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1Departments of Physics of Complex Systems and 2Neuroscience, The Weizmann Institute of Science, Rehovot, Israel
Submitted 8 September 2006; accepted in final form 3 February 2007
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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; Komuro and Rakic 1996; Meister et al. 1991; Shatz 1990; Yuste et al. 1992), in the initiation of epileptic seizures (Gutnick et al. 1982; Miles and Wong 1983), and in cortical integration of sensory information (Engel et al. 1992). Neurons cultured in vitro display collective bursting activity akin to that seen in vivo, which appears to be a typical behavior for a random neural network and is observed in a large variety of preparations. This large-amplitude activity has proven to be useful in the study of neuronal (e.g., Papa and Segal 1996) as well as of network (e.g., Shahaf and Marom 2001) properties.
The clinical as well as the developmental importance of spontaneous network activity contrasts with the relative paucity of knowledge of mechanisms for generation of such population bursts. In both dissociated culture (Darbon et al. 2002; Maeda et al. 1995; Murphy et al. 1992; Streit et al. 2001; Tscherter et al. 2001) and slice preparation (Darbon et al. 2002; Harris and Stewart 2001; Kiehn and Kjaerulff 1998; Menendez de la Prida and Sanchez-Andres 2000; O'Donovan et al. 1994; Stoop and Pralong 2000; Streit et al. 2001; Tscherter et al. 2001; Wu et al. 1999), such events can be generated at spontaneous burst initiation zones (BIZs). From these BIZs, activity propagates via synaptic transmission to affect large neural populations.
The use of two-dimensional cultures for studying localization of spontaneous activity generation poses considerable experimental difficulties. The most prosaic difficulty is that bursts often initiate in parts of the culture that are unmonitored (e.g., Wu et al. 1999). Another experimental difficulty lies in retracing the origin of the burst from observations of the propagating front of activity that it generates. Fronts of neuronal activity in two dimensions are known to be linearly unstable to finite wavelength perturbations ("form instabilities") (see Kistler 2000), leading to indeterminacy in the trajectory and a corresponding inability to retrace the origin. This is further complicated by the experimental constraint that measurements are typically taken over areas the scale of which is comparable to one axonal length (
1 mm), whereas activity may spread far beyond that scale by jumps over several axonal connections (Buonomano 2003; Tscherter et al. 2001). These jumps in propagation make it extremely difficult to follow the causal advance of the signal. Another experimental complication arises because different events initiating from the same center may exhibit marked variations in propagation pathways (Beggs and Plenz 2004; Maeda et al. 1995; Tscherter et al. 2001; Wu et al. 1999). This obscures pacemaker location, especially outside the part of the culture that is monitored. Using spinal cord slice and dissociated two-dimensional cultures plated over a multi-electrode arrays that span a relatively large area (2 mm2), a large percentage of population bursts has been associated with specific pacemakers (Darbon et al. 2002; Streit et al. 2001; Tscherter et al. 2001). These groups obtain qualitative results that indicate a mixture of local and nonlocal initiation along with variation in trajectory from burst to burst.
Following the initial suggestions by Maeda et al. (1995) and modifications by Segev et al. (2002) and Nam et al. (2004), we have developed a system of patterned unidimensional hippocampal cultures (Feinerman et al. 2005) that reproducibly exhibit robust burst propagation for distances of 
8 cm (Feinerman and Moses 2006). We have previously used these networks to link the large-scale behavior of cultures to their small scale components by the use of relatively simple one-dimensional models (Feinerman and Moses 2006; Feinerman et al. 2005).
In this study, we use these unidimensional cultures to simplify the experimental difficulties involved in BIZ identification. The unidimensional networks span distances that are much longer than the axonal lengths. This leads to continuously propagating activity that does not skip over any area along the line (Feinerman et al. 2005). Events from a single BIZ are constrained to propagate along the single track set by the line. This was accomplished while keeping all events within the experimental field of view so that each event can be traced back to its corresponding BIZ.
We have used these novel experimental capabilities to investigate spontaneous activity in the unidimensional culture. One can create, by tracking a large number of population bursts, a BIZ distribution along the culture, assigning each area with its probability to initiate a large-scale population burst. We show that this distribution is not uniform; rather, few discrete areas control activity in the entire culture.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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; Papa et al. 1995). Cells were plated onto previously patterned, No. 1 13-mm glass coverslips (Menzel-Glaser) at 330,000 cells/ml yielding linear densities of 300 cells/mm (Feinerman et al. 2005). Coverslip patterning was performed as described previously (Feinerman and Moses 2003; Feinerman et al. 2005). In short, coverslips were evaporated with thin chrome and gold layers that were then coated with octadecanethiol (Sigma, 0.1%) and Pluronics F108 Prill (BASF, 30 mg/ml) to make them protein repellant. Lines were scratched through this coating to reveal the coverslip in areas intended for neuron adhesion. The coverslip was then immersed in a solution of laminin (Sigma, 25 µg/ml), fibronectin (Sigma, 25 µg/ml), and Pluronics F108 Prill (30 mg/ml) that adhere to the exposed lines to serve as a substrate for neuron growth. The Pluronics polymers actually serve a double role: they function as a protein repellent when coated on the hydrophobic octadecanethiol but enhance cell adhesion when coated directly unto the coverslip.
