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J Neural Eng. Author manuscript; available in PMC 2008 Nov 3.
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PMCID: PMC2577565
NIHMSID: NIHMS50038

Region-specific network plasticity in simulated and living cortical networks

comparison of the center of activity trajectory (CAT) with other statistics

Abstract

Electrically interfaced cortical networks cultured in vitro can be used as a model for studying the network mechanisms of learning and memory. Lasting changes in functional connectivity have been difficult to detect with extracellular multi-electrode arrays using standard firing rate statistics. We used both simulated and living networks to compare the ability of various statistics to quantify functional plasticity at the network level. Using a simulated integrate-and-fire neural network, we compared five established statistical methods to one of our own design, called center of activity trajectory (CAT). CAT, which depicts dynamics of the location-weighted average of spatiotemporal patterns of action potentials across the physical space of the neuronal circuitry, was the most sensitive statistic for detecting tetanus-induced plasticity in both simulated and living networks. By reducing the dimensionality of multi-unit data while still including spatial information, CAT allows efficient real-time computation of spatiotemporal activity patterns. Thus, CAT will be useful for studies in vivo or in vitro in which the locations of recording sites on multi-electrode probes are important.

Introduction

Modification of connectivity between cortical neurons plays an important role in the processes of learning (Ahissar et al 1992, Buonomano 1998) and memory (Merzenich and Sameshima 1993). Connectivity at the synaptic level has been studied by administering stimuli while simultaneously recording neural activity, and then quantifying plasticity by analyzing the stimulus–response relationships. Culturing on multi-electrode arrays (MEAs) (figures 1(a) and (b)) was introduced to help understand connectivity and plasticity in networks of neurons (Gross 1979, Pine 1980). This allows long-term (months), non-invasive observation of the electrical activity of multiple neurons simultaneously (Potter and DeMarse 2001)in a system with less experimental complexity and greater control than preparations in vivo. External factors such as sensory inputs, attention and behavioral drives are absent, while many aspects of complex spatiotemporal spike patterns observed in animals remain (Gross and Kowalski 1999, Shefi et al 2002).

Figure 1
Living MEA culture versus simulated network. The simulated neural network and stimulation electrodes were constructed to mimic the dissociated cultured network and MEA setup. (a) A view of a living MEA culture with 60 electrodes. (b) Neurons, tagged with ...

Many activity statistics have been used to quantify stimulus–response relationships from simultaneous recordings of multiple neurons (Brown et al 2004). Most analyze the dependences between spike trains, such as the maximum likelihood method (Chornoboy et al 1988, Okatan et al 2005), product–moment correlation coefficient (Kudrimoti et al 1999), functional holography (Baruchi and Ben-Jacob 2004), etc. However, only a few were applied for measuring network plasticity. The most common of these was the firing rate (FR), which showed plastic modifications of network response induced by tetanic stimulation in cortical cultures (Reich et al 1997, Jimbo et al 1998, Maeda et al 1998, Jimbo et al 1999, Wagenaar et al 2006a) and dopamine-regulated plasticity in anesthetized rats (Rosenkranz and Grace 1999). Firing rate histogram (FRH) uses firing rates integrated over successive sequential latency epochs to add detailed temporal information, and was applied to demonstrate adaptable image processing and pattern recognition through training by tetanic stimulation in MEA cultures (Ruaro et al 2005). Mutual information (MI) characterized the statistical dependence between neuron pairs, exposing the strength of coupling between neurons and the functional connectivity among cortical areas (David et al 2004). Cross-correlation histograms (CCH) from pairs of neurons showed functional plasticity in the auditory cortex of behaving monkeys (Ahissar et al 1998), and the more advanced shift-predictor corrected cross-correlogram (SCCC) was used to quantify receptive field plasticity in the rat auditory cortex (Bao et al 2003). Joint peri-stimulus time histogram (JPSTH) characterized the causality of firing between neuron pairs, and successfully demonstrated long-term facilitation of neural activity involved in respiratory control (Morris et al 2003). Robust neuronal computation and encoding is believed to involve the distribution of information over populations of neurons and synapses in a combination of spatial and temporal domains. Observing only pairs of neurons (MI, CCH, SCCC and JPSTH), neglecting temporal information (FR) and neglecting spatial information (all) limit the ability of these to measure the complex plasticity of the brain.

We recently devised a statistic called the center of activity trajectory (CAT), which incorporates both the physical locations of the recording sites and the timing of neural activity in order to depict dynamics of the population activity in the neuronal circuitry space (Chao et al 2005). The neuronal circuitry space is defined by the physical locations of the neurons, in our case being the MEA’s two-dimensional plane. The center of activity (CA) component is analogous to the center of mass, in that the ‘mass’ at an electrode location is determined by the recorded firing rate. CAT is the sequence of CAs over successive time intervals. We discuss how the inclusion of spatial and temporal information improved the detection of neural network plasticity. The importance of the spatial location of neural activity has been widely emphasized in other studies. For example, spatiotemporal dipole models were used to represent the spatial distribution of underlying focal neural sources producing electroencephalographic (EEG) and magnetoencephalographic (MEG) signals (Scherg 1990, Leahy et al 1998).

