Memory is a crucial cognitive function for daily life [1, 2] that has been the subject of extensive investigation at various levels, ranging from cognitive psychological to neurobiological approaches. Cognitive psychology has mainly focused on abstract explanations of memory [3–5], and discriminates between short-term memory, acting on time scales of seconds, and long-term memory, on time scales of minutes to days [6–8]. New experiences are first stored in the hippocampus in a process called synaptic consolidation [9, 10]. Then, memories are transferred to the neocortex for long-term storage by repeated replay in the hippocampus, particularly during slow-wave sleep (system consolidation) [10, 11]. On the other hand, neurobiology has revealed detailed insights into neuronal functioning and synaptic plasticity that are likely to underlie memory [12]. Bridging the gap between cognitive and neurobiological studies has been challenging, at least in part because experimental paradigms usually do not facilitate assessment of parameters that cover the entire range from the molecular or cellular level to cognitive functioning.

It is widely accepted that plasticity of neuronal connectivity is crucial for memory. Connection strengths between neurons can be determined in patch clamp experiments [13], but this approach reveals only one, or at best a few, connection strengths at a time. In past decades, multi electrode arrays (MEAs)have been used to record activity from networks of cultured neurons [14], and recorded activity patterns can be used to infer functional connectivity and study memory [15–17]. We will use the term 'connectivity' throughout the current work to refer to functional connectivity in a network. We will use network activity and connectivity to investigate short-term and long-term memory. In these networks, short-term memory of a stimulus is seen as the reverberating activity in response to the stimulus and the subsequent relative silence. Long-term memory, on the other hand, can be investigated by connectivity analysis. Connectivity and activity in neuronal networks mutually affect each other. The finding that input deprived networks develop quasi stable activity patterns [18, 19] and connectivity [20] suggests that activity and connectivity are in equilibrium [21]. External stimuli induce new activity patterns, and disturb the equilibrium between activity and connectivity [22, 23]. Upon repetition of the stimulus, the adapting connectivity in the network reaches a new equilibrium with spontaneous activity patterns that include the stimulus response. This resembles in-vivo systems consolidation, and is interpreted as the formation of long-term memory of the input [22]. Consequently, repeated exposure to this stimulus induces no further connectivity changes. These observations suggest that memory traces are part of balanced connectivity and activity at the network level, and that detection of memory trace formation requires estimation of connectivity throughout networks. With this in mind, long-term memory can be seen as stored in adapted connectivity that, in contrast to short-term memory, persists for many hours. It is not feasible to determine network connectivity based on patch clamp recording of pre- and post synaptic signals, but MEA recordings do enable estimation of network connectivity. Recent work showed that cultured networks on MEAs are able to form memory traces when repeatedly exposed to a stimulus [24] during a few hours and that this ability depends on slow-wave sleep-like conditions [23], very similar to in-vivo system consolidation. In addition, these preparations facilitate measurement and manipulation of cellular and synaptic properties, which provides the opportunity to bridge part of the gap between neurobiological and cognitive studies.

In addition to memory, prediction is also crucial to successfully conclude every-day actions. Prediction can be defined as the ability to reduce the uncertainty on upcoming external inputs, and is strongly related to memory [25–27]. In principle there can be no prediction without memory [26]. Most evidence to support the notion that neural networks are able to predict comes from theoretical work [1, 2, 25], and a few pioneering experimental studies using retinal [27–31] or hippocampal preparations [32–34].

Recent work also showed that random networks of dissociated cortical neurons are able to predict the timing of the upcoming stimulus, suggesting that prediction is independent of specific network architecture [35]. In that study, prediction was shown to initially depend on short-term memory of given stimuli, which typically lasted several hundreds of milliseconds. During multiple hours of repeated focal stimulation, long-term memory traces were formed and prediction became less dependent on short-term memory. This suggests that focal stimulation-induced long-term memory traces also play a role in prediction. It remains unclear which mechanisms underlie prediction and to what extent long-term memory is involved.

