Information

Are all action potentials the same shape and amplitude when graphed with respect to time?


The most common visualization of an action potential is a graph of the difference in membrane potential (y axis) at a particular time (x axis).

According to my textbook Cognitive Psychology by E. Bruce Goldstein, an action potential sent from neuron down the axon remains the same. That is, if we plot the action potential as described above, then at each as it is propagated down it will have the same shape on the graph (within some range of error obviously, but he is saying the error is trivial). But he then says on page 34

One way to answer the question of how action potentials determine different qualities [(e.g. taste of something sweet)] is to propose that the action potentials for each quality might look different. However, [Edgar] Adrian rules out that possibility by determining that all action potentials have basically the same height and shape.

My Question

Can someone confirm these two facts:

  1. Once an action potential is sent from a given neuron down the axon, does the shape and amplitude remain constant as it is propagated?
  2. Do all action potentials have the same amplitude and shape?

  1. Generally speaking, yes. For reference see this paper in Nature This is Fig. 7 from it with comment:

Reason is that most axons are not passive tubes of electrolyte with leakage (in which case AP would be attenuated along it) but rather active media with membrane potential across that have ion channels that reproduce initial action potential along the axon. However, in more passive tubes, like in dendrites, action potentials might be attenuated.

  1. Generally, no. Amplitude of action potential depends on properties of ion channels, at what potential, for example, $K^+$ channels will open to start repolarization (peak of AP). Duration also depends on properties of ion channels. But since there are not a lot of variability in ion channels and extracellular ion composition is mainly same in animals, most of APs will have same shape/duration/amplitude.

Short answer
Action potentials differ in shape between neuronal cell types, and action potentials may even change shapes during action potential propagation within one and the same axon.

Background

  1. Once an action potential is sent from a given neuron down the axon, does the shape and amplitude remain constant as it is propagated?

Although the textbooks will typically say action potentials are transmitted without their amplitude being changed this claim is theoretically virtually impossible due to the many variables encountered in and around the axon. For example, axons in the sciatic nerve may extend to a meter and it is virtually impossible to keep the exact conditions along that length exactly identical. The amplitude of the action potential is mainly dependent on the influx of Na+. Slight variations in membrane potential, concentration of sodium, or channel (subtype) densities may therefore change the amplitude. In addition, temperature affects action potential amplitude (Hodgkin & Katz, 1949) and slight temperature differences along long axons may therefore be expected to alter amplitude. Likewise, shape may alter as well. For example, glutamate released alongside axons of hippocampal pyramidal neurons results in widening of action potentials (Sasaki et al., 2011).

  1. Do all action potentials have the same amplitude and shape?

Therefore, given the answer under question 1 no, they do not have to. Even a propagated action potential in a given axon may change amplitude and shape, as said. Most notably, different neuronal types may in fact be classified according to their action potential morphology, such as the various neuronal types in the dorsal root ganglia of the spine that can be differentiated based on their duration (Villiere & McLachlan, 1996).

References
- Hodgkin & Katz, J Physiol; 109: 240-9
- Sasaki et al., Science 2011; 331: 599-601
- Villiere & McLachlan, J Physiol 1996; 76: 1924-41


Mirroring Action Potentials: Label-Free, Accurate, and Noninvasive Electrophysiological Recordings of Human-Derived Cardiomyocytes

The electrophysiological recording of action potentials in human cells is a long-sought objective due to its pivotal importance in many disciplines. Among the developed techniques, invasiveness remains a common issue, causing cytotoxicity or altering unpredictably cell physiological response. In this work, a new approach for recording intracellular signals of outstanding quality and with noninvasiveness is introduced. By taking profit of the concept of mirror charge in classical electrodynamics, the new proposed device transduces cell ionic currents into mirror charges in a microfluidic chamber, thus realizing a virtual mirror cell. By monitoring mirror charge dynamics, it is possible to effectively record the action potentials fired by the cells. Since there is no need for accessing or interacting with the cells, the method is intrinsically noninvasive. In addition, being based on optical recording, it shows high spatial resolution and high parallelization. As shown through a set of experiments, the presented methodology is an ideal candidate for the next generation devices for the reliable assessment of cardiotoxicity on human-derived cardiomyocytes. More generally, it paves the way toward a new family of in vitro biodevices that will lay a new milestone in the field of electrophysiology.

The in vitro recording of action potentials (APs) from electrogenic cells is a central aspect of many different fields that span from neurophysiology to cardiology, pharmacology, and other medical disciplines. After the invention of patch-clamp, [ 1 ] awarded with the Noble prize in 1991, many complementary approaches have been developed to meet this challenge. They include microelectrode arrays (MEA), [ 2, 3 ] CMOS nanoelectrode array (CNEA), [ 4 ] calcium imaging, [ 5, 6 ] voltage-sensing optical (VSO) platforms [ 7 ] or impedance spectroscopy, [ 8 ] and others. However, each approach presents specific advantages as well as it suffers from intrinsic limitations. For example, despite the unmatched sensitivity of patch-clamp, the possibility to monitor large amounts of cells in a complex culture (neuronal network or cardiac syncytium) with this technique remains very difficult to envision. Recently, MEA recordings have also improved dramatically thanks to novel materials, [ 9-12 ] 3D nanostructures, [ 13-16 ] and advanced silicon and organic electronics. [ 3, 17, 18 ] In particular, the recent work of Abbott et al. [ 19 ] showed for the first time that neuronal action potentials and synaptic signals can be recorded from thousands of connected neurons, providing unprecedented insights on network dynamics and connections. Unfortunately, the invasiveness of the reported approach, based on electroporation, poses strong limitations on repeatability and long-term characterizations. Notably, both patch-clamp and MEA methods require the probe getting in intimate contact with the intracellular compartment. Namely, they require to porate the cell membrane for introducing the probe into the cell, with consequent invasiveness issues related to cellular membrane disruption. [ 20 ] Optical methods for recording action potentials exploit molecules that bind to or in the cells and that emit light with intensity dependence on the variation of the membrane potential. [ 21 ] These methodologies do not require cell membrane disruption and have been used extensively for their high spatial resolution (given by the performance of the optical microscopes) and to the ease of implementation (measurements performed directly with cell cultures on glass coverslips or on simple multiwell plates). In few recent works, optical recording with voltage-indicators could also be successfully combined with optical stimulation for obtaining a powerful all-optical electrophysiology platform, [ 22 ] although high-throughput measurements were limited to ≈50 simultaneous cells at the most. However, standard optical methods are not easy to combine with other light-based approaches such as super-resolution microscopy or nongenetic control with light. [ 23, 24 ] Importantly, the dye-molecules may interact strongly with the cell machinery, altering significantly the cellular activities or even inducing cytotoxic effects. [ 25, 26 ] This poses strong limitations to the use of optical detection methods for those studies in which physiological conditions must be kept strictly unperturbed, as for example the assessment of toxicity of drugs or compounds on neural and cardiac cells. In this regard, it is worth noticing that we are witnessing a constant decline in the number of new drugs approved by the U.S. Food and Drug Administration (FDA), while the average drug development cost has risen to over 2.5 billion dollars. [ 27 ] It is widely accepted that this decline is due to failures in clinical trials, which can come from misleading output from traditional preclinical models (in vitro cultures and animals). [ 28, 29 ] These enormous costs have obvious societal consequences that create the need for novel electrophysiological methodologies. In this regard, an ideal approach for pharmacological screenings should show low to no invasiveness [ 30 ] or perturbations (such as membrane poration or cytotoxicity) combined with high spatial resolution [ 31 ] (possibly down to single cell or even below), high scalability (large number of cells monitored within the same culture), massive throughput [ 32 ] (large number of cell cultures monitored with multiwells approaches), and easy automation.

In this work, we introduce a new paradigm for action potential recording that addresses all of the mentioned limitations. The approach relies on the concept of “image charge” or “mirror charge” in classical electrodynamics: electric charges placed in proximity of a conductor affect its charge spatial distribution thus generating mirror charges into the conductor itself (see inset picture in Figure 1a). Hence, by monitoring the spatio–temporal dynamics of the mirror charges, one can monitor the dynamics of the “source charges” and the related electric potential. Following this idea, we cultured the cells on a suspended membrane that divides the environment in two spaces (see Figure 1): the CIS-chamber, that is a conventional well for cell culturing, and the TRANS-chamber, which is filled with charged fluorophores dissolved in a nonvolatile liquid. The two chambers are completely separated from each other, with no possibility for cells to get in contact with the fluorophores or with the solvent. However, as explained in the next session, the two systems are electrically coupled hence ions accumulated inside the cell generate mirror charges in the TRANS-chamber. In other words, the TRANS-chamber behaves like a virtual mirror cell that fires mirror action potentials perfectly resembling the action potentials. A conventional inverted microscope can then be used to monitor the dynamics of mirror action potentials. Remarkably, the method is fully noninvasive: there is no need to porate the cell membrane or administrate dyes to the cell medium.

Figure 1a offers an overall view of the device working principle and the virtual mirror cell concept. As described above, the ions moving through the cell membrane and accumulating into the cell polarize the floating electrodes. The latter work as transducers by generating a local electric field that attracts or repels the fluorophores dissolved in the TRANS-chamber. Following the cell potential, the fluid volume below the electrode is subjected to inward and outward flows of molecules, which modulate its fluorophore density and thus its fluorescence intensity. It is therefore possible to define the fluid volume below the electrode as a virtual mirror cell, characterized by a density of fluorophore, which mirrors the ionic concentration into the cell. Hence, the fluorophore fluxes through the volume boundaries of the mirror cell replicate the cellular ionic transmembrane currents. It follows that the electrical action potential of the cell, triggered by transmembrane currents, is transduced into an optical signal, generated by fluorophore fluxes in-and-out the virtual mirror cell. We can refer to this signal as a mirror action potential (MAP). In this vision, an entire cell culture is “mirrored” into an ensemble of virtual mirror cells, which replicate optically the electrical behavior of the real cells. As shown in Figure 1b, MAPs detection is performed by using a standard optical camera: this solution allows to monitor in parallel all the electrodes in the camera field of view (FOV), and thus to record in an easy and convenient way the electrical activity from large cell cultures. For sake of clarity, we sketched in Figure 1c the whole dynamics of the real and mirror charges when the cell is in resting condition, fires the action potential, and finally restores its resting potential, respectively. Here, we can easily observe that the cells never get in contact with the fluorophores during the whole recording procedure. It is also worth noticing that the electrodes are floating, i.e., not wired or grounded. This strongly simplifies the architecture (with respect to conventional MEAs) and shifts the achievable spatial resolution to that of an optical camera, namely in the order of 10 megapixels.

