EckerBCSDCSBT20143ASEckerPBerensRJCottonMSubramaniyanGHDenfieldCRCadwellSMSmirnakisMBethgeASTolias2014-04-00182235–248Shared, trial-to-trial variability in neuronal populations has a strong impact on the accuracy of information processing in the brain. Estimates of the level of such noise correlations are diverse, ranging from 0.01 to 0.4, with little consensus on which factors account for these differences. Here we addressed one important factor that varied across studies, asking how anesthesia affects the population activity structure in macaque primary visual cortex. We found that under opioid anesthesia, activity was dominated by strong coordinated fluctuations on a timescale of 1–2 Hz, which were mostly absent in awake, fixating monkeys. Accounting for these global fluctuations markedly reduced correlations under anesthesia, matching those observed during wakefulness and reconciling earlier studies conducted under anesthesia and in awake animals. Our results show that internal signals, such as brain state transitions under anesthesia, can induce noise correlations but can also be estimated and accounted for based on neuronal population activity.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published-235State Dependence of Noise Correlations in Macaque Primary Visual Cortex150171882315017154211501715420SubramaniyanEBT20133MSubramaniyanASEckerPBerensASTolias2013-03-0038110Transmission of neural signals in the brain takes time due to the slow biological mechanisms that mediate it. During such delays, the position of moving objects can change substantially. The brain could use statistical regularities in the natural world to compensate neural delays and represent moving stimuli closer to real time. This possibility has been explored in the context of the flash lag illusion, where a briefly flashed stimulus in alignment with a moving one appears to lag behind the moving stimulus. Despite numerous psychophysical studies, the neural mechanisms underlying the flash lag illusion remain poorly understood, partly because it has never been studied electrophysiologically in behaving animals. Macaques are a prime model for such studies, but it is unknown if they perceive the illusion. By training monkeys to report their percepts unbiased by reward, we show that they indeed perceive the illusion qualitatively similar to humans. Importantly, the magnitude of the illusion is smaller in monkeys than in humans, but it increases linearly with the speed of the moving stimulus in both species. These results provide further evidence for the similarity of sensory information processing in macaques and humans and pave the way for detailed neurophysiological investigations of the flash lag illusion in behaving macaques.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published9Macaque Monkeys Perceive the Flash Lag Illusion15017188231501715421BerensECMBT20123PBerensASEckerRJCottonWJMaMBethgeASTolias2012-08-0031321061810626Orientation tuning has been a classic model for understanding single-neuron computation in the neocortex. However, little is known about how orientation can be read out from the activity of neural populations, in particular in alert animals. Our study is a first step toward that goal. We recorded from up to 20 well isolated single neurons in the primary visual cortex of alert macaques simultaneously and applied a simple, neurally plausible decoder to read out the population code. We focus on two questions: First, what are the time course and the timescale at which orientation can be read out from the population response? Second, how complex does the decoding mechanism in a downstream neuron have to be to reliably discriminate between visual stimuli with different orientations? We show that the neural ensembles in primary visual cortex of awake macaques represent orientation in a way that facilitates a fast and simple readout mechanism: With an average latency of 30–80 ms, the population code can be read out instantaneously with a short integration time of only tens of milliseconds, and neither stimulus contrast nor correlations need to be taken into account to compute the optimal synaptic weight pattern. Our study shows that—similar to the case of single-neuron computation—the representation of orientation in the spike patterns of neural populations can serve as an exemplary case for understanding the computations performed by neural ensembles underlying visual processing during behavior.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published8A Fast and Simple Population Code for Orientation in Primate V1150171882315017154211501715420EckerBTB20113ASEckerPBerensASToliasMBethge2011-10-0040311427214283The amount of information encoded by networks of neurons critically depends on the correlation structure of their activity. Neurons with similar stimulus preferences tend to have higher noise correlations than others. In homogeneous populations of neurons, this limited range correlation structure is highly detrimental to the accuracy of a population code. Therefore, reduced spike count correlations under attention, after adaptation, or after learning have been interpreted as evidence for a more efficient population code. Here, we analyze the role of limited range correlations in more realistic, heterogeneous population models. We use Fisher information and maximum-likelihood decoding to show that reduced correlations do not necessarily improve encoding accuracy. In fact, in populations with more than a few hundred neurons, increasing the level of limited range correlations can substantially improve encoding accuracy. We found that this improvement results from a decrease in noise entropy that is associated with increasing correlations if the marginal distributions are unchanged. Surprisingly, for constant noise entropy and in the limit of large populations, the encoding accuracy is independent of both structure and magnitude of noise correlations.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published11The effect of noise correlations in populations of diversely tuned neurons150171542015017188231501715421BerensEGTB20113PBerensASEckerSGerwinnASToliasMBethge2011-03-001110844234428Cortical circuits perform the computations underlying rapid perceptual decisions within a few dozen milliseconds with each neuron emitting only a few spikes. Under these conditions, the theoretical analysis of neural population codes is challenging, as the most commonly used theoretical tool—Fisher information—can lead to erroneous conclusions about the optimality of different coding schemes. Here we revisit the effect of tuning function width and correlation structure on neural population codes based on ideal observer analysis in both a discrimination and a reconstruction task. We show that the optimal tuning function width and the optimal correlation structure in both paradigms strongly depend on the available decoding time in a very similar way. In contrast, population codes optimized for Fisher information do not depend on decoding time and are severely suboptimal when only few spikes are available. In addition, we use the neurometric functions of the ideal observer in the classification task to investigate the differential coding properties of these Fisher-optimal codes for fine and coarse discrimination. We find that the discrimination error for these codes does not decrease to zero with increasing population size, even in simple coarse discrimination tasks. Our results suggest that quite different population codes may be optimal for rapid decoding in cortical computations than those inferred from the optimization of Fisher information.