Several studies have attributed the formation of long-term memory traces to spike timing dependent plasticity (STDP) [6, 36–43]. STDP governs changes in synaptic weights based on the timing of pre- and postsynaptic action potentials, and may lead to either long-term potentiation or depression of synaptic strengths [44–47]. Calcium influx mediated by N-methyl-D-aspartate (NMDA) receptor activation plays an important role in STDP [37, 44, 46, 48], and has been shown to affect the density of AMPA receptors in the synaptic region [37, 48, 49]. Depending on the amplitude and kinetics of the calcium influx, synapses can be either potentiated or depressed [37, 48, 50]. The strong association between memory and prediction suggests that STDP and NMDA receptor activation may also play a role in prediction.

In the current work, we present an in-vitro model to investigate memory and prediction. In particular we aimed to determine the involvement of NMDA receptor activation in memory and prediction. We applied focal electrical stimulation to networks of rat cortical neurons plated on MEAs, with and without pharmacological blockade of NMDA receptors, and investigated whether networks were able to (i) form long-term memory traces, and (ii) predict future stimuli. In addition, we determined to what extent prediction depended on (short-term or long-term) memory.

2.1. Culture preparation

Cortical cells, obtained from newborn rats (usually postnatal day 1 and always with 48 h after birth) were dissociated by trypsin treatment and trituration, and then 60 µl droplets of cell suspension (about cells) were plated on multi electrode arrays (MEAs; Multi Channel Systems, Reutlingen, Germany), precoated with poly ethylene imine. The glass substrate contained 60 titanium nitride electrodes (diameter 30 µm and pitch 200 µm), on which a Plexiglas ring (diameter 20 mm) was glued to create a culture well (figure 1(a)). The well was filled with 1 ml of Neurobasal commercial medium (Neurobasal-A medium -gluc -pyr, Thermo Fisher), supplemented with B27, 1.24 g l−1 glucose, Pen/strep/glutamine, 100 mg l−1 vitamin C and 10 ng l−1 NGF. MEAs were stored in an incubator, under standard conditions of C, high humidity, and 5 CO2 in air. The culture medium was refreshed twice a week by removing 300 µl and adding 400 µl of fresh medium, thus compensating for evaporation. All cultures were grown for at least 3 weeks before experiments started, to allow for culture maturation [20, 51, 52]. Mature cultures contained excitatory () and inhibitory () neurons [53], and astrocytes (ratio astrocytes neurons: 4:1) [54] (see figure S3 in the appendix). Before experiments, culture chambers were firmly sealed with watertight but O2 and CO2 permeable foil (MCS; ALA scientific). At the end of each experiment, cultures were returned to the incubator. Animal care followed the guidelines for the accommodation and care of animals as recommended by the Netherlands Food and Consumer Product Safety Authority (NVWA). All surgical and experimental procedures were approved by the Dutch committee on animal use (Centrale Commissie Dierproeven; AVD110002016802), and complied with Dutch and European laws and guidelines. Results are presented in compliance with the ARRIVE guidelines.

Figure 1. Example of MEA, experimental protocols and recorded activity. (a) Shows an example of a 60 electrodes single well MEA used in this study. (b) Shows the protocols for memory experiments (top) and prediction experiments (bottom). (c) Shows an example of recorded spontaneous activity under control conditions. Each tick represents a recorded spike at the indicated electrode. Bottom trace shows summed activity (array wide firing rate; AWFR). (d) Represents an example of spontaneous activity recorded after APV administration. (c) and (d) Show that APV administration reduced the spontaneous firing rates, but firing patterns still contained synchronous activity (networks bursts).

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To record activity, we placed MEAs into a setup outside the incubator, consisting of a MC1060BC preamplifier and FA60s filter amplifier (both MultiChannelSystems GmbH, Reut-lingen, Germany). This setup has a temperature controller that maintains a standard temperature of C and was positioned inside a Plexiglas hood that received a constant flow (2 l min−1) of a humidified gas mixture that contained 95% compressed air and 5% CO2. Every recording began after a 15 min accommodation period. Signals from the network were recorded by 59 electrodes using a custom-made Lab-View program, at a sampling frequency of 16 kHz per electrode. Acquired analogue signals were band-pass filtered (2nd order Butterworth 0.1–6 kHz) before sampling. Action potentials were detected whenever recorded voltages exceeded a threshold, set at 5.5 times the estimated root- mean-square noise level (ranging 3–5 µV). During recordings this noise estimation was continuously updated for each electrode. For each detected event the setup stores a time stamp, the electrode number, and the wave shape (6 ms). For off-line artifact detection and removal we used a wave shape based algorithm adapted from [55].