The device was fabricated on a thin silicon nitride (Si3N4) membrane, which defines the boundary between the CIS and the TRANS chambers. Here, pass-through nanoelectrodes were realized by gold galvanic electrodeposition, according to the workflow illustrated in Figure S1 (Supporting Information). Figure 2c reports a cross-section view of the final nanoelectrodes: the 3D nanostructure grown on top completely seals the nanopore, ensuring perfect isolation of the two microfluidic compartments. The galvanic growth process was optimized in order to obtain nanostructures with enhanced surface roughness and average diameter around 1.3 µm. In fact, such features are considered particularly favorable for cell adhesion and cell-device electrical coupling. [ 33, 34 ] In particular, our nanostructures were inspired by the works of Spira et al., who introduced mushroom-like shapes to promote the engulfment by the cells. [ 35 ] The arrays of nanostructures were fabricated for each sensing electrode (Figure 2b). The nanostructures are reasonably homogenous in shape and size: their average diameter is 1.3 µm, while their height 0.6 µm. On the bottom side of the membrane, a gold square pad with thickness 150 nm and lateral size 28 µm incorporates each nanoelectrodes array (Figure 2a). The final device consists of an array of gold square pads equally spaced on the side of the membrane facing the TRANS-chamber, and connected to the CIS-chamber by pass-through nanoelectrodes, for a total covered area of ≈1 × 1 mm 2 .

The microfluidic chamber was realized simply by a drop of the fluorophore dispersion confined between the Si3N4 membrane and a bottom transparent electrode made of indium tin oxide (ITO) and Au. For the present realization, we chose rhodamine 6G (R6G) as fluorophore, and ethylene glycol as solvent. Rhodamine 6G is a photostable dye with high quantum yield, which can be easily dissolved in water, as well as in many different organic solvents. [ 36 ] On the other hand, ethylene glycol was chosen because characterized by a very low volatility, which makes this solvent particularly suitable for open microfluidic devices. By performing simple electrophoretic experiments in custom-made electrochemical cells, which included two parallel metallic wires immersed in ethylene glycol, the dissolved R6G molecules were observed to move toward the negative pole and thus to acquire a positive electric charge (data not shown).

To test the working mechanism of the device, we simulated the firing of action potentials by applying a voltage pulse train between the gold nanostructures, connected from the CIS-chamber, and the bottom transparent electrode (Figure 2d). Only for this specific test-bed configuration, a thin layer of gold (as shown in the device sketch) was deposited on the top side of the membrane in order to allow for the electrical connection of the electrodes. When applying external voltage pulses, the gold square pads change their light intensity following the applied voltage. In particular, when a positive electric pulse is applied, the electrodes fluorescence intensity decreases. When the electric pulse stops, fluorescence intensity is re-established. This behavior can be explained by the voltage-induced motion of the positively charged fluorophores, which are pushed away from the electrodes when the voltage pulse is on, and diffuse back under the electrode when the voltage turns off. The demonstrated device functioning is in accordance with the previously described device working principle (see Figure 1c).

We used human-induced pluripotent stem cell (hiPSC) cardiomyocytes to demonstrate the capability of our device to detect action potentials from electrogenic cells. The cells are plated on the side of the Si3N4 membrane with the 3D protruding gold nanoelectrodes. Before electrophysiological recordings, we performed LIVE/DEAD assays and immunofluorescence of two key markers of the human cardiac lineage to assess the viability and correct maturation of the cardiomyocytes on the novel device. As reported in Figure S2 (Supporting Information), the cell viability is close to 90% after 7 days in vitro and confirms the good biocompatibility of the device. In Figure 3a, the immunostaining highlights a significant expression of cardiac troponin T (green signal) as expected for a mature culture of hiPSC cardiomyocytes and a very low expression of NKX2-5 (red signal), a marker of cardiac progenitor cells.

After the incubation time, the hiPSC cardiomyocytes have spread over the Si3N4 membrane forming a cellular monolayer and acquiring spontaneous beating. The day of the measurement, the device is assembled onto the microscope stage, by connecting the bottom electrode to ground, adding the fluorophore dispersion, and enclosing the liquid with the sample with cells.

By illuminating the device from the top (see Figure S3 for details about the measurement setup, Supporting Information), it is possible to visualize, in transmission mode, the cell culture on the thin Si3N4 membrane equipped with the sensing electrodes (Figure 3c). In this first view modality, it is possible to monitor the spontaneous activity and contraction of the cardiomyocytes. For electrophysiological recordings, the device is illuminated from the bottom, and videos of fluorescence intensity are acquired simultaneously from several nanoelectrodes arrays, i.e., from all the virtual mirror cells in the camera FOV. This second view modality (recording modality) allows being sensitive only to the light emitted by the fluorophores, without any disturbance from other image elements. Throughout our experiments, we did not observe significant variations of the fluorescence intensity baseline beneath gold pads of the same devices. Thus, the fluorophores distributed homogeneously in the microfluidic chambers. In each experimental session, several videos were recorded from different regions of the cell culture, with various frame acquisition rates (from 10 to 100 frame per seconds, as allowed by the camera) and for different time courses.

Figure 3b shows the fluorescence intensity integrated under a single electrode pad. For sake of clarity, the signals are here inverted to provide a more direct visual comparison to electrophysiological signals. The fluorescence intensity undergoes to regular oscillations corresponding to light intensity reductions, with very regular shape, constant repetition rate, and high SNR. As supported by the following arguments, these fluorescence variations can be acknowledged as MAPs.

As a first observation, we note that the pulse repetition rate is the same of the cell beating, as previously monitored by observing the cells with bright-field illumination. Moreover, in Movie S1, Supporting Information, these fluorescence modulations can be clearly observed with also the microscope top light turned on, in order to visualize the cells contractile motion over the electrodes. This video allows for correlating the fluorescence variations with the cells beating rate. Remarkably, it is possible to observe that the light decreasing underneath the electrodes (corresponding to the rising slope of the pulses reported in Figure 3b) starts when the cells begin their contraction. Therefore, the measured optical pulses are perfectly synchronous with cells contractile activity, and thus with action potentials firing. Furthermore, recorded optical pulses have a time duration, measured at half the signal amplitude, equal to ≈500 ms, a value compatible with typical cardiac action potential duration at 50% amplitude (a value known as APD50). [ 2 ] Finally, to support the claim of the fluorophore motion in-and-out the virtual mirror cell, we also integrated the fluorescence intensity coming from the region surrounding the electrode pads (see Figure S4, Supporting Information). By comparing this signal with the one recorded under the gold pads (i.e., the MAP), we observed fluorescence intensity variations perfectly aligned, and with opposite phase. This observation confirms the device functioning depicted in Figure 1c: the fluorophores that are pushed away from the electrode when the cell depolarizes (thus producing a negative variation of the fluorescence intensity beneath the electrode) accumulate in the fluid volume surrounding the virtual mirror cell (thus producing an opposite, i.e., positive, variation of the fluorescence signal). All these observations strongly support the correct functioning of the device according to the concept described in Figure 1, and thus its ability to record MAPs.

The recorded MAPs are characterized by very high differential signal ΔS/S and SNR. The differential signal, calculated as the ratio between the fluorescence signal amplitude and the fluorescence baseline intensity, can be estimated to be ≈0.3. The SNR, calculated as the ratio between the fluorescence signal amplitude and the peak-to-peak noise of the fluorescence baseline intensity when the cell is at rest, is of ≈130. In this respect, it is important to highlight the fact that the presented results are raw data acquired directly by the camera, with no averaging required over several repeated signals. To appreciate the outstanding quality of the acquired MAPs, we can compare them with data obtained using alternative solutions for label-free optical recording, such as platforms based on plasmonic nanoantennas proposed in the last 10 years. [ 37, 38 ] MAPs show much larger ΔS/S and SNR, respectively ≈100 and 20 times higher than those previously reported for recordings of cell activity. [ 37, 38 ] Moreover, these results place the new method at the same level of the most recent and advanced MEA recording systems [ 4, 39 ] or optical methods. [ 40 ] The high quality of the MAP signals comes from the fact that, being the cells separated from the region of the measurements, there are no limitations in terms of fluorophore types, concentrations, or light excitation (power and wavelength).

Remarkably, even though no poration protocol was applied, the recorded MAPs have shape and duration that resemble those of intracellular cardiac action potentials. Concerning the shape, they are characterized by a steep rise followed by a slower decay. The two different time phases can be associated to the fast depolarization and the slower repolarization that characterize intracellular cardiac action potentials. Concerning the duration, the recorded average MAP duration at 50% amplitude (MAPD50) was equal to 680 ± 106 ms. This value is in line with the typical APD50 durations of human cardiac cells. [ 2 ] To explain the ability of the device to detect intracellular-like action potentials, we suggest a combination of two main factors. First, the floating nature of the top electrodes allows them to polarize following the membrane potential of the cell in tight adhesion on them. This occurs because of a finite resistance at the cell/electrode interface. Second, due to the 3D shape and rough structure of the electrodes, a strong adhesion with the cells is established. This is corroborated by several works in literature, where they state the possibility to record intracellular-like action potentials from extracellular electrodes in intimate contact with the cellular membrane. [ 41-43 ] In respect to the main literature, a main difference of our work is the absence of any specific electrode's functionalization, which have been used in the past to promote the endocytosis of the recording structures. [ 35, 44 ] For a deeper analysis of the device's ability to detect intracellular-like signals, we also performed circuital simulations of the device when driven by a cellular action potential (see Figure S5, Supporting Information).

The new proposed device features the long-sought characteristics of an ideal recording platform. First, it allows monitoring a large number of cells, realizing the large scalability requirement. In Figure 3c, a given region of the cell culture is monitored: all the electrodes in the camera FOV, each one corresponding to a different virtual mirror cell, are recorded in parallel (i.e., at the same time, given the camera internal circuitry time constants). This feature comes from the adoption of an optical readout scheme, carried out by a camera. Moreover, by simply moving the microscope stage over the light source (an operation that can be easily automated, in order to speed up the recording), different regions of the cell culture can be explored, and thus a very large number of cells can be recorded. In this respect, the floating nature of the sensing electrodes promotes the adoption of high-density configurations, which can provide a very large number of AP detection sites. In fact, floating electrodes do not need any external circuitry that could constrain their allocation in space. These characteristics represent a significant advantage with respect to conventional electrical recording methods, such as patch-clamp and MEAs. While standard patch-clamp allows to record only from few cells, MEAs require conductive feedlines to record electrical signals on multiple sites, which limit the electrodes number, as well as their spatial arrangement.

As another advantage, the presented device could enable cellular recording at very high spatial resolution. This feature comes from the fact that camera pixels are the ultimate detection sites of the cells action potentials. Considering that modern camera can easily provide several millions of pixels, further developments of the proposed device featuring high-density electrodes configurations could enable the extremely resolved imaging of the cells electrical activity, even below the cellular level. This could allow to overcome the limits of CMOS-MEAs technology, whose most advanced MEA designs can offer up to ≈100 thousand electrodes, [ 45 ] with dimensions and spacing bounded by amplification circuitry constraints. To support this, in Figure S6 (Supporting Information), we show a device with smaller electrode pads (lateral size 8 µm) arranged at higher density (pitch 20 µm). When triggered with external voltage pulses, the device reproduces the same operation principle of larger electrode pads, illustrated in Figure 2d.

Finally, some considerations can be made about signal variability. The measured MAPs depicted in Figure 3c show some differences in amplitude. These fluctuations can be ascribed mainly to variabilities in the electrical coupling between each cell and the underneath nanoelectrodes. This phenomenon is very common in MEA-based recording and is thus not surprising. In addition, some variabilities are observed in the electrochemically grown gold nanostructures that form the interface with the cells (see Figure 2b). As a further source of signal variability, inhomogeneity in the FOV illumination can result in different signal amplitudes below the electrodes pads.

