response reliability observed with voltage-sensitive dye...

Response reliability observed with voltage-sensitive dye imaging of corticallayer 2/3: the probability of activation hypothesis

Clare A. Gollnick, Daniel C. Millard, Alexander D. Ortiz, Ravi V. Bellamkonda, andX Garrett B. StanleyCoulter Department of Biomedical Engineering, Georgia Institute of Technology & Emory University, Atlanta, Georgia

Submitted 3 June 2015; accepted in final form 4 February 2016

Gollnick CA, Millard DC, Ortiz AD, Bellamkonda RV, StanleyGB. Response reliability observed with voltage-sensitive dye imagingof cortical layer 2/3: the probability of activation hypothesis. JNeurophysiol 115: 2456–2469, 2016. First published February 10,2016; doi:10.1152/jn.00547.2015.—A central assertion in the study ofneural processing is that our perception of the environment directlyreflects the activity of our sensory neurons. This assertion reinforcesthe intuition that the strength of a sensory input directly modulates theamount of neural activity observed in response to that sensory feature:an increase in the strength of the input yields a graded increase in theamount of neural activity. However, cortical activity across a range ofsensory pathways can be sparse, with individual neurons havingremarkably low firing rates, often exhibiting suprathreshold activityon only a fraction of experimental trials. To compensate for thisobserved apparent unreliability, it is assumed that instead the localpopulation of neurons, although not explicitly measured, does reliablyrepresent the strength of the sensory input. This assumption, however,is largely untested. In this study, using wide-field voltage-sensitivedye (VSD) imaging of the somatosensory cortex in the anesthetizedrat, we show that whisker deflection velocity, or stimulus strength, isnot encoded by the magnitude of the population response at the levelof cortex. Instead, modulation of whisker deflection velocity affectsthe likelihood of the cortical response, impacting the magnitude, rateof change, and spatial extent of the cortical response. An idealobserver analysis of the cortical response points to a probabilistic codebased on repeated sampling across cortical columns and/or time,which we refer to as the probability of activation hypothesis. Thishypothesis motivates a range of testable predictions for both futureelectrophysiological and future behavioral studies.

coding; noise; reliability; tactile; VSD

WE USE INFORMATION DERIVED from our sensory systems tointeract dynamically with the external sensory world. Oursenses help us avoid being hit by a speeding car in a crosswalkor instantly recognize a face in a sea of strangers. Our indi-vidual sensory experiences are fleeting, yet much of what weunderstand about neural processing of sensory stimuli has beeninferred from data averaged across repeated presentations of aspecific sensory input. Implicit in this analysis is the assump-tion that the trial average is a valid model for the code the brainuses to represent our sensory experiences. However, the trialaverage itself is not ethologically relevant. There is no a priorireason to expect a trial-averaged neural signal to reflect fea-tures of the dynamic neural code. Even given trial-averagedifferences, it is the across-trial variability that determineswhich stimulus parameters are effectively encoded (Abbott and

Dayan 1999; Averbeck et al. 2006; Beck et al. 2012). In thisstudy, we consider this concept of reliability, or how wellindividual trials can be differentiated or decoded given knowl-edge of characteristics of a trial average. From a theoreticalperspective, the role of trial-to-trial variability has been ex-plored, particularly in the context of single neurons or the jointactivity of pairs of neurons (Butts and Goldman 2006; Church-land et al. 2010; Cohen and Kohn 2011), but at a populationlevel the concept is not well understood.

The rodent vibrissa (whisker) system is a powerful modelsystem for detailed investigation of neural circuitry in earlysensory pathways (for review see Petersen 2007) and is emerg-ing as an important model system for behavior. Rodents arecapable of choosing between different textures and patterns ofwhisker stimulation (Carvell and Simons 1990; Morita et al.2011; Wolfe et al. 2008) and of performing object detectionand localization (O’Connor et al. 2010a, 2010b). Nevertheless,the specific stimulus features that are encoded in these tasks arenot known. One hypothesis is that sporadic high-velocity“slip-stick” events observed during texture discrimination as awhisker is moved across a surface are relevant stimulus fea-tures (Jadhav et al. 2009; Wolfe et al. 2008). Experiments inour laboratory and others’ have shown that both the frequencyof stimulus detection in behavioral experiments (Ollerenshawet al. 2012; Stüttgen et al. 2006; Stüttgen and Schwarz 2008;Waiblinger et al. 2015) and the spike frequency in the thalamusand cortex with extracellular recordings (Boloori et al. 2010;Pinto et al. 2000; Shoykhet et al. 2000; Simons 1978; Wang etal. 2010) are modulated by the velocity of the whisker move-ments. However, neither of these approaches can allow a directmeasurement of population response on single trials.

In this study, we consider reliability in the context of theencoding of whisker deflection velocity using in vivo voltage-sensitive dye (VSD) imaging of the rat barrel cortex in ananesthetized preparation. The VSD imaging employed mea-sures population activity in putative cortical layer 2/3 on asingle trial with sufficient fidelity as to differentiate stimulus-evoked activity on a single stimulus presentation (Ollerenshawet al. 2014). Consistent with previous VSD studies (Olleren-shaw et al. 2012; Petersen et al. 2003a) and many decades oftrial-averaged electrophysiological evidence, we show that thetrial-average amplitude of cortical activation increased withwhisker deflection velocity. Despite these trial-average trends,we show that knowledge of trial-average trends was not suffi-cient to accurately classify response observed on only singletrials. By examining the variability of the single-trial distribu-tion, we find that the stimulus velocity instead modulatedresponse frequency. We propose a probabilistic framework that

Address for reprint requests and other correspondence: G. B. Stanley,Coulter Dept. of Biomedical Engineering, Georgia Institute of Technology& Emory Univ., 313 Ferst Drive, Atlanta, GA 30332 (e-mail:[email protected]).

J Neurophysiol 115: 2456–2469, 2016.First published February 10, 2016; doi:10.1152/jn.00547.2015.

2456 0022-3077/16 Copyright © 2016 the American Physiological Society www.jn.org

http://orcid.org/0000-0003-2039-7706

mailto:[email protected]

changes the conceptual map between observed trial-averageactivity and the expected distribution of activity on singletrials. The probability of activation framework suggests addi-tional testable predictions and hypotheses for sensory neuralcoding and behavior.

METHODS

Animals. All procedures were approved by the Institutional AnimalCare and Use Committee at the Georgia Institute of Technology. Datafrom six adult female Sprague-Dawley rats (250g-330 g) were used inthis study. Data from four additional animals were excluded on thebasis of predetermined criterion due to inadequate signal quality asreflected in the signal-to-noise ratio, predominantly caused by inade-quate or uneven dye penetration.

