History-Dependent Multiple-Time-Scale Dynamics in a Single-Neuron Model

Gilboa, Gail; Chen, Ronen; Brenner, Naama

doi:10.1523/jneurosci.0763-05.2005

Cited by 74 publications

(68 citation statements)

References 37 publications

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“…However, in our case, the correlation time is Ͻ5 ms, on the order of the refractory period, so that every superthreshold event results in on the order of one spike (data not shown). A similarly shaped threshold curve was observed for the HodgkinHuxley neuron (Gilboa et al, 2005). The nonmonotonicity of the threshold function helps the model to preserve the spiketiming precision observed in the real system.…”

Section: Measuring the Threshold Function For The Stasupporting

confidence: 61%

Two-Dimensional Time Coding in the Auditory Brainstem

Slee¹,

Higgs²,

Fairhall³

et al. 2005

J. Neurosci.

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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.

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Section: Measuring the Threshold Function For The Stasupporting

confidence: 61%

Two-Dimensional Time Coding in the Auditory Brainstem

Slee¹,

Higgs²,

Fairhall³

et al. 2005

J. Neurosci.

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“…SFA is not only observed at the early stages of sensory processing, but is also widespread in cortical neurons embedded in highly recurrent networks. Often modeled by a single process with one specific timescale 16,17 , SFA also occurs on multiple timescales [18][19][20] . In pyramidal neurons of the rat somatosensory cortex, three or more processing steps away from sensory receptors, SFA is scale free 21 , meaning that the effective speed at which individual neurons adapt is not fixed but depends on the input.…”

Section: A R T I C L E Smentioning

confidence: 99%

“…In particular, the power-law decay that we found in the moving threshold (s) might reflect the scale-free dynamics observed during sodium-channel de-inactivation 39 . In this alternative view, scale-free dynamics is likely to emerge from the presence of multiple inactivated states of ion channels 19,40 .…”

Section: Input Currentmentioning

confidence: 99%

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Temporal whitening by power-law adaptation in neocortical neurons

et al. 2013

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Neural signaling requires a large amount of metabolic energy 1 . Consequently, neurons are thought to communicate using efficient codes in which redundant information is discarded 2 . Theories of efficient coding 3 successfully predict several features of sensory systems. At early stages of visual processing, inputs coming from the external world are decorrelated in both space and time [4][5][6][7] ; through sensory adaptation 8 , codes are dynamically modified so as to maximize information transmission [9][10][11][12] ; and sensory adaptation on multiple timescales 11,13,14 could possibly reflect the statistics of the external world 15 .Sensory adaptation is at least partially a result of intrinsic properties of individual neurons and, in particular, of SFA. SFA is not only observed at the early stages of sensory processing, but is also widespread in cortical neurons embedded in highly recurrent networks. Often modeled by a single process with one specific timescale 16,17 , SFA also occurs on multiple timescales [18][19][20] . In pyramidal neurons of the rat somatosensory cortex, three or more processing steps away from sensory receptors, SFA is scale free 21 , meaning that the effective speed at which individual neurons adapt is not fixed but depends on the input. Scale-free adaptation can be captured by simple threshold models with a power law-decaying spike-triggered process 22 that possibly describes the combined action of Na + -channel inactivation [23][24][25] and ion channels mediating adaptation currents [26][27][28] .Thus, three questions arise. First, can the temporal features of spiketriggered currents and spike-triggered changes in firing threshold, possibly spanning multiple timescales, be directly extracted from experimental data? Second, can SFA be explained by these spiketriggered effects? And finally, do the timescales of SFA match the temporal statistics of the inputs received by individual neurons? If temporal characteristics of inputs and SFA were matched, SFA could lead to a perfect decorrelation of the information contained in one spike with that of the previous one of the same neuron, a phenomenon known as temporal whitening 29 . Temporal whitening in turn implies that, at a high signal-to-noise ratio (SNR), information transmission is enhanced 30 . RESULTSThe question of whether SFA is optimally designed for efficient coding can only be addressed if both the dynamics of SFA and the statistical properties of the inputs generated in biologically relevant situations are known. We used a combined theoretical and experimental approach to extract the dynamics of spike-triggered processes and SFA directly from in vitro recordings of cortical neurons. We then analyzed the synaptically driven membrane potential dynamics recorded in vivo from somatosensory neurons during active whisker sensation (data from ref. 31). Our overall goal was to study whether adaptation optimally removes the temporal correlations in the input to single neurons embedded in the highly recurrent network of the cortex.SFA i...

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“…This phenomenon is expected to be related to nonexponential relaxation processes at the molecular level. The relationship between these two levels has been investigated in the context of particular models, for example for ion channel kinetics describing an internal structure of the unavailable manifold (21,22). In this context an effective nonlinear low-dimensional model was suggested to account for molecular memory and adaptive response (23).…”

Section: ]mentioning

confidence: 99%

Adaptive response by state-dependent inactivation

Friedlander

Brenner

2009

Proc. Natl. Acad. Sci. U.S.A.

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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, activitydependent 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 systemspecific 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. adaptation | feedback | signal-processing | biochemical networks M any sensing molecules, such as membrane channels and receptors, have mechanisms of activity attenuation following exposure to strong, persistent stimulation. Sometimes termed "adaptation" or "desensitization," the quantitative hallmark of these responses is that an abrupt change in stimulus elicits a strong rapid rise in activity followed by a slower relaxation to steady state. Such responses have been studied extensively in the context of sensory systems (1) as well as cellular signaling systems (2, 3). They are thought to reflect the continuous need of a sensory system to adjust to changing external conditions while coping with limited resources and suggest connections to such concepts as homeostasis (4) and feedback control (5).A widely encountered mechanism underlying adaptive response is the slow activity-dependent modulation in the total number of molecules available to respond. This is a well-known phenomenon that characterizes a large class of biological systems and can be implemented physically in many ways; Fig. 1 illustrates voltage-gated ion channels (6, 7), bacterial chemotactic (8, 9) and G protein-coupled receptors (10) as typical examples. These receptors and channels can all become temporarily unavailable to respond to the external signal via either a change of protein conformation that blocks the channel pore (ion channels), covalent modifications (chemotactic receptors), or their physical removal from the cell surface (internalization of GPCR or trafficking in some synaptic receptors)(11). In all these examples transitions to the unavailable state are strongly dependent on the activity state of the molecule (e.g., primarily through open channels or through ligand-bound receptors). Despite these apparent common principles, differences in morphology and context have tr...

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History-Dependent Multiple-Time-Scale Dynamics in a Single-Neuron Model

Cited by 74 publications

References 37 publications

Two-Dimensional Time Coding in the Auditory Brainstem

Two-Dimensional Time Coding in the Auditory Brainstem

Temporal whitening by power-law adaptation in neocortical neurons

Adaptive response by state-dependent inactivation

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