To definitively demonstrate the capabilities of the proposed approach with particular regard of pharmacological screenings and toxicity tests, we administered to the cell culture the compound Nifedipine, an L-type calcium channel blocker [ 46, 47 ] known to increase cardiomyocytes beating rate and shorten APs time duration [ 48 ] (final Nifedipine concentration in the cellular medium = 90 × 10 −9 m ). After Nifedipine administration, cells were observed to accelerate their contractile activity. The results for the action potential recording before and after the drug administration are summarized in Figure 4.

After drug administration, MAP rate increased from 0.65 to 0.85 Hz (Figure 4a), in agreement with the observed increase of the cellular beating rate. On the other hand, MAPs duration decreased. In fact, the average MAPD50 changed from 600 to 480 ms, with a 20% reduction (Figure 4b). The obtained results are in agreement with known Nifedipine effects on cardiomyocytes, as detected by other methods, such as patch-clamp or MEAs. [ 49, 50 ] Moreover, this experiment is a further confirmation that the detected optical signals (MAPs) can be acknowledged as measurements of cellular APs. Here, it is important to highlight that no poration/stimulation/delivery protocol has been applied to the cardiomyocytes for measuring the deformation of the APs due to drug administration. In fact, the only perturbation to which the cells were exposed had been the administration of the selected drug. All other parameters were the same of the physiological condition. This is a pivotal point for allowing completely noninvasive screenings, which are required to assess both acute and long-term effects such as chronic cardiotoxicity. Moreover, in Figure S7 (Supporting Information), we show that the device is able to detect very fast electrical signals, with duration down to 0.7 ms. Such a good temporal resolution can allow to monitor accurately also rapid features of an AP and their possible modifications due to drug effects.

In this work, we present a new paradigm for monitoring action potentials from electrogenic cells by a label free scheme. In contrast to other optical-based detection methods, the fluorescent molecules do not interact at all with the cell culture. This ensures that the fluorescent molecules cannot alter the biochemical processes or the ion channel functioning in any way, guaranteeing the highest reliability of toxicity studies when drugs are administered to the culture. This aspect is fundamental as it enables both the acute and the long-term monitoring of the same cells or multiple cells in physiological conditions. The new electro-optical transduction enables the acquisition of high SNR and high temporal resolution signals with the same quality provided by the most recent MEA biosensors presented in literature but with much higher number of electrodes and with no need for wiring. Moreover, thanks to the concept of mirror charge, the approach provides signals that closely resemble pure intracellular action potentials without requiring the poration of the cellular membrane. The latter represents a long-standing limit of MEA technologies that are invasive methods. Furthermore, the structural simplicity of the device offers ample margins for improving the spatial resolution and the number of recording units. In fact, the floating electrodes may be fabricated with submicrometer size and interelectrode distance using standard fabrication techniques, without adding significant complexities that could lead to performance degradation.

The novel approach has the potential to replace the MEA and VSO methodologies for the reliable assessment of cardiotoxicity on human-derived cardiomyocytes. In the longer term, this approach paves the way toward a completely new family of in vitro biodevices suitable for many different applications, even far from those mentioned above. For examples, studies on bacteria and biofilms [ 51, 52 ] are challenging because of the smaller size of the bacterial cells, which makes the use of MEA and patch-clamp more difficult. In perspective, the advantages of the MAP approach make this method extremely promising for neuronal recordings, where the noninvasiveness is paramount both for not damaging the cells and for not interfering with the complex communication processes of neuronal networks. Few factors will have to be considered for the successful application of MAP to neuron electrophysiology. The biocompatibility for long-term incubation (required for network maturation), the high temporal resolution (needed for the shorter neuronal action potentials), and the different cellular adhesion on the nanostructures are the main points to take into account. Remarkably, our experiments with external electrical pulses and with cardiac cultures did not highlight specific limitations, since we could use the MAP device for detecting very fast external stimuli (down to 0.7 ms, see Figure S7, Supporting Information) and for culturing cells for long time (more than 1 week). Ultimately, the emerging community of brain on chip or brain on a dish [ 53 ] may benefit from these devices. In light of the presented performances, advantages and clear translational capability, we think that the MAP concept will lay a new milestone in the field of electrophysiology.


References

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Berry, M. & Pentreath, V. (1978) The characterised dopamine neuron in Planorbis corneus In Osborne, N. ed. Biochemistry of Characterised Neurons. NY: Pergamon Press pg 89

Schwarz, J. & Eikhof, G. (1987) Na currents and action potentials in rat myelinated nerve fibres at 20 and 37 Celsius. Pflugers Arch. vol. 409, pp. 569-577
Cole, K. (1968) Membranes, Ions and Impulses: A Chapter of Classical Biophysics. Los Angeles, CA: University of California Press
Hodgkin, A. (1951) The ionic basis of electrical activity in nerve and muscle Biol Rev vol. 26 pp 339-409
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Contents

Neurons are remarkable among the cells of the body in their ability to propagate signals rapidly over large distances. They do this by generating characteristic electrical pulses called action potentials: voltage spikes that can travel down axons. Sensory neurons change their activities by firing sequences of action potentials in various temporal patterns, with the presence of external sensory stimuli, such as light, sound, taste, smell and touch. It is known that information about the stimulus is encoded in this pattern of action potentials and transmitted into and around the brain, but this is not the only method. Specialized neurons, such as those of the retina, can communicate more information through graded potentials. This differs from action potentials because information about the strength of a stimulus directly correlates with the strength of the neurons output. The signal decays much faster for graded potentials, necessitating short inter-neuron distances and high neuronal density. The advantage of graded potentials are higher information rates capable of encoding more states (i.e. higher fidelity) than spiking neurons. [4]

Although action potentials can vary somewhat in duration, amplitude and shape, they are typically treated as identical stereotyped events in neural coding studies. If the brief duration of an action potential (about 1ms) is ignored, an action potential sequence, or spike train, can be characterized simply by a series of all-or-none point events in time. [5] The lengths of interspike intervals (ISIs) between two successive spikes in a spike train often vary, apparently randomly. [6] The study of neural coding involves measuring and characterizing how stimulus attributes, such as light or sound intensity, or motor actions, such as the direction of an arm movement, are represented by neuron action potentials or spikes. In order to describe and analyze neuronal firing, statistical methods and methods of probability theory and stochastic point processes have been widely applied.

With the development of large-scale neural recording and decoding technologies, researchers have begun to crack the neural code and have already provided the first glimpse into the real-time neural code as memory is formed and recalled in the hippocampus, a brain region known to be central for memory formation. [7] [8] [9] Neuroscientists have initiated several large-scale brain decoding projects. [10] [11]

The link between stimulus and response can be studied from two opposite points of view. Neural encoding refers to the map from stimulus to response. The main focus is to understand how neurons respond to a wide variety of stimuli, and to construct models that attempt to predict responses to other stimuli. Neural decoding refers to the reverse map, from response to stimulus, and the challenge is to reconstruct a stimulus, or certain aspects of that stimulus, from the spike sequences it evokes.

A sequence, or 'train', of spikes may contain information based on different coding schemes. In motor neurons, for example, the strength at which an innervated muscle is contracted depends solely on the 'firing rate', the average number of spikes per unit time (a 'rate code'). At the other end, a complex 'temporal code' is based on the precise timing of single spikes. They may be locked to an external stimulus such as in the visual [12] and auditory system or be generated intrinsically by the neural circuitry. [13]

Whether neurons use rate coding or temporal coding is a topic of intense debate within the neuroscience community, even though there is no clear definition of what these terms mean. [14]

Rate coding Edit

The rate coding model of neuronal firing communication states that as the intensity of a stimulus increases, the frequency or rate of action potentials, or "spike firing", increases. Rate coding is sometimes called frequency coding.

Rate coding is a traditional coding scheme, assuming that most, if not all, information about the stimulus is contained in the firing rate of the neuron. Because the sequence of action potentials generated by a given stimulus varies from trial to trial, neuronal responses are typically treated statistically or probabilistically. They may be characterized by firing rates, rather than as specific spike sequences. In most sensory systems, the firing rate increases, generally non-linearly, with increasing stimulus intensity. [15] Under a rate coding assumption, any information possibly encoded in the temporal structure of the spike train is ignored. Consequently, rate coding is inefficient but highly robust with respect to the ISI 'noise'. [6]

During rate coding, precisely calculating firing rate is very important. In fact, the term "firing rate" has a few different definitions, which refer to different averaging procedures, such as an average over time (rate as a single-neuron spike count) or an average over several repetitions (rate of PSTH) of experiment.

In rate coding, learning is based on activity-dependent synaptic weight modifications.

Rate coding was originally shown by ED Adrian and Y Zotterman in 1926. [16] In this simple experiment different weights were hung from a muscle. As the weight of the stimulus increased, the number of spikes recorded from sensory nerves innervating the muscle also increased. From these original experiments, Adrian and Zotterman concluded that action potentials were unitary events, and that the frequency of events, and not individual event magnitude, was the basis for most inter-neuronal communication.

In the following decades, measurement of firing rates became a standard tool for describing the properties of all types of sensory or cortical neurons, partly due to the relative ease of measuring rates experimentally. However, this approach neglects all the information possibly contained in the exact timing of the spikes. During recent years, more and more experimental evidence has suggested that a straightforward firing rate concept based on temporal averaging may be too simplistic to describe brain activity. [6]

Spike-count rate (average over time) Edit

The spike-count rate, also referred to as temporal average, is obtained by counting the number of spikes that appear during a trial and dividing by the duration of trial. [14] The length T of the time window is set by the experimenter and depends on the type of neuron recorded from and to the stimulus. In practice, to get sensible averages, several spikes should occur within the time window. Typical values are T = 100 ms or T = 500 ms, but the duration may also be longer or shorter.(Chapter 1.5 in the textbook 'Spiking Neuron Models' [14] )

The spike-count rate can be determined from a single trial, but at the expense of losing all temporal resolution about variations in neural response during the course of the trial. Temporal averaging can work well in cases where the stimulus is constant or slowly varying and does not require a fast reaction of the organism — and this is the situation usually encountered in experimental protocols. Real-world input, however, is hardly stationary, but often changing on a fast time scale. For example, even when viewing a static image, humans perform saccades, rapid changes of the direction of gaze. The image projected onto the retinal photoreceptors changes therefore every few hundred milliseconds (Chapter 1.5 in [14] )

Despite its shortcomings, the concept of a spike-count rate code is widely used not only in experiments, but also in models of neural networks. It has led to the idea that a neuron transforms information about a single input variable (the stimulus strength) into a single continuous output variable (the firing rate).