Surgical preparation. Animals were sedated with isoflurane (5%)and injected with pentobarbital sodium (50mg/kg ip) for long-termanesthesia. A tail vein catheter was inserted, and pentobarbital sodium(4.5mg/ml) was delivered continuously and adjusted to maintain ananesthetic depth at which no toe- or tail-pinch reflex was observed.Heart rate, oxygen saturation, respiratory rate, and temperature (37°C)were monitored continuously to ensure a constant level of anestheticdepth throughout the experiment. Once anesthetized, the animal wasstabilized in a stereotaxic frame. A craniotomy was performed overthe barrel cortex (stereotaxic coordinates: 0.5–4.0 mm caudal to thebregma and 3.0–7.0 mm lateral to the midline), and the dura wasremoved. A dental cement well was created around the craniotomy tohold dye and saline. The cortical surface was kept moist with steriledye or saline throughout the entire experiment.

VSD imaging. Voltage-sensitive dye (VSD) imaging measuressubthreshold activity from supragranular layers of the barrel cortex(Kleinfeld and Delaney 1996; Petersen et al. 2003a). The dye is nottargeted to supragranular layers specifically; instead, the limitingfactor for the origin of the VSD signal (as with all optical imagingtechniques in the visible spectrum) is the loss of signal at deeperdepths due to light scattering in biological tissue. Previous studieshave shown using simultaneous whole cell recordings that the VSDsignal are linearly correlated with subthreshold voltage traces of layer2/3 pyramidal neurons (Cohen et al. 1978; Petersen et al. 2003a).However, the VSD signal is not exclusive and potentially representsactivity from other sources such as apical dendrites from other layers.Importantly, previous studies have estimated that these contributionsare likely not more than 10% of the signal (Petersen et al. 2003a). Inour study, VSD (RH1691, 2 mg/ml; Optical Imaging) was placed onthe surface of the brain and mixed regularly with a micropipette every5–10 min for 1.5–2 h to allow sufficient time for diffusion into thecortex. Next, the unbound dye was removed by multiple washes withsterile saline. The cortex was illuminated with a 150-W halogen lamppassed through an excitation filter (621–643 nm). A long-pass emis-sion filter was used (�665 nm). Images were recorded with ahigh-speed charge-coupled device camera (MiCAM2; SciMedia) asdepicted in Fig. 1. A �1 objective lens was combined with a �0.63condenser lens, resulting in a total magnification of �1.6. The camerawas focused �300 �m below the surface to target activity from layer2/3. Forty to 60 trials for each stimulus condition were recorded foranalysis. Image resolution was �20 �m/pixel.

Whisker deflections. Controlled whisker deflections were deliveredwith piezoelectric bending actuator (range of motion: 1 mm; band-width: 200 Hz; Polytec PI) attached to a glass pipette. The whiskerswere trimmed to 15 mm, and the whisker tip was placed inside thepipette and positioned 10 mm from the whisker base. The saw-toothdeflection consisted of an 8-ms exponential rise phase and an 8-msexponential decay phase. The velocity of the whisker deflection wasvaried by changing the rostral-caudal distance the whisker moved bythe piezoelectric actuator. The duration of the deflection remainedconstant. The angle of deflection at the whisker base was calculatedfrom the measured distances (distance from whisker pad, deflection

distance), assuming triangular geometry. The six velocities (V1 to V6)were calibrated using high-speed videography to be 75, 150, 300, 600,900, and 12,00°/s, respectively, in the rostral-caudal plane. During ourcalibration procedures, we observed that the whisker was reliablydeflected with every presentation of the stimulus using this method.This method of whisker deflections has been used extensively previ-ously to deliver precisely controlled whisker deflections (Millard et al.2013; Ollerenshaw et al. 2014; Wang et al. 2010). However, given thenature of the data presented in this study, we took additional precau-tions to ensure that the whisker deflections were delivered reliably.The distance from the whisker base was carefully placed at 10 mmfrom the whisker pad. Even given this precaution, a 1-mm misplace-ment can dramatically affect the absolute velocity delivered. There-fore, our analyses focus on trends within single experiments and donot compare absolute values across animals. Because the animal wasanesthetized and immobilized in these experiments, the location of thewhisker within the diameter of the pipette was maintained within agiven preparation.

In most animals, noise trials in which no stimulus was deliveredwere also recorded. In data sets in which noise trials were notrecorded, 40 prestimulus frames were used to approximate noisetrials. Dual whisker deflections were delivered using two individuallycalibrated piezoelectric actuators at equal velocity, both in the rostral-caudal plane.

Image analysis and transformation into time series. All data anal-ysis was done in custom-written software in MATLAB (The Math-Works, Natick, MA). For each trial, a background image (F0) wascreated by averaging 40 prestimulus frames (200-ms interval). Thestimulus-evoked VSD signal was calculated as the percent changefrom this background image: %�F/F � (F � F0)/F0 � 100. Analysesof response amplitude were performed on time series derived fromVSD image series. VSD time series were calculated by averaging overa circular region of interest (ROI) with a 10-pixel radius (�200 �m)from the center of activation in the onset frame (determined manually,usually 10 or 15 ms after stimulus delivery) from an average of alltrials. The onset frame has previously been shown to be restricted toa single cortical column (Petersen et al. 2003a). The use of a spatiallyrestricted ROI resulted in an increased signal-to-noise ratio andallowed the detection of even small activations that were stimulusevoked. For calculation of the center of mass and image presentationonly, images were filtered with a spatial averaging filter (400 � 400�m, �1 barrel). To display response amplitude for all data sets on thesame scale, single-trial response amplitudes were normalized by themaximum single-trial response amplitude observed in each data set.Average response amplitudes were normalized by the maximumaverage response.

Ideal observer classification by stimulus velocity. An ideal ob-server was tasked with classification of trials by response ampli-tudes (r) into six stimulus velocity categories V1, V2, ..., V6 (Wanget al. 2010). Response amplitude r is the peak response frame fromthe barrel-specific time series derived from VSD images describedabove. The temporal dynamics of the VSD response were excep-tionally stereotyped, and the peak frame is consistent across allstimuli within a single preparation. For each velocity Vi, a proba-bility distribution, P(r|Vi), was estimated using bootstrapped esti-mates of the sample mean. Bootstrapped sampling was performedwith replacement. The set of six velocity distributions formed thetrial-average classifier. The same classifiers were used in alldecoding frameworks throughout the study. The input to themodel, the response estimate r was modulated by changing thenumber of trials used to calculate r. A given subsampled responseamplitude r was sorted into the velocity class with the maximallikelihood estimator (given a flat prior):

Vˆ MLE � arg maxViP(r|Vi).

The result was a 6 � 6 performance matrix in which the [j, k]element was the frequency of assigning a single trial to Vk when the

2457CORTICAL VARIABILITY AND PROBABILITY OF ACTIVATION

J Neurophysiol • doi:10.1152/jn.00547.2015 • www.jn.org

actual stimulus was Vj. The “actual classification performance” wasdefined as the frequency that a given trial was correctly classified,summed across stimuli, or simply the average of the diagonal of theperformance matrix.

