The accuracy of membrane potential reconstruction based on spiking
Deepankar Mohanty, Benjamin Scholl, and Nicholas J. Priebe
Center for Perceptual Systems, Section of Neurobiology, School of Biological Sciences, College of Natural Sciences,
The University of Texas at Austin, Austin, Texas
Submitted 21 December 2011; accepted in final form 20 January 2012
Mohanty D, Scholl B, Priebe NJ. The accuracy of membrane
potential reconstruction based on spiking receptive fields. J Neuro-
physiol 107: 2143–2153, 2012. First published January 25, 2011;
doi:10.1152/jn.01176.2011.—A common technique used to study the
response selectivity of neurons is to measure the relationship between
sensory stimulation and action potential responses. Action potentials,
however, are only indirectly related to the synaptic inputs that deter-
mine the underlying, subthreshold, response selectivity. We present a
method to predict membrane potential, the measurable result of the
convergence of synaptic inputs, based on spike rate alone and then test
its utility by comparing predictions to actual membrane potential
recordings from simple cells in primary visual cortex. Using a noise
stimulus, we found that spike rate receptive fields were in precise
correspondence with membrane potential receptive fields (R2? 0.74).
On average, spike rate alone could predict 44% of membrane potential
fluctuations to dynamic noise stimuli, demonstrating the utility of this
method to extract estimates of subthreshold responses. We also found
that the nonlinear relationship between membrane potential and spike
rate could also be extracted from spike rate data alone by comparing
predictions from the noise stimulus with the actual spike rate. Our
analysis reveals that linear receptive field models extracted from noise
stimuli accurately reflect the underlying membrane potential selectiv-
ity and thus represent a method to generate estimates of the underlying
average membrane potential from spike rate data alone.
primary visual cortex; spike threshold; intracellular recording; simple
THE PRIMARY MODE OF COMMUNICATION between neurons in cortex
is synaptic transmission triggered by action potentials. Action
potentials, or spikes, result when a neuron’s many synaptic
inputs combine to cause it to reach a critical membrane
potential threshold. Whereas a neuron’s spiking response to a
sensory stimulus defines the information it is communicating to
downstream neurons, the selectivity of its response is deter-
mined by the convergence of its synaptic inputs via upstream
neurons. Understanding the basis for sensory selectivity, there-
fore, requires knowledge of the selectivity of the afferent
We know that the aggregate synaptic input, and therefore the
response selectivity of such input, to a neuron is represented by
its membrane potential fluctuations in response to sensory
stimulation; however, direct measurement of membrane poten-
tial requires intracellular recordings, which are difficult to
obtain relative to extracellular (spiking) recordings. Therefore,
a method of estimating the underlying membrane potential
selectivity from extracellular recordings of spikes alone would
be important for providing visibility into the selectivity of
synaptic inputs in cortex.
Such estimation, however, has historically been challenged
by the presence of the intervening action potential threshold.
Threshold acts as a filter for the neuron: stimuli that do not
evoke a sufficient depolarization for the neuron to reach thresh-
old do not generate spikes, and as such, the effectiveness of
these stimuli is overlooked. This filtering action of threshold is
evident in several experimental models of cortex. For example,
in primary visual cortex (V1), neuronal spike rate selectivity is
higher than membrane potential selectivity for orientation
(Carandini and Ferster 2000; Monier et al. 2003), direction
(Jagadeesh et al. 1997; Priebe and Ferster 2005), and spatial
receptive fields (Bringuier et al. 1999). In auditory (Tan et al.
2004) and barrel cortex (Moore and Nelson 1998), spike rate
selectivity is also increased relative to membrane potential
selectivity. This intervening threshold nonlinearity, while crit-
ical to cortical response selectivity, has precluded the transla-
tion of physiologically measured spiking responses into their
underlying membrane potential responses and, in turn, the
important characterization of the underlying synaptic inputs.
We demonstrate here that it is indeed possible to recover
membrane potential selectivity from recorded spiking selectiv-
ity alone, using a dynamic noise stimulus. With the use of a
dynamic noise stimulus, spike rate receptive field estimates
should not be distorted by the threshold nonlinearity, and their
membrane potential and spike rate selectivities, as represented
by their receptive fields, should be the same (Chichilnisky
2001; Simoncelli et al. 2004).