We used a simulated network to compare CAT’s ability to detect network plasticity to the alternative statistics: FR, FRH, MI, SCCC and JPSTH. No ground truth about network plasticity in living networks exists, because neuronal connectivity cannot be measured for more than a few pairs of neurons simultaneously. Therefore, we could only cross-validate the amount of plasticity detected by each statistic in a simulated network, in which the weights of all synapses were observable. In simulation, we modulated neural plasticity in a controlled manner, and quantified the ability of each statistic to reveal underlying changes in synaptic connectivity.

In simulation, CAT showed the ability to detect smaller changes in the distribution of network synaptic weights than did FR, FRH, MI, SCCC or JPSTH. CAT also detected more pronounced changes in the network following tetanus than the alternate statistics in living MEA cortical cultures.

By applying a shuffling method to the CAT analysis to erase spatial information about recording location in its calculation, we found that changes in activity patterns recorded from neighboring electrodes were not independent and contributed to the better performance of CAT to detect plasticity. The network plasticity was region specific: despite the apparent random connectivity of neurons, plasticity was not symmetrically distributed, and the location of neurons played a role in stimulus-induced plasticity.

Methods

Simulation

Simulated networks

We used the Neural Circuit SIMulator (Natschlager et al 2002) to produce five artificial neural networks, as described previously (Chao et al 2005) (also see supplemental materials 1 available at stacks.iop.org/JNE/4/294). Briefly, 1000 leaky-integrate-andfire (LIF) model neurons, with a total of 50 000 synapses, were placed randomly in a 3 mm by 3 mm area (see figure 1(c)). All synapses were frequency dependent (Markram et al 1998, Izhikevich et al 2004) to model synaptic depression. 70% of the neurons were excitatory, with spike-timing-dependent plasticity (STDP) (Song et al 2000). We included an 8 by 8 grid of electrodes; 60 of these were used for recording and stimulation as in a real MEA (four excluded electrodes were corner electrodes 11, 18, 81 and 88, see figure 1(d)).

Setup of networks with different synaptic states

The synaptic state of a network was determined by its connections and synaptic weight distribution. In order to generate different synaptic states, we used five networks with different connectivity as reference networks. We ran the networks for 5 h in simulated time until the synaptic weights reached a steady state (see supplemental materials 1 available at stacks.iop.org/JNE/4/294). The set of synaptic weights stabilized after 5 h of spontaneous activity, without external stimuli, and was used as the initial state for the corresponding reference network.

For each reference network, we applied simulated tetanization at two randomly picked electrodes at 20 Hz, and a series of subsequent networks (different synaptic states) were collected after different tetanus durations (1, 2, 5, 10, 15, 20, 30 s and 1, 2, 5 min). That is, starting from a reference network (S0), S1 was the network with the synaptic state at 1 s after the start of tetanization, S2 at 2 s, and so forth. Therefore, for each pair of randomly chosen tetanization electrodes, ten new networks with different synaptic states were obtained. This process was repeated for each reference state using ten different tetanization electrode pairs. By altering the five reference networks in this manner, a total of 500 new networks with different synaptic states were obtained.

Tetanic stimulation induces long-lasting changes in synaptic transmission (Bliss and Lømo 1973), which shapes how neural circuits process information and is involved in behavioral modifications, including simple forms of learning in motor control (Fisher et al 1997). Administration of 20 Hz tetanization, as in our study, was widely used to induce long-term facilitation (LTF) of post-synaptic potentials at crayfish neuromuscular junctions (Wojtowicz and Atwood 1985, Delaney et al 1989), short-term synaptic plasticity in anesthetized fish (Fortune and Rose 2000), long-term potentiation (LTP) in hippocampal slices (Miles and Wong 1987) and modification of synaptic strength in cortical cultures (Jimbo et al 1999). In our simulated networks, tetanization induced both LTP and long-term depression (LTD) of synapses through STDP: firing of a post-synaptic neuron immediately after a pre-synaptic neuron results in LTP of synaptic transmission and the reverse order of firing results in LTD (Levy and Steward 1983, Markram et al 1998, Bi and Poo 1998, Gerstner et al 1996).

Simulations with random probing sequence (RPS)

For each network, we ran ten simulations with different 10 min random probing sequences (RPSs). Therefore, a total of 5050 simulations were performed separately on 505 networks (500 new networks and 5 reference networks). The probe stimuli were applied to all 60 electrodes, one at a time, with inter-stimulus intervals on a given electrode drawn from independent exponential distributions with a mean of 60 s. Thus, each electrode stimulated the simulated network with different random sequences, averaging 1 pulse per second for the whole array.