The “optimal classification performance” for a given classifier waslimited only by the overlap between the velocity distributions. Con-ceptually, it was the frequency of correctly classified trials if theresponse amplitudes were sampled directly from the classifier distri-butions:

Optimal performance � 100 · �Vi

�r�Ri

P�r�Vi�P�Vi�dr ,

where Ri is the range of response amplitudes over which velocity Vi

had the maximum probability and P(Vi) � 1/6, the relative frequencyat which a given velocity stimulus was presented. Extreme errors weretrials in which the assigned velocity class, Vk, differed from the actualstimulus class, Vj, such that |k � j| � 2. For simulations of multiplewhisker presentations, the maximum likelihood estimation was cal-culated from the effective response amplitude, �r, which was the meanof n (1, 3, or 10) randomly selected trials.

Response frequency analysis. Single-trial time series were calcu-lated by averaging over the same barrel-sized ROI used to createaverage time series described previously. Each trial was determined tobe either a “response” or “no-response” trial based on the presence orabsence of a measurable stimulus-evoked activity. As the temporalresponse was extremely stereotyped across velocities, an average timeseries from 0 to 250 ms after stimulus delivery was used as a filter (ortemplate). The filter included frames in which the activity had not yetreached the cortex, to ensure that changes in fluorescence werestimulus locked. Individual trials were matched to the template bypointwise multiplication and summed (dot product). The resultingmatch score quantified how well each single trial matched the tem-plate:

Match Score � �k�0

K�1

x�k� � h�k� � x · h ,

where x is the single-trial time series, h is the averaged time seriesfilter, and K is the length of the filter. Match score distributions fromboth noise trials and stimulus trials were calculated. A classificationthreshold was set at 3 SD above mean scores of noise trials. Stimulustrials with match scores above this threshold were considered re-sponse trials. Note that the use of a high threshold (a match scoreabove the 99.7 percentile of the noise distribution) resulted in a greaternumber of false negatives (a misclassification of a true response as ano-response trial) while limiting the probability of false-positivemisclassifications. The high threshold level was chosen to highlightthe existence of large response amplitudes to small velocity stimuli;however, the results presented in this report were consistent for allthreshold levels (0–3 SD above noise). Note that the threshold choiceis required only for qualitative assessment, because significance testswere not used on the sorted data sets.

Probability of activation simulations. We discussed two possiblemodels that could generate the observed average VSD responses, thecontinuum model and the probability of activation model. As ademonstration of the unique characteristics of each model, we simu-lated single-trial distributions with identical trial-average statistics butoriginating with the assumptions of the two possible models. Thesesimulations are meant to demonstrate the qualitative differencesbetween the models and are not quantitatively representative of anyspecific parameter of actual data. The single trials from all data setswere normalized (as described above) such that they could be plottedon the same axis and considered a single data set. Briefly, each trialwas normalized relative to the largest single trial observed within agiven preparation such that the maximum response amplitude is fixedat 1. For the simulated continuum hypothesis data, distributions wereassumed to be normally distributed about the observed mean of each

velocity category with a standard deviation (SD) equal to that of thenoise distribution. For the probability of activation data, the “no-response distribution” was Gaussian with identical mean and varianceof the actual noise distribution (trials where no stimulus was pre-sented). The “response distribution” was also Gaussian, with a meanand SD estimated from only trials assumed to be response trials. Inthis analysis, unlike in the formal analysis above, response trials aresorted by an absolute threshold (3 SD above the noise distributionmean). Simulated response frequencies at each velocity were ran-domly drawn from binomial distributions measured from real data. Atrial was randomly assigned as response or no response and thenassigned an amplitude randomly drawn from the corresponding dis-tribution described above.

Calculation of activated area. To determine the spatial spread ofthe cortical activation, we estimated the extent of the VSD imageactivated following a whisker deflection. Specifically, the activatedarea analysis was performed on a time-averaged VSD image thatincluded data from two frames (15 and 20 ms after stimulus delivery).Each image was filtered with a spatial averaging filter (100 � 100�m) to reduce high-frequency spatial noise prior to analysis. Themean and SD of the noise were calculated using all pixel intensities inthe noise image. The threshold was set at 2 SD above mean noise(determined from a prestimulus noise frame). Regions of the imagethat surpassed this activity threshold were considered active. Trial-average area represents the mean of all the activated areas of singletrials.

Analysis of rising slope in VSD signal. We defined the rising slopeof the measured VSD signal as the maximum derivative, or change insignal between any two frames, that occurred during the stimulusonset to peak response. This calculation was performed on bothtrial-averaged time series and single-trial time series that were usedfor the response amplitude analysis.

Multiwhisker spatial classification. A spatial template-matchingalgorithm was used to classify single trials from simultaneous whiskerdeflection. This algorithm was adapted from a previously publishedmethod (Millard and Stanley 2013). In each data set (n � 3 animals),trials (data set 1, 100 trials; data sets 2 and 3, 50 trials) were collectedfor individual whisker deflections and for both whiskers deflectedsimultaneously. Two-dimensional images were transformed from aone-dimensional vector representing individual barrel columns. Arepresentative barrel map of 32 barrel columns was registered asdescribed previously, and the mean change in fluorescence withineach barrel region was calculated. N is the number of barrel columns(maximum of 32) that fell within the VSD image. Trial-average andtime-average (15–20 ms) images from individual whisker deflectionsand simultaneous whisker deflections were transformed in this way tocreate spatial templates for each stimulus category: whisker 1 alone(T1), whisker 2 alone (T2), both whiskers (T3), and no stimulus (T4).We assumed a constant noise model with covariance (�) to accountfor uneven staining of the cortex. Single trials (y) were time-averagedand mapped to one dimension in the same manner as for the templatesand then sorted by choosing the least-squares template, TLS, thatminimized the weighted mean squared error:

TLS � argmin Ti�

T1,...,T4

�y � Ti�'��1 �y � Ti� .