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published5Reassessing optimal neural population codes with neurometric functions1501718823150171542162573ASEckerPBerensGAKelirisMBethgeNKLogothetisASTolias2010-01-005965327584587Correlated trial-to-trial variability in the activity of cortical neurons is thought to reflect the functional connectivity of the circuit. Many cortical areas are organized into functional columns, in which neurons are believed to be densely connected and to share common input. Numerous studies report a high degree of correlated variability between nearby cells. We developed chronically implanted multitetrode arrays offering unprecedented recording quality to reexamine this question in the primary visual cortex of awake macaques. We found that even nearby neurons with similar orientation tuning show virtually no correlated variability. Our findings suggest a refinement of current models of cortical microcircuit architecture and function: Either adjacent neurons share only a few percent of their inputs or, alternatively, their activity is actively decorrelated.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published3Decorrelated Neuronal Firing in Cortical Microcircuits1501715421150171882351573JHMackePBerensASEckerASToliasMBethge2009-02-00221397423Spike trains recorded from populations of neurons can exhibit substantial pairwise correlations between neurons and rich temporal structure. Thus, for the realistic simulation and analysis of neural systems, it is essential to have efficient methods for generating artificial spike trains with specified correlation structure. Here we show how correlated binary spike trains can be simulated by means of a latent multivariate gaussian model. Sampling from the model is computationally very efficient and, in particular, feasible even for large populations of neurons. The entropy of the model is close to the theoretical maximum for a wide range of parameters. In addition, this framework naturally extends to correlations over time and offers an elegant way to model correlated neural spike counts with arbitrary marginal distributions.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de//fileadmin/user_upload/files/publications/macke2009_5157[0].pdfpublished26Generating Spike Trains with Specified Correlation Coefficients1501715420150171882356143PBerensGAKelirisASEckerNKLogothetisASTolias2008-12-0022199207Extra-cellular voltage fluctuations (local field potentials; LFPs) reflecting neural mass action are ubiquitous across species and brain regions. Numerous studies have characterized the properties of LFP signals in the cortex to study sensory and motor computations as well as cognitive processes like attention, perception and memory. In addition, its extracranial counterpart the electroencelphalogram (EEG) is widely used in clinical applications. However, the link between LFP signals and the underlying activity of local populations of neurons remains largely elusive. Here, we review recent work elucidating the relationship between spiking activity of local neural populations and LFP signals. We focus on oscillations in the gamma-band (30-90Hz) of the local field potential in the primary visual cortex (V1) of the macaque that dominate during visual stimulation. Given that in area V1 much is known about the properties of single neurons and the cortical architecture, it provides an excellent opportunity to
study the mechanisms underlying the generation of the local field potential.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published8Feature selectivity of the gamma-band of the local field potential in primate primary visual cortex1501715421150171882352053PBerensGAKelirisASEckerNKLogothetisASTolias2008-06-0022111The local field potential (LFP), comprised of low-frequency extra-cellular voltage fluctuations, has been used extensively to study the mechanisms of brain function. In particular, oscillations in the gamma-band (3090 Hz) are ubiquitous in the cortex of many species during various cognitive processes. Surprisingly little is known about the underlying biophysical processes generating this signal. Here, we examine the relationship of the local field potential to the activity of localized populations of neurons by simultaneously recording spiking activity and LFP from the primary visual cortex (V1) of awake, behaving macaques. The spatial organization of orientation tuning and ocular dominance in this area provides an excellent opportunity to study this question, because orientation tuning is organized at a scale around one order of magnitude finer than the size of ocular dominance columns. While we find a surprisingly weak correlation between the preferred orientation of multi-unit activity and gamma-band LFP
recorded on the same tetrode, there is a strong correlation between the ocular preferences of both signals. Given the spatial arrangement of orientation tuning and ocular dominance, this leads us to conclude that the gamma-band of the LFP seems to sample an area considerably larger than orientation columns. Rather, its spatial resolution lies at the scale of ocular dominance columns.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published10Comparing the feature selectivity of the gamma-band of the local field potential and the underlying spiking activity in primate visual cortex1501715421150171882347883ASToliasASEckerAGSiapasAHoenselaarGAKelirisNKLogothetis2007-12-0069837803790Understanding the mechanisms of learning requires characterizing how the response properties of individual neurons and interactions across populations of neurons change over time. In order to study learning in-vivo, we need the ability to track an electrophysiological signature that uniquely identifies each recorded neuron for extended periods of time. We have identified such an extracellular signature using a statistical framework which allows quantification of the accuracy by which stable neurons can be identified across successive recording sessions. Our statistical framework uses spike waveform information recorded on a tetrodes four channels in order to define a measure of similarity between neurons recorded across time. We use this framework to quantitatively demonstrate for the first time the ability to record from the same neurons across multiple consecutive days and weeks. The chronic recording techniques and methods of analyses we report can be used to characterize the changes in brain circuits du
e to learning.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published10Recording Chronically from the same Neurons in Awake, Behaving Primates150171542160767PBerensSGerwinnASEckerMBethgeVancouver, BC, Canada2010-04-009098The relative merits of different population coding schemes have mostly been analyzed in the framework of stimulus reconstruction using Fisher Information. Here, we consider the case of stimulus discrimination in a two alternative forced choice paradigm and compute neurometric functions in terms of the minimal discrimination error and the Jensen-Shannon information to study neural population codes.