As previously described in Feinerman et al. (2005), cells at 14–16 DIV, were incubated for 60 min in the presence of the cell-permeant, calcium-sensitive dye Fluo4-AM (Moleculer Probes, 2 µg/ml). The culture was imaged with a Zeiss Axiovert 135TV microscope and photographed through a x10 lens fitted with a x0.5 adapter to enlarge the field of view as well as enhance fluorescence intensity. Images were captured at a 50-Hz video rate, and digitized with a PCI-1141 frame grabber (National Instruments) and IMAQ software (Labview) for subsequent analysis. All experiments were performed while maintaining the culture at 28°C. The slower dynamics at this temperature (in comparison to 37°C) facilitates imaging at video rate. In about half of the experiments, GABAA receptors were also blocked by bath application of 40 µM bicuculline (Sigma-Aldrich). Experiments where bicuculline wasn't added are termed undrugged.
Toxic signs in the cultures, such as calcium accumulation and drastic decrease in activity, were evident only after >4 h of recording and were avoided by restricting experiments to 2.5 h. Using calcium measurements must involve some buffering of calcium inside the cells and may affect network behavior. Jacobi and Moses (2007) used identical patterning and culturing techniques but recorded electrically from multiple cells using multi-electrode array (MEA) plates. They confirm that the use of calcium-sensitive dye has no major effects on bursting behaviors such as neuronal firing rates or burst propagation.
Long linear cultures were used (170 µm wide and 17 mm long, unless otherwise stated) exhibiting spontaneous population bursts that typically excite the entire culture (Feinerman and Moses 2006; Feinerman et al. 2005). Such lines are too long to be fully viewed in a microscope's field of view and were patterned in an elongated C shape so that their two ends and central part are visible for fluorescent measurements (see Fig. 1A). Regions of interest (ROIs) containing 100 neurons each were chosen on these three areas, and their average fluorescence intensity was monitored.
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). The probability that two neurons form a synaptic connection then depends solely on their distance along the linear track. This is not altered by the above-mentioned winding C pattern. Network connectivity depending on a single spatial dimension can be described as unidimensional or "linear." The average axon length in this system is <400 µm (Feinerman et al. 2005), much shorter than the length of the culture. This constrains activity in the culture to comply with its linear structure: bursts propagate along the culture in a causal progression as one group of neurons excites a neighboring group. BIZ identification and location
Population bursts were evident as a sharp rise in the fluorescence level in all ROIs along the line. The onset of the burst in each ROI was taken as the point of highest derivative during this fluorescent rise. We associate with each burst a timing signature that is used to calculate the position of its BIZ. To construct a time signature the three times at which the burst excites the two ends and the central part of the line were recorded (Fig. 1A). The time t1 is when the burst arrives at end 1, t3 at end 3, t2 is when it arrives at the central area 2, where the location of areas 1–3 are depicted in Fig. 1A. As the absolute time of the burst is not important, only the two intervals 
t1,2 = t1 – t2 and t3,2 = t3 – t2 were considered (see Fig. 1B). Each pair of interval signatures was then used to calculate the location of its BIZ. For example, a burst initiated anywhere between end 1 and the central part of the line must traverse the full length between the central part and end 3. This distance of 8.5 mm is passed in t3,2 s, which is also the longer of the two time intervals. Measuring this longer interval for each burst provides an estimate for its speed which is c = 8.5/t3,2 mm/s in this example. As propagation speed varies between bursts, it was estimated separately for each individual burst. Assuming a constant speed throughout the propagation of a single burst, the second interval (t1,2) was then used to locate the position of the BIZ between end 1 and the central part 2. A short interval of t1,2 
0, for example, indicates a burst starting at midpoint between end 1 and the center of the line 2, regardless of the speed. The constant speed assumption was verified by Jacobi and Moses (2007).
Video imaging sets the time resolution of our measurement at 20 ms. This time resolution translates to the spatial precision at which BIZs can be identified. The error in estimating BIZ location is obtained by multiplying this timing uncertainty by the population burst propagation velocities (Feinerman et al. 2005). The resulting spatial resolution can be as low as 1.1 mm when inhibitory synapses are blocked with bicuculline and 0.5 mm when no drugs are added to the medium. An average spatial resolution was calculated for each culture using the propagation speed as averaged over all bursts detected during the course of that experiment. Histograms depicting the relative strength of different BIZs (see Figs. 1 and 2) were prepared by binning together BIZs the locations of which were calculated to be separated by less than this average spatial resolution. A probability to initiate bursts was assigned to each bin. This is defined simply as the number of bursts initiated in this bin divided by the total number of bursts that have occurred in the course of single experiment. Error bars in all BIZ location histograms were estimated by the SD of a binomial model 
2 = p(1 – p)/N, where p is the probability of event initiation in a specific bin and N the total number of events.