RESULTS

Population responses to whisker deflections were studiedusing voltage-sensitive dye imaging (VSD) as illustrated inFig. 1A. Single punctate whisker deflections of different ve-locities were delivered by a computer-controlled piezoelectricactuator in the rostral-caudal plane (see METHODS). Images wererecorded every 5 ms and the fluorescence quantified as percentchange from background. Figure 1B shows trial-average im-ages for six different velocity whisker deflections (V1 to V6):

2458 CORTICAL VARIABILITY AND PROBABILITY OF ACTIVATION


75, 150, 300, 600, 900, and 1,200°/s, which span the expectedbehavioral threshold for detection of the punctate deflection ofan individual whisker (Ollerenshaw et al. 2012; Stüttgen andSchwarz 2008). Consistent with previous studies, the neuralactivity started locally over the primary barrel column �10 msafter stimulus presentation (Fig. 1B) and then spread intoneighboring barrel columns (Ollerenshaw et al. 2012, 2014;Petersen et al. 2003a; Wang et al. 2012). In our hands as wellas in previous VSD studies, location of the onset of corticalactivity is topographic and determined by the identity of thedeflected whisker, allowing a direct alignment with the under-lying barrel map. Time series shown in Fig. 1C were created byaveraging temporally (images over trials) and then spatially(over a circular ROI approximately the size of 1 cortical barrelcolumn: 400-�m diameter) corresponding to the deflectedwhisker (see METHODS). Increasing the velocity of the stimulusincreased the trial-average peak amplitude (or simply responseamplitude) of the VSD response (Fig. 1D) across all experi-ments (n � 6 whiskers, 4 animals). These trial-average VSDdata are consistent with previous electrophysiological (Bolooriet al. 2010; Pinto et al. 2000) and VSD findings (Petersen et al.2003a; Wang et al. 2012) which demonstrated that as thevelocity of a whisker deflection increased, the trial-averageactivity increased.

Trial-average differences were not sufficient to allow forsingle-trial velocity discrimination. The previous analysis is areplication of imaging and electrophysiological studies (Leeand Simons 2004; Petersen et al. 2003a; Pinto et al. 2000;Wang et al. 2010). Figure 1 shares an important characteristicwith these previous analyses: the analysis begins by collapsingthe data across trials. Here, we collapse across trials by aver-aging VSD time series from multiple trials, but with othermethodologies this takes the form of a computing firing rate,average single-cell trace, or another summary metric. Manytechniques, including (but not limited to) intracellular record-ing, extracellular recordings, calcium imaging, and two-photonimaging, do not have sufficient signal-to-noise ratio to estimatea population response within a single trial. Because of thisshortcoming, computing a summary metric across trials is anecessary first step. VSD imaging, on the other hand, hassufficient signal-to-noise ratio to estimate population activityon a single trial. This unique characteristic of VSD allows us totest the assumption that the trial average can substitute effec-tively for single trials for a model of the neural code. Thishypothesis cannot be evaluated well with other methods. In thisstudy we specifically tested whether single-trial response couldbe classified into a whisker deflection velocity category usingknowledge of the trial-average population response.

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Fig. 1. Trial-average cortical response amplitude was modulated by stimulus strength. A: a schematic of the voltage-sensitive dye (VSD) imaging system. Apiezoelectric actuator delivered controlled mechanical deflections of a whisker with variable velocity. The surface of the cortex was stained with VSD, and imageswere recorded on a high-speed charge-coupled device camera every 5 ms. B: representative cortical responses to whisker deflections of variable velocity (V1,lowest). Images were averaged over 60 trials. Scale bar (1 mm) applies to all images. %�F/F0, response amplitude. C: corresponding time series to the imagesshown in B. Time series were calculated by averaging over a circular region of interest the size of 1 cortical column (�400-�m diameter) centered over the barrelcorresponding to the deflected whisker. The peak response frame determines the response amplitude. D: the trial-average response amplitude for each data set(dashed lines, n � 6 whiskers, 4 animals) and the resulting mean (solid black line). Trial-average response amplitude increased with velocity in all data sets.



To test this hypothesis, we define a trial-average classifierfor each data set. The trial-average classifier is a set of responsedistributions created from bootstrapped estimates of the trialaverage (mean) for each of six velocities. Bootstrapping is asubsampling methodology (n � 10, with replacement) thatestimates the variability of a sample parameter (trial-averageresponse amplitude). As the number of trials increases, thebootstrapped distribution will tend to center on the overallsample mean. The SD of the trial-average classifiers are esti-mates of the standard error of the mean (SE). A representativeexample of a set of trial-average distributions is shown in Fig.2A. The observed trial-average sample peak of this specificdata set is represented as a black dot.

If the single trials were perfectly modeled by the trialaverage, the theoretical performance would be limited only bythe area of overlap of each of the distributions (referred to asthe optimal classifier performance). In other words, if it werepossible to infer something about the single trial (the ethologi-cally relevant measure) from a collapsed metric such as thetrial-average response amplitude, we would expect an idealobserver to be able to effectively classify trials using theinformation available in these classifiers.

We tested this hypothesis using maximum likelihood esti-mation. Briefly, given an input response amplitude r, drawnfrom the boot-strapped distributions, the trial is classified as thestimulus velocity with the maximum likelihood of havingcreated that response. Optimal performance is visualized inmatrices showing the frequency of trials predicted to be in eachclass (columns) for each actual input velocity (rows). A rep-resentative performance matrix is shown in Fig. 2B. In all

our data sets, the optimal performance matrix has a strongdiagonal representing a high number of correctly classifiedtrials (72.9% 10.4%, mean 1 SD). If the trial averageswere perfect models of single trials and differed only due toexperimental noise, one would expect an ideal observer tocorrectly classify a trial �72% of the time.

Because VSD imaging allows us access to single trials, wewere able to use the same decoding framework to classifyexperimentally observed single-trial response amplitudes. Thedecoding performance on single trials was substantially lessthan optimal. On average, we correctly classified 27.7% 3.7% of trials, which is about 11% more than if the classifi-cations among six equally likely velocities were purely ran-dom. The performance of each individual data set is shown inFig. 2E.

This result is not surprising. The SD of the trial-averageclassifiers distributions are estimates of the SE of the samplemean. Given a sample size greater than one, the SE necessarilyunderestimates the SD of the population (the true single-trialvariability). Because these trial-average classifiers are also thedistributions that would be used to assess the statistical signif-icance of the trial averages, this simulation demonstrates thattrial-average metrics, represented in this analysis by the trial-average classifier, are not representative of single trials (thescientifically relevant unit of the neural code).

It is interesting to observe that the actual performance of anideal observer using this framework was not just noisy butapproached random classification, particularly when we con-sidered the scale of the errors. In the example shown in Fig.2C, a trial from even the lowest velocity (V1) was classified as

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Fig. 2. Classification of single trials by an ideal observer performed near chance. A: representative example of a trial-average classifier. Black dots represent actualobserved trial-average time series peaks and appear in velocity order (closest to origin V1, maximum V6). B: the optimal performance of the classifier shown inA is limited only by the overlap of the velocity response distributions. The probability of classifying an observation from velocity Vj as coming from Vk isrepresented graphically as element [j, k] in the performance matrix. The presence of a strong diagonal represents a high number of correctly sorted trials. C: theactual performance matrix of the ideal observer given true single-trial response amplitudes. D: distribution of the errors associated with classification. Using thenotation described above, the error � j � k. E: the percentage of trials correctly classified under both the optimal and actual conditions across all data sets.Optimal and actual performance from individual data sets are connected with a line. F: the percentage of error trials that are extreme |j � k| � 2 in both the optimaland actual performance conditions.



one of the highest velocities (V5); similarly, a trial from thehighest velocity was mistaken classified as the lowest (V1). Toquantify this across data sets, we considered any trial that wasmisclassified by two velocity classes or more away as anextreme error (Fig. 2D). In the optimal case, the percentage oferrors predicted to be extreme was 7.8% with an SD of 10.3%.The actual observed percentage of extreme errors was fivetimes greater, on average, 38.9% 7.4%. The percentage ofmisclassified trials that are expected to be extreme errors usinga random classifier is 56.2% (Fig. 2F).