We used intracellular recordings, which allow access to both
the suprathreshold spike rate and subthreshold membrane po-
tential, to determine how our receptive fields based on spike
rate compare with membrane potential receptive fields. Recep-
tive fields of V1 simple cells are virtually identical for mem-
brane potential and spike rate. Furthermore, the average mem-
brane potential time course can be accurately predicted from
spike rate receptive fields. Finally, we demonstrate that the
nonlinear relationship between recorded membrane potential
and spike rate may be accurately estimated from our spike rate
measures. Overall, we found that this technique provides an
accurate prediction of the average underlying membrane po-
tential solely on the basis of the spiking responses, demonstrat-
ing that it is possible to estimate subthreshold selectivity solely
on the basis of suprathreshold responses for simple cells in V1.
Physiological recordings and visual stimulation. Whole cell patch-
clamp recordings were made in vivo from neurons in V1 in anesthe-
Address for reprint requests and other correspondence: N. J. Priebe, Section
of Neurobiology, The Univ. of Texas at Austin, 2400 Speedway, Austin, TX
78705 (e-mail: email@example.com).
J Neurophysiol 107: 2143–2153, 2012.
First published January 25, 2011; doi:10.1152/jn.01176.2011.
21430022-3077/12 Copyright © 2012 the American Physiological Societywww.jn.org
tized, paralyzed cats (2–2.5 kg) as has previously been described
(Priebe and Ferster 2005). Anesthesia was induced with ketamine
(5–15 mg/kg) and acepromazine (0.7 mg/kg) and followed by intra-
venous (IV) administration of thiopental sodium (10–20 mg/kg)
during surgery. After surgery, the animal was placed in the stereotaxic
frame until the end of the experiment. Recording stability was in-
creased by both suspending the thoracic vertebrae from the stereotaxic
frame and performing a pneumothoracotomy. Eye drift was mini-
mized with the IV infusion of vecuronium bromide (Norcuron, 0.2
mg·?1kg·h?1). Anesthesia was maintained for the duration of the
experiment with the continuous infusion of thiopental sodium (Hos-
pira, 1–3 mg·?1kg·h?1). Body temperature, ECG, EEG, CO2, and
autonomic signs were continuously monitored. The nictitating mem-
brane was retracted using phenylephrine hydrochloride, and the pupils
were dilated using topical atropine. Contact lenses with artificial
pupils were inserted to protect the corneas. Supplementary lenses
were selected by direct ophthalmoscopy to focus the display screen
onto the retina.
Borosilicate glass electrodes (A-M Systems, Carlsborg, WA)
were filled with a K-gluconate-based solution (in mM: 130 K-
gluconate, 2 MgCl2, 0.5 EGTA, 10 HEPES, 2 Mg-ATP, 2 Na-GTP,
20 Tris-phosphocreatine). After a craniotomy was made above area
17 (?2 mm lateral of the midline), a small hole in the dura was
made and an electrode was advanced into the cortex with a mo-
torized microdrive (Sutter Instruments, Novato, CA). After the
electrode was in place, warm agarose solution (3% in normal
saline) was placed over the craniotomy to protect the surface of the
cortex and reduce pulsations. All procedures were approved by The
University of Texas at Austin Institutional Animal Care and Use
Visual stimuli were generated by a Macintosh computer (Apple,
Cupertino, CA) using the Psychophysics Toolbox (Brainard 1997;
Pelli 1997) for Matlab (The MathWorks, Natick, MA) and pre-
sented on a Sony GDM-F520 video monitor placed 50 cm from the
animal’s eyes. The video monitor had a noninterlaced refresh rate
of either 100 or 120 Hz and a spatial resolution of at least 1,280 ?
1,024 pixels, which subtended 38 cm horizontally and 30 cm
vertically. The video monitor had a mean luminance of 45 cd/m2.