There is a growing body of evidence that in Purkinje neurons, at least, information is not simply encoded in firing but also in the timing and duration of non-firing, quiescent periods. [17] [18] There is also evidence from retinal cells, that information is encoded not only in the firing rate but also in spike timing. [19] More generally, whenever a rapid response of an organism is required a firing rate defined as a spike-count over a few hundred milliseconds is simply too slow. [14]

Time-dependent firing rate (averaging over several trials) Edit

The time-dependent firing rate is defined as the average number of spikes (averaged over trials) appearing during a short interval between times t and t+Δt, divided by the duration of the interval. [14] It works for stationary as well as for time-dependent stimuli. To experimentally measure the time-dependent firing rate, the experimenter records from a neuron while stimulating with some input sequence. The same stimulation sequence is repeated several times and the neuronal response is reported in a Peri-Stimulus-Time Histogram (PSTH). The time t is measured with respect to the start of the stimulation sequence. The Δt must be large enough (typically in the range of one or a few milliseconds) so that there is a sufficient number of spikes within the interval to obtain a reliable estimate of the average. The number of occurrences of spikes nK(tt+Δt) summed over all repetitions of the experiment divided by the number K of repetitions is a measure of the typical activity of the neuron between time t and t+Δt. A further division by the interval length Δt yields time-dependent firing rate r(t) of the neuron, which is equivalent to the spike density of PSTH (Chapter 1.5 in [14] ).

For sufficiently small Δt, r(t)Δt is the average number of spikes occurring between times t and t+Δt over multiple trials. If Δt is small, there will never be more than one spike within the interval between t and t+Δt on any given trial. This means that r(t)Δt is also the fraction of trials on which a spike occurred between those times. Equivalently, r(t)Δt is the probability that a spike occurs during this time interval.

As an experimental procedure, the time-dependent firing rate measure is a useful method to evaluate neuronal activity, in particular in the case of time-dependent stimuli. The obvious problem with this approach is that it can not be the coding scheme used by neurons in the brain. Neurons can not wait for the stimuli to repeatedly present in an exactly same manner before generating a response. [14]

Nevertheless, the experimental time-dependent firing rate measure can make sense, if there are large populations of independent neurons that receive the same stimulus. Instead of recording from a population of N neurons in a single run, it is experimentally easier to record from a single neuron and average over N repeated runs. Thus, the time-dependent firing rate coding relies on the implicit assumption that there are always populations of neurons.

Temporal coding Edit

When precise spike timing or high-frequency firing-rate fluctuations are found to carry information, the neural code is often identified as a temporal code. [14] [20] A number of studies have found that the temporal resolution of the neural code is on a millisecond time scale, indicating that precise spike timing is a significant element in neural coding. [3] [21] [19] Such codes, that communicate via the time between spikes are also referred to as interpulse interval codes, and have been supported by recent studies. [22]

Neurons exhibit high-frequency fluctuations of firing-rates which could be noise or could carry information. Rate coding models suggest that these irregularities are noise, while temporal coding models suggest that they encode information. If the nervous system only used rate codes to convey information, a more consistent, regular firing rate would have been evolutionarily advantageous, and neurons would have utilized this code over other less robust options. [23] Temporal coding supplies an alternate explanation for the “noise," suggesting that it actually encodes information and affects neural processing. To model this idea, binary symbols can be used to mark the spikes: 1 for a spike, 0 for no spike. Temporal coding allows the sequence 000111000111 to mean something different from 001100110011, even though the mean firing rate is the same for both sequences, at 6 spikes/10 ms. [24] Until recently, scientists had put the most emphasis on rate encoding as an explanation for post-synaptic potential patterns. However, functions of the brain are more temporally precise than the use of only rate encoding seems to allow. [19] In other words, essential information could be lost due to the inability of the rate code to capture all the available information of the spike train. In addition, responses are different enough between similar (but not identical) stimuli to suggest that the distinct patterns of spikes contain a higher volume of information than is possible to include in a rate code. [25]

Temporal codes (also called spike codes [14] ), employ those features of the spiking activity that cannot be described by the firing rate. For example, time-to-first-spike after the stimulus onset, phase-of-firing with respect to background oscillations, characteristics based on the second and higher statistical moments of the ISI probability distribution, spike randomness, or precisely timed groups of spikes (temporal patterns) are candidates for temporal codes. [26] As there is no absolute time reference in the nervous system, the information is carried either in terms of the relative timing of spikes in a population of neurons (temporal patterns) or with respect to an ongoing brain oscillation. (phase of firing) [3] [6] One way in which temporal codes are decoded, in presence of neural oscillations, is that spikes occurring at specific phases of an oscillatory cycle are more effective in depolarizing the post-synaptic neuron. [27]

The temporal structure of a spike train or firing rate evoked by a stimulus is determined both by the dynamics of the stimulus and by the nature of the neural encoding process. Stimuli that change rapidly tend to generate precisely timed spikes [28] (and rapidly changing firing rates in PSTHs) no matter what neural coding strategy is being used. Temporal coding in the narrow sense refers to temporal precision in the response that does not arise solely from the dynamics of the stimulus, but that nevertheless relates to properties of the stimulus. The interplay between stimulus and encoding dynamics makes the identification of a temporal code difficult.

In temporal coding, learning can be explained by activity-dependent synaptic delay modifications. [29] The modifications can themselves depend not only on spike rates (rate coding) but also on spike timing patterns (temporal coding), i.e., can be a special case of spike-timing-dependent plasticity. [30]

The issue of temporal coding is distinct and independent from the issue of independent-spike coding. If each spike is independent of all the other spikes in the train, the temporal character of the neural code is determined by the behavior of time-dependent firing rate r(t). If r(t) varies slowly with time, the code is typically called a rate code, and if it varies rapidly, the code is called temporal.

Temporal coding in sensory systems Edit

For very brief stimuli, a neuron's maximum firing rate may not be fast enough to produce more than a single spike. Due to the density of information about the abbreviated stimulus contained in this single spike, it would seem that the timing of the spike itself would have to convey more information than simply the average frequency of action potentials over a given period of time. This model is especially important for sound localization, which occurs within the brain on the order of milliseconds. The brain must obtain a large quantity of information based on a relatively short neural response. Additionally, if low firing rates on the order of ten spikes per second must be distinguished from arbitrarily close rate coding for different stimuli, then a neuron trying to discriminate these two stimuli may need to wait for a second or more to accumulate enough information. This is not consistent with numerous organisms which are able to discriminate between stimuli in the time frame of milliseconds, suggesting that a rate code is not the only model at work. [24]

To account for the fast encoding of visual stimuli, it has been suggested that neurons of the retina encode visual information in the latency time between stimulus onset and first action potential, also called latency to first spike or time-to-first-spike. [31] This type of temporal coding has been shown also in the auditory and somato-sensory system. The main drawback of such a coding scheme is its sensitivity to intrinsic neuronal fluctuations. [32] In the primary visual cortex of macaques, the timing of the first spike relative to the start of the stimulus was found to provide more information than the interval between spikes. However, the interspike interval could be used to encode additional information, which is especially important when the spike rate reaches its limit, as in high-contrast situations. For this reason, temporal coding may play a part in coding defined edges rather than gradual transitions. [33]

The mammalian gustatory system is useful for studying temporal coding because of its fairly distinct stimuli and the easily discernible responses of the organism. [34] Temporally encoded information may help an organism discriminate between different tastants of the same category (sweet, bitter, sour, salty, umami) that elicit very similar responses in terms of spike count. The temporal component of the pattern elicited by each tastant may be used to determine its identity (e.g., the difference between two bitter tastants, such as quinine and denatonium). In this way, both rate coding and temporal coding may be used in the gustatory system – rate for basic tastant type, temporal for more specific differentiation. [35] Research on mammalian gustatory system has shown that there is an abundance of information present in temporal patterns across populations of neurons, and this information is different from that which is determined by rate coding schemes. Groups of neurons may synchronize in response to a stimulus. In studies dealing with the front cortical portion of the brain in primates, precise patterns with short time scales only a few milliseconds in length were found across small populations of neurons which correlated with certain information processing behaviors. However, little information could be determined from the patterns one possible theory is they represented the higher-order processing taking place in the brain. [25]

As with the visual system, in mitral/tufted cells in the olfactory bulb of mice, first-spike latency relative to the start of a sniffing action seemed to encode much of the information about an odor. This strategy of using spike latency allows for rapid identification of and reaction to an odorant. In addition, some mitral/tufted cells have specific firing patterns for given odorants. This type of extra information could help in recognizing a certain odor, but is not completely necessary, as average spike count over the course of the animal's sniffing was also a good identifier. [36] Along the same lines, experiments done with the olfactory system of rabbits showed distinct patterns which correlated with different subsets of odorants, and a similar result was obtained in experiments with the locust olfactory system. [24]

Temporal coding applications Edit

The specificity of temporal coding requires highly refined technology to measure informative, reliable, experimental data. Advances made in optogenetics allow neurologists to control spikes in individual neurons, offering electrical and spatial single-cell resolution. For example, blue light causes the light-gated ion channel channelrhodopsin to open, depolarizing the cell and producing a spike. When blue light is not sensed by the cell, the channel closes, and the neuron ceases to spike. The pattern of the spikes matches the pattern of the blue light stimuli. By inserting channelrhodopsin gene sequences into mouse DNA, researchers can control spikes and therefore certain behaviors of the mouse (e.g., making the mouse turn left). [37] Researchers, through optogenetics, have the tools to effect different temporal codes in a neuron while maintaining the same mean firing rate, and thereby can test whether or not temporal coding occurs in specific neural circuits. [38]

Optogenetic technology also has the potential to enable the correction of spike abnormalities at the root of several neurological and psychological disorders. [38] If neurons do encode information in individual spike timing patterns, key signals could be missed by attempting to crack the code while looking only at mean firing rates. [24] Understanding any temporally encoded aspects of the neural code and replicating these sequences in neurons could allow for greater control and treatment of neurological disorders such as depression, schizophrenia, and Parkinson's disease. Regulation of spike intervals in single cells more precisely controls brain activity than the addition of pharmacological agents intravenously. [37]

Phase-of-firing code Edit

Phase-of-firing code is a neural coding scheme that combines the spike count code with a time reference based on oscillations. This type of code takes into account a time label for each spike according to a time reference based on phase of local ongoing oscillations at low [39] or high frequencies. [40]

It has been shown that neurons in some cortical sensory areas encode rich naturalistic stimuli in terms of their spike times relative to the phase of ongoing network oscillatory fluctuations, rather than only in terms of their spike count. [39] [41] The local field potential signals reflect population (network) oscillations. The phase-of-firing code is often categorized as a temporal code although the time label used for spikes (i.e. the network oscillation phase) is a low-resolution (coarse-grained) reference for time. As a result, often only four discrete values for the phase are enough to represent all the information content in this kind of code with respect to the phase of oscillations in low frequencies. Phase-of-firing code is loosely based on the phase precession phenomena observed in place cells of the hippocampus. Another feature of this code is that neurons adhere to a preferred order of spiking between a group of sensory neurons, resulting in firing sequence. [42]

Phase code has been shown in visual cortex to involve also high-frequency oscillations. [42] Within a cycle of gamma oscillation, each neuron has its own preferred relative firing time. As a result, an entire population of neurons generates a firing sequence that has a duration of up to about 15 ms. [42]

Population coding Edit

Population coding is a method to represent stimuli by using the joint activities of a number of neurons. In population coding, each neuron has a distribution of responses over some set of inputs, and the responses of many neurons may be combined to determine some value about the inputs. From the theoretical point of view, population coding is one of a few mathematically well-formulated problems in neuroscience. It grasps the essential features of neural coding and yet is simple enough for theoretic analysis. [43] Experimental studies have revealed that this coding paradigm is widely used in the sensor and motor areas of the brain.