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Neuron densities along the line were determined by double immunostaining for neurons by staining for NeuN, Neuronal Nuclei, and inhibitory neurons staining for GAD, glutamic acid decarboxylase. After calcium imaging in which BIZ locations were determined, cultures were fixed and processed for immuostaining with monoclonal anti–NeuN antibody (Chemicon, 1 µg/ml) and then by staining with Alexa 546 tagged secondary antibody (Molecular Probes, 10 µg/ml). For identifying GABAergic neurons, cells were first incubated with polyclonal anti-GAD65/67 (Chemicon, partially purified immunoglobulin 1:2000) and then with a Marina Blue tagged secondary antibody (Molecular Probes, 13 µg/ml).
The average Alexa 546 and Marina Blue absolute fluorescent intensity in consecutive 250-µm-long patches along the line was collected and used to estimate the local density of both the total and inhibitory neuron populations. Bleaching did not cause biases in these measurements as exposure times were short. This was verified by comparing the small overlaps between consecutive images. The absolute Alexa 546 fluorescent intensity was averaged over each bin and normalized by the sum of these averages in all bins along the line to estimate neuronal density along the culture (also referred to as probability in Fig. 2). As explained in the caption to Fig. 2C, the relative density of inhibitory neurons in a certain area was estimated as the Marina Blue intensity over the Alexa 546 intensity; both values are averaged over this area.
Recovery periods
Spontaneous events were tracked on 17-mm lines, each event was labeled "L" if it was initiated on one side of the line (0–8.5 mm) and "R" for the other side (8.5–17 mm). Interburst intervals (IBIs) include two consecutive bursts and may be labeled accordingly. Comparing the histogram of the IBIs labeled LL and RL (for example) would give two typical recovery periods for BIZs situated on the L side: recovery from a previous L event or from a previous R event. In the analysis, we assume that each side has only one BIZ. Although this simplifying assumption does not always strictly hold, in fact coarse graining two BIZs as one has no effect on our subsequent analysis.
Decoupling
Cultures were decoupled into two parts by blocking conductance between them at a central location (on a 17-mm line it is 8.5 mm from both ends). These blocks were performed either reversibly by locally applying tetradotoxin (TTX) at 0.3–1 µM (see, for example, Fig. 4) using a designated concentric double pipette (Feinerman and Moses 2003; Feinerman et al. 2005) or by irreversible mechanical dissection using a sharp blade. Using mechanical dissection caused a marked decrease of activity in n = 3 of 9 cultures, which were not used in subsequent analysis. Such negative effects were absent when using chemical dissections (n = 5). When considering only the successful experiments, there were no apparent differences between the two techniques. We used such dissection tools to measure the interaction between different pacemakers, studying the way pacemakers situated in the same culture sense and affect one other.
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We have previously shown (Feinerman et al. 2005) that the linear network model of Osan and Ermentrout (2002) describes burst propagation in our system to a high quantitative degree. However, this model does not describe the two major processes that control BIZ interactions: spontaneous burst initiation and the refractoriness following such events. Here we model the interaction between two BIZs using the "boxing arena" model described in detail in the following text. In short, this model describes interaction through the coupling of recovery periods of two BIZs. The first BIZ to recover after a population burst will initiate the next burst.
A simple computer simulation was implemented to compare the experimental measurements to the predictions of this model. First, in the experiment, a lesion was induced on a 17-mm-long line, and the activity of two uncoupled sides was monitored. The full lists of experimentally measured IBIs of the two decoupled sides were used as input for the simulation. To predict activity when these two sides are coupled, the program was iterated a large number of times (see following text), and at each loop each side was assigned a resting period. This period was chosen randomly from the list of the experimentally measured IBIs of its corresponding side with all IBIs given an equal probability (1 over the total number of IBIs). Using the assumption of the boxing arena model, the shorter of these times is chosen as the next IBI of the simulated, coupled culture while the longer one is discarded. We obtained simulated predictions of the IBI distribution in a culture where the two sides are allowed to interact, as well as the relative contribution of each of these sides to the initiation of these events. The program was looped between 10,000 and 400,000 times until the SEs of all three numbers were less than one half of a second. These predictions were compared with the experimental data from both before and after the lesion.
The average IBI of the connected culture, 
T
as estimated by this simulation can be described mathematically by
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1, 2 we obtain
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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). The average propagation speed was 64 ± 9 mm/s (all averages are presented as means ± SE, n = 8) in the undrugged case and 103 ± 11 mm/s (n = 5) in presence of bicuculline. The speed of different events as measured in a culture were not constant, they varied between bursts with a coefficient of variation (CV, defined as SD over the mean) of 0.71 ± 0.12 in the undrugged case and 0.30 ± 0.02 with bicuculline. These speeds are the same for both chemically evoked and spontaneously generated events (Feinerman et al. 2005). The mean IBI in standard recording medium was 20.7 ± 2.4 s as averaged over 17-mm-long lines (n = 21) and 24.2 ± 3.6 s for 4-mm-long lines (n = 12). In cultures that were monitored both with and without bicuculline (n = 5), the mean IBI rose from 18.4 ± 5.4 s by an average factor of 1.9 ± 0.2 to 31.2 ± 4.3 s once inhibition was blocked. BIZs
BIZs were localized via their time signatures in activation of the two ends and the central parts of the line (see METHODS). Figure 1C shows the time signatures of one specific experiment. Each signature can be traced to a specific initiation point along the line. In this example, three BIZs, sized between 1 and 3 mm, can be located (see Fig. 1D). We inspected lines of this length, with or without inhibition, in which average speeds were slow enough to allow a spatial resolution of <1.5 mm (n = 11 of 21 cultures), and found between 2 and 4 such main BIZs at varying locations that were responsible for all events. All these BIZs were localized to areas with a typical length of 1 mm (always <3.5 mm) and a width of 170 µm.