We first explore the relationship between minimum discrimination error, Jensen-Shannon Information and Fisher Information and show that the discrimination framework is more informative about the coding accuracy than Fisher Information as it defines an error for any pair of possible stimuli. In particular, it includes Fisher Information as a special case. Second, we use the framework to study population codes of angular variables. Specifically, we assess the impact of different noise correlations structures on coding accuracy in long versus short decoding
time windows. That is, for long time window we use the common Gaussian noise approximation. To address the case of short time windows we analyze the Ising model with identical noise correlation structure. In this way, we provide a new rigorous framework for assessing the functional consequences of noise correlation structures for the representational accuracy of neural population codes that is in particular applicable to short-time population coding.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de//fileadmin/user_upload/files/publications/berens2009b_6076[0].pdfpublished8Neurometric function analysis of population codes1501718823GatysETB20137LGatysAEckerTTchumatchenkoMBethgeTübingen, Germany2013-09-00Neural activity in the cortex appears to be notoriously noisy. A widely accepted explanation for this finding is that excitatory and inhibitory inputs to downstream neurons are balanced in a way that the upstream population activity does not affect the mean but only the variance of the input current. This can be thought of as a multiplicative noise channel. However, the capacity limits imposed by this information channel are not known. Here we develop a general understanding of the encoding process in terms of scale mixture processes and derive information-theoretic bounds on their performance. Our results show that signal transmission via instantaneous changes in the variance can behave quite differently from the common additive noise channel. We perform systematic numerical analyses to maximize the information across the variance channel and thus obtain tight lower bounds to its capacity. Furthermore, we found that additional noise, resembling the unreliable synaptic transmission of spikes, can surprisingly enhance the coding performance of the channel.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published0Information Coding in the Variance of Neural Activity15017188231501715420FroudarakisBCESBT20137EFroudarakisPBerensJRCottonASEckerPSaggauMBethgeAToliasSalt Lake City, UT, USA2013-03-00nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published0Encoding of natural scene statistics in the primary visual cortex of the mouse1501718823EckerBTB2012_27ASEckerPBerensASToliasMBethgeSantorini, Greece2012-06-0056How attention shapes the structure of population activity has attracted substantial interest over the past decades. Attention has traditionally been associated with an increase in firing rates, reflecting a change in the gain of the population. More recent studies also report a
change in noise correlations, which is thought to reflect changes in functional connectivity.
However, since the degree of attention can vary substantially from trial to trial even within one experimental condition, the measured correlations could actually reflect fluctuations in the attention-related feedback signal (gain) rather than feed-forward noise, as often assumed.
To gain insights into this issue we analytically analyzed the standard model of spatial attention, where directing attention to the receptive field of a neuron increases its response gain. We assumed conditionally independent neurons (no noise correlations) and asked how uncontrolled
fluctuations in attention affect the correlation structure.
First, we found that this simple model of spatial attention explains the empirically measured correlation structure quite well. In addition to a positive average level of correlations, it predicts both an increase in correlations with firing rates, as observed in many studies, and a
decrease in correlations with the difference of two neurons’ tuning functions — a structure generally referred to as limited range correlations.
Second, we asked how fluctuations in attention would affect the accuracy of a population code, if treated as noise
by a downstream readout. Based on previous theoretical results, it would be expected that they negatively affect
readout accuracy because of the limited range correlations they induce. Surprisingly, we found that this is not
the case: correlations due to random gain fluctuations do not affect readout accuracy because their major axis is
orthogonal to changes in the stimulus orientation.