For example, in the visual area medial temporal (MT), neurons are tuned to the moving direction. [44] In response to an object moving in a particular direction, many neurons in MT fire with a noise-corrupted and bell-shaped activity pattern across the population. The moving direction of the object is retrieved from the population activity, to be immune from the fluctuation existing in a single neuron's signal. When monkeys are trained to move a joystick towards a lit target, a single neuron will fire for multiple target directions. However it fires the fastest for one direction and more slowly depending on how close the target was to the neuron's "preferred" direction. [45] [46] If each neuron represents movement in its preferred direction, and the vector sum of all neurons is calculated (each neuron has a firing rate and a preferred direction), the sum points in the direction of motion. In this manner, the population of neurons codes the signal for the motion. [ citation needed ] This particular population code is referred to as population vector coding.

Place-time population codes, termed the averaged-localized-synchronized-response (ALSR) code, have been derived for neural representation of auditory acoustic stimuli. This exploits both the place or tuning within the auditory nerve, as well as the phase-locking within each nerve fiber auditory nerve. The first ALSR representation was for steady-state vowels [47] ALSR representations of pitch and formant frequencies in complex, non-steady state stimul were later demonstrated for voiced-pitch, [48] and formant representations in consonant-vowel syllables. [49] The advantage of such representations is that global features such as pitch or formant transition profiles can be represented as global features across the entire nerve simultaneously via both rate and place coding.

Population coding has a number of other advantages as well, including reduction of uncertainty due to neuronal variability and the ability to represent a number of different stimulus attributes simultaneously. Population coding is also much faster than rate coding and can reflect changes in the stimulus conditions nearly instantaneously. [50] Individual neurons in such a population typically have different but overlapping selectivities, so that many neurons, but not necessarily all, respond to a given stimulus.

Typically an encoding function has a peak value such that activity of the neuron is greatest if the perceptual value is close to the peak value, and becomes reduced accordingly for values less close to the peak value. [ citation needed ] It follows that the actual perceived value can be reconstructed from the overall pattern of activity in the set of neurons. Vector coding is an example of simple averaging. A more sophisticated mathematical technique for performing such a reconstruction is the method of maximum likelihood based on a multivariate distribution of the neuronal responses. These models can assume independence, second order correlations, [51] or even more detailed dependencies such as higher order maximum entropy models, [52] or copulas. [53]

Correlation coding Edit

The correlation coding model of neuronal firing claims that correlations between action potentials, or "spikes", within a spike train may carry additional information above and beyond the simple timing of the spikes. Early work suggested that correlation between spike trains can only reduce, and never increase, the total mutual information present in the two spike trains about a stimulus feature. [54] However, this was later demonstrated to be incorrect. Correlation structure can increase information content if noise and signal correlations are of opposite sign. [55] Correlations can also carry information not present in the average firing rate of two pairs of neurons. A good example of this exists in the pentobarbital-anesthetized marmoset auditory cortex, in which a pure tone causes an increase in the number of correlated spikes, but not an increase in the mean firing rate, of pairs of neurons. [56]

Independent-spike coding Edit

The independent-spike coding model of neuronal firing claims that each individual action potential, or "spike", is independent of each other spike within the spike train. [57] [58]

Position coding Edit

A typical population code involves neurons with a Gaussian tuning curve whose means vary linearly with the stimulus intensity, meaning that the neuron responds most strongly (in terms of spikes per second) to a stimulus near the mean. The actual intensity could be recovered as the stimulus level corresponding to the mean of the neuron with the greatest response. However, the noise inherent in neural responses means that a maximum likelihood estimation function is more accurate.

This type of code is used to encode continuous variables such as joint position, eye position, color, or sound frequency. Any individual neuron is too noisy to faithfully encode the variable using rate coding, but an entire population ensures greater fidelity and precision. For a population of unimodal tuning curves, i.e. with a single peak, the precision typically scales linearly with the number of neurons. Hence, for half the precision, half as many neurons are required. In contrast, when the tuning curves have multiple peaks, as in grid cells that represent space, the precision of the population can scale exponentially with the number of neurons. This greatly reduces the number of neurons required for the same precision. [59]

Sparse coding Edit

The sparse code is when each item is encoded by the strong activation of a relatively small set of neurons. For each item to be encoded, this is a different subset of all available neurons. In contrast to sensor-sparse coding, sensor-dense coding implies that all information from possible sensor locations is known.

As a consequence, sparseness may be focused on temporal sparseness ("a relatively small number of time periods are active") or on the sparseness in an activated population of neurons. In this latter case, this may be defined in one time period as the number of activated neurons relative to the total number of neurons in the population. This seems to be a hallmark of neural computations since compared to traditional computers, information is massively distributed across neurons. Sparse coding of natural images produces wavelet-like oriented filters that resemble the receptive fields of simple cells in the visual cortex. [60] The capacity of sparse codes may be increased by simultaneous use of temporal coding, as found in the locust olfactory system. [61]

Given a potentially large set of input patterns, sparse coding algorithms (e.g. sparse autoencoder) attempt to automatically find a small number of representative patterns which, when combined in the right proportions, reproduce the original input patterns. The sparse coding for the input then consists of those representative patterns. For example, the very large set of English sentences can be encoded by a small number of symbols (i.e. letters, numbers, punctuation, and spaces) combined in a particular order for a particular sentence, and so a sparse coding for English would be those symbols.

Linear generative model Edit

Most models of sparse coding are based on the linear generative model. [62] In this model, the symbols are combined in a linear fashion to approximate the input.

The codings generated by algorithms implementing a linear generative model can be classified into codings with soft sparseness and those with hard sparseness. [62] These refer to the distribution of basis vector coefficients for typical inputs. A coding with soft sparseness has a smooth Gaussian-like distribution, but peakier than Gaussian, with many zero values, some small absolute values, fewer larger absolute values, and very few very large absolute values. Thus, many of the basis vectors are active. Hard sparseness, on the other hand, indicates that there are many zero values, no or hardly any small absolute values, fewer larger absolute values, and very few very large absolute values, and thus few of the basis vectors are active. This is appealing from a metabolic perspective: less energy is used when fewer neurons are firing. [62]

Another measure of coding is whether it is critically complete or overcomplete. If the number of basis vectors n is equal to the dimensionality k of the input set, the coding is said to be critically complete. In this case, smooth changes in the input vector result in abrupt changes in the coefficients, and the coding is not able to gracefully handle small scalings, small translations, or noise in the inputs. If, however, the number of basis vectors is larger than the dimensionality of the input set, the coding is overcomplete. Overcomplete codings smoothly interpolate between input vectors and are robust under input noise. [64] The human primary visual cortex is estimated to be overcomplete by a factor of 500, so that, for example, a 14 x 14 patch of input (a 196-dimensional space) is coded by roughly 100,000 neurons. [62]

Other models are based on matching pursuit, a sparse approximation algorithm which finds the "best matching" projections of multidimensional data, and dictionary learning, a representation learning method which aims to find a sparse matrix representation of the input data in the form of a linear combination of basic elements as well as those basic elements themselves. [65] [66] [67]

Biological evidence Edit

Sparse coding may be a general strategy of neural systems to augment memory capacity. To adapt to their environments, animals must learn which stimuli are associated with rewards or punishments and distinguish these reinforced stimuli from similar but irrelevant ones. Such tasks require implementing stimulus-specific associative memories in which only a few neurons out of a population respond to any given stimulus and each neuron responds to only a few stimuli out of all possible stimuli.

Theoretical work on sparse distributed memory has suggested that sparse coding increases the capacity of associative memory by reducing overlap between representations. [68] Experimentally, sparse representations of sensory information have been observed in many systems, including vision, [69] audition, [70] touch, [71] and olfaction. [72] However, despite the accumulating evidence for widespread sparse coding and theoretical arguments for its importance, a demonstration that sparse coding improves the stimulus-specificity of associative memory has been difficult to obtain.

In the Drosophila olfactory system, sparse odor coding by the Kenyon cells of the mushroom body is thought to generate a large number of precisely addressable locations for the storage of odor-specific memories. [73] Sparseness is controlled by a negative feedback circuit between Kenyon cells and GABAergic anterior paired lateral (APL) neurons. Systematic activation and blockade of each leg of this feedback circuit shows that Kenyon cells activate APL neurons and APL neurons inhibit Kenyon cells. Disrupting the Kenyon cell–APL feedback loop decreases the sparseness of Kenyon cell odor responses, increases inter-odor correlations, and prevents flies from learning to discriminate similar, but not dissimilar, odors. These results suggest that feedback inhibition suppresses Kenyon cell activity to maintain sparse, decorrelated odor coding and thus the odor-specificity of memories. [74]


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PhysioEx Exercise 3 Test Answers

Which of the following statements about receptor potentials is FALSE?

-Odor molecules can act as stimuli.
-The receptor potential is carried by neuroglia.
-The receptor proteins respond to stimuli.
-They can trigger an action potential.

Which of the following is NOT a functional region of a neuron?

secretory region
conducting region
receiving region
medullary region

The conducting region of the neuron is the _______.

cell body
axon
axon terminal
dendrite

The typical concentration of sodium is _______.

– the same as potassium intracellularly.
– lower than potassium extracellularly.
– lower than potassium intracellularly.
– higher than potassium intracellularly.

Which of the following describes a change from the resting membrane potential?

– an action potential
– a synaptic potential
– a receptor potential
– a receptor potential, a synaptic potential or an action potential

What effect did increasing the extracellular potassium have on the resting membrane potential?

– The resting membrane potential became less negative.
– The resting membrane potential became more negative.
– The resting membrane potential did not change.
– The resting membrane potential disappeared.

What effect did decreasing the extracellular sodium have on the resting membrane potential?

– Only a small change occurred, because the sodium channels were mostly open.
– The resting membrane potential disappeared.
– Only a small change occurred, because the resting neuron is not very permeable to sodium.
– The resting membrane potential became less negative.

The channels that provide for the movement of potassium in the resting neuron are _______.

– leakage and chemically gated.
– chemically gated
– voltage gated
– leakage

Establishing the resting membrane potential requires energy through the use of the _______.

– sodium-glucose pump
– potassium-glucose pump
– sodium-potassium pump
– sodium leakage channels

The receptor potential is generated at the _______.

receiving region
conducting region
output region
secretory region

Sensory transduction is defined as _______.

– the conversion of a stimulus to a change in membrane potential
– the disappearance of the perception of a stimulus
– the conversion of a light stimulus into pain
– a change in the amplitude of a receptor potential

The receptor potential _______.

– can be graded with stimulus intensity
– amplitude can vary with the stimulus intensity, requires the appropriate stimulus and can be graded with a stimulus intensity
– amplitude can vary with the stimulus intensity
– requires the appropriate stimulus

Which of the following describes a depolarization?

– The membrane potential becomes more polarized.
– The membrane potential becomes more negative.
– The membrane becomes less polarized.
– The membrane, which was formerly not polarized, now is polarized.

Which of the following was able to detect pressure?

– the Pacinian corpuscle and the free nerve ending
– free nerve ending
– olfactory receptor
– Pacinian corpuscle

Which of the following does NOT describe graded potentials?

– They vary with the intensity of the stimulus.
– They are changes to the membrane potential.
– They are always depolarizing.
– They are local changes.