The poor performance of the ideal observer using a trial-average classifier on single trials demonstrates that the singletrials are not well modeled by the trial-average response. Toinvestigate how this occurs, we considered single-trial distri-butions directly. Figure 3A shows the time series associatedwith single trials from a representative data set. There is largevariability in the response amplitude across all velocities.Consistent with the high number of extreme errors made whendecoding with a trial-average classifier, the response amplitudefrom a single trial in response to a low velocity can equal themagnitude of the response from a trial observed in response toa high velocity. A jittered scatter plot shows the same data witha single data point representing the peak response amplitudeframe (open circle) for each single trial at each velocity (Fig.3B). The mean response is indicated with a solid black line. Aspreviously observed, the mean (trial average) increased withvelocity, but a given response amplitude on a single trial can bethe result of any velocity. The corresponding plot with allsingle trials from all data sets (n � 6 whiskers, 4 animals) isshown in Fig. 3C. From this representation of the data, it isclear that knowledge of the peak response amplitude is notsufficient to classify individual trials into velocity categories.

Single-trial responses were well-described by a probabilityof activation model. It must be determined how, given suchvariability in the response amplitude, there are substantialdifferences in the trial-average amplitude between velocitiesacross all animals. In all data sets, for a given velocity, weobserved a subset of trials in which the stimulus-evokedresponse was not measurably increased from the prestimulusactivity. These trials were distinctly different from the trials inwhich there was clearly an evoked response (Fig. 3A). Wesorted trials on the basis of presence or absence of a stimulus-evoked response on individual trials using a matched-filteralgorithm (see METHODS). We defined two categories: 1) re-sponse trials, in which poststimulus fluorescence was distin-guishable from noise, and 2) no-response trials, in whichpoststimulus fluorescence was not different from noise. Anexample set of sorted time series, as well as example corre-sponding single-trial images, is shown in Fig. 4A. The magni-tude of the response and no-response trials was not distinguish-able by an absolute threshold, but the response trials allexhibited a clear, spatially specific activation over the primarybarrel column as well a stimulus-locked increase in fluores-cence in the corresponding time series. No-response trialsexhibited either nonspecific background activity or no stimu-lus-specific changes at all. In a small number of trials sorted asno-response trials, there was actually a very small spatiallylocalized signal. We consider these trials to be response trialsmisclassified as no-response trials, but the change in activitywas so small as to not be distinguished from noise fluctuationsby our sorting criteria (Fig. 4B).

When response or no-response trials were considered alone,the differences between the velocities were dramatically re-duced. The ordered nature of the velocities was sometimes

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even lost: low velocities had larger mean response amplitudesthan higher velocities, as shown in Fig. 4C. The means ofresponse and no-response groups for individual data sets areshown as dashed lines in Fig. 4D. Once sorted, the absoluteamplitude of response and no-response trials was no longerstrongly modulated by the stimulus velocity. However, thenumber of trials sorted into the response category, which wecall the “response frequency,” increased with stimulus strength(Fig. 4E). This was true for every data set collected. Note thatthe response frequency was considered relative to the velocity(not always the highest velocity) with the highest number ofresponse trials for each data set. Importantly, no velocity in anydata set showed a perfect response rate. Although the fre-quency of response trials always increased with velocity, theabsolute response frequency was highly variable between datasets.

The presence of two distinct types of responses suggests amodel for the encoding of the whisker deflection velocity thatis distinctly different from that predicated from knowledge ofthe trial-average responses alone. Historically, we (Boloori etal. 2010; Ollerenshaw et al. 2014; Wang et al. 2010) and others(Ito 1985; Pinto et al. 2000; Simons 1978) have implicitlyassumed a model in which the stimulus strength was en-coded by the strength of the population response on a singletrial (the trial-average classifier). We refer to this as thecontinuum model because it proposes graded response withincreasing deflection velocity (Fig. 5, top). This continuummodel also represents the traditional interpretation of intra-

cellular and extracellular recordings when responses fromone or a few cells across trials are used as a model for theentire population on a single trial. However, the same meanresponse profile we observed can also be created from a

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Fig. 4. Response frequency was modulatedby stimulus strength. A: single trials werequalitatively and quantitatively separableinto 2 groups: trials with stimulus-evokedactivity (response trials; black) and thosewithout (no-response trials; gray). B: exam-ple single-trial images from trials shown in Ademonstrate variability within the groups.Shown are 3 response trials with variableresponse amplitude (top). Three no-responsetrials (bottom) were chosen to represent thetypes of trials that comprise this category,including a misclassified trial. C: when alltrials were included in the average time seriesof a single data set, there were large differ-ences between the velocities (left), but whenthe average of only response trials (middle)or only no-response trials (right) was consid-ered, the differences were dramatically re-duced. D: results were consistent across alldata sets (n � 6 whiskers, 4 animals; dashedlines) for both the response (black) and no-response (gray) average responses. The meanfor both groups is depicted with a solid line.Note that higher variability is associated withconditions with the fewest number of trials(low velocities for response trials, high ve-locities for no-response trials). E: the fre-quency of response trials increased withstimulus velocity for all data sets (dottedlines), as well on average (mean; solid line).

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Fig. 5. Two possible encoding schemes. The continuum model (top) has gradedresponse amplitude with increasing stimulus strength [low, medium (med), andhigh velocities]. For the probability of activation model (bottom), the fre-quency of response trials increases with increasing stimulus strength; however,the response and no-response distributions are conserved across stimulusstrength.



discrete “probability of activation” model formed from twopossible response categories, a response and a no-responseclass (Fig. 5, bottom). The differences in the mean responseoccur by changes in the number of observations sampledfrom each distribution.