Our results can be readily generalized to include feature-based attention. The model has very few free parameters and can potentially account for a large fraction of the experimentally observed spike count (co-)variance.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published-56The correlation structure induced by fluctuations in attention150171882315017154211501715420EckerBTB20127AEckerPBerensAToliasMBethgeSalt Lake City, UT, USA2012-02-00180Attention has traditionally been associated with an increase in firing rates, reflecting a change in the gain of the
population. More recent studies also report a change in noise correlations, which is thought to reflect changes
in functional connectivity. However, since the degree of attention can vary substantially from trial to trial even
within one experimental condition, the measured correlations could actually reflect fluctuations in the attentionrelated feedback signal (gain) rather than feed-forward noise, as often assumed. To gain insights into this issue we analytically analyzed the standard model of spatial attention, where directing attention to the receptive field of a neuron increases its response gain. We assumed conditionally independent neurons (no noise correlations) and asked how uncontrolled fluctuations in attention affect the correlation structure. First, we found that this simple model of spatial attention explains the empirically measured correlation structure quite well. In addition to a positive average level of correlations, it predicts both an increase in correlations with firing rates, as observed in many studies, and a decrease in correlations with the difference of two neurons’ tuning functions—a structure generally referred to as limited range correlations. Second, we asked how fluctuations in attention would affect the accuracy of a population code, if treated as noise by a downstream readout. Based on previous theoretical results, it would be expected that they negatively affect readout accuracy because of the limited range correlations they induce. Surprisingly, we found that this is not the case: correlations due to random gain fluctuations do not affect readout accuracy because their major axis is orthogonal to changes in the stimulus orientation. Our results can be readily generalized to include feature-based attention. The model has very few free parameters and can potentially account for a large fraction of the observed spike count (co-)variance.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published-180The correlation structure induced by fluctuations in attention15017188231501715420BerensEGTB2011_27PBerensASEckerSGerwinnASToliasMBethgeSalt Lake City, UT, USA2011-02-00Cortical circuits perform computations within few dozens of milliseconds with each neuron emitting only a few spikes. In this regime conclusions based on Fisher information, which is commonly used to assess the quality of population codes, are not always valid. Here we revisit the effect of tuning function width and correlation structure on neural population codes for angular variables using ideal observer analysis in both reconstruction and classification tasks employing Monte-Carlo simulations and analytical derivations. We show that the optimal tuning width of individual neurons and the optimal correlation structure of the population depend on the signal-to-noise ratio for both the reconstruction and the classification task. Strikingly, both ideal observers lead to very similar conclusions at low signal-to-noise ratio. In contrast, Fisher information favors severely suboptimal coding schemes in this regime. To further investigate the coding properties of Fisher-optimal codes, we compute the full neurometric functions of an ideal observer in the stimulus discrimination task, which allows us to evaluate population codes separately for fine and coarse discrimination. We find that codes with Fisher-optimal tuning width show strikingly bad performance for simple coarse discrimination tasks with a ëpedestal errorí, which is independent of population size. We show analytically that this is a necessary consequence of the fact that in such codes only few neurons are activated by each stimulus, irrespective of the population size. Further we show that the initial region of the neurometric function goes to zero with increasing population size. As a consequence, the overall error achieved by Fisher-optimal ensembles saturates for large populations. In summary, based on exact ideal observer analysis for both stimulus reconstruction and discrimination tasks we obtained (1) an accurate assessment of neural population codes at all signal-to-noise ratios and (2) analytical insights into the suboptimal behavior of Fisher-optimal population codes.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published0Optimal Population Coding, Revisited15017188231501715421150171542070557ASEckerPBerensGAKelirisMBethgeNKLogothetisASToliasSan Diego, CA, USA2010-11-00Correlated trial-to-trial variability in the activity of cortical neurons is thought to reflect the functional connectivity of the circuit. Many cortical areas are organized into functional columns, in which neurons are believed to be densely connected and share common input. Numerous studies report a high degree of correlated variability between nearby cells. We developed chronically implanted multi-tetrode arrays offering unprecedented recording quality to re-examine this question in primary visual cortex of awake macaques. We found that even nearby neurons with similar orientation tuning show virtually no correlated variability.
In a total of 46 recording sessions from two monkeys, we presented either static or drifting sine-wave gratings at eight different orientations. We recorded from 407 well isolated, visually responsive and orientation-tuned neurons, resulting in 1907 simultaneously recorded pairs of neurons. In 406 of these pairs both neurons were recorded by the same tetrode.
Despite being physically close to each other and having highly overlapping receptive fields, neurons recorded from the same tetrode had exceedingly low spike count correlations (rsc = 0.005 ± 0.004; mean ± SEM). Even cells with similar preferred orientations (rsignal > 0.5) had very weak correlations (rsc = 0.028 ± 0.010). This was also true if pairs were strongly driven by gratings with orientations close to the cells’ preferred orientations.
Correlations between neurons recorded by different tetrodes showed a similar pattern. They were low on average (rsc = 0.010 ± 0.002) with a weak relation between tuning similarity and spike count correlations (two-sample t test, rsignal < 0.5 versus rsignal > 0.5: P = 0.003, n = 1907).
To investigate whether low correlations also occur under more naturalistic stimulus conditions, we presented natural images to one of the monkeys. The average rsc was close to zero (rsc = 0.001 ± 0.005, n = 329) with no relation between receptive field overlap and spike count correlations. We obtained a similar result during stimulation with moving bars in a third monkey (rsc = 0.014 ± 0.011, n = 56).
Our findings suggest a refinement of current models of cortical microcircuit architecture and function: either adjacent neurons share only a few percent of their inputs or, alternatively, their activity is actively decorrelated.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published0Decorrelated neuronal firing in cortical microcircuits1501715421150171882368107ASEckerPBerensGAKelirisMBethgeNKLogothetisASToliasSantorini, Greece2010-06-0058Correlated trial-to-trial variability in the activity of cortical neurons is thought to reflect the
functional connectivity of the circuit. Many cortical areas are organized into functional columns,
in which neurons are believed to be densely connected and share common input. Numerous
studies report a high degree of correlated variability between nearby cells. We developed
chronically implanted multi-tetrode arrays offering unprecedented recording quality
to re-examine this question in primary visual cortex of awake macaques. We found that
even nearby neurons with similar orientation tuning show virtually no correlated variability.
In a total of 46 recording sessions from two monkeys, we presented either static or drifting
sine-wave gratings at eight different orientations. We recorded from 407 well isolated, visually
responsive and orientation-tuned neurons, resulting in 1907 simultaneously recorded
pairs of neurons. In 406 of these pairs both neurons were recorded by the same tetrode.
Despite being physically close to each other and having highly overlapping receptive fields,
neurons recorded from the same tetrode had exceedingly low spike count correlations (rsc =
0.005 ± 0.004; mean ± SEM). Even cells with similar preferred orientations (rsignal > 0.5) had
very weak correlations (rsc = 0.028 ± 0.010). This was also true if pairs were strongly driven
by gratings with orientations close to the cells’ preferred orientations.