Which of the following responded to a chemical stimulus?

– Pacinian corpuscle
– free nerve ending
– olfactory receptor
– both the Pacinian corpuscle and the olfactory receptor

When the intensity of the appropriate stimulus was increased, the amplitude of the response _______.

was zero
did not change
decreased
increased

another term for a neuron
a cluster of cell bodies
a bundle of axons
another term for nerve fiber

The region on the neuron where action potentials are generated is called the ______.

trigger zone
depolarization zone
stimulator zone
dendrite

In this simulation, ___________________ will be used to stimulate the axon.

light
heat
voltage
chemicals

We describe the regeneration of the action potential down the membrane of the axon of the neuron as _______.

hyperpolarization
conduction or propagation
conduction
propagation

The minimum voltage that is required to generate an action potential is called the _______.

depolarization voltage
propagation voltage
threshold voltage
trigger voltage

Increasing the voltage resulted in which of the following?

– an increase in the rate of propagation of the action potential
– an increase in the size of the action potential
– a decrease in the rate of propagation of the action potential
– no change to the action potential

An axon that is more negative than the resting membrane potential is said to be _______.

depolarized
hyperpolarized
at threshold
graded

If an increase in extracellular potassium hyperpolarizes a neuron, which of the following would be correct?

-It would change the membrane potential to a more negative value.
-It would decrease the flow of sodium out of the cell.
-It would change the membrane potential to a less negative value.
-It would increase the flow of sodium out of the cell.

An action potential requires _______.

– voltage-gated sodium channels to open
– sodium to flow with its electrochemical gradient
– chemically gated sodium channels to open
– voltage-gated sodium channels to open and sodium to flow with its electrochemical gradient

To reach threshold, the amount of sodium _______.

– entering the cell must overcome the potassium exiting
– exiting the cell must overcome the potassium exiting
– entering the cell must overcome the potassium entering
– exiting the cell must overcome the potassium entering

Which of the following blocks voltage-gated sodium channels?

lidocaine
tetrodotoxin
tetrodotoxin and lidocaine
potassium

Which of the following is used to block pain?

tetrodotoxin
tetrodotoxin and lidocaine
lidocaine
potassium

Which of the following occurred in the presence of tetrodotoxin?

The size of the action potential decreased.
The number of action potentials increased.
The number of action potentials decreased.
The size of the action potential increased.

Which of the following occurred in the presence of tetrodotoxin?

An action potential was always seen at R1.
All action potentials were missing.
An action potential was always seen at R1 and R2.
An action potential was always seen at R2.

In the presence of lidocaine, the action potential was NOT affected at R1 because _______.

– lidocaine was applied downstream of R1
– there are no voltage-gated sodium channels to be affected
– lidocaine doesn’t have an effect on the generation of action potentials
– lidocaine was applied upstream of R1

The effects of lidocaine and tetrodotoxin were _______.

– identical
– similar, but lidocaine had a greater effect
– similar, but tetrodotoxin had a greater effect
– very different, because lidocaine had no effect

Which of the following occurs first in the generation of an action potential?

Voltage-gated sodium channels open.
Voltage-gated potassium channels open.
The membrane depolarizes.
The membrane repolarizes.

Which of the following occurs during depolarization?

Both A and C occur.
Voltage-gated sodium channels close.
Voltage-gated potassium channels close.
Sodium flows into the cell.
All of the above occur.

Which of the following occurs during repolarization?

– Voltage-gated sodium channels open. Sodium flows into the cell.
– Voltage-gated potassium channels remain open and some voltage-gated sodium channels inactivate. Potassium flows into the cell.
– Voltage-gated sodium channels open and some voltage-gated potassium channels inactivate. Sodium flows out of the cell.
– Voltage-gated potassium channels open and some voltage-gated sodium channels inactivate. Potassium flows out of the cell.
– Voltage-gated potassium channels open and potassium flows into the cell.

Which of the following allow the movement of potassium through the neuronal membrane?

simple diffusion
leakage channels
leakage channels and voltage-gated potassium channels
voltage-gated potassium channels

Why does the threshold increase when the interval between the stimuli decreases?

– Potassium is flowing into the cell.
– Calcium is flowing out the cell.
– Sodium is flowing out of the cell.
– Some sodium channels have been inactivated and cannot be reopened immediately.

During the relative refractory period, _______.

– a second action potential cannot be generated, no matter how strong the stimulus.
– the flow of potassium is also depolarizing the neuron.
– another action potential can be generated provided the stimulus is large enough.
– another action potential can be generated provided the stimulus is relatively smaller than the original stimulus.

When the interval between the stimuli decreases, _______.

– a second action potential is generated as long as the stimulus is above threshold
– a second action potential is generated until the interval reaches the relative refractory period
– a second action potential is generated until the interval reaches the absolute refractory period
– a second action potential is generated regardless of the stimulus and the interval

When the stimulus voltage is increased, _______.

– sodium permeability into the cell increases to overcome the potassium exiting
– a greater-than-threshold depolarization results and sodium permeability into the cell increases to overcome the potassium exiting.
– a greater-than-threshold depolarization results
– sodium permeability into the cell decreases

When the stimulus intensity increases, _______.

– the number of action potentials decreases
– the size of the action potential decreases
– the size of the action potential increases
– the number of action potentials increases

In this activity, which of the following will increase the stimulus intensity?

– increasing the absolute refractory period
– decreasing the absolute refractory period
– increasing the duration of the stimulus
– increasing the relative refractory period

At threshold, axons will _______.

– Usually be at the end of their absolute refractory period.
– Begin to hyperpolarize the membrane potential.
– Likely generate an action potential if refractory periods have elapsed.
– Always generate an action potential.

Longer stimuli will allow for _______.

-the absolute refractory period to finish
– more action potentials to occur, the absolute refractory period to finish and the relative refractory period to finish
– the relative refractory period to finish
– more action potentials to occur

The time interval between action potentials is called the _______.

potential frequency
threshold interval
interspike interval
threshold frequency

Increase in stimulus intensity _______.

– increases the duration of the action potential
– increases the frequency of action potentials
– has no effect on action potentials
– increases the size of the action potential

The frequency of action potentials is _______.

– measured in hertz, and the same as the relative refractory period
– the reciprocal of the interspike interval, and measured in hertz
– the same as the relative refractory period
– the reciprocal of the interspike interval
– measured in hertz

During the relative refractory period, _______.

– adaptation occurs
– the stimulus must be above threshold to generate an action potential
– the stimulus must be below threshold to generate an action potential
– no action potentials are generated

Which of the following is described correctly?

– Schwann cells provide the myelination in the peripheral nervous system.
– Astrocytes provide the myelination in the central nervous system.
– Oligodendrocytes provide the myelination in the peripheral nervous system.
– Schwann cells provide the myelination in the central nervous system.

The rate with which an action potential travels along an axon _______.

– is measured in meters/sec
– is called the conduction velocity
– is called the conduction velocity and is measured in volts/sec
– is measured in volts/sec
– is called the conduction velocity and is measured in meters/sec

Which of the following describes a B fiber?

– small diameter, unmyelinated
– large diameter, lightly myelinated
– medium diameter, lightly myelinated
– small diameter, lightly myelinated

The nodes of Ranvier are _______.

– locations on the axon where the myelin sheath is very heavy
– trigger zones of an axon
– a type of glial cell
– locations on the axon where the myelin sheath is absent

Which fibers generate the smallest value for conduction velocity?

A fibers
B fibers
D fibers
C fibers

The time interval for conduction would be shortest with

– the largest unmyelinated axons
– the smallest and most heavily myelinated axons
– the largest and most heavily myelinated axons
– the smallest unmyelinated axons

Increasing the amount of myelination _______.

– increases the time between action potentials
– increases the time between action potentials only for small-diameter axons
– decreases the time between action potentials
– has no effect on the time between action potentials

In this activity, the stimulus voltage used was _______.

– altered to accommodate the structural differences
– the same for all of the axons
– suprathreshold for all of the axons
– the same for all of the axons and suprathreshold for all of the axons


Synaptic plasticity: taming the beast

Synaptic plasticity provides the basis for most models of learning, memory and development in neural circuits. To generate realistic results, synapse-specific Hebbian forms of plasticity, such as long-term potentiation and depression, must be augmented by global processes that regulate overall levels of neuronal and network activity. Regulatory processes are often as important as the more intensively studied Hebbian processes in determining the consequences of synaptic plasticity for network function. Recent experimental results suggest several novel mechanisms for regulating levels of activity in conjunction with Hebbian synaptic modification. We review three of them—synaptic scaling, spike-timing dependent plasticity and synaptic redistribution—and discuss their functional implications.


Affiliations

Program in Cellular and Molecular Medicine, The Johns Hopkins University School of Medicine, Baltimore, MD, USA

Sarah A. Park & David T. Yue

Department of Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore, MD, USA

Shin-Rong Lee, Leslie Tung & David T. Yue

Department of Neuroscience, The Johns Hopkins University School of Medicine, Baltimore, MD, USA

Center for Cell Dynamics, The Johns Hopkins University School of Medicine, Baltimore, MD, USA


MEArec features

Generation of realistic Multi-Electrode Array recordings

The recent development of Multi-Electrode Arrays (MEAs) enables researchers to record extracellular activity at very high spatio-temporal density both for in vitro (Berdondini et al. 2009 Frey et al. 2009) and in vivo applications (Neto et al. 2016 Jun et al. 2017). The large number of electrodes and their high density can result in challenges for spike sorting algorithms. It is therefore important to be able to simulate recordings from these kind of neural probes.

To deal with different probe designs, MEArec uses another Python package ( MEAutility - https://meautility.readthedocs.io/), that allows users to easily import several available probe models and to define custom probe designs. Among others, MEAutility include Neuropixels probes (Jun et al. 2017), Neuronexus commercial probes (http://neuronexus.com/products/neural-probes/), and a wide variety of square MEA designs with different contact densities (the list of available probes can be found using the mearec available-probes command).

Similarly to the tetrode example, we first have to generate templates for the probes. These are the commands to generate templates and recordings for a Neuropixels design with 128 electrodes ( Neuropixels-128 ). The recordings contain 60 neurons, 48 excitatory and 12 inhibitory. With similar commands, we generated templates and recordings for a Neuronexus probe with 32 channels (A1x32-Poly3-5mm-25s-177-CM32 - Neuronexus-32 ) with 20 cells (16 excitatory and 4 inhibitory), and a square 10x10 MEA with 15 μm inter-electrode-distance ( SqMEA-10-15 ) and 50 cells (40 excitatory and 10 inhibitory).

Figure 3 shows the three above-mentioned probes (A), a sample template for each probe design (B), and one-second snippets of the three recordings (C-D-E), with zoomed in windows to highlight spiking activity.

Generation of high-density multi-electrode array recordings. a Example of three available probes: a commercial Neuronexus probe (left), the Neuropixels probe (middle), and a high-density square MEA. b Sample templates for each probe design. (C-D-E) One-second snippets of recordings from the Neuronexus probe c, the Neuropixels probe d, and the square MEA probe e. The highlighted windows display the activity over three adjacent channels and show how the same spikes are seen on multiple sites

While all the recordings shown so far have been simulated with default parameters, several aspects of the spiking activity are critical for spike sorting. In the next sections, we will show how these features, including bursting, spatio-temporal overlapping spikes, drift, and noise assumptions can be explored with MEArec simulations.