It is not possible to distinguish between the probability ofactivation model and the continuum model with only a trial-average response. For example, Fig. 6 shows two possiblesingle trial-distributions simulated from hypothetical realiza-tions of both the continuum (Fig. 6, A–C) and probability ofactivation models (Fig. 6, G–I). Both models result in the sametrial-average measurements (Fig. 6, A, D, G), making thesource of the responses ambiguous. The primary differencesbetween the two models are revealed in a more thoroughexamination of trial-to-trial variability. For the continuummodel, in addition to increased mean response with velocity,three additional observations are evident. First, the minimumand maximum observed responses increased with the mean andwith velocity (Fig. 6B). Second, when pooled across velocities,the aggregate distribution of the responses is multimodal,reflecting the graduated increase in amplitudes with velocity(Fig. 6C). Third, knowledge of the amplitude of a single-trialresponse reduces the uncertainty about which of the stimulicould have produced that response. In contrast, the range ofachievable responses does not change with increasing velocityin the probability of activation model (Fig. 6H). When pooled,this distribution is bimodal (Fig. 6I). Note that although bimo-dality is supporting evidence of a probability of activationmodel, it is not actually necessary, because it is also dependenton the overall difference between signal and noise distributionsin a given data set, which is often determined by data quality,not data content. The key difference between the two models,however, is that in the probability of activation model, thesingle-trial amplitude does not convey information, or reduce

the uncertainty, about strength of the stimulus. Observed VSDsingle-trial distributions in Fig. 6, E and F (same data as in Fig.3C), are more consistent with the probability of activationmodel.

Trial-average trends in rising slope do not reflect differenceson single trials. Response amplitude is not the only parameterthat has been studied historically only as a trial average.Extracellular recordings and intracellular recordings inter-preted as a trial average have reported differences in the risingslope with deflection velocity (Pinto et al. 2000; Wilent andContreras 2004). Using our VSD imaging data, we also con-sidered these additional trends both as a trial average and onthe single trials. Rising slope was calculated as the maximumderivative or change in the magnitude of the signal betweenany two frames (from stimulus delivery to the peak). Consis-tent with previous trial-average single-unit extracellular andintracellular literature, we observed a correlation betweenwhisker deflection velocity and rising slope when this analysiswas performed on trial-average time series. Representativetrial-average time series highlighting this trend are shown inFig. 7A with a summary across animals shown in Fig. 7B(dotted lines represent individual animals, bold line indicatesthe animal average). Qualitatively, these responses are verysimilar to trial-average time series previously reported in in-tracellular recordings (Wilent and Contreras 2004). However,reliable differences in rising slope were not observed when weconsidered the single-trial distributions. Figure 7C shows ascatter plot of the rising slope of all single trials from a typicalanimal. As with response amplitude, the minimal and maxi-mum rising slope of the single-trial distributions did not changewith deflection velocity. Therefore, given knowledge of therising slope of a single trial, an ideal observer would not beable to classify these trials by velocity.

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Trial-average trends of activated area do not reflect differ-ences on single trials. As exhibited in Fig. 1B and previousstudies (Petersen et al. 2003a; Wang et al. 2012), the area ofcortex activated by the whisker deflection also appears tocovary with the whisker deflection velocity when summarizedas a trial average. We quantified the relationship betweenactivated cortical area and velocity. We defined activated areaas the region of cortex within an image with %�F/F0 greaterthan 3 SD of the background noise. Similar to both rising slopeand response amplitude, we observed a trial-average correla-tion between activated area and deflection velocity. Represen-tative trial-average images are shown in Fig. 8A, summarizedacross animals in Fig. 8B. Although this trial-average trend isapparent in both our trial-average images in Fig. 8A as well asin the original examples in Fig. 1A, these differences are not

representative of differences in area of the single trials. In Fig.8C, we also show amplitude-matched single-trial images fromtwo different velocities (V2: 150°/s; V5: 900°/s). From compar-ison of the high-amplitude, low-amplitude, and no-responsesingle-trial images, it is clear that the activated area variesgreatly between trials. Despite the strong trial-average trend, itis straightforward to find examples of V5 (900°/s) trials withdramatically less activated area than a chosen trial from V2(150°/s). The distributions of activated areas from all trials andall velocities in a single animal are shown in Fig. 8D, similarlyto Fig. 3B. Although measurements of area performed onsingle trials can be noisy, it is still apparent that all velocitiesare capable of activating both large (maximum) and small(minimum) cortical areas. This trend was observed in allanimals.

Encoding stimulus strength within the probability of ac-tivation model requires multiple redundant sensors orevents. The probability of activation model predicts thatdeflection is not encoded by the response in a single barrelcolumn. This is troubling since velocity is likely an impor-tant parameter for sensory perception (Jadhav et al. 2009).Outside of controlled laboratory experiments, however, a ratwould rarely perceive a stimulus, whether it is an object orwind stimulus, using only a single whisker. Multiple obser-vations of the same stimulus, whether on the same whiskerover time or over an array of multiple whiskers, couldprovide an estimate of the strength of stimulus. For instance,a weak stimulus may activate 2 barrel columns out of 10, orresult in an observable activation in 2 of 10 whisks across anobject. Similarly, a strong stimulus may activate all 10barrels or respond on every single whisk across an object.This hypothesis can easily be simulated by adapting thesame maximum likelihood decoding framework used in Fig.2 to include a variable number of observations. We simu-lated having access to multiple observations by averaging 3or 10 single trials into a single response variable prior toclassification. Overall accuracy of the classification in-creased with increasing number of observations of thestimulus. In Fig. 9A, there are increasingly prominent diag-onals in the performance matrices as the number of trialsincreased from 1 to 3 to 10 observations. This was trueacross all data sets (Fig. 9B). This conceptual model sug-gests that velocity discrimination performance would in-crease with additional samples or observations of the stim-ulus given the probability of activation model. Note thatbecause the difficulty of the classification task depends onarbitrary experimental decisions such as the number ofvelocities, we do not consider the specific number of whis-kers or the exact performance values reported here to bebiologically relevant. The observation that increasing thenumber of observations increases the performance wouldhold in all nontrivial classification paradigms given theprobability of activation hypothesis.

The key assumption in this conceptual simulation in Fig. 9was that population response measurements that encode thestimulus velocity are not coupled and instead are redundantestimates of the same stimulus parameter. In other words, theproposed velocity-encoding scheme requires that it is possiblefor one barrel column to respond while another adjacent barrelcolumn does not. If the responses of neighboring whiskerswere trivially coupled by a network state variable, VSD imag-

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ing artifact, or other confounding variable, then no new stim-ulus intensity information could be gained by increasing thenumber of observations.

To our knowledge, within-trial population response correla-tions between neighboring barrel have not been experimentallystudied using VSD or otherwise. When considered as a trialaverage, the findings across an array of studies are collectivelyinconclusive: some studies observe sublinear population re-sponses (Civillico and Contreras 2006; Mirabella et al. 2001;Simons 1985), others supralinear (Ego-Stengel et al. 2005;Shimegi et al. 1999 2000), and some no change at all (Drewand Feldman 2007).

