The interplay between excitation and inhibition in the...
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Neuronal processing changes with different stimulus contexts. For example, stimulus processing in IC neurons can adapt to changes in background noise [1]. Such adaptation is advantageous for stimulus processing in different stimu- lus contexts. What is the neuronal computation underlying changes with adaptation? Linear models average all inputs to a cell into one receptive field, making it dif- ficult to understand where these changes are coming from. We employ a generalized nonlinear model (GNM) [2], which: - extracts separate excitation and inhibition from extracellular data - can predict responses more accurate and with higher temporal precision than standard models based on linear receptive fields - suggests that temporal shifts in processing associated with adaptation to noise involve a change in the relative strength of excitatory and inhibitory input tuning, rather than explicit changes in temporal selectivity Thus, considering the interplay of excitation and inhibition provides a better de- scription of IC neuron responses, and provides insight into their adaptation in different stimulus contexts. Conclusions: - The GNM can extract putative excitatory and inhibitory tuning from extracellular recordings, leading to a much better description of the extracellular data than models based on single receptive fields. - Tuning of excitatory and inhibitory elements in the GNM are generally very simi- lar. As a result, the linear receptive field averages their effects, and does not ac- curately reflect their underlying tuning. - The temporal precision of IC responses can be explained by the interplay of ex- citation and delayed inhibition. - Adaptation to noise may be the result of a change in the balance between exci- tation and inhibition, rather than explicit changes in temporal tuning. - The GNM modeling results are consistent with a common source for excitation and inhibition. (Circuitry?) Nonlinear Modeling Framework: Modeling techniques leverage efficient optimization techniques developed for maximum-likelihood estimation of the GLM (generalized linear model) [4]. In the GNM internal nonlinearities enable the fitting of separate excita- tion and inhibition. Without them the model would reduce to a GLM. Models are fit with 0.5 ms precision to single spike trains (40 s) for a population of 23 cells. Model performance was measured on 100 repeats of a cross validation sample (3 s). References: [1] Lesica NA, Grothe B (2008). PLoS One 3: e1655. [2] Butts DA, Weng C, Jin JZ, Alonso JM, Paninski L (submitted) The interplay of excitation and inhibition underlies the precise timing of LGN spike trains. [downloadable at: http://biology.umd.edu/ntlab] [3] Wehr M, Zador AM (2003), Nature 426: 442 - 446 [4] Paninski L (2004), Network: Comput Neural Syst 15:243 - 262 [5] Ahrens MB, Paninski L, Sahani M (2008), Network: Comput Neural Syst 19(1), 35 - 67 Temporal Precision through Inhibition: Common Source for Excitation and Inhibition? Tuning of GNM differs significantly from linear STRF GNM finds overlapping excitation and inhibition. This cannot be repre- sented by linear models as they average all inputs into a single STRF. GNM finds time kernels for excitation and inhibition of very similar shape (and possible delay). A model using identical time kernels for excitation and inhibition (GNM1) performs not significantly worse than the original GNM. High temporal precision is achieved by short time delay between excitation and inhibition. Refractory period (spike history term) also contributes to temporal precision. effective time kernel At all time resolutions GNM performs better than linear models. Improvement of GNM performance over linear models increases with temporal resolution. GLM GNM exc GNM inh GNM exc − inh 2 ms 2 ms The interplay between excitation and inhibition in the inferior colliculus and its relationship to adaptation for naturalistic stimuli Nadja Schinkel-Bielefeld 1 , Mai El-Zonkoly 1 , Nicholas Lesica 2 , Benedikt Grothe 3 , and Daniel A. Butts 1 1) NeuroTheoryLab, University of Maryland, 2) Ear Institute, University College London, 3) BCCN Munich, Ludwig-Maximilian University Munich + F STRF internal nonlinearity current postsynaptic stimulus spiking nonlinearity spike train observed h spk k F STRF spiking nonlinearity stimulus Model (GLM) + spike train observed spike history h spk Detailed Modeling Methods: The GNM is a cascade model with linear elements: where represents temporal convolution: The W i ’s represent nonlinear transformations of the stimulus s(t), and F is the spiking non- linearity, which is given by: where is the spike threshold. The nonlinear transforms W i of the stimulus are simple LN models, each specified by an internal receptive field k i and a nonlinearity f i . We optimize the parameters of the GNM to maximize the log-likelihood of the model given the data, given by: where r(t) is the rate predicted by the model, and {t s } are the observed spike times. The likelihood can be efficiently optimized in the context of a GLM framework [4], find- ing optimal parameters for both the postsynaptic current p i and internal nonlinearities f i . For this bilinear optimization, internal nonlinearities are represented as a linear combina- tion of appropriately chosen basis functions [5]. This leaves only fitting the internal recep- tive fields by brute force. Experimental Procedures Stimuli: Responses: Vocalizations (V) Ambient Noise (N) -- single-unit recodings in gerbil Stimuli were amplitude-modulated pure tones that were presented monaurally at each neuron’s best-frequency. In the V condition, stimuli were created using measured power spectrum of animal vocalizations. Noise stimuli were generated using power spectra of ambient noise (i.e. wind, vacuum cleaner), and the VN condition is a superposition of both stimuli, with different noise presented in each trial. Adaptation to Noise In the presence of noise (VN condi- tion), linear receptive fields shift their temporal tuning to generally have longer latencies and become less bi- phasic [1]. 