In each simulation, there were 10.0 ± 3.1 (mean and standard deviation) stimuli delivered at each electrode. The same Gaussian noise, introduced into neurons as fluctuations in membrane voltage, was used for each simulation to control the effects of self-firing or of sub-threshold fluctuation of membrane potential on activity. In order to ensure that the statistics calculated from the same network correspond to the same synaptic state, the STDP algorithm was turned off throughout the simulation to prevent ongoing activity changing the network state.

Plasticity statistics

Five commonly used statistics and the center of activity trajectory (CAT) were measured from each simulation (see figure 7). The five commonly used statistics were FR, FRH, mutual information (MI), SCCC and JPSTH (see supplemental materials 2 available at stacks.iop.org/JNE/4/294).

Figure 7
Comparison of the six different statistics. CAT was the most sensitive activity statistic and was highly efficient. Examples of six statistics calculated from the same RPS during three synaptic states are shown: S0 (reference network), S7 (network with ...

Center of activity trajectory (CAT)

CAT represents spatiotemporal patterns of network-wide population activity. As applied here, it is a spatially weighted measure of temporally binned responses to single-electrode stimuli in neuronal circuitry space. During each simulation, stimuli at each electrode occurred multiple times (10.0 ± 3.1 times) in one RPS. FRH from the recording electrode Ek to the stimulus at electrode Pi, FRHEjPi , was defined as the average number of spikes counted in a 5 ms moving time bin with 500 μs time step over trials. FRHEkPi= (n) represents the value of FRHEjPi in k the n bin, and Col(Ek) and Row( th Ek) are the column number and the row number of the electrode Ek, respectively. For example, the electrode in column number 2 and row number 8 is 28 (see figure 1(d)). The value of CA in the nth bin for the stimulation electrode Pi has X and Y components, which are defined as

[CAXPi(n),CAYPi(n)]=k=160FRHEkPi(n)[Col(Ek)Rcol,Row(Ek)Rrow]k=160FRHEkPi,
(1)

where Rcol and Rrow are the coordinates of a reference point (the physical center of the 8 by 8 grid of electrodes, in our case). CA was calculated with an electrode number in the neuronal circuitry space, which is equivalent to using the physical location since the inter-electrode spacing is constant. The corresponding X and Y components for CAT are defined as

CATXPi=[CAXPi(1),CAXPi(2),,CAXPi(n),,CAXPi(N)]CATYPi=[CAYPi(1),CAYPi(2),,CAYPi(n),,CAYPi(N)],
(2)

where N is the total number of bins in FRHEjPi. Intuitively, CA is analogous to the center of mass, where the ‘mass’ at an electrode location is determined by the recorded FR. CAT is the sequence of CAs over successive time intervals.

CA reflects spatial asymmetry of neural activity about the reference point (the center of the dish), and CAT represents the dynamics of CA. That is, if the network is firing symmetrically, the CA will be at the center of the dish, whereas if the network fires mainly in one corner then the CA will be found off-center toward that corner. CA reduces the dimensionality from 60 to 2, and it is not an injective (information-preserving) function of activity distribution. See supplemental materials 3 (available at stacks.iop.org/JNE/4/294)forCATin a simulated network, and Supplemental Materials 5 (available at stacks.iop.org/JNE/4/294) for CAT in an MEA culture.

Evaluating the performances of different statistics

Performance of a statistic was defined by the smallest change in network synaptic weights that could be detected as significant. To evaluate performance in each simulation, we evaluated the statistic for evoked responses to all 60 stimulation electrodes and joined these together into a large vector representing the whole stimulus–response information (input–output function) of the network. We called this joint vector the whole-input–output (WIO) vector of the statistic. Figure 2 demonstrates the calculation of the WIO vector for CAT. A visualization of the change in WIO vectors for CAT from S0 to S1S10 appears in figure 3.

Figure 2
Whole-input–output (WIO) vectors for analyzing performances of different statistics. WIO vectors calculated from each statistic were used to represent the network input–output function. As an example, the WIO vector of CAT calculated from ...
Figure 3
Multi-dimensional whole-input–output (WIO) vectors measured in different synaptic states in simulated networks. The WIO vectors measured from different synaptic states were different. This is a cross-viewing 3D stereogram of an example of the ...