Correlations between neurons recorded by different tetrodes showed a similar pattern. They
were low on average (rsc = 0.010 ± 0.002) with a weak relation between tuning similarity
and spike count correlations (two-sample t test, rsignal < 0.5 versus rsignal > 0.5: P = 0.003, n =
1907).
To investigate whether low correlations also occur under more naturalistic stimulus conditions,
we presented natural images to one of the monkeys. The average rsc was close to zero
(rsc = 0.001 ± 0.005, n = 329) with no relation between receptive field overlap and spike
count correlations. We obtained a similar result during stimulation with moving bars in a
third monkey (rsc = 0.014 ± 0.011, n = 56).
Our findings suggest a refinement of current models of cortical microcircuit architecture and
function: either adjacent neurons share only a few percent of their inputs or, alternatively,
their activity is actively decorrelated.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published-58Decorrelated Firing in Cortical Microcircuits1501715421150171882358447PBerensJHMackeASEckerRJCottonMBethgeASToliasSalt Lake City, UT, USA2009-03-00Understanding the structure of multi-neuronal firing patterns in ensembles of cortical neurons is a major challenge for systems neuroscience. The dependence of network properties on the statistics of the sensory input can provide important insights into the computations performed by neural ensembles. Here, we study the functional properties of neural populations in the primary visual cortex of awake, behaving macaques by varying visual input statistics in a controlled way. Using arrays of chronically implanted tetrodes, we record simultaneously from up to thirty well-isolated neurons while presenting sets of images with three different correlation structures: spatially uncorrelated white noise (whn), images matching the second-order correlations of natural images (phs) and natural images including higher-order correlations (nat).
We find that groups of six nearby cortical neurons show little redundancy in their firing patterns (represented as binary vectors, 10ms bins) but rather act almost independently (mean multi-information 0.85 bits/s, range 0.16 - 1.90 bits/s, mean fraction of marginal entropy 0.34 %, N=46). Although network correlations are weak, they are statistically significant. While relatively few groups showed significant redundancies under stimulation with white noise (67.4 ± 3.2%; mean fraction of groups ± S.E.M.), many more did so in the other two conditions (phs: 95.7 ± 0.6%; nat: 89.1 ± 1.4%). Additional higher-order correlations in natural images compared to phase scrambled images did not increase but rather decrease the redundancy in the cortical representation: Network correlations are significantly higher in phs than in nat, as is the number of significantly correlated groups.
Multi-information measures the reduction in entropy due to any form of correlation. By using second order maximum entropy modeling, we find that a large fraction of multi-information is accounted for by pairwise correlations (whn: 75.0 ± 3.3%; phs: 82.8 ± 2.1%; nat: 80.8 ± 2.4%; groups with significant redundancy). Importantly, stimulation with natural images containing higher-order correlations only lead to a slight increase in the fraction of redundancy due to higher-order correlations in the cortical representation (mean difference 2.26 %, p=0.054, Sign test).
While our results suggest that population activity in V1 may be modeled well using pairwise correlations only, they leave roughly 20-25 % of the multi-information unexplained. Therefore, choosing a particular form of higher-order interactions may improve model quality. Thus, in addition to the independent model, we evaluated the quality of three different models: (a) The second-order maximum entropy model, which minimizes higher-order correlations, (b) a model which assumes that correlations are a product of common inputs (Dichotomized Gaussian) and (c) a mixture model in which correlations are induced by a discrete number of latent states. We find that an independent model is sufficient for the white noise condition but neither for phs or nat. In contrast, all of the correlation models (a-c) perform similarly well for the conditions with correlated stimuli.
Our results suggest that under natural stimulation redundancies in cortical neurons are relatively weak. Higher-order correlations in natural images do not increase but rather decrease the redundancies in the cortical representation.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published0Sensory input statistics and network mechanisms in primate primary visual cortex150171882353597ASEckerPBerensAHoenselaarMSubramaniyanASToliasMBethge2008-09-001nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published-1Towards the neural basis of the flash-lag effect15017154201501718823MackeBEOTB20087JHMackePBerensASEckerMOpperASToliasMBethgePrinceton, NJ, USA2008-07-00nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published0Modeling populations of spiking neurons with the Dichotomized Gaussian distribution1501718823150171542151017MBethgeJHMackePBerensASEckerASToliasSantorini, Greece2008-06-0048In order to understand how neural systems perform computations and process sensory
information, we need to understand the structure of firing patterns in large populations of
neurons. Spike trains recorded from populations of neurons can exhibit substantial pair wise
correlations between neurons and rich temporal structure. Thus, efficient methods for
generating artificial spike trains with specified correlation structure are essential for the
realistic simulation and analysis of neural systems.
Here we show how correlated binary spike trains can be modeled by means of a latent
multivariate Gaussian model. Sampling from our model is computationally very efficient, and
in particular, feasible even for large populations of neurons. We show empirically that the
spike trains generated with this method have entropy close to the theoretical maximum. They
are therefore consistent with specified pair-wise correlations without exhibiting systematic
higher-order correlations. We compare our model to alternative approaches and discuss its
limitations and advantages. In addition, we demonstrate its use for modeling temporal
correlations in a neuron recorded in macaque primary visual cortex.
Neural activity is often summarized by discarding the exact timing of spikes, and only
counting the total number of spikes that a neuron (or population) fires in a given time window.