0 5 10 15 20 25 30 time [ms] v vn The GNM fits suggest that the effects on the linear receptive field using adap- tation to noise can be primarily explained by a relative shift in the gain of excit- atory versus inhibitory inputs. In the noise condition, inhibition is reduced compared with excitation. s(t)*k v exc v inh vn exc vn inh Which aspects of GNM change in the VN condition? Each component of the GNM fit in the V condition was separately changed to describe the VN condition for each neuron (N = 23). The predictive power of the resulting GNM was compared with the GNM where all the components of the model were refit. Changes in the internal nonlin- earities with adaptation 10 15 20 25 time [ms] 10 15 20 25 time [ms] GNM exc GNM inh GNM exc − inh In the noise condition the relative strength of inhibition to excitation is decreased. This results in a later inhibitory peak in the linear kernels. Results: GNM fit for an Example Cell The GNM typically accounts for two times the explanable variance as single-filter models such as the LN model and GLM (N = 23). Time kernels Postsynaptic current Spike history Nonlinearity Predictive Power (Fraction of the ex- plainable variance explained) GNM: 51% GLM: 27% LN: 23% Population Data 0 20 40 60 0 20 40 60 pred. power GNM pred. power lin. model [%] LN GLM 0 5 10 1 1.5 2 2.5 3 3.5 bin size [ms] ratio of predictive power GNM/GLM GNM/LN 0 5 10 0 20 40 60 80 bin size [ms] predictive power [%] GNM GLM LN 40 50 60 70 40 50 60 70 pred. power GNM pred. power GNM1 (k ex = k in ) This suggests a common source for excitation and inhibition. Possible correspondence to known circuitry? GNM finds higher and sharper peaks than linear models. This mechanism has also been found in intracellular studies, i.e. [3]. Vocalization alone (V) Generalized Linear EXCITATION INHIBITION } LN models of inputs Generalized Nonlinear Model (GNM) s(t) ? k in k ex f in p ex p in f ex −40 −30 −20 −10 0 10 LN model psc psc+time NL NL+psc 8 10 12 14 16 18 20 22 24 time [ms] 0 0.5 1 5 ms output time data GNM exc inh module 0 200 400 600 time data GNM GLM LN 5 ms 0 10 20 30 time [ms] exc inh combined effect of temporal kernel and postsynaptic current Vocalization + Noise (VN) 5 10 15 20 25 time [ms] s(t)*k 0 10 20 time [ms] 0 10 20 30 time [ms] Motivation
Transcript of The interplay between excitation and inhibition in the...
Neuronal processing changes with different stimulus contexts. For example, stimulus processing in IC neurons can adapt to changes in background noise [1]. Such adaptation is advantageous for stimulus processing in different stimu-lus contexts.
What is the neuronal computation underlying changes with adaptation?
Linear models average all inputs to a cell into one receptive field, making it dif-ficult to understand where these changes are coming from.
We employ a generalized nonlinear model (GNM) [2], which:
- extracts separate excitation and inhibition from extracellular data- can predict responses more accurate and with higher temporal precision than standard models based on linear receptive fields- suggests that temporal shifts in processing associated with adaptation to noise involve a change in the relative strength of excitatory and inhibitory input tuning, rather than explicit changes in temporal selectivity
Thus, considering the interplay of excitation and inhibition provides a better de-scription of IC neuron responses, and provides insight into their adaptation in different stimulus contexts.
Conclusions:- The GNM can extract putative excitatory and inhibitory tuning from extracellular recordings, leading to a much better description of the extracellular data than models based on single receptive fields.- Tuning of excitatory and inhibitory elements in the GNM are generally very simi- lar. As a result, the linear receptive field averages their effects, and does not ac- curately reflect their underlying tuning.- The temporal precision of IC responses can be explained by the interplay of ex- citation and delayed inhibition. - Adaptation to noise may be the result of a change in the balance between exci- tation and inhibition, rather than explicit changes in temporal tuning.- The GNM modeling results are consistent with a common source for excitation and inhibition. (Circuitry?)
Nonlinear Modeling Framework:
Modeling techniques leverage efficient optimization techniques developed for maximum-likelihood estimation of the GLM (generalized linear model) [4]. In the GNM internal nonlinearities enable the fitting of separate excita-tion and inhibition. Without them the model would reduce to a GLM.
Models are fit with 0.5 ms precision to single spike trains (40 s) for a population of 23 cells. Model performance was measured on 100 repeats of a cross validation sample (3 s).