We measured the Euclidian distances E(Si) between ten WIO vectors (from ten simulations with different RPSs) calculated at Si to the centroid calculated at S0 (shown as a cross in figure 3). We then compared E(Si) for S1S10 to E(S0) separately, and the p-values (n 10 RPSs, Wilcoxon signed rank test, which tests the magnitudes of the differences between paired observations without assumptions about the form of the distribution of the measurements) were computed to quantify the significance of differences. For each state, the relation between the mean p-values (n 50, from five reference networks and ten tetanization electrode pairs per reference network) and the mean absolute synaptic change (MASC) was quantified

MASC(Si)=1Nk=1NWk(Si)Wk(S0)0.5×100%,
(3)

where N is the number of excitatory synapses and Wk(Si) represents the synaptic weight of the kth excitatory synapse at network Si. We normalized the absolute change in each synapse by the possible range, 0 to 0.5, for excitatory synapses. We determined the performance of different statistics as the minimum MASC for p-values below a significance threshold of 0.05; this is termed ‘detectable MASC’. The smaller the MASC a statistic can detect, the better the statistic’s performance.

Evaluation of the sensitivities and specificities of different statistics

Successful performance can be artificially enhanced if a statistic mistakes some non-significant changes as being significant. Therefore, analyzing sensitivity (ability to detect significant plasticity) and specificity (ability to discount insignificant plasticity) can further determine the quality of a statistic. Sensitivity was defined as the probability that a statistic indicated a significant difference when calculated from two significantly different network synaptic states (probability of a true positive). Specificity was defined as the probability that a statistic showed no significant difference when calculated from networks with no significant difference in synaptic state (probability of a true negative). Together, sensitivity and specificity described the accuracy of a statistic.

For each reference network, the 500 new states (S1 to S10) were individually evaluated to determine whether their synaptic weight distributions were significantly different from the distribution of the reference state (two-sample Kolmogorov–Smirnov test, which tests whether the two samples have the same distribution, two-tailed, α = 0.05). If a statistic showed a significant difference (p-value < 0.05; see the previous section) for a state that was significantly different than the reference state (according to the Kolmogorov– Smirnov test), then the result was classified as being a true positive (TP). Conversely, if it showed no significance, then the result was considered a false negative (FN). If a statistic showed significance when calculated from a state that was not significantly different than the reference state, then the result was considered a false positive (FP). If it showed no significance, then the result was considered a true negative (TN). The numbers of TP, FN, FP, and TN were counted for the 500 new networks, and the sensitivity and specificity were defined as

Sensivity=TPTP+FN×100%,Specificity=TNFP+TN×100%.
(4)

Experiments in living cultures

Culture and experimental protocol

Dense networks of dissociated cortical neurons were prepared and cultured as described in Potter and DeMarse (2001). Briefly, embryonic rat cortices were dissected and dissociated using papain and trituration. Fifty thousand cells (∼7000 cells mm−2) were plated on multi-electrode arrays (MultiChannel Systems, Reutlingen, Germany) pre-coated with poly-ethylene-imine (PEI) and laminin. Cultures were grown in Dulbecco’s Modified Eagle’s Medium (DMEM) containing 10% horse serum.

Six experiments were performed on five cultures from four dissociations. Culture ages ranged from 1 to 3 months (Potter and DeMarse 2001). We delivered biphasic stimuli (monopolar) at 500 mV and 400 μs per phase by using our custom-made stimulator (Wagenaar et al 2004, Wagenaar and Potter 2004). Data acquisition, visualization, artifact suppression (Wagenaar and Potter 2002) and spike detection were performed using MultiChannel Systems hardware and our publicly available acquisition and analysis software, Meabench (Potter et al 2006). Experiments were conducted in an incubator to control environmental conditions.

Each experiment consisted of a 2 hperiod of RPS followed by a 15 min tetanic stimulation followed by another 2 h period of RPS (Wagenaar et al 2006a). In six experiments, the RPS periods consisted of six electrodes stimulated in a random order at an aggregate frequency of 0.5 Hz (in one experiment, the RPS periods consisted of only four probe electrodes). Fewer electrodes were used in RPS for living networks than simulated networks because not every electrode was able to evoke responses. Two of these electrodes were used for the tetanic stimulation: 150 trains of 20 paired pulse stimuli with 10 ms intervals between paired pulses, 50 ms intervals between pairs and 6 s intervals between the start of each train. Prior to an experiment, every electrode was stimulated in a random order 20 times, and electrodes with six (or four) highest responses (the total number of spikes counted within 100 ms latency after stimuli over recording electrodes) were selected as probe electrodes. The tetanus electrodes were randomly chosen from these.

Measures of CAT, FR, FRH and SCCC

We used evoked responses within 100 ms after the stimuli of RPS for statistics calculations (see supplemental materials 2 available at stacks.iop.org/JNE/4/294). We measured CAT from the evoked responses in the cultured networks and compared it to the three most commonly used statistics: FR, FRH and SCCC. MI was not measured, due to its poor performance in detecting network plasticity in simulations (see results). JPSTH was not measured because of its high dimensionality and computation time (see figure 7 and supplemental materials 2 available at stacks.iop.org/JNE/4/294).

