency adaptation are primarily triggered by the spiking activity of the neuron (benda and herz, 2003) and thus contribute to output-driven adaptation. sec; sound frequencies and intensities are indicated in the plot. however, ao stays near enough to its equilibrium value so that the longer time constant is revealed, and an order-of-magnitude estimate of τi is possible. subthreshold activation of some potassium currents may be locally induced by synaptic events or triggered by the fluctuations of the membrane potential, thus potentially contributing to both input-driven and output-driven adaptation, depending on the specific organization of the cell under study. for a functional characterization of spike-frequency adaptation, it is essential to understand the dependence of adaptation on the input and output of the neuron. it has been proposed that motor commands in the form of travelling waves can be spatially filtered by the descending fibres to selectively control muscle force. this is consistent with input-driven adaptation being governed by simple first-order dynamics, as were used in the minimal model.
in general, oscillations can be characterized by their frequency, amplitude and phase. answer this question, we investigate how the model reacts to two stimuli, x and y, for which it has different sensitivity, here modeled by using values kx = 1 and ky = 0. comparison, the total effect of adaptation for pure stimuli after the onset of the stimulus was quantified by the firing-rate difference between onset and steady state, δr, which was also obtained by fitting an exponential function to the firing rate. "relevance of nonlinear lumped-parameter models in the analysis of depth-eeg epileptic signals". to distinguish more clearly between these two cases, we provide the parameters δr and τ with indices lh for switches from lower to higher intensity and indices hl for switches from higher to lower intensity and also mark the data differently in the plots. the method is based on identifying intensities for different sounds that yield the same steady-state firing rate and thus the same level of adaptation as caused by the output firing rate. "synchronization of cortical activity and its putative role in information processing and learning".-frequency adaptation is ubiquitous in neural systems, and several biophysical mechanisms are known to contribute to this phenomenon in different neural systems. "cyclic variations in eeg during sleep and their relation to eye movements, body motility and dreaming". of neuronal firing may serve as a means to group spatially segregated neurons that respond to the same stimulus in order to bind these responses for further joint processing, i. these are found by setting dao/dt = dai/dt = 0:Note that the values of k and s of the tone before the switch have to be inserted in these equations to obtain ao,0 and ai,0 as initial conditions for the system after the switch. like pacemaker neurons in central pattern generators, subtypes of cortical cells fire bursts of spikes (brief clusters of spikes) rhythmically at preferred frequencies. for example, neuronal activity generated by two populations of interconnected inhibitory and excitatory cells can show spontaneous oscillations that are described by the wilson-cowan model. oscillations are observed throughout the central nervous system at all levels, and include spike trains, local field potentials and large-scale oscillations which can be measured by electroencephalography (eeg). in particular, it describes how the activity of a group of interacting neurons can become synchronized and generate large-scale oscillations. by the same token, output-driven adaptation need not causally depend on spiking activity, as long as the source of this adaptation component is a process that completely determines the output of the neuron. harmonic oscillations appear very frequently in nature—examples are sound waves, the motion of a pendulum, and vibrations of every sort. in this study, in contrast, we observed the effect of this adaptation component on the spiking activity of single neurons. investigate the transient effects on the firing rate induced by the switching of tones, we analyzed firing-rate differences between switch stimuli and pure stimuli. pfurtscheller and colleagues found a reduction in alpha (8–12 hz) and beta (13–30 hz) oscillations in eeg activity when subjects made a movement. three different levels have been widely recognized: the micro-scale (activity of a single neuron), the meso-scale (activity of a local group of neurons) and the macro-scale (activity of different brain regions). simulations using the kuramoto model with realistic long-range cortical connectivity and time-delayed interactions reveal the emergence of slow patterned fluctuations that reproduce resting-state bold functional maps, which can be measured using fmri. hz) that can be detected from the occipital lobe during relaxed wakefulness and which increases when the eyes are closed. as we have seen from the model, time constants for the firing-rate deflections may reflect the mixture of input-driven and output-driven adaptation. firing of neurons also forms the basis of periodic motor commands for rhythmic movements. for comparison, the gray line shows the firing rate that is obtained for the pure stimulus with sound frequency and intensity as in the second stimulus section. "intrinsic electrical properties of mammalian neurons and cns function: a historical perspective". phase resetting is fundamental for the synchronization of different neurons or different brain regions because the timing of spikes can become phase locked to the activity of other neurons. a-d, firing-rate differences r(t) = rswitch(t) - rpure(t) between responses to switch stimuli and responses to pure stimuli for four cells.