An important control is that in all the experiments, both with and without bicuculline, 562 of 564 (>99%) recorded events had time signatures that were consistent with locally initiated activity (see the crossed-out signature in Fig. 1B, which never appeared). This substantiates convincingly the statement that all events on the one-dimensional culture are initiated by local BIZs. The two exceptional events in which activity commenced simultaneously at distant parts of the culture are most likely collisions of two independent events originating in two separate BIZs (Wu et al. 1999) as specified in the following text.
It is interesting to check whether some areas are indeed more liable than others to initiate bursts. Pearson's 
2 was used to test the hypothesis that BIZ histograms, similar to the one presented in Fig. 1D, were derived from a uniform pdf. The average P value over 21 experiments either with or without bicuclline was P = 0.047 ± .002 and as low as P = 0.0083 ± 0.0003 if three of these cultures were discarded. In 
85% of the tested cultures (n = 21), the uniform distribution null-hypothesis must be rejected. We conclude that not all areas are equally likely to initiate bursts.
BIZ distribution was compared in the presence or absence of bicuculline on n = 5 lines. Adding bicuculline to a specific culture (Fig. 2) changed the relative initiation probabilities of existing BIZs, adding new BIZs and removing existing ones (Fig. 2A).
Contribution of neuronal density
To determine whether BIZ location is correlated with neuronal density, nine cultures were immunostained for NeuN directly after completion of the experimental determination of their BIZ distribution. Their neuronal density was measured, and a density map of neurons along the line was created. Density and trigger zones were both summed in bins determined by the specific speed measured on each of the lines in the presence of bicuculline (between 5 and 17 bins). Correlation analysis was performed between this density map and the BIZ distribution measured on the corresponding cultures. Pearson correlations were, on average, positive and low: 0.26 ± 0.15 with bicuculline (P = 0.35 ± 0.1) and 0.12 ± 0.12 (P = 0.53 ± 0.1) in the undrugged case. The high P values can be expected in the case of low correlation and a relatively small number of bins.
Dense areas of the culture are likely to have an increased probability of BIZ. However, aggregation of inhibitory neurons may cause deviations from such correlations even in a dense area of the culture. We thus compared more carefully the correlation between BIZ and neuron distribution between the undrugged and the bicuculline case. To this end, two cultures that exhibited no correlation between density and activity both with and without bicuculline were discarded from further analysis. In the other seven cultures, correlations are present but small with no bicuculline (average correlation: 0.2 ± 0.14) and become more pronounced when inhibition is blocked (average: 0.48 ± 0.08). An example of one such culture is given in Fig. 2B. However, these correlations are still quite low (0.53 ± 0.1 without and 0.35 ± 0.08 with bicuculline) and the corresponding P values high. A further test was needed for the significance of this increase. Applying the Student's t-test to the two correlation lists (undrugged and bicuculline), we obtain a P value of 0.055, indicating that the increase in correlation, on blocking the inhibitory network, is nearly significant statistically. The difference obtained with the addition of bicuculline suggests that inhibitory neurons play an important role in pacemaker architecture.
Contribution of inhibitory neurons
Cultures that were immunostained for NeuN were also stained for GAD (anti-GAD65/67), although the quality and specificity of staining were lower. The high neuronal densities associated with BIZs tend to build a multi-layer structure that makes it difficult to count the precise fraction of inhibitory neurons in the pacemaker. The effect of inhibitory neurons on BIZ location was therefore evaluated by comparing the concentration of inhibitory neurons (1 example is shown in Fig. 2C) inside pacemaking zones relative to the concentration in areas adjacent to them. Differences in specific areas were estimated by integrating over the fluorescence intensities of NeuN or GAD staining. We find that, on average, BIZs differ from other areas of the culture by having by having a low density of GAD-positive neuron, while having a high density of GAD-negative neurons. The average density of inhibitory neurons was 2.68 ± 1.1 times lower in the BIZ than in the adjacent areas (n = 4 Fig. 2E). Looking at a specific sample (Fig. 2D) shows that although the neuronal density of two areas may be similar and high, it is that area where inhibitory neurons have a lower density that actually becomes a BIZ. These measurements indicate that inhibitory neurons interfere with the initiation of spontaneous bursts.
Interaction between initiation zones
As demonstrated in the previous section, population bursts in a single culture initiate in one of a few BIZs. In a large culture, we can expect multiple centers that interact to create the dynamics of the full culture. To understand the complicated general case, it is imperative to first check the simple case in which only two BIZs interact, namely, how the existence of one spontaneous center in the culture affects the IBI distribution of a second one. We can look at two time intervals—the first is the time it takes an IBI to recuperate enough so as to initiate the next burst and the second is the time it takes to recuperate enough to respond to a burst initiated by the second IBI.