Statistics

For each statistic, we calculated one WIO vector every 240 s (a ‘block’) for the experiments with six probe stimulation electrodes, and every 160 s for the experiments with four probe stimulation electrodes. Thus, there were 19.9 ± 4.2 (mean and standard deviation) stimuli delivered at each electrode for each WIO vector. Three periods were used for statistics: Pre1, Pre2 and Post1 (see figure 8(a)). Each period had a duration of 52.5 min, and the intervals between Pre1 and Pre2 and between Pre2 and Post1 were 15 min. The 15 min interval between Pre2 and Post1 was the tetanization. For each statistic, the mean distance of the WIO vectors in Pre1 to the centroid of the WIO vectors in Pre2 (C) was compared to the mean distance to their own centroid (D). The ratio of change to drift, C/D, was used to quantify the change from Pre1 to Pre2 before the tetanus (no change if this ratio ≅1). A similar measure between Pre2 and Post1 was used to quantify the change across the tetanus. The performance of each statistic to detect the tetanus-induced change was quantified by comparing the two C/Ds (n = 6 experiments, Wilcoxon signed rank test).

Figure 8
Comparison of the changes in CAT, FR, FRH and SCCC across tetanization in living MEA cultures. (a) An example of comparison of CAT, FR, FRH and SCCC (from evoked responses to RPS in one experiment) before and after tetanization is shown. Principal components ...

Results

We tested the performances of six network plasticity statistics in simulated networks: FR, FRH, MI, SCCC, JPSTH and CAT (all acronyms are shown in table 1). We then compared several of these statistics in their ability to detect tetanus-induced network plasticity in living cultures on MEAs.

Table 1
Acronym list.

Network simulation: CAT showed the highest performance and sensitivity for detecting changes in the network synaptic state

In simulation, the synaptic connectivity can be easily controlled and monitored, and the way(s) changes in synaptic connectivity affect a statistic’s value can be directly studied. Various statistics were used to study functional connectivity in simulated networks under different synaptic states. The performance of different activity statistics to small differences in network synaptic connectivity was evaluated by measuring the statistical significance of the change in each statistic under different network synaptic states, altered gradually by simulated tetanic stimulation with STDP.

Our 1000 neuron LIF model and the living networks expressed similar spontaneous, and evoked, activity patterns, demonstrating the ability of the LIF model to represent the activity of biological networks. Raster plots and FRH of spontaneous activity and evoked responses obtained from both MEA cultures and simulated networks are shown together for comparison, and demonstrate a remarkable similarity of activity patterns (figure 4) (Chao et al 2005). For example, the rates of barrages (the ongoing synchronized bursts of action potentials) were 0.70 Hz and 0.73 Hz, and the proportions of spikes in barrages were 76% and 71%, in spontaneous activity of living and simulated networks respectively.

Figure 4
Comparison of the network activities from a MEA culture and a simulated network. Simulated spontaneous activity and evoked responses resemble the experimentally recorded data. First row: 1 min of spontaneous activity was recorded from a living network ...

A set of simulated networks with different synaptic states was created by using different electrode pairs and durations for tetanizations. In order to verify that different tetanization electrode pairs with different durations changed the synaptic weight distribution in the simulated networks, the centers of weights (CWs) (Chao et al (2005), see supplemental materials 7 available at stacks.iop.org/JNE/4/294) that were found for network states (S0 to S10) were calculated and are shown in figure 5(a).

Figure 5
Setup of different synaptic states in simulation. A series of networks with different synaptic states were obtained by tetanization at different electrode pairs and with different durations from the reference network. From each reference network S0, ten ...

CW represents the asymmetry of the network synaptic weights distribution. CW changed differently for different initial network synaptic weight distributions, for different tetanization electrode pairs and for different tetanization durations. Therefore, the various networks provide a basis to test the ability of various activity statistics to discriminate between synaptic states. The MASC of all different states (S1 to S10) relative to the initial S0 is shown in figure 5(b). For each tetanization duration, the mean and standard deviation of MASC were calculated (n = 50 networks, from five reference networks and ten tetanization electrode pairs per reference network). Even with significantly different CWs, MASCs from different networks ‘collected’ at the same tetanization duration were similar in magnitude (standard deviation < 1%, n = 50), suggesting that the magnitude of plasticity was dependent mainly on tetanus duration, as opposed to the network structure.

Simulations with RPSs were performed on simulated networks with different synaptic weight distributions. The various activity statistics of evoked responses to the RPS were calculated from each simulation. An activity statistic with good discrimination of underlying synaptic states should show different results in different networks, even with only small differences in the distribution of synaptic weights.