We examined the cortical activity in response to simultane-ous deflection of two whiskers on single trials to determinewhether or not adjacent barrel columns are deterministicallycoupled within a single trial. In three additional experiments (3animals, 4 pairs of whiskers), two adjacent whiskers weredeflected both individually and simultaneously. The neuralactivity was recorded using VSD imaging as before. Consistentwith previous studies, the trial-average VSD image from si-multaneous deflection was spatially similar to summed re-sponses of the two individual whiskers (Fig. 10A). On a subsetof single trials, however, even though both whiskers werephysically deflected, the spatial extent of the cortical response

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more closely resembled trials in which only one whisker wasdeflected (Fig. 10B). This preliminary evidence suggests that itis possible for only one barrel column to respond given thesimultaneous deflection of two whiskers: the responses acrosswhisker barrels are not strongly coupled. Although this spatialassessment is qualitative, it was repeatable across animals. Werepeated the same experiment in three separate animals, usingfour pairs of whiskers (data sets) in total. In each animal, weobserved subsets of trials in which one or the other barrelcolumn responded.

We additionally observed that the frequency of the possibletrial types was supportive of the general probability of activa-tion model. To estimate frequency, we sorted images fromsingle trials recorded in response to dual whisker deflectionsbased on a spatially matched filter algorithm (see METHODS) andrecorded the number of trials that most resembled the spatialprofile of four categories: each whisker individually responds(barrel column 1 alone, barrel column 2 alone), both barrelcolumns respond, and neither respond. The observed frequen-cies for two data sets (from 3 animals) are shown in Table 1.Two observations support the probability of activation modelin the interpretation of the data. First, trials in which twowhiskers are deflected but only one barrel column responds arecommon. In all data sets, single barrel column responses todual whisker deflections were at least 10% of trials, as much as41% in some data sets. Individual barrel column responsesfrom both whiskers were observed. Second, the frequency ofsingle barrel column responses was consistent with the ob-served probability of activation in the single whisker deflectiondata (Table 1). In data set 1, for example, the response

frequency for individual whisker deflection was lower than inthe other data sets (62% and 76%, respectively, for whisker 1and whisker 2). Consistent with a probabilistic model, thenumber of single barrel column response trials for the dualdeflection data was higher (22% and 19%). Additionally, indata set 3, the response of whisker 2 alone was very low (32%),and this is reflected in the number of overall no response trials(neither whisker responses) in the dual whisker deflectionstimulus (32%). Taken together, these observations support thehypothesis that barrel column circuits are not coupled within asingle trial and can act as redundant encoders of stimulusintensity. It is important to note that whereas the existingevidence suggests that the spatial profile of responses resem-bles the combined and probabilistic responses of single whis-ker deflections, this is not evidence of independence of re-sponse amplitude or probability of response.

In summary, we have demonstrated that trial-average trendsare insufficient as evidence to support inferences about char-acteristics of the neural code directly. With respect to whiskerVSD data specifically, the variability within the single-trialdistributions in amplitude, rising slope, and area instead sup-port a probability of activation framework in which thestrength of the sensory input is encoded not in a graded corticalresponse amplitude, but instead probabilistically and redun-dantly (across trials or experiences). In addition, we provideevidence that cortical columns that represent input from dif-ferent whiskers are separable, potentially allowing for velocityinformation to be encoded probabilistically across the whiskerarray.

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Table 1. Spatial classification of simultaneous whisker deflection trials

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Data set 1 0.62 0.76 0.51 0.22 0.19 0.08Data set 2 0.90 0.66 0.68 0.08 0.22 0.02Data set 3 0.62 0.32 0.52 0.14 0.02 0.32Data set 4 0.66 0.76 0.70 0.14 0.08 0.08

Frequencies are presented as probability estimates: the number of observed trials in each category divided by the total number of recorded trials. Wk, whisker.



DISCUSSION

In this report, we present evidence that the stimulus strengthis not encoded by graded changes in response amplitude withina cortical/barrel column. Specifically, the correlation betweendeflection velocity and trial-average VSD response amplituderesults primarily from modulation of response frequency, notabsolute amplitude. An ideal observer analysis showed thatdifferences in trial-average response amplitudes were not suf-ficient information to allow classification of trials into velocitycategories; instead, the observer made large classification er-rors. Although highly variable, there was structure in thesingle-trial distributions. We observed that single trials from allvelocities divided into two groups: response and no-responsetrials. Once sorted, amplitude differences between velocitieswere dramatically reduced. Additionally, trial-average trendsin rising slope and activated area did not reflect differences insingle trials.

Two surprising aspects of the VSD single trial responseswere at odds with the continuum model and led us to theprobability of activation model. First, we failed to observeactivity in response to some (even very strong) whisker deflec-tions. Because no-response trials are effectively an absence ofevidence, when considered in isolation, these trials might beattributable to technical limitations of the VSD methodology,such as requiring many neurons to be active simultaneously fora detectable signal or variable background activity. However,we also observed high-amplitude responses to minimal veloc-ities, including those velocities predicted to be significantlysubthreshold in an awake, behaving animal. In fact, somenumber of trials in all velocities achieved maximal responseamplitude. This observation is distinct from the observation ofno-response trials because it is dependent not on an absence ofevidence but on positive evidence of activity. Under the con-tinuum model, it would be unlikely to observe the maximumresponse amplitude to a slow, subthreshold, whisker deflection;it would be exceptionally unlikely to observe them with thefrequency we observed in the VSD data. Although subtle, it isimportant to note that the VSD data reported presently are notsupportive of an all-or-none bimodality. Instead, responseamplitude was extremely variable, taking on any possiblevalue: a “something-or-nothing” distribution. Taken together,we believe the dual inconsistencies of the observed responsedistribution are impossible to reconcile with the continuumhypothesis, leading us to propose a probabilistic hypothesis forthe encoding of whisker intensity information.

Given our proposed model, it is essential to consider theVSD evidence and the probability of activation hypothesis inthe context of existing extracellular and intracellular data. TheVSD signal is limited to activity in supragranular layers ofcortex due to light loss by scattering from deeper depths(Petersen and Diamond 2000), and we specifically targetedlayer 2/3 with the imaging as a representation of the suprath-reshold output of layer 4 projections to 2/3. Although VSD isnot specific to cell soma or any cell type, in vivo VSD activityhas previously been shown to be linearly correlated with layer2/3 pyramidal neurons in the barrel cortex (Cohen et al. 1978;Petersen et al. 2003a). Given only the data in this study, wecannot rule out the possibility that the probabilistic responsesare specific to layer 2/3, particularly given that layer 2/3 hascharacteristically low firing rates and high trial-to-trial vari-

ability (Crochet et al. 2011; Kerr et al. 2007; Petersen et al.2003a; Sato et al. 2007; Wilent and Contreras 2004).