Neurons in a specific BIZ may also have a different recovery period for initiating a population burst depending on the source of the previous burst. It is possible, for example, that neurotransmitter deficits in the local area of a pacemaker differ in the case that it had initiated a burst from the case in which it reacted to one initiated elsewhere. By tracking population bursts to their BIZs, we checked the dependence of recovery periods on the origin of the burst that immediately preceded them. An example of this dependence in one experiment is shown in Fig. 3. Following an average recovery period of 4 s the L side initiates a population burst. This is independent of whether the origin of the previous burst was in area L or R. This analysis was repeated for (n = 6) halves of three cultures with no significant difference between the IBI means. In all cases, the difference between the two means is less than the sum of errors in their measurement. This indicates that the time required for a pacemaker to recover from a burst that it had initiated is the same as the recovery time following bursting in response to activity initiated elsewhere. This simple result is used in the boxing arena model described in the following text.
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The best way to study the interaction of centers is to compare their behavior when they are separated and when they are coupled. For example, in the simple case of no interaction, the combined frequency of two centers controlling the activity in a single culture would be the sum of their decoupled frequencies.
To this end, n = 8 lines 17 mm long and n = 3 lines 6 mm long were studied, in n = 6 inhibition was blocked, whereas in n = 5, all synapses were active. More than 90% of the population bursts travel to excite the entire culture (Feinerman et al. 2005). However, once a culture is decoupled, either chemically or mechanically, it separates into two parts the spontaneous activity of which is fully decoupled (see Fig. 4). This is due to the simple fact that population bursts cannot bypass the barrier. This decoupling effect was reversible for chemically induced barriers.
For each culture, three IBI distributions were measured, one of the full, connected culture, and the two of the separated half cultures. A summary of the results is given in Fig. 5. The most striking observation is that, on average, the joint IBI was only 6% shorter than that of the faster side, whereas it was 27% faster than that of the slower side. This signifies that the more active centers in the culture dominate burst initiation over ones with longer recovery periods.
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The decoupling experiments were used to estimate the probability of collisions. These are events that initiate at the same time from different BIZs. Although our calcium imaging does not enable us to measure this directly, we do expect that when these two fronts meet they will collide since the culture behind a front is refractory. A collision detectable by our measurements is one the time signature of which resides in the "forbidden" quadrant of Fig. 1B so that the two ends of the line activate before its central part. For two BIZ situated at the two extremes of the line, a collision could occur only if they initiate an event within 200 ms (calculated as half the line length over a speed which is on the order of 50 mm/s). The time window for BIZ located in other places would be shorter. In cultures where bicuculline was present this time window reduces to 100 ms.
The chance for observing a collision was estimated for each of the 17-mm lines on which a dissection was performed (n = 8). The IBI distribution of each decoupled half of a culture was estimated by a Gaussian with the measured average (T1 and T2 for the 2 sides) and SD values (1 and 2). A collision in a single event occurs if the random times chosen from the two pdf's are equal, to an accuracy of T = 100 or 200 ms (with or without the presence of bicuculline, respectively). An upper bound for the probability p for such a collision to occur can thus be estimated by binning the Gaussians into the appropriate bins (T = 100 or 200 ms) and multiplying them bin by bin
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Boxing arena model
Let's assume that a boxer in the gym hits the punch bag at times taken from a natural distribution centered on some frequency, resting between punches to gather his strength before launching another punch. If two such boxers are put in the arena, then each will gather enough strength and then launch the next punch. Once one of them succeeds, the force of both boxers will dwindle down—one by the effort of throwing the punch and the other by the blow taken. The "clock" of both boxers is then reset, and they have to regain their strength for the next punch, each one using his natural frequency as was determined in the gym. It is then the amount of overlap of the two distinct ("gym") pdfs (probability density functions) that determines the nature of the joint ("arena") pdf.
We argue that a similar mechanism controls the interaction between two BIZs in a culture. By analogy, each boxer represents a BIZ, throwing a punch represents initiating a burst and taking one is like reacting to a burst. After each large-scale population event, each BIZ has its characteristic recovery time, and the first to recover will initiate the next population burst. This burst will then propagate to activate the whole culture including all other BIZ, so that the recovery clocks of all pacemakers in the culture are reset to zero and the cycle will repeat. The duration of this recovery time could depend, for example, on the characteristic time for reuptake of depleted neurotransmitters (Kamioka et al. 1996; Maeda et al. 1995; Staley et al. 1998). The simple simulation described in METHODS was used to test the boxing arena model, which predicts that BIZs interact simply by resetting each other's clock.
We demonstrate the possible outcome of this scenario by elaborating on three experiments in light of the simulation.
DOMINATION.
In experiment 6 (see Fig. 5), the two uncoupled periods were 12.1 ± 0.8 and 21.3 ± 2 s (a factor of 1.8). Their IBI histograms were fed into the simulation, which gave a joint period of 11.9 s, where the faster side has a period of 13.3 s and the slower one a period of 116 s (a factor of 8.7). The actual measured results gave a joint period of 11.4 ± 0.5 s with all events during 12 min of measurement initiating from the faster side. The large difference in periods is characterized by a practically zero overlap between the IBI pdfs of each side. The recovery period of the faster side was always smaller (experimentally) than that of the slower side, so that all bursts in the coupled culture were initiated by this one side.