CAT demonstrated the highest performance in detecting changes in state among the 6 statistics. The performances of the statistics are shown in figure 6. For each state Si, the Euclidian distances E(Si) between each WIO vector of the statistic from Si to the centroid of the WIO vectors from the corresponding S0 were measured. Ten E(Si), measured from ten RPSs in the same network with the same tetanization electrode pair, were compared to ten corresponding E(S0), and the p-value was calculated (n 10 RPSs, Wilcoxon signed rank test). For each state Si,50 = p-values and 50 MASCs were collected from 50 networks (5 reference networks with 10 different tetanization electrode pairs per reference network). The mean and standard deviation of the p-values were plotted versus the corresponding MASC averaged across the networks (n = 50 networks). The detectable MASCs for CAT, JPSTH, SCCC, FRH, MI and FR were 4.68, 6.65, 6.75, 9.3, 11.7 and 15.7% respectively. CAT detected the smallest MASC and is therefore the best statistic.

Figure 6
Evaluating the performances of different statistics. CAT showed the highest performance to detect changes in the synaptic state among six statistics. The performance of different statistics to detect changes in the synaptic state was evaluated by finding ...

The relative performance (the smaller the detectable MASC, the higher the performance), average compute time and dimensionality are shown in figure 7. The performance of the statistic shown in descending order is CAT, JPSTH, SCCC, FRH, MI and FR. The dimensionality of each statistic from one stimulation electrode is described in supplemental materials 2 (available at stacks.iop.org/JNE/4/294). The average compute times for CAT, FR, FRH, MI, SCCC and JPSTH were 31.8 s, 1.2 s, 30.6 s, 3.9 min, 26.4 min and 70.4 min per simulation respectively (MATLAB 7.0, AMD Athlon processor, 2.08 GHz, 512 MB RAM). Among all six statistics, only FR and FRH had a shorter compute time than CAT, and only FR had smaller dimensionality than CAT. However, CAT showed significantly higher performance than FR and FRH.

Table 2 shows the occurrences of true positives, false negatives, false positives, true negatives and the sensitivity and specificity (see methods) of each statistic. CAT showed a sensitivity of 88.7%, the highest among all, with a specificity of 82.4%, comparable to JPSTH and SCCC. FRH, MI and FR showed high specificity, which was an artifact of their low sensitivities. Sixty-eight out of the 500 new network states were found to not have significantly different distributions of network synaptic weights as compared to their original reference states (two-sample Kolmogorov–Smirnov test, two-tailed, α = 0.05).

Table 2
Sensitivity versus specificity in simulated networks.

By evaluating the performance, sensitivity, specificity and compute time, CAT was found to be most sensitive and highly efficient at detecting synaptic changes in simulated networks.

The five alternative statistics are often applied to spike-sorted data. Spike sorting is used to distinguish the spike trains of individual neurons (Ahissar et al 1998, Jimbo et al 1998, 1999, Celikel et al 2004), and can aid studies of neural populations (Lewicki 1998), especially for neural computations that use spike timing. In simulated networks, activity of individual neurons can be directly observed. The analysis in figure 6 was repeated using sorted neurons to investigate if the performance of the alternative statistics would improve. In the five reference simulated networks constructed, 4.1 ± 1.8 neurons were recorded per electrode, and the six statistics were recalculated based on about 250 neurons instead of 60 electrodes. CAT remained unchanged as the sorted spikes were spatially summed as before (see equation (1) in methods). Despite improved performance and sensitivity of the other five statistics, CAT still detected the most plasticity. JPSTH, SCCC, FRH, MI and FR improved 11.1, 17.6, 11.0, 35.0 and 31.2% in performance, respectively, and improved 1.9, 5.2, 9.7, 27.7 and 62.5% in sensitivity (see supplemental materials 4 available at stacks.iop.org/JNE/4/294).

Experiments in living cultures: CAT revealed tetanus-induced long-term plasticity significantly better than the other statistics

CAT was measured from the evoked responses to RPS in six experiments on living cultured cortical networks (CATs from all experiments are shown in supplemental materials 6 available at stacks.iop.org/JNE/4/294) and compared to the three most commonly used statistics: FR, FRH and SCCC. For visualization purposes, principal components analysis (PCA) was applied to the series of multi-dimensional WIO vectors to capture the largest variances and graphically demonstrate trends in changes. The first two principal components were normalized by subtracting their means and then dividing by their standard deviations. The normalized first principal component (PC1) was plotted versus the normalized second principal component (PC2). An example comparing CAT, FR, FRH and SCCC is shown in figure 8(a). The corresponding CATs before and after tetanization from every block (a 240 s window, see methods) and the average CATs are shown in figure 8(b).

The change across the tetanus was significantly greater than the drift before the tetanus for CAT (p < 1 × 10−4, Wilcoxon signed rank test), FRH (p < 0.01) and SCCC (p < 0.01), but not for FR (p = 0.013). C/D was used to quantify the change before the tetanus and the change across the tetanus (if the change is small, C/D ≅ 1). The statistics of C/D from six experiments are shown in figure 8(c).