However, after critically reevaluating existing literature, wefind the probability of activation hypothesis does appear re-markably consistent with existing extracellular and intracellu-lar data across layers. Spiking data are almost exclusivelyconsidered as part of a trial average. We and others haveassumed that that a small subset of neurons represent thepopulation: that the trial-average or a combined peristimulustime histogram (PSTH) can be used to estimate the variabilityand extremes of the population responses on single trials (Maet al. 2006; Pouget et al. 2003; Wang et al. 2010). It isinteresting to observe retrospectively that there is actually nopositive evidence for this assumption. Instead, probabilisticand often absent responses are characteristic not only of indi-vidual neurons but also of the behavioral output: psychometriccurves recorded from animals performing a whisker detectiontask. Focusing on electrophysiological evidence, previous stud-ies of layer 2/3 neurons reported trials in which a whiskerdeflection did not cause any spikes within the experimentallyobserved subset of the population. This was true even withhigh stimulus intensities (Kerr et al. 2007; Petersen et al.2003b; Sato et al. 2007; Wilent and Contreras 2004). In thecortical input layer, layer 4, neurons often respond to transienthigh-velocity events, such as the set of stimuli used in thisstudy, with a single spike or no spike at all (Lee and Simons2004; Wang et al. 2010). In single-unit recordings, trials withno experimentally observed activity not only exist, but thefrequency of such trials is inversely correlated with deflectionvelocity, consistent with our present interpretation. Conse-quently, the trial-average firing rate of a single neuron, orPSTH, is similar to an estimate of the reliability of an individ-ual neuron across trials. This reinterpretation demonstrates thatthe continuum model was built from an assumption made in anabsence of evidence: neural activity was assumed to haveoccurred even when none was experimentally measured. Thenonspecificity of the VSD signal, although in some contextsconsidered a limitation, is uniquely capable of analyzing thepopulation responses separate from this ubiquitous, but unsub-stantiated, assumption of reliability of the population response.

The results presented in this report also allow an intriguinglysimple interpretation of canonical behavioral experiments. Be-havioral experiments have shown that the probability of detec-tion increases with stimulus velocity (Ollerenshaw et al. 2012;Stüttgen and Schwarz 2008), which we observed as an in-creased probability of response in our VSD signal. A probabi-listic behavioral output is matched with a probabilistic neuralsignal. In fact, existing behavioral data from our laboratory andothers (Ollerenshaw et al. 2012; Stüttgen and Schwarz 2008)show that the detection threshold (the deflection velocity atwhich behaving animals respond to a whisker stimulus 50%of the time) is between 200 and 300°/s. This is the samerange of stimulus intensities in which we observed a 50%probability of response in this study. It is possible tointerpret these behavioral results in the context the contin-uum model, but the simplest interpretation, where detectionoccurs when the activity crosses an absolute threshold,cannot account for the observed behavioral results. Previ-ously, more complex models such as an accumulation ofevidence model were used to match observed behavior withthe neural recordings (Ollerenshaw et al. 2012).



The probability of activation model makes the specificprediction that a behaving animal could not discriminate de-flection velocity with information from only a single whisker.This is consistent with behavioral evidence currently available.Existing behavioral paradigms show that animals respond moreoften to stronger stimuli and that the dynamic range of detect-able stimuli can be modulated by previous or ongoing stimuli(Ollerenshaw et al. 2014; Waiblinger et al. 2015). Thoughthese paradigms demonstrate complex behaviors and capabil-ities of rodents, they are not evidence of velocity discrimina-tion. To our knowledge, no study has shown that an animal canbe trained to discriminate whisker deflection velocities. Such astudy requires a demonstration that animals can respond lessoften to stronger stimuli or differently (i.e., alternative forcedchoice) within a set of stimuli with variable intensity.

One of the biggest limitations of this study is the use of ananesthetized preparation. Although it is impossible to know forcertain how anesthesia influences the observed effect, an at-tractive hypothesis is that the observed bimodality is related todifferent processing of stimuli in the “up” and “down” brainstates characteristic of an anesthetized cortex (Civillico andContreras 2012; Petersen et al. 2003b). Brain-state fluctuationslikely contribute to the variability of the VSD signal. Becausewe did not record any indicator of cortical state, we cannotspecifically exclude this hypothesis. However, several obser-vations suggest that a causal role for up and down states indetermining the observed response frequency is unlikely. First,the frequency of no-response trials is stimulus specific,whereas the stimuli are delivered in pseudorandom order. Eachstimulus condition samples from relatively equal occurrencesof the up and down states; therefore, state should affect allstimuli equally. Without a more complex nonlinear relation-ship between state and response frequency, simple state fluc-tuations are not sufficient to explain the stimulus-dependentdifferences. Second, the dual whisker deflection data suggestthat one part of the cortex can respond while a neighboringregion of the cortex does not. If up and down states weredetermining this response/no-response characteristic, then onewould have to conclude that neighboring whisker barrels couldbe in opposing states at the same time. Although possible, thisis inconsistent with existing literature (Petersen et al. 2003b).Since neither the probability of activation hypothesis nor thecontinuum hypothesis has been observed experimentally inawake animals, both potential models should be consideredwhen techniques that allow for recording of entire populationson a single trial in awake animals are perfected.

Intriguingly, the instantaneous velocity of whisker deflectionis analogous to simplistic characterizations of the strength ofinputs in other pathways, such as sound intensity in audition orluminance/contrast in vision, both of which are represented byan increased trial-average response amplitude. Most existingtheories of neural computation, both in the barrel cortex and inother sensory modalities, rely on local differences in theamplitude of the population response to encode stimulus pa-rameters (Ma et al. 2006; Pouget et al. 2003; Seriès et al. 2004).If the absolute strength or magnitude of a population responseis not informative within a single experience or a corticalcolumn, it reduces the power of such proposed codes. Perhapsmost strikingly, the results of the ideal observer model dem-onstrate that changes to parameters measured or inferred fromthe trial average, including but not limited to the current

examples of response amplitude, rising slope, and activatedarea, would not represent a feature available for decodingstimulus information during active perception.

We propose a framework in which the strength of thesensory input is encoded not in a graded cortical responsecontinuum but probabilistically by distinct, spatially separablesubpopulations of neurons (different cortical columns). Differ-ent spatial patterns across columns could encode the equivalentstimulus information or percept while limiting the scientificusefulness of direct inference from a trial-average signal. Wedo not suggest that the data presented in this work, or anysingle scientific study, are sufficient to entirely prove a newhypothesis. Instead, the VSD data become a starting point topropose the probability of activation model as a testable alter-native interpretation of existing intracellular, extracellular, andbehavioral data.

ACKNOWLEDGMENTS

We thank He Zheng for contributing a VSD data set.

GRANTS

This work was supported by National Institute of Neurological Disordersand Stroke Grant R01NS48285. C. A. Gollnick and D. C. Millard weresupported by the National Science Foundation Graduate Research FellowshipProgram.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

C.A.G., D.C.M., R.V.B., and G.B.S. conception and design of research;C.A.G. and A.D.O. performed experiments; C.A.G. and D.C.M. analyzed data;C.A.G. and G.B.S. interpreted results of experiments; C.A.G. preparedfigures; C.A.G. and G.B.S. drafted manuscript; C.A.G. and G.B.S. edited andrevised manuscript; C.A.G., D.C.M., A.D.O., R.V.B., and G.B.S. approvedfinal version of manuscript.

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