PARTIAL DOMINATION. In experiment 1 (Fig. 5), the uncoupled periods were 35.2 ± 5.1 and 45.8 ± 4 s (a factor of 1.3). Their IBI histograms were fed into the simulation which gave a joint period of 28.6 s where the faster side has a period of 42 s and the slower 87 s (a factor of 2.07). The actual measured results gave a joint period of 31 ± 3.1 s with the faster side initiating a burst every 41 ± 6.1 s and the slower one every 129 ± 42 s (a factor of 3.14). Here the initial ratio between pacemaker periods is smaller and some overlap between their IBI pdf's exists. The recovery time of the slower side can be shorter, so that it may initiate one out of several bursts. This leads to partial domination of the faster side.
COOPERATION. The two half lines of experiment 5 (Fig. 5) had similar periods, 19.3 ± 1.4 and 20.8 ± 1.7 s (a factor of 1.07). The simulation gave a joint period of 14.8 s with the faster side initiating an event every 27.3 s and the other one every 32.6 s. The actual results are a joint period of 14.3 ± 1.1 s with the previously fast side responsible for a burst once every 29.9 ± 4.4 s and the other side every 28.5 ± 5.3 s. In this case, there is a large overlap between the uncoupled IBI pdfs of the two sides and their averages are similar. The joint probability that both sides will need the full average time to recover is lower than the single probability of each side, so that the frequency of the coupled culture is higher than each of the separate sides. For example, in the case of Gaussian pdfs in 75% of the instances the recovery period of at least one side will be shorter than the average.
The full comparison of the model's predictions to the experimental results is given in Fig. 6. On average, the simulation was successful in estimating the joint and the fast coupled periods: underestimating the joint period by 15.5 ±1.8% and the fast period by 6.5 ± 0.56%. The simulation underestimated the slow period by 27% (only 0.8 SD because they were larger in this case). This simulation error for the slow period is actually an underestimation because it doesn't include the culture that exhibited total domination and for which a period for the slow BIZ could not be measured (see Fig. 6).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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The prominent feature of our measurements is that all spontaneous events originated from local BIZs. This holds in the undrugged case as well as when inhibitory neurons are removed from the network by application of bicuculline. Such pacemakers were previously identified, but their exclusive domination in burst initiation could not be established. Our experimental setup enables a resolution of the size of these pacemakers down to the millimeter scale, and some simple experimental improvements can specify it even better, perhaps even to the single neuron scale.
The small number of events that do seem to initiate simultaneously at distant parts of the culture (2 of 564 events) were shown to be consistent with independent events initiated at two different BIZ. Therefore we have found no evidence for global, subthreshold, background activity that can simultaneously erupt in distant parts of the culture. Although collisions do exist in this system, the relatively long time between events makes them rare enough so that they do not play a major role in spontaneous activity on the line. Collisions may be more important in system with higher burst frequencies.
Global subthreshold activity involves connectivity mechanisms other than synaptic transmission to maintain long distance correlations in membrane potential across the culture. Such mechanisms can include gap junctions (Bennet and Zukin 2004), glial waves (Willmott et al. 2000), or the spread of diffusive factors. We can conclude that they are not important for the initiation of spontaneous activity in the culture. On the other hand, localized BIZs are consistent with the synaptic transmission and local connectivity (Feinerman et al. 2005) that characterize our system.
BIZ composition and burst initiation
Spontaneous network bursts have been shown to be initiated by either intrinsically bursting cells (Latham et al. 2000; Menendez de la Prida and Sanchez-Andres 2000; Sanabria et al. 2001) or by sporadic random spiking (Agmon and Wells 2003; Bacci et al. 1999; Darbon et al. 2002; Streit et al. 2001; Traub and Dingledine 1990) enhanced by recurrent network activity (Giugliano et al. 2004). On blocking of synaptic transmission in conventional 2-D cultures identical to the ones used here 0.1% of the neurons still showed spontaneous spiking activity (unpublished data from our lab). Our results suggest that when the network is fully connected such sporadic events can be enhanced to become full-blown population bursts.
We have shown that some areas of the culture are more likely than others to initiate population bursts (see also Darbon et al. 2002; Tcherter et al. 2001). Local variations in network architecture can affect the likelihood of certain areas to initiate population bursts. It is reasonable that denser parts of the culture are more probable to excite population bursts because, in general, they include more neurons that are apt to spontaneously fire and greater connectivity that may amplify such events. Our measured correlation between neuronal density and the BIZ distribution enforces the importance of a local aggregation of neurons to the architecture of a BIZ.