We did not perform spike sorting for experiments in living cultures. Standard spike sorting methods sort neural signals based on variations in spike waveform. In MEAs, local field potentials and overlapping action potentials distort the waveform to an extreme degree, and the electrodes are too far apart to allow triangulating common signal sources. Spike sorting was attempted, but proved to be unreliable.

Electrode shuffling demonstrates the importance of electrode locations shown by CAT

In order to get some idea of the degree of localization of function in cultured cortical networks, the performance of CAT statistic with electrode locations shuffled (CAT-ELS) was calculated (see supplemental materials 2 available at stacks.iop.org/JNE/4/294). In CAT-ELSs, the information about the physical locations of the recording electrodes was removed. In both simulations and experiments in living cultures, the electrode locations were shuffled ten times, and ten different corresponding CAT-ELSs were generated. The performance of these CAT-ELSs was evaluated and compared to the original CAT.

CAT, unlike the other statistics, incorporates the physical locations of the recording electrodes. This is the primary difference between methods, and we attribute CAT’s superior performance in both living and simulated networks to this feature. For simulated networks, the comparison of the performance between CAT-ELS and original CAT is shown in figure 9(a). The detectable MASC (threshold p-value = 0.05) for mean CAT-ELS was 10.8%, which was worse than (4.68%). The decrease in performance (increase in detectable MASC) indicates that electrode locations significantly affect the performance of CAT in simulated networks. Furthermore, the sensitivity of CAT-ELS was 35.4%, significantly smaller than CAT’s 88.7% (see table 2).

Figure 9
Comparison of CAT and CAT-ELS in simulated and living networks. (a) A comparison of the performance of CAT and CAT-ELS in simulated networks (the representation is the same as figure 6). Ten performance curves corresponding to different random shuffled ...

For living MEA cultures, one example of the comparison between CAT and CAT-ELS is shown in figure 9(b). The corresponding CAT-ELSs before and after tetanization from every block are shown in figure 9(c). The electrode location shuffling ‘collapsed’ the patterns of CAT-ELSs before and after tetanization (compare to figure 8(b)). The difference between pre-tetanization and post-tetanization clusters found in CAT was also reduced in CAT-ELS (figure 9(b)).

The statistics of C/D for CAT-ELS (n = 60, six experiments, ten shuffles for each experiment) are shown in figure 9(d). The change across the tetanus was significantly greater than the drift before the tetanus for CAT (p < 1 × 10−4, Wilcoxon signed rank test), but not for CAT-ELS (p = 0.19).

Discussion

Statistics of functional plasticity in extracellular multi-electrode recordings

While comparisons of firing rates show plasticity in intracellular recordings, more detailed statistics incorporating spatiotemporal population activity patterns are needed to reveal plasticity in extracellular multi-electrode recordings. Electrode spacing on the order of hundreds of microns means that any induced or observed plasticity will span pathways of multiple neurons instead of neighboring monosynaptic neurons (Jimbo et al 1999). Intracellularly, synaptic strength is directly observable by stimulating a pre-synaptic neuron while recording from an adjacent post-synaptic neuron. Extracellularly, synaptic noise across a chain of neurons and convergent pathways will obscure firing rate measures of stimulus-induced plasticity.

Alternatively, by incorporating the timing and spatial flow of activity, spatiotemporal patterns have been found both in vivo and in vitro. Spike sequences, imposed upon the network by behavioral manipulations, recur spontaneously during subsequent sleep episodes (Nádasdy et al 1999, Nádasdy 2000, Lee and Wilson 2002). Calcium imaging of cortical slices reveals reactivation of sequences of neurons, ‘cortical songs’, with distinct spatiotemporal structures over tens of seconds (Ikegaya et al 2004). Robust recurrent spike patterns were also found in a detailed cortical simulation (Izhikevich et al 2004) and in living slices (Fellous et al 2004). CAT provides a new and simple statistic to detect spatiotemporal patterns in networks and extends the previous studies by quantifiably demonstrating its ability to discern plasticity.

Region-specific plasticity

Although FRH included detailed temporal information about the activity dynamics at all electrodes, it was less capable of capturing network plasticity than CAT, which has the same temporal resolution as the FRH but ‘condenses’ the spatial dimension by linear combination (see equation (1)). We hypothesize that this was due to the inclusion of spatial information of the electrode locations. The performance and the sensitivity of CAT with electrode locations shuffled were significantly worse than unshuffled CAT, both in simulation (the detectable MASC increased from 4.68% to 10.8% and the sensitivity decreased from 88.7% to 35.4%) and in living networks (the change across the tetanus was significantly greater than the drift before the tetanus for CAT, but not for CAT-ELS) (see figure 9 and table 2). This indicates that activity varied systematically with the electrode location, and also suggested that the observed network plasticity was region specific: the plasticity was not symmetrically distributed throughout the network. This further suggests that despite the apparent random connectivity of cultured neurons, neuron location played a role in tetanus-induced plasticity.