Bursting modulation of spike amplitude and shape

Bursting activity is one of the most complicated features of spiking activity that can compromise the performance of spike sorting algorithms. When a neuron bursts, i.e., fires a rapid train of action potentials with very short inter-spike intervals, the dynamics underlying the generation of the spikes changes over the bursting period (Hay et al. 2011). While the bursting mechanism has been largely studied with patch-clamp experiments, combined extracellular-juxtacellular recordings (Allen et al. 2018) and computational studies (Hagen et al. 2015) suggest that during bursting, extracellular spikes become lower in amplitude and wider in shape.

In order to simulate this property of the extracellular waveforms in a fast and efficient manner, templates can be modulated both in amplitude and shape during the convolution operation, depending on the spiking history.

To demonstrate how bursting is mimicked, we built a toy example with a constant spike train with 10 ms inter-spike-interval (Fig. 4a). A modulation value is computed for each spike and it is used to modulate the waveform for that event by scaling its amplitude, and optionally stretching its shape. The blue dots show the default modulation (bursting disabled), in which the modulation values are drawn from a Gaussian distribution with unitary mean to add some physiological variation to the spike waveforms. When bursting is enabled (by setting the bursting parameter to true), the modulation values are computed based on the spike history, and it depends on the number of consecutive spikes in a bursting event and their average inter-spike-intervals (see Supplementary Methods – Recordings generation - Modulated convolution – for details on the modulation values calculation).

Bursting behavior. a Modulation values computation for a sample spike train of 300 ms with constant inter-spike-intervals of 10 ms. The blue dots show the modulation values for each spike when bursting is not activated: each value is drawn from a (mathcal (1, 0.05^<2>)) distribution. When bursting is activated, a bursting event can be limited by the maximum number of spikes (orange - 5 spikes, green - 10 spikes), or by the maximum bursting event duration (red - 75 ms). b Modulated templates. The blue lines show templates modulated in amplitude only. The orange and green lines display the same templates with added shape modulation. c Modulation in tetrode recordings. The top panel shows spikes in a one-second period. The middle panel displays the modulation values for those spikes. The bottom panel shows the modulated template on the electrode with the largest peak after convolution. (D-E) PCA projections on the first principal component for the tetrode recordings without bursting (the same as Section Getting started with MEArec ) d and re-simulated with bursting e and shape modulation enabled. Note that the PCA projections were computed in both cases from the waveforms without bursting. The clusters, with bursting, become more spread and harder to separate than without bursting

Bursting events can be either controlled by the maximum number of spikes making a burst (orange dots - 5 spikes per burst green dots - 10 spikes per burst) or by setting a maximum bursting duration (red dots - maximum 75 ms). Note that in Fig. 4a the spike train is constant just to illustrate the computation of the modulation values. In actual simulations, instead, the modulation values will depend on the firing rate and the timing between spikes.

By default, spikes are only modulated in amplitude. The user can also enable shape modulation by setting the shape_mod parameter to true. The modulation value, computed for each spike, controls both the amplitude scaling and shape modulation of the spike event. For amplitude modulation, the amplitude of the spike is simply multiplied by the modulation value. Additionally, when shape modulation is enabled, the waveform of each spike is also stretched. The shape_stretch parameter controls the overall amount of stretch, but the actual stretch of single waveforms depends on the modulation value computed for each spike. In Fig. 4b, examples of bursting templates are shown. The blue traces display templates only modulated in amplitude, i.e., the amplitude is scaled by the modulation value. The orange and green traces, instead, also present shape modulation, with different values of the shape_stretch parameter (the higher the shape_stretch , the more stretched waveforms will be). We refer to the Supplementary Methods – Recordings generation - Modulated convolution – for further details on amplitude and shape modulation.

Figure 4c shows a one-second snippet of the tetrode recording shown previously after bursting modulation is activated. The top panel shows the spike events, the middle one displays the modulation values computed for each spike, and the bottom panel shows the output of the modulated convolution between one of the templates (on the electrode with the largest amplitude) and the spike train.

Figures 4d and e show the waveform projections on the first principal component of each channel for the tetrode recording shown in Section Getting started with MEArec with and without bursting enabled, respectively. In this case all neurons are bursting units and this causes a stretch in the PCA space, which is a clear complication for spike sorting algorithms. Note that shape modulation does not affect all neurons by the same amount, since it depends on the spike history and therefore on the firing rate.

Controlling spatio-temporal overlaps

Another complicated aspect of extracellular spiking activity that can influence spike sorting performance is the occurrence of overlapping spikes. While temporal overlapping of events on spatially separated locations can be solved with feature masking (Rossant et al. 2016), spatio-temporal overlapping can cause a distortion of the detected waveform, due to the superposition of separate spikes. Some spike sorting approaches, based on template-matching, are designed to tackle this problem (Pachitariu et al. 2016 Yger et al. 2018 Diggelmann et al. 2018).

In order to evaluate to what extent spatio-temporal overlap affects spike sorting, MEArec allows the user to set the number of spatially overlapping templates and to modify the synchrony rate of their spike trains. In Fig. 5 we show an example of this on a Neuronexus-32 probe (see Fig. 3A). The recording was constructed with two excitatory and spatially overlapping neurons, whose templates are shown in Fig. 5a (see Supplementary Methods – Recordings generation - Overlapping spikes and spatio-temporal synchrony – for details on the spatial overlap definition). The spike synchrony rate can be controlled with the sync_rate parameter. If this parameter is not set (Fig. 5b - left), some spatio-temporal overlapping spikes are present (red events). If the synchrony rate is set to 0, those spikes are removed from the spike trains (Fig. 5b - middle). If set to 0.05, i.e., 5% of the spikes will be spatio-temporal collisions, events are added to the spike trains to reach the specified synchrony rate value of spatio-temporal overlap. As shown in Fig. 5c, the occurrence of spatio-temporal overlapping events affects the recorded extracellular waveform: the waveforms of the neurons, in fact, get summed and might be mistaken for a separate unit by spike sorting algorithms when the spikes are overlapping.

Controlling spatio-temporal overlapping spikes. a Example of two spatially overlapping templates. The two templates are spatially overlapping because on the electrode with the largest signal (depicted as an black asterisk) for the blue template, the orange template has an amplitude greater than the 90% of its largest amplitude. b Without setting the synchrony rate, the random spike trains (left) present a few spatio-temporal collisions (red events). When setting the synchrony rate to 0 (middle), the spatio-temporal overlaps are removed. When the synchony rate is set to 0.05 (right), spatio-temporal overlapping spikes are added to the spike trains. c One-second snippet of the recording with 0.05 synchrony. In the magnified window, a spatio-temporal overlapping event is shown: the collision results in a distortion of the waveform

The possibility of reproducing and controlling this feature of extracellular recordings within MEArec could aid in the development of spike sorters which are robust to spatio-temporal collisions.

Generating drifting recordings

When extracellular probes are inserted in the brain, especially for acute experiments, the neural tissue might move with respect to the electrodes. This phenomenon is known as drift. Drift can be due to a slow relaxation of the tissue (slow drift) or to fast re-adjustments of the tissue, for example due to an abrupt motion of the tissue (fast drift). These two types of drifts can also be observed in tandem (Pachitariu et al. 2019).

Drifting units are particularly critical for spike sorting, as the waveform shapes change over time due to the relative movement between the neurons and the probe. New spike sorting algorithms have been developed to specifically tackle the drifting problem (e.g. Kilosort2 (Pachitariu et al. 2019), IronClust (Jun et al. 2017)).

In order to simulate drift in the recordings, we first need to generate drifting templates:

Drifting templates are generated by choosing an initial and final soma position with user-defined rules (see Supplementary Methods – Template generation - Drifing templates – for details) and by moving the cell along the line connecting the two positions for a defined number of constant drifting steps that span the segment connecting the initial and final positions (30 steps by default). An example of a drifting template is depicted in Fig. 6a, alongside with the drifting neuron’s soma locations for the different drifting steps.

Drifting. a Example of a drifting template. The colored asterisks on the left show the trajectory from the initial (blue large asterisk) to the final (red large asterisk) neuron positions. The positions are in the x-y coordinates of the probe plane, and the electrode locations are depicted as black dots. The corresponding templates are displayed at the electrode locations with the same colormap, showing that the template peak is shifted upwards following the soma position. b Slow drift. (top) 60-second slow drifting recording with four neurons moving at a velocity of 20 μ m/min. Templates on the largest electrode are superimposed in different colors on the recordings. Note that the maximum channel changes over time. (bottom) Amplitude of the waveforms over time on the electrode with the largest initial peak. c Fast drift. (top) 60-second fast drifting recording with four neurons undergoing a fast drift event every 15 s. Templates on the largest electrode are superimposed in different colors on the recordings. Also for fast drifts, the maximum channel changes over time. (bottom) Amplitude of the waveforms over time on the electrode with the largest initial peak

Once a library of drifting templates is generated, drifting recordings can be simulated. MEArec allows users to simulate recordings with three types of drift modes: slow, fast, and slow+fast. When slow drift is selected, the drifting template is selected over time depending on the initial position and the drifting velocity (5 μ/min by default). If the final drifting position is reached, the drift direction is reversed. For fast drifts, the position of a drifting neuron is shifted abruptly with a user-defined period (every 20 s by default). The new position is chosen so that the difference in waveform amplitude of the drifting neuron on its current maximum channel remains within user-defined limits (5-20μV by default), in order to prevent from moving the neuron too far from its previous position. The slow+fast mode combines the slow and fast mechanisms.

In Fig. 6b and c we show examples of slow drift and fast drift, respectively. In the top panel the recordings are displayed, with superimposed drifting templates on the electrode with the largest peak. Note that the maximum channel can change over time due to drift. In the bottom panels, instead, the amplitude of the waveforms on the channels with the initial largest peak for each neuron are shown over time. Slow drift causes the amplitude to slowly vary, while for fast drifts we observe more abrupt changes when a fast drift event occurs. In the slow+fast drift mode, these two effects are combined.

Modeling experimental noise

Spike sorting performance can be greatly affected by noise in the recordings. Many algorithms first use a spike detection step to identify putative spikes. The threshold for spike detection is usually set depending on the noise standard deviation or median absolute deviation (Quiroga et al. 2004). Clearly, recordings with larger noise levels will result in higher spike detection thresholds, hence making it harder to robustly detect lower amplitude spiking activity. In addition to the noise amplitude, other noise features can affect spike sorting performance: some clustering algorithms, for example, assume that clusters have Gaussian shape, due to the assumption of an additive normal noise to the recordings. Moreover, the noise generated by biological sources can produce spatial correlations in the noise profiles among different channels and it can be modulated in frequency (Camuñas-Mesa and Quiroga 2013 Rey et al. 2015).

To investigate how the above-mentioned assumptions on noise can affect spike sorting performance, MEArec can generate recordings with several noise models. Figure 7 shows 5-second spiking-free recordings of a tetrode probe for five different noise profiles that can be generated (A - recordings, B - spectrum, C - channel covariance, D - amplitude distribution).