Even when inhibition is blocked, the average correlations between BIZ distribution and neuronal density do not exceed 0.48 ± 0.08. Therefore neuronal density cannot be the only factor affecting BIZ distribution. Moreover, we measured a change in pacemaker distributions in the same culture when the connectivity of the network is altered (by global application of bicuculline). The importance of the local inhibitory network in BIZ was indeed verified by the double immunostaining experiments. This suggests that the existence of a pacemaker and its bursting frequency does not depend only on the density of endogenously or randomly active neurons but also on recurrent network activity involving the local network in the vicinity of these neurons (Bacci et al. 1999; Giugliano et al. 2004; Maeda et al. 1995; Menendez de la Prida and Sanchez-Andres 2000; Murphy et al. 1992; Tabak and Latham 2003). Because inhibitory interneurons participate in the local network involving an endogenously spiking cell, they may damp recurrent activity and prevent the initiation of a population burst (see Amit and Brunel 1997). Further experiments will be needed to specify the degree of connectivity in different areas and how it correlates with BIZ location.
BIZ interaction
A high percentage of intrinsic bursters can lead to a large number of dominant pacemaking areas (Darbon et al. 2002; Harris and Stewart 2001; Maeda et al. 1995; Menendez de la Prida and Sanchez-Andres 2000; Stoop and Pralong 2000; Streit et al. 2001; Tscherter et al. 2001; Wu et al. 1999) that interact with each other. The natural step beyond locating pacemakers lies in understanding their interaction and the ways in which they cooperate to drive global activity. These interactions are furthermore important for issues ranging from the synchronization of different brain regions (Engel et al. 1992), through the control of oscillatory activity (Bartos et al. 1999; Marder and Bucher 2001) to the spread of epileptic activity (Stoop and Pralong 2000).
The boxing arena model suggests a very simple and mechanistic interaction between pacemakers in the culture. The simulation shows that pacemaker activity is completely specified by its decoupled IBI pdfs and depends on local rather than global properties, e.g., the size of the culture is irrelevant (see also Segev et al. 2002). A BIZ changes its frequency when it is brought into contact with a second culture because bursts from other BIZs that did not previously affect it now keep resetting its recovery clock (Tabak and Latham 2003; Tabak et al. 2001). When two cultures are coupled, the relative number of times at which each side will initiate events simply depends on the overlap between their IBI distributions. The less the overlap, the more the faster side will take over burst initiation of the connected larger culture. This discussion does not treat, of course, the mutual interaction of BIZs during the developmental stages of the network.
As discussed in the preceding text, random variations in the local composition and connectivity of the neural network can cause differences in their ability to generate bursts. This random variation alone could have led to a situation where every part of the culture participates in burst initiation, only with different probabilities. The BIZ interaction, however, sharpens such differences. The most extreme example being that of total dominance (Fig. 5, experiment 6), where one BIZ forces the probability that other areas initiate a burst to be practically zero. Once dissected away from the dominant BIZ, these other areas recovered their ability to initiate bursts. This can help in explaining the small number of BIZ we have identified on each of the 17-mm-long cultures.
Burst termination and refractoriness
The reciprocal resetting mechanism underlying pacemaker interaction can be understood in terms of activity dependent auto regulatory adaptation mechanisms that result from large scale population bursts (Darbon et al. 2002; Tabak and Latham 2003). Different pacemakers recover from this refractoriness at different rates before they initiate a second burst. Recovery periods as a mechanism for network synchronization have already been suggested (Gutnick et al. 1982; Traub et al. 1984). The recovery period we have identified is not refractory in the classical sense because a BIZ can react to population bursts initiated elsewhere before this period has ended. The fact that network activity is controlled by the fast BIZs rather than by the slower ones highlights an interesting point, namely that the recovery period for initiating a burst must be longer than the refractory period for reacting to one.
A possible explanation for this could include the division of the refractory time for a BIZ following a population burst into three periods. In the earliest period, the BIZ is totally refractive (Darbon et al. 2002; Maeda et al. 1995), and it cannot be excited by a distant source let alone initiate activity. The next period is of partial refractoriness, for example, as a consequence of partial neurotransmitter replenishment. At this stage, the BIZ can react to an incoming burst as it includes a massive bombardment of EPSPs. However, the BIZ cannot generate a burst as this process may entail the recurrent enhancement of a small number of random spikes into large-scale activity. This is less likely if low amount of neurotransmitters (for example) are available. A third period may be one in which there is full recuperation and the BIZ is at rest. The BIZ can then both react to an external stimulus or initiate one when a random event (single neuron spiking or perhaps several neurons spiking simultaneously) takes place (Agmon and Wells 2003; Giugliano et al. 2004; Lewis and Rinzel 2000).
We have shown that the duration of these refractory periods is the same in case a BIZ had initiated a burst or in the case it had reacted to one initiated elsewhere. This supports the hypothesis of recurrent activity in burst initiation; small-scale spiking is locally amplified into high-amplitude activity before it travels across the culture. This buildup period is also evident by monitoring fluorescent amplitudes and front speeds (Feinerman et al. 2005). Such a build-up process can eliminate any correlation between the refractory period following a burst and the small number of spikes that originally activated it. It is more likely that the amplitude of the burst is determined by other mechanisms of saturation that terminate it, such as delayed inhibitory activity or neurotransmitter depletion. Such mechanisms are independent of the location at which the burst has commenced and can lead to the observed independence between it and the refractory period that follows it.