Noise stimuli were presented for between 8 and 20 s and were
preceded and followed by at least 250-ms blank (mean luminance)
periods. For each recorded V1 neuron, after its preference was
initially characterized for orientation, spatial frequency, spatial
location, and stimulus size for each eye, a one-dimensional noise
stimulus at the preferred orientation was presented to the preferred
eye (Citron and Emerson 1983; Mclean and Palmer 1988; Priebe
and Ferster 2005). At each location the luminance was light, gray,
or dark with probabilities 0.25, 0.5, and 0.25, respectively. Voltage
responses were sampled at 4,096 Hz and stored for subsequent
analysis. A new noise stimulus was presented at the frame rate of
the monitor. The temporal sequence of bars in each trial was
controlled by setting an initial random seed, which could either
vary or be fixed across trials. Receptive field estimates were based
on trials collected in which the random seed varied. Validation of
receptive fields was accomplished by comparing the response to
the trials in which the random seed was fixed with the predicted
response based on the receptive field. All of the neurons reported
here had a spiking modulation ratio (F1/F0) at the preferred spatial
frequency ?1 and were therefore classified as simple cells (Skot-
tun et al. 1991).
Analysis. Spikes were identified from the large characteristic de-
flections in membrane potential. Membrane potential was passed
through a 5-ms median filter to remove the action potentials. Mem-
brane potential and spike rate were then binned at the frame rate of the
stimulus, either 100 or 120 Hz. Further analyses are described where
appropriate in the RESULTS.
Comparing membrane potential and spike rate selectivity in
a simple model. The central aim of this work was to demon-
strate the degree to which membrane potential fluctuations in
response to visual stimuli and selectivity may be accurately
predicted by spike rate. To date, discrepancies in selectivity for
membrane potential and spike rate, combined with the feasi-
bility challenges of measuring membrane potential directly in
vivo, have precluded visibility into the synaptic basis for
response selectivity in cortical neurons. As such, the ability to
map membrane potential from spiking data alone will have
far-reaching utility across studies of cortical function.
The discrepancies in selectivity for membrane potential
versus spike rate stem from experiments in which each stim-
ulus condition is presented individually and the average re-
sponse following the stimulus is measured. To demonstrate
why this is the case, we constructed a model V1 neuron that
depolarizes in response to a light bar flashed in either of two
locations, but to a greater degree to location 1 than to location
2. When plotted based on stimulus location (Fig. 1A), the
selectivity of the model neuron is represented by a vector that
leans closer to the ordinate than the abscissa, indicating that the
neuron prefers a light bar presented in location 1 versus
location 2. Using this model neuron, we can now evaluate two
different methods to estimate both spike rate and membrane
potential selectivity, the first of which produces discrepant
The first method to characterize neuronal response selectiv-
ity is to measure the neuronal response to stimulation of each
spatial location individually. This stimulus protocol is dia-
gramed in Fig. 1A. Light bars flashed in each location sepa-
rately are represented by two filled circles, one on the ordinate
and one on the abscissa. The response of the model neuron is
determined by drawing a projection from the stimulus (filled
circle) onto the model neuron’s selectivity vector. Because of
the neuronal threshold nonlinearity, spikes are only elicited in
response to the stimulus flashed at location 1 (Fig. 1A, red) and
not at location 2 (Fig. 1A, blue), yet membrane potential
depolarizations are elicited in response to the stimulus at both
locations. Therefore, the selectivity of the model neuron differs
substantially when measured via depolarizations versus spike
rate. This is evident in Fig. 1A, inset, in which the vectors
representing spike rate selectivity and membrane potential
selectivity point in different directions.
An alternative method to characterize neuronal response
selectivity is to use a noise stimulus that samples the visual
space of stimulus conditions more broadly (see also Chichilni-
sky 2001 and Simoncelli et al. 2004 for descriptions of this
method). To do so, the luminance of the bars is randomly
varied using a Gaussian distribution and simultaneously dis-
played at each bar location (Fig. 1B). As when we presented
the bars individually (Fig. 1A), the response to each stimulus
condition is determined by the projection onto the selectivity
vector and is indicated by color (Fig. 1B). Importantly, the
stimulus distribution is Gaussian, and therefore the threshold
nonlinearity will not distort the spike rate selectivity and
membrane potential selectivity as we observed when the bars
were presented individually. That is, the subthreshold response
to both bars will be revealed in spike rate, since in this stimulus
method, the simultaneous presentation of bars at both locations
2144LINEAR RECONSTRUCTION OF MEMBRANE POTENTIAL FROM SPIKES
J Neurophysiol • doi:10.1152/jn.01176.2011 • www.jn.org
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