Region specificity was not limited to plasticity induced by tetanization. In simulation, we also altered the weights of randomly selected synapses in reference networks to different degrees to generate different new network states. CAT still showed the highest sensitivity to changes in MASC, and furthermore, the sensitivity of CAT-ELS was still significantly lower (data not shown). Despite the synaptic plasticity not being region specific, the spatiotemporal flow of neural activity was region dependent, effectively making the plasticity of neural activity region specific. This result supports the notion of synfire chains or braids of neural activity (Ikegaya et al 2004, Izhikevich 2005), where information is transmitted in a pipeline of neighboring pathways as opposed to a single string of connections. In this study, tetanization was used to obtain different synaptic states since it provided a realistic form of plasticity and a straightforward comparison to our study of local functional plasticity in living networks.

A common misconception regarding dissociated cultures is that they are random, homogeneous and lack structure, and thus cannot support stable changes to synaptic weights associated with memory formation. While plated from a random cell suspension, microscopic observation reveals that a heterogeneous arrangement develops over time (Gross and Kowalski 1999, Segev et al 2003). Although very different than structures found in vivo, the ability of neurons and glia to interact remains and a network having a diverse array of activity arises spontaneously (Wagenaar et al 2006b). Altering sensory input of thalamic relays to cortical areas has demonstrated that the cortex develops structure according to the type of the sensory input (Sur et al 1988), which suggests an important relationship between neural structure and function. CAT demonstrates that structure is also relevant to neural function in a cultured network, and that tetanic stimulation alters network function. Future experiments will incorporate closed-loop sensory-motor feedback and optical imaging to investigate the network mechanisms of our cultures to functionally and structurally adapt to environmental interaction (Potter et al 2006).

CAT versus population coding

It is important to note that CAT is distinct from the population vector description of neural activity (Georgopoulos et al 1986, Caminiti et al 1990). Population coding, which is widespread in the brain and in invertebrate nervous systems, has been found in the motor cortex (Georgopoulos 1994), premotor cortex (Caminiti et al 1990), hippocampus (Wilson and McNaughton 1993) and other cortical areas. It demonstrates how the firing rates of a group of broadly tuned (e.g., to a direction of arm movement) neurons, taken together, provide an accurately tuned representation. With population codes, a fixed-weight linear combination of neuronal activity is projected in a sensory input space or a motor output space (Carmena et al 2003). In contrast, CAT incorporates information about the physical recording locations into its linear combination calculation, and projects neuronal activities recorded at different sites into the actual neuronal location space in order to depict the dynamics of the population activity. Furthermore, the linear combination of activities in CAT is normalized by the total firing rate across all electrodes (see equation (1)).

CA is a measure of the asymmetry of the spatial activity distribution, and CAT is a measure of its dynamics. A similar measure of population activity flow was applied in human study to quantify the trajectory patterns of the traveling electroencephalographic alpha waves across the scalp (Manjarrez et al 2007).

Plasticity versus spontaneous bursting

Without external stimulation, the most prominent feature of spontaneous activity found in MEA cultures and in simulated networks is synchronous bursting (Wong et al 1993, Kamioka et al 1996, Gross and Kowalski 1999, Van Pelt et al 2004, Wagenaar et al 2005), and bursts were found to have effects on tetanus-induced synaptic plasticity in cortical neurons (Maeda et al 1998). In simulation, the network synaptic state after tetanization was found to change gradually due to the presence of spontaneous bursts, which makes quantifying tetanus-induced plasticity difficult (Chao et al 2005). In the six experiments we performed on living MEA cultures, 8.57 ± 3.33 spontaneous bursts per minute and 16.06 ± 4.55 stimulus-evoked bursts per minute were observed. Even with the presence of the spontaneous bursts, the tetanus-induced plasticity was still detected by using CAT. Since the level of bursting can be finely controlled in MEA cultures with multi-site stimulation (Wagenaar et al 2005), we plan to use CAT to investigate how the degree of bursting affects a network’s ability to produce and/or maintain plasticity.

CAT’s superior performance, sensitivity and low computational load make it an attractive method for real-time applications. CAT can also be applied to in vivo multi-electrode or optical recording studies for neural activity aligned to behavioral or sensory cues. As techniques for observing distributed activity become faster and more fine-grained, studying the details of the spatial flow of activity through neuronal networks will reveal more and more about processes of learning and memory.

Supplementary Material

01

Acknowledgments

This work was partially supported by grants NS38628 from NIH/NINDS, EB000786 from NIH/NIBIB and DA18250 from NIH/NIDA, and by the Whitaker Foundation and the NSF Center for Behavioral Neuroscience. We thank Radhika Madhavan for technical assistance and Douglas Swehla for valuable inputs.

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