References:[1] Lesica NA, Grothe B (2008). PLoS One 3: e1655.[2] Butts DA, Weng C, Jin JZ, Alonso JM, Paninski L (submitted) The interplay of excitation and inhibition underlies the precise timing of LGN spike trains. [downloadable at: http://biology.umd.edu/ntlab][3] Wehr M, Zador AM (2003), Nature 426: 442 - 446 [4] Paninski L (2004), Network: Comput Neural Syst 15:243 - 262[5] Ahrens MB, Paninski L, Sahani M (2008), Network: Comput Neural Syst 19(1), 35 - 67
Temporal Precision through Inhibition:
Common Source for Excitation and Inhibition?
Tuning of GNM differs significantly from linear STRF
GNM finds overlapping excitation and inhibition. This cannot be repre-sented by linear models as they average all inputs into a single STRF.
GNM finds time kernels for excitation and inhibition of very similar shape (and possible delay). A model using identical time kernels for excitation and inhibition (GNM1) performs not significantly worse than the original GNM.
High temporal precision is achieved by short time delay between excitation and inhibition.
Refractory period (spike history term) also contributes to temporal precision.
effective time kernel
At all time resolutions GNM performs better than linear models.
Improvement of GNM performance over linear models increases with temporal resolution.
GLMGNM excGNM inhGNM exc − inh
2 ms2 ms
The interplay between excitation and inhibition in the inferior colliculus and its relationship to adaptation for naturalistic stimuli
Nadja Schinkel-Bielefeld1, Mai El-Zonkoly1, Nicholas Lesica2, Benedikt Grothe3, and Daniel A. Butts1
1) NeuroTheoryLab, University of Maryland, 2) Ear Institute, University College London, 3) BCCN Munich, Ludwig-Maximilian University Munich
+
F
STRF
internalnonlinearity
currentpostsynaptic
stimulus
spiking nonlinearity
spike trainobserved
hspk
k
F
STRF
spiking nonlinearity
stimulus
Model (GLM)
+
spike trainobserved
spikehistory
hspk
Detailed Modeling Methods:The GNM is a cascade model with linear elements:
where represents temporal convolution:
The Wi’s represent nonlinear transformations of the stimulus s(t), and F is the spiking non-linearity, which is given by: where � is the spike threshold. The nonlinear transforms Wi of the stimulus are simple LN models, each specified by an internal receptive field ki and a nonlinearity fi.
We optimize the parameters of the GNM to maximize the log-likelihood of the model given the data, given by:
where r(t) is the rate predicted by the model, and {ts} are the observed spike times. The likelihood can be efficiently optimized in the context of a GLM framework [4], find-ing optimal parameters for both the postsynaptic current pi and internal nonlinearities fi. For this bilinear optimization, internal nonlinearities are represented as a linear combina-tion of appropriately chosen basis functions [5]. This leaves only fitting the internal recep-tive fields by brute force.
Experimental ProceduresStimuli: Responses:
Vocalizations (V) Ambient Noise (N) -- single-unit recodings in gerbil
Stimuli were amplitude-modulated pure tones that were presented monaurally at each neuron’s best-frequency. In the V condition, stimuli were created using measured power spectrum of animal vocalizations. Noise stimuli were generated using power spectra of ambient noise (i.e. wind, vacuum cleaner), and the VN condition is a superposition of both stimuli, with different noise presented in each trial.
Adaptation to NoiseIn the presence of noise (VN condi-tion), linear receptive fields shift their temporal tuning to generally have longer latencies and become less bi-phasic [1].
0 5 10 15 20 25 30time [ms]
vvn
The GNM fits suggest that the effects on the linear receptive field using adap-tation to noise can be primarily explained by a relative shift in the gain of excit-atory versus inhibitory inputs. In the noise condition, inhibition is reduced compared with excitation.
s(t)*k
v excv inhvn excvn inh
Which aspects of GNM change in the VN condition?
Each component of the GNM fit in the V condition was separately changed to describe the VN condition for each neuron (N = 23). The predictive power of the resulting GNM was compared with the GNM where all the components of the model were refit.
Changes in the internal nonlin-earities with adaptation
10 15 20 25time [ms]
10 15 20 25time [ms]
GNM excGNM inhGNM exc − inh
In the noise condition the relative strength of inhibition to excitation is decreased. This results in a later inhibitory peak in the linear kernels.
Results:GNM fit for an Example Cell
The GNM typically accounts for two times the explanable variance as single-filter models such as the LN model and GLM (N = 23).
Time kernels Postsynaptic current Spike historyNonlinearity
Predictive Power (Fraction of the ex-plainable variance explained)GNM: 51% GLM: 27% LN: 23%
Population Data
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This suggests a common source for excitation and inhibition. Possible correspondence to known circuitry?
GNM finds higher and sharper peaks than linear models. This mechanism has also been found in intracellular studies, i.e. [3].
Vocalization alone (V)
Generalized Linear
EXCITATION INHIBITION
}LN modelsof inputs
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Motivation