-frequency adaptation affects the response characteristics of many sensory neurons, and different biophysical processes contribute to this phenomenon. these cases indicate that input-driven adaptation is also part of the initial total adaptation and may account for differences between tones in the time course of the firing rate after stimulus onset. different neural ensembles are coupled through long-range connections and form a network of weakly coupled oscillators at the next spatial scale. instead of modelling individual neurons, this approach approximates a group of neurons by its average properties and interactions. through synaptic interactions the firing patterns of different neurons may become synchronized and the rhythmic changes in electric potential caused by their action potentials will add up (constructive interference). quantify input-driven adaptation, we calculated firing-rate differences between the responses to a switch stimulus, which contained a switch from one sound frequency to the other, and the responses to a pure stimulus (i. synchronization can be modulated by task constraints, such as attention, and is thought to play a role in feature binding, neuronal communication, and motor coordination. coupling between theta and gamma activity is thought to be vital for memory functions, including episodic memory. furthermore, the pure stimuli contain the same type of ramps and show no firing-rate transients. local interactions between neurons can result in the synchronization of spiking activity and form the basis of oscillatory activity. oscillations recorded from multiple cortical areas can become synchronized to form large scale brain networks, whose dynamics and functional connectivity can be studied by means of spectral analysis and granger causality measures. "oscillatory gamma activity in humans and its role in object representation". indeed, eeg studies suggest that visual perception is dependent on both the phase and amplitude of cortical oscillations. spontaneous activity is usually considered to be noise if one is interested in stimulus processing; however, spontaneous activity is considered to play a crucial role during brain development, such as in network formation and synaptogenesis. more generally, sensory stimulus spaces are often high dimensional, considering their possible variations in time, space, and additional components. in particular, models of interacting pyramidal cells and inhibitory interneurons have been shown to generate brain rhythms such as gamma activity. note that the presented approach to detecting input-driven adaptation is not restricted to analyzing primary sensory neurons. the deflections are fitted by exponential curves (thick black lines), and the obtained values for the initial firing-rate difference δr and the time constant τ are indicated in the graphs. that the upward and downward deflections of the firing rate for the same cell do not necessarily have the same shape; the two extracted time constants may diverge considerably (fig. of a hindmarsh–rose neuron showing typical bursting behavior: a fast rhythm generated by individual spikes and a slower rhythm generated by the bursts. from exponential fits of the firing-rate transients after onset and switch, we obtained time constants of 53 and 71 msec for the two stimulus onsets, indicating that initially the faster and stronger adaptation component ao dominates. is linearly added to ongoing oscillatory activity between t1 and t2. the open triangles in e depict the comparison between δτlh and δτhl. neuronal oscillations became a hot topic in neuroscience in the 1990s when the studies of the visual system of the brain by gray, singer and others appeared to support the neural binding hypothesis. in the present example, the output was simply the firing rate, and the input channels were given by different sound frequencies for which the auditory neuron had different sensitivity. the data supports the idea that input-driven adaptation is caused by a process that is activated at higher intensities and that reduces neural sensitivity in the high-intensity regime. different dependences of adaptation on the sensory input and neural output will have different effects on the coding properties of a sensory neuron. tight coordination of single-neuron spikes with local theta oscillations is linked to successful memory formation in humans, as more stereotyped spiking predicts better memory., 1998; sah and davies, 2000) or slow voltage-dependent (brown and adams, 1980; storm, 1990) potassium currents or the inactivation of sodium currents (fleidervish et al.
indeed, eeg signals change dramatically during sleep and show a transition from faster frequencies to increasingly slower frequencies such as alpha waves..Fleidervish ia, friedman a, gutnick mj (1996) slow inactivation of na+ current and slow cumulative spike adaptation in mouse and guinea-pig neocortical neurones in slices. firing-rate differences were quantified by their initial firing-rate differences, δr, immediately after the switch and their decay time constants, τ. in addition to local synchronization, oscillatory activity of distant neural structures (single neurons or neural ensembles) can synchronize. study was supported by deutsche forschungsgemeinschaft through sonderforschungsbereich 618 (robustness, modularity, and evolutionary design of living systems) and by boehringer ingelheim fonds (t. "generative models of cortical oscillations: neurobiological implications of the kuramoto model". as a consequence, those signal components that are the same in each single measurement are conserved and all others, i. many cellular mechanisms underlying adaptation are triggered by the spike output of the neuron in a feedback manner (e. such s1 and s2 were found by additional tuning measurements at the beginning of each recording session. phase resetting in medicine and biology: stochastic modelling and data analysis. such models only capture the basic neuronal dynamics, such as rhythmic spiking and bursting, but are more computationally efficient. is a naturally recurring state characterized by reduced or absent consciousness and proceeds in cycles of rapid eye movement (rem) and non-rapid eye movement (nrem) sleep. examples are walking, breathing, and swimming, most evidence for central pattern generators comes from lower animals, such as the lamprey, but there is also evidence for spinal central pattern generators in humans. msec to avoid artifacts caused by sharp intensity changes and discontinuities in the drive of the loudspeaker. similar insight is to be expected for other neurons exhibiting a mixture of input-driven and output-driven adaptation. "synchronization between motor cortex and spinal motoneuronal pool during the performance of a maintained motor task in man". to many other sensory neurons, auditory receptor cells of locusts respond to prolonged external stimulation with spiking activity that contains both a tonic and a phasic component. d, göpfert mc (2002) novel schemes for hearing and orientation in insects. functions of neural oscillations are wide ranging and vary for different types of oscillatory activity., 2001; kim and rieke, 2003) and lead to a negative feedback on the firing rate (benda and herz, 2003). in contrast, input-driven adaptation components in principle open up new possibilities for coding strategies, because the relative sensitivities of the neuron to different sound frequencies will change over time depending on previous intensity levels. as in the present study, no dendritic or somatic measurements are needed; extracellular recordings of spiking activity would suffice to identify and discriminate different (sub)cellular adaptation components. "functional role of gamma and theta oscillations in episodic memory". the simplifying linearity assumptions g(x) = x, ao,∞(r) = α · r, and ai,∞(s) = β · s, the model equations read as follows:This system can be solved analytically for constant input s. "magnetoencephalography - theory, instrumentation, and applications to noninvasive studies of the working human brain". these rhythmic outputs are produced by a group of interacting neurons that form a network, called a central pattern generator. similar influences of mechanical structures have been described in vertebrate muscle spindles (matthews, 1931, 1933) and the pacinian corpuscle (hubbard, 1958; loewenstein and mendelson, 1965). to investigate whether the intensity difference has an effect on the firing-rate transient beyond determining the sign, we also analyzed the correlation between s2 - s1 and δr for the two cases s2 - s1 > 0 and s2 - s1 < 0 separately. laser interferometry and stroboscopic illumination allow the observation of the tympanic oscillations under acoustic stimulation (schiolten et al.