In the culture with active inhibition (undrugged case), delayed activity of the inhibitory network can terminate bursts before they reach high amplitude and before major adaptation or depletion takes place. This could explain why burst amplitudes become higher and refractory periods grow longer on addition of bicuculline. This applies to the first refractory stages described in the previous paragraph (the random burst initiation mechanism may actually speed up with no inhibition). Note that the interaction as described in the boxing arena model holds both in the inhibited undrugged case and when inhibition is blocked. This is because this simple, and therefore universal, description relies on the existence of an activity-dependent refractory mechanism rather than on its precise nature.
The fact that the simulation predicts periods that are slightly shorter than the observed ones (especially for the slow BIZs) points at a further conclusion that may be drawn: that if a pacemaker is activated faster than its natural period, then it slows down. This is probably due to accumulating neurotransmitter deficits when the slow pacemakers are driven at a rate that is much higher than their natural period, causing the larger errors of the model. For example, if the refractory mechanism involves neurotransmitter depletion, neurons that react to a burst before full replenishment (second refractory stage as described above), may overuse reserve neurotransmitter pools (Zucker and Regehr 2002). A similar explanation can include the over exhaustion of internal presynaptic calcium stores (Emptage et al. 2001; Zucker and Regehr 2002). Using up these stores can result in accumulating shortages and reduce the ability of a certain area to initiate bursts. Referring to the boxing arena analogy, one might say that taking a punch before recovering causes more cumulative fatigue than launching one.
Comparison with other systems
Our results are in line with earlier culture studies of spontaneous activity in cultures. We have identified multiple burst sources that cooperate to drive activity in the culture (Darbon et al. 2002; Giugliano et al. 2004; Maeda et al. 1995; Tcherter et al. 2004) and have been able to construct a spatio-temporal map that includes BIZ location and relative strength (Darbon et al. 2002; Tcherter et al. 2001). Our results imply a network synchronization process that involves two separate processes of recurrently generated bursts followed by an activity-dependent refractory period (Darbon et al. 2002; Giugliano et al. 2004; Maeda et al. 1995; Tabak and Latham 2003). The unidimensional culture has allowed us to expand on these results. The ability to track each and every burst establishes the exclusiveness of local BIZs as the sole mechanism for initiating global population activity in these cultures. Using a two-stage procedure, we first imaged propagating bursts to identify BIZ location and then used immunohistochemistry to characterize their structure. Dissection of the culture into two parts was used to study the interaction between different BIZ. The locality of this dissection, possible only with a linear preparation, is required to ensure that network is not altered by the experimental manipulation. This is further verified by the reversibility of this manipulation.
A single cut across the line can be induced either chemically, by local application of tetradotoxin (TTX) (Feinerman and Moses 2003; Feinerman et al. 2005), or mechanically by a physical incision. This splits the culture into two disjoint parts while harming only a very small fraction of the neurons. Dissections in one-dimensional cultures are clean and cause little damage in comparison to two-dimensional preparations. The results obtained help in understanding similar sectioning experiments in two-dimensional cultures and slice preparations. Stoop and Pralong (2000) and Harris and Stewart (2001) dissected between different areas of a rat brain slice to show that activity in one specific area drives a second area that has a much lower rate of self activity. Stoop and Pralong (2000) study spontaneous bursting activity in an uninhibited, modified horizontal slice preparation that preserves the interconnectivity of the hippocampus, entorhinal cortex and amygdala in a rat temporal lobe. Although not discussed by Stoop and Pralong (2000), their data reveal a slight decrease in the frequency of the dominating pacemaker area (hippocampal CA3/2 region) once it is separated from the driven areas (entorhinal cortex and amygdala). In line with our results, this suggests that the slower, driven area had also contributed events to the total frequency before the decoupling. These similarities in bursting activity substantiate the use of dissociated culture preparations to study spontaneous bursting in naturally interconnected networks. These results agree with the boxing arena model in which the specific interconnections between two areas are irrelevant so long as activity initiated in each of them spreads to excite the other.
Maeda et al. (1995) report that separating a dissociated (2 dimensional) culture into two parts caused no consistent changes in burst frequencies. The difference may lie in the fact that their cultures (as well as their separated parts) were much larger than the ones we used, thus each severed part of the cultures probably contained several high-frequency pacemakers and separating them caused no changes in the total frequency of each side.
Some interesting conclusions may be inferred for bursts that occur in vivo. Our experiments, along with the analysis of the boxing arena model, show that the existence of several BIZs may be obscured by the dominance of one. Epileptic patients, for example, may have two or more loci of activation, but only the frequent one will be observable due to its dominance. Other areas may not be apparent before an operation, but will appear as active sites on removal of the dominant and evident area.
Summary
The use of unidimensional cultures facilitates the experimental analysis of large-scale spontaneous population bursts. All bursts initiate in a few localized BIZs from which they emanate to excite the whole culture. BIZ tend to have a high neuronal density and a low number of inhibitory neurons. Distinct BIZs compete in driving spontaneous activity in the culture. Their interaction, as measured on the randomly connected neuronal culture, provides a good description of previous observations of spontaneous activity in slice preparations where connectivity is more realistic and complex.
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Present address and address for reprint requests and other correspondence: O. Feinerman, Memorial Sloan Kettering Cancer Center, 415 E 68th St., Rm: 1419, New York, NY 10021 (E-mail: feinermo{at}mskcc.org)
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