Noise models. The 5 columns refer to different noise models: 1) Uncorrelated Gaussian noise, 2) Distance-correlated Gaussian noise, 3) Colored uncorrelated Gaussian noise, 4) Colored distance-correlated Gaussian noise, and 5) Noise generated by distant neurons. a One-second spiking-free recording. b Spectrum of the first recording channel between 10 and 5000 Hz. c Covariance matrix of the recordings. d Distribution of noise amplitudes for the first recording channel. The different noise models vary in the spectrum, channel correlations, and amplitude distributions

The first column shows uncorrelated Gaussian noise, which presents a flat spectrum, a diagonal covariance matrix, and a symmetrical noise amplitude distribution. In the recording in the second column, spatially correlated noise was generated as a multivariate Gaussian noise with a covariance matrix depending on the channel distance. Also in this case, the spectrum (B) presents a flat profile and the amplitude distribution is symmetrical (D), but the covariance matrix shows a correlation depending on the inter-electrode distance. As previous studies showed (Camuñas-Mesa and Quiroga 2013 Rey et al. 2015), the frequency content of extracellular noise is not flat, but its spectrum is affected by the spiking activity of distant neurons, which appear in the recordings as below-threshold biological noise. To reproduce the spectrum profile that is observed in experimental data, MEArec allows coloring the noise spectrum of Gaussian noise with a second order infinite impulse response (IIR) filter (see Supplementary Methods – Recordings generation - Noise models and post-processing – for details). Colored noise represents an efficient way of obtaining the desired spectrum, as shown in the third and fourth columns of Fig. 7, panel B. Distance correlation is maintained (panel C - fourth column), and the distribution of the noise amplitudes is symmetrical. Finally, a last noise model enables one to generate activity of distant neurons. In this case, noise is built as the convolution between many neurons (300 by default) whose template amplitudes are below an amplitude threshold (10μV by default). A Gaussian noise floor is then added to the resulting noise, which is scaled to match the user-defined noise level. The far-neurons noise profile is shown in the last column of Fig. 7. While the spectrum and spatial correlation of this noise profile are similar to the ones generated with a colored, distance-correlated noise (4th column), the shape of the noise distribution is skewed towards negative values (panel D), mainly due to the negative contribution of the action potentials.

The capability of MEArec to simulate several noise models enables spike sorter developers to assess how different noise profiles affect their algorithms and to modify their methods to be insensitive to specific noise assumptions.


Discussion

The determinant of AP formation is the high expression of voltage-gated Na + and K + channels in a spatially compact and restricted area such as in the axon initial segment (Kole and Stuart, 2012). The high expression of Na + and K + channels in Xenopus oocytes affirmed these minimal channel requirements for inducing a rapid, all-or-none, regenerative electrical event. The findings in this paper extend the work of Shapiro et al. (2012), who demonstrated the ability of infrared radiation to depolarize a cell, and of Corbin-Leftwich et al. (2016), who studied the impact of a Kv7 modulator on cellular excitability. Unique to the present study is the assessment of membrane potentials generated in loose clamp by high expression of Nav channels ( Fig. 2 ), examination of the role of non-voltage-gated K + conductances in the genesis of APs ( Figs. 3 , ​ ,4, 4 , and S5), demonstration of the diversity of AP waveforms that can be generated in oocytes ( Figs. 5 and ​ and6), 6 ), and documentation of reliable methods necessary to achieve the AP recordings ( Figs. 1 , S1, S2, and S3). Collectively, these findings provide valuable information about the parameters of APs induced in oocytes that can be used in diverse research and educational settings.

Notably, our study used skeletal muscle Nav1.4 α subunits, because plasmid DNA constructs for neuronal Nav channels are remarkably unstable in bacterial hosts. However, if methods are successfully used to prepare neuronal Nav plasmid DNA without rearrangements or uncontrolled mutations (Feldman and Lossin, 2014), it is reasonable to expect that neuronal Nav channels (e.g., Nav1.1, 1.2, and 1.6) could be used to generate APs in oocytes as well. This remains to be tested in future studies.

In neurons, the axon hillock (Fuortes et al., 1957) and the axon initial segment (Araki and Otani, 1955) are sites of AP initiation (Colbert and Johnston, 1996), although this functional polarization may be a vertebrate specialization (Kole and Stuart, 2012). The unique role of these structures is governed by the very high expression of voltage-gated Na + and K + channels in a spatially restricted area. Although there are differences in the channel density and geometry of the neuronal structures and the Xenopus oocyte, a requirement for very high expression of Na + channels is a cornerstone of the present study. The genesis of all-or-none events that resemble APs in excitable cells required the coexpression of at least one type of voltage-gated or non-voltage-gated K + conductance. Indeed, coexpression of the TREK-1 type of K2P channels with Nav channels was sufficient to allow rapid APs ( Fig. 3 ). These results compare favorably with the conclusions from a mixed computer simulation/biological experiment in which virtual Na + currents were introduced to HEK cell patch-clamp recordings with biologically expressed K2P channels to assess the ability to fire APs without the introduction of voltage-gated K + channels (MacKenzie et al., 2015). Although background Kv channels may have been present in the HEK cells, and the study examined in silico but not biological Na + channels, K2P channels generated the hyperpolarized VREST needed for APs, and they contributed to repolarization of the AP (MacKenzie et al., 2015). Likewise, in cerebellar Purkinje cells, high expression of K2P channels supports rapid AP firing (Brickley et al., 2007). The results of the present study support the hypothesis that the minimal requirement for an AP includes a sufficiently large K + conductance, although it need not be a voltage-activated conductance. Mechanistically, our results suggest that a K2P conductance is sufficient to promote the deactivation of Na + channels, at least for the capability of firing single APs.

Kir channels have a complex relationship with cellular excitability. Neurons with naturally large Kir currents tend to have strongly hyperpolarized VREST values (Hibino et al., 2010), which may suppress excitability (Leao et al., 2012 Li et al., 2013), and genetic overexpression of Kir channels can be used to silence neuronal electrical activity (Nitabach et al., 2002). Correspondingly, genetic inhibition of Kir2.1 reduces membrane hyperpolarization and promotes rhythmic firing in ventricular myocytes (Miake et al., 2002). The dampening of excitability by Kir channels may seem paradoxical, because membrane hyperpolarization promotes recovery from inactivation of Nav channels. However, a membrane that is strongly hyperpolarized at rest may not generate a large enough depolarization in a spatially restricted area to engage the regenerative cycle of depolarization and Na + channel activation, even when Na + channels are available. Kir channels thus influence cellular excitability not simply by maintaining a hyperpolarized VREST or altering VTHR, but by regulating the relationship between VREST and Nav channel availability ( Figs. 4 and S5).

Kir channel expression promoted spontaneous firing ( Fig. 6 A ) and high-frequency firing in response to long current injections ( Fig. 6 C ), probably by finely regulating the Nav channel availability. Indeed, other mechanisms that allowed the membrane potential to hover near threshold while also maintaining sufficient Nav channel availability for AP firing could reveal excitability in the oocyte membrane even Kv7 channels could support spontaneous firing ( Fig. 6 B ). Correspondingly, we observed that in oocytes with a high expression of Nav channels and the capability of generating APs, we could prevent AP generation by artificially hyperpolarizing the membrane in the loose-clamp recordings. Together, these experiments in oocytes help us understand how Kir channels influence the dynamic relationship between Nav channel availability and VREST, with significant impact on cellular excitability.

We have shown that AP generation in Xenopus oocytes provides a way to additively change an AP waveform in living cells and study the role of different channels on AP diversity (Yue and Yaari, 2004 Bean, 2007 Larsson, 2013). Such an approach could be particularly useful in reconstituting APs from ion channels cloned from invertebrates in which recording from neural tissue is challenging or using channels from unicellular organisms such as diatoms or algal cells. Other specific applications include investigating the role of accessory subunits for many of the channels (Patton et al., 1994), RNA editing (Patton et al., 1997 Garrett and Rosenthal, 2012), glycosylation (Johnson and Bennett, 2008), or disease-causing, gain-of-function mutations in ion channels (Lossin et al., 2012 Cannon, 2015 Dell’Orco et al., 2017). Especially useful would be the expression of mutations in accessory subunits whose influences are difficult to predict. An example is the C121W mutation in a neuronal Nav 㬡 subunit, which is associated with a form of epilepsy (Wallace et al., 1998). Additional applications of this approach are to test hypotheses about the impact of drugs and modulators on AP waveforms (Corbin-Leftwich et al., 2016) using controlled combinations of channel RNAs. Perhaps researchers may also be able to induce propagated APs in gap junction𠄺ssociated oocytes (Swenson et al., 1989) or stimulate APs in oocytes using channelrhodopsins or ligand-gated channels.

When adding different ionic conductances to the model system, the ease of repeatedly switching between voltage clamp and AP recording makes it possible to assess relative magnitudes of ionic currents and membrane potential changes. However, precise measurements of the kinetics and amplitudes of ionic current recordings are compromised by space clamp artifacts (Baumgartner et al., 1999). The key adaptation of the TEVC method that is needed for AP recordings in oocytes is to weaken the voltage clamp so that the membrane potential changes as a function of the ionic currents. Thus, the approach described here is best considered as an AP recording method requirements for simultaneous voltage clamp recordings of time- and voltage-dependent currents should be used only to confirm that certain channel types are functional and to estimate expression levels. A second limitation is in studying the role of calcium-dependent conductances on AP firing, due to the presence of endogenous Ca 2+ -activated Cl − conductances in the oocyte (Weber, 1999). Additional limitations of the oocyte expression system or any other in vitro expression system are not restricted to the loose-clamp method of AP recording. Despite these limitations, the model has identified research applications and remains open to the possibility of future, creative adaptations as well.

An unexpected benefit that we experienced in exploring this AP model is the facilitation of student learning about the properties of APs. Undergraduate and graduate students alike benefit from the hands-on recording and analysis of APs, an experience that is not tractable for many students when using cultured cells or brain slices and patch-clamp methods. The approach offers the enjoyment of interacting with the data in real time and in a living cell the ability to use the model for hypothesis-testing promotes inquiry-based learning, which deepens understanding and increases knowledge retention (Kober, 2015 Waldrop, 2015). The minimal AP model can certainly help to clarify common misconceptions about APs. For example, students, faculty, and researchers alike often believe that the value of � or � mV (as shown in textbooks) is the value of “threshold” in all cells. This minimal AP model, therefore, could certainly help investigators recognize the impact of ion channel composition and resting potential on threshold and appreciate that it is neither a set value for every excitable cell nor invariable in an individual cell. Academics also often believe that all neurons fire APs. The present approach helps students formulate their own explanation for why certain neurons do not show spiking behavior in native systems (Bufler et al., 1992 Baden et al., 2013) and what is distinctive about an excitable membrane. This helps encourage discussion and understanding about how channel localization and clustering may affect AP firing and facilitates appreciation for the structure and function of the axon hillock, initial segments, and nodes of Ranvier.

In conclusion, this work demonstrates reliable, useful, and simple approaches to induce APs in Xenopus oocytes with many applications for research and teaching.


Watch the video: Ράγισε καρδιές με την παρέμβασή της στον focus fm η υγειονομικού που δυο μήνες είναι στην ανεργία (November 2021).