In modeling studies, these spike counts have often been assumed to be Poisson distributed
and neurons to be independent. However, correlations between spike counts have been
reported in various visual areas. We show how both temporal and inter-neuron correlations
shape the structure of spike counts, and how our model can be used to generate spike counts
with arbitrary marginal distributions and correlation structure. We demonstrate its capabilities
by modeling a population of simultaneously recorded neurons from the primary visual cortex
of a macaque, and we show how a model with correlations accounts for the data far better
than a model that assumes independence.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published-48Flexible Models for Population Spike Trains1501715420150171882351007PBerensASEckerMSubramaniyanJHMackePHauckMBethgeASToliasSantorini, Greece2008-06-0046Understanding the structure of multi-neuronal firing patterns has been a central quest and
major challenge for systems neuroscience. In particular, how do pairwise interactions between
neurons shape the firing patterns of neuronal ensembles in the cortex? To study this
question, we recorded simultaneously from multiple single neurons in the primary visual
cortex of an awake, behaving macaque using an array of chronically implanted tetrodes1. High
contrast flashed and moving bars were used for stimulation, while the monkey was required to
maintain fixation.
In a similar vein to recent studies of in vitro preparations2,3,5, we applied maximum entropy
analysis for the first time to the binary spiking patterns of populations of cortical neurons
recorded in vivo from the awake macaque. We employed the Dichotomized Gaussian
distribution, which can be seen as a close approximation to the pairwise maximum-entropy
model for binary data4. Surprisingly, we find that even pairs of neurons with nearby receptive
fields (receptive field center distance < 0.15°) have only weak correlations between their
binary responses computed in bins of 10 ms (median absolute correlation coefficient: 0.014,
0.010-0.019, 95% confidence intervals, N=95 pairs; positive correlations: 0.015, N=59;
negative correlations: -0.013, N=36). Accordingly, the distribution of spiking patterns of
groups of 10 neurons is described well with a model that assumes independence between
individual neurons (Jensen-Shannon-Divergence: 1.06×10-2 independent model, 0.96×10-2
approximate second-order maximum-entropy model4; H/H1=0.992). These results suggest that
the distribution of firing patterns of small cortical networks in the awake animal is
predominantly determined by the mean activity of the participating cells, not by their
interactions.
Meaningful computations, however, are performed by neuronal populations much larger than
10 neurons. Therefore, we investigated how weak pairwise correlations affect the firing
patterns of artificial populations4 of up to 1000 cells with the same correlation structure as
experimentally measured. We find that in neuronal ensembles of this size firing patterns with
many active or silent neurons occur considerably more often than expected from a fully
independent population (e.g. 130 or more out of 1000 neurons are active simultaneously
roughly every 300 ms in the correlated model and only once every 3-4 seconds in the
independent model). These results suggest that the firing patterns of cortical networks
comparable in size to several minicolumns exhibit a rich structure, even if most pairs appear
relatively independent when studying small subgroups thereof.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published-46Pairwise Correlations and Multineuronal Firing Patterns in the Primary Visual Cortex of the Awake, Behaving Macaque1501715420150171882345917PBerensASEckerGAKelirisNKLogothetisASToliasSan Diego, CA, USA2007-11-00The local field potential (LFP) and, in particular, the gamma-band frequency range (30-90 Hz) have recently received much attention, as numerous studies have shown correlations between LFP and sensory, motor and cognitive variables in various cortical regions. However, the extent to which it reflects the activity of local populations of neurons remains elusive. The issue of spatial scale is central for understanding the origins of the LFP and how this signal can be used to study the functional organization of the brain.
We addressed this question by simultaneously recording multi-unit spiking activity (MUA) and LFP from the primary visual cortex (V1) of awake, behaving macaques using arrays of tetrodes. Oriented gratings were used for visual stimulation, applied either binocular or monocular. The columnar organization of stimulus orientation and ocularity in V1 provides an excellent opportunity to study the spatial precision of the LFP signal, because neurons with similar orientation preference are organized at the fine spatial scale of cortical microcolumns (50-100 μm), whereas ocular dominance columns span around 450 μm.
As shown before, we find that the increase of LFP gamma-band power is a function of orientation and ocularity of the stimulus. However, the power of the gamma-band contains much less information about the orientation of the stimulus than the MUA recorded at the same site. The average discriminability d' between preferred and orthogonal orientation was 2.46±0.15 for MUA and 1.01±0.05 for LFP (mean ±std). Moreover, we find only a weak correlation between the preferred orientation of the MUA tuning function and that of the LFP (r=0.21, p<0.05). In contrast, we find a strong correlation between the preferred ocularity of the two signals (r=0.53, p<1e-9).
We therefore conclude that the gamma-power of the LFP does not reflect well the local activity on the scale of orientation columns but does capture the ocular dominance structure of V1. We suggest that gamma-band activity is generated by ensembles of neurons larger than 50-100 μm. In agreement with a previous study (Liu & Newsome, 2006) we find that it more likely resembles the activity of neurons from an area spanning a few hundred micrometers.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published0On the spatial scale of the local field potential - orientation and ocularity tuning of the local field potential in the primary visual cortex of the macaque150171542147337ASEckerAGSiapasAHoenselaarPBerensGAKelirisNKLogothetisASToliasSan Diego, CA, USA2007-11-00Understanding the mechanisms of learning and memory consolidation requires characterizing how the response properties of individual neurons and interactions across populations of neurons change over time, during periods spanning multiple days.
We used multiple chronically implanted tetrodes to record single unit activity from area V1 of the awake, behaving macaque and developed a method to quantitatively determine recording stability. Our method is based on a statistical framework which uses similarity of action potential waveforms to detect stable recordings given a pre-defined type I error rate. The similarity measure that was used takes into account both the shape of the action potential waveform and the amplitude ratio across channels, which depends on the location of the neuron relative to the tetrode.
271 well-isolated single units were recorded from 7 tetrodes during two periods of up to 23 days. We computed the distribution of pairwise similarities of average waveforms recorded on consecutive recording sessions during the first 34 days after implantation of the chronic drive. During this period, there was no recording stability due to regular adjustments of the tetrodes. We used this distribution as an empirical null distribution for hypothesis testing.
Using this statistical procedure and a type I error rate of alpha = 0.05, we find that of all single units recorded on a given day, 51% could be recorded for at least 2 days, 40% for at least 3 days, and 25% for at least 7 days.
In addition, we adapted a recently proposed multivariate statistical test (Gretton et al., 2007) to test whether the waveforms obtained at consecutive days come from the same underlying probability distribution. Using this test we obtained qualitatively similar results.
To validate these results, we compared orientation tuning functions of neurons that were tracked across days. Consistent with the claim that the same neurons were recorded across days and the fact that the monkey was not performing a learning task, the distribution of tuning differences of stable and orientation-tuned neurons across days was highly significantly different (Wilcoxon rank sum test, n1 = 79, n2 = 582, p < 10^-34) from the distribution of tuning differences across different neurons.
Our results show that using only waveform information it is possible to reliably track stable neurons across days with a limited type I error probability. This statistical approach is particularly important since, in a learning experiment, properties of neurons such as orientation tuning are potentially changed and therefore cannot be used to evaluate stability.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published0Recording chronically from the same neurons in awake, behaving primates150171542147317ASEckerPBerensMBethgeNKLogothetisASToliasHossegor, France2007-09-002122Responses of single neurons to a fixed stimulus are usually both variable and highly ambiguous. Therefore,
it is widely assumed that stimulus parameters are encoded by populations of neurons. An important
aspect in population coding that has received much interest in the past is the effect of correlated noise
on the accuracy of the neural code.
Theoretical studies have investigated the effects of different correlation structures on the amount of
information that can be encoded by a population of neurons based on Fisher Information. Unfortunately,
to be analytically tractable, these studies usually have to make certain simplifying assumptions such as
high firing rates and Gaussian noise. Therefore, it remains open if these results also hold in the more realistic scenario of low firing rates and discrete, Poisson-distributed spike counts.
In order to address this question we have developed a straightforward and efficient method to draw samples
from a multivariate near-maximum entropy Poisson distribution with arbitrary mean and covariance
matrix based on the dichotomized Gaussian distribution [1]. The ability to extensively sample data from
this class of distributions enables us to study the effects of different types of correlation structures and
tuning functions on the information encoded by populations of neurons under more realistic assumptions
than analytically tractable methods.
Specifically, we studied how limited range correlations (neurons with similar tuning functions and low
spatial distance are more correlated than others) affect the accuracy of a downstream decoder compared
to uniform correlations (correlations between neurons are independent of their properties and locations).
Using a set of neurons with equally spaced orientation tuning functions, we computed the error of an
optimal linear estimator (OLE) reconstructing stimulus orientation from the neurons firing rates. We
findsupporting previous theoretical resultsthat irrespective of tuning width and the number of neurons in
the network, limited range correlations decrease decoding accuracy while uniform correlations facilitate
accurate decoding. The optimal tuning width, however, did not change as a function of either the
correlation structure or the number of neurons in the network. These results are particularly interesting
since a number of experimental studies report limited range correlation structures (starting at around
0.1 to 0.2 for similar neurons) while experiments carried out in our own lab suggest that correlations are
generally low (on the order of 0.01) and uniform.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published1Studying the effects of noise correlations on population coding using a sampling method15017154201501715421150171882342727ASEckerPBerensGAKelirisNKLogothetisASToliasGöttingen, Germany2007-04-001222Recent advances in both electrophysiological recording techniques and hardware capabilities have enabled
researchers to simultaneously record from a large number of neurons in different areas of the brain. This opens
the door for a wide range of complex analyses potentially leading to a better understanding of the principles
underlying neural network computations. At the same time, due to the increasing amount of data with
increasing complexity, significantly more emphasis has to be put on the data analysis task. Although
high-level scripting languages such as Matlab can speed up the development of analysis tools, in our
experience, a too large amount of time is still spent on (re)structuring and (re)organizing data for specific
analyses.
Therefore, our goal was to develop a system which enables experimental neuroscientists to spend less time on
organizing their data and more on data collection and creative analysis. We developed an object oriented
Matlab toolbox which supplies the user with basic data types and functions to organize and structure various
types of electrophysiological data. By using an object oriented, hierarchical layout, basic functionality, such as
integration of metadata, or storage and retrieval of data and results, is implemented independent of specific
data formats or experimental designs. This provides maximal flexibility and compatibility with future
experiments and new data formats. All data and experimental results are stored in a database, so the
experimenter can choose which data to keep in memory for faster access and which to save to disk to save
resources. Additionally, we have created an extensive library of basic analysis and visualization tools that can
be used to get an overview of the data.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de//fileadmin/user_upload/files/publications/EckerTolias_2007_ADataManagement_4272[0].pdfpublished-1222A Data Management System for Electrophysiological Data Analysis150171542142737PBerensGAKelirisASEckerNKLogothetisASToliasGöttingen, Germany2007-04-00735Oscillations in the local field potential (LFP) are abundant across species and brain regions. The possible
relationship of these low-frequency extracelluar voltage fluctuations with the activity of the underlying local
population of neurons remains largely elusive. To study this relationship, we used an array of chronically
implanted tetrodes spanning a distance of 700 μm and simultaneously recorded action potentials from multiple
well-isolated single units, multi unit activity (MUA) and LFP from area V1 of the awake, behaving macaque.
Moving and static gratings of different orientations were used for visual stimulation.
In agreement with previous studies we find that the increase of LFP gamma-band power is a function of the
orientation of the stimulus. However, the power of the gamma-band contains much less information about the
orientation of the stimulus than the MUA and SUA recorded at the same site (Figure 1A). The average
discriminability d‘ between preferred and orthogonal orientation was 2.46 for MUA, 2.45 for SUA and 1.01
for the LFP. Moreover, in contrast to recent results from area MT (Liu and Newsome, 2006) we find only a
weak correlation between the preferred orientation of the MUA tuning function and that of the LFP (Figure
1B, different colors indicate different animals). Interestingly, all nearby LFP recording sites in our array were
tuned to a similar orientation while the preferred orientations of MUA tuning functions were widely scattered.
These results suggest that the power of LFP signals does not capture local population activity at the scale of
orientation columns in area V1.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de//fileadmin/user_upload/files/publications/T16-4C_[0].pdfpublished-735Orientation tuning of the local field potential and multi-unit activity in the primary visual cortex of the macaque150171542139497PBerensASEckerAHoenselaarGAKelirisAGSiapasNKLogothetisASToliasSantorini, Greece2006-06-0039Oscillations in the local field potential (LFP) are abundant across species and brain regions. The possible
role of these oscillations in information processing in the primary visual cortex (V1) of the macaque still
remains largely elusive despite that V1 is one of the most extensively studied brain areas. To this end, we
used chronically implanted, multiple tetrodes and recorded the spiking activity of single neurons and LFPs
from area V1 of the awake, behaving macaque. Moving and static gratings of different orientations were
used for visual stimulation.
In agreement with previous reports we find that the increase of the LFP gamma-band power is a function
of the orientation of the stimulus. Surprisingly though, there is only a weak correlation between the peak
of the multi-unit spiking activity orientation tuning functions and the peak of the orientation tuning function
of the gamma-band power of the LFP. There is however a different kind of relationship between spikes
and LFP. Namely, the timing of the spikes is not randomly distributed in time but instead is locked to the
phase of the gamma-band of the LFP. Specifically, the spikes of 60 out of 151 well-isolated single units
showed significant phase locking to the LFP (P<0.05, circular Rayleigh test). On average, the spikes occurred
on the downward slope of the LFP oscillation. In contrast to the presence of phase precession reported
in the rat hippocampus, the phase tuning in V1 is stable over time. Specifically, the preferred
phase of the spikes does not seem to change over time during the presentation of the stimulus. Moreover,
the preferred phase is not significantly modulated as a function of the orientation of the stimulus (Figure
A).
This temporal structuring of the spiking activity of neurons in V1 could allow coding of information in the
temporal regime (Panzeri & Schultz, 2001). In addition it could also potentially synchronize populations of
neurons (Fries 2005). We are currently investigating these conjectures.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published-39Spikes are phase locked to the gamma-band of the local field potential oscillations in the primary visual cortex of the macaque1501715421ToliasEKSSL20067ASToliasAEckerGAKelirisTGSiapasSMSmirnakisNKLogothetisSalt Lake City, UT, USA2006-03-0013Despite recent progress in systems neuroscience, basic properties of the neural code still remain obscure. For instance, the responses of single neurons are both highly variable and ambiguous (similar responses can be elicited by different types of stimuli). This variability/ambiguity has to be resolved by considering the joint pattern of firing of multiple single units responding simultaneously to a stimulus. Therefore, in order to understand the underlying principles of the neural code it is important to characterize the correlations between neurons and the impact that these correlations have on the amount of information that can be encoded by populations of neurons. Here we applied the technique of chronically implanted, multiple tetrodes to record simultaneously from a number of neurons in the primary visual cortex (V1) of the awake behaving macaque, and to measure the correlations in the trial-to-trial fluctuations of their firing rates under the same stimulation conditions (noise correlations). We find that, contrary to widespread belief, noise correlations in V1 are very small (around 0.01) and do not change systematically neither as a function of cortical distance (up to 600 um) nor as a function of the similarity in stimulus preference between the neurons (uniform correlation structure). Interestingly, a uniform correlation structure is predicted by theory to increase the achievable encoding accuracy of a neuronal population and may reflect a universal principle for population coding throughout the cortex.nonotspecifiedhttp://www.kyb.tuebingen.mpg.de/published-13Structure of interneuronal correlations in the primary visual cortex of the rhesus macaque1501715421510414ASEcker2008-03-00nonotspecifiedpublishedPredictive Coding and Spike Timing Dependent Plasticity in Primary Visual Cortexdiplom1501718823Ecker201310AEckerToliasEKPPL200710ASToliasAEckerGAKelirisFPanagiotaropolulosSPanzeriNKLogothetis372310ASToliasGAKelirisASEckerAGSiapasSMSmirnakisNKLogothetis