Focal stimulation was applied by electrical stimulation through one of the electrodes, using biphasic rectangular current pulses of 200 µs per phase [23]. After probing all electrodes at various amplitudes (16–24 µA), we selected one (prediction experiments) or two (memory experiments) electrode(s) for stimulation, using the lowest amplitude that induced a network response after at least 50 of all stimuli. Amplitudes were low enough to avoid electrolysis. We did not select stimulation electrodes on the 1st or 8th row or column of the MEA. If more than one (two)electrode(s) induced a network response, we selected the one(s) that induced the highest number of action potentials. For memory experiments we always used 2 electrodes from opposite quartiles with at least one row and column in between.

2.3. Experimental design

We used 20 µM 2-amino-5-phosphonovaleric acid (APV) to block NMDA receptors. This concentration clearly affected firing patterns and stimulation induced connectivity changes, but had no significant effect on network excitability (see the appendix figure S1). Addition of APV was done under a laminar flow hood to maintain sterility. We performed experiments under control conditions (control cultures) or using an NMDA antagonist (APV cultures). All used cultures were tested for activity and stimulus responses before experiments started. Cultures with less than 20 active electrodes, presenting less than 2 network bursts per minute or without a clear response to stimulation were not used for experiments. Each culture corresponds to a single MEA. Throughout the manuscript, we use the term MEA to refer to the device, and the term culture to refer to the network of neurons on the MEA.

2.3.1. Long-term memory

We adapted a protocol to induce memory traces from earlier studies [22, 23]. We acquired 1 h of spontaneous activity at the beginning of the experiment (Baseline). After APV administration we recorded a second hour of spontaneous activity (BaselineAPV). Then both control and APV cultures underwent focal stimulation applied to two different electrodes (A and B). For each electrode we applied 5 stimulation periods of ten minutes each at a constant frequency of 0.2 Hz, alternated by 1 h spontaneous activity recordings. First, electrode A was used, then electrode B, and then again electrode A, leading to a total of 15 stimulation periods of 10 min. The total duration of the experimental protocol was 17 h and 30 min (figure 1(b)).

2.3.2. Prediction

To study prediction we adapted the protocol developed in earlier work [35]. In short, we first acquired 1 h of spontaneous activity under control conditions. After APV administration we recorded another hour of spontaneous activity. Then, cultures were subjected to 20 h of focal electrical stimulation (figure 1(b)). For these experiments we used inter stimulus intervals (ISIs) drawn independently and identically from a density distribution, with a mean frequency of 0.2 Hz. This distribution was designed to produce long-range temporal correlations, which were read from a pre-generated list (see figure 4(c)). The long and intensive stimulation protocol adopted for the prediction experiments might be too stressful for the cultures to be applied twice. We therefore compared current results under NMDA blockade to control experiments from a previous study [35]. Before analysis of the effects of NMDA blockage was performed, we compared mean firing rate (MFR) and BI during baseline recording of both control and APV-treated cultures (baseline before APV addition).

2.4. Data analysis2.4.1. Memory trace formation

Functional connectivity was inferred from spontaneous activity recordings using conditional firing probability (CFP) [20]. In short, CFP calculates the probability that electrode j spikes at time , given that electrode i spiked at t = 0. The maximum of this probability curve was interpreted as the strength of the connection from electrode i to j (see the appendix for details). For this analysis only active electrodes were considered. An electrode was defined as active if spikes were recorded in 1 h of spontaneous activity during baseline. Then long-term recordings were divided into chunks that contained 213 action potentials. This value was shown to be sufficient for statistical analysis of network connectivity in each chunk [23]. Still, with this chunk size, an hour of spontaneous activity could typically be divided into multiple chunks (average chunks duration was  min in control cultures and  min in APV cultures). This yielded a connectivity matrix M for each chunk, that contained the strengths of connections between all possible pairs of electrodes. To assess the formation of memory traces, we quantified connectivity changes induced by each stimulation period by computation of Euclidean distances (EDs) between connectivity matrices [23] (equation (S2) in the appendix).

Each stimulation period was preceded and followed by periods of spontaneous activity that contained multiple chunks of 213 action potentials. Thus, we could in principle compute the distances between all possible pairs of baseline and post-stimulation chunks. However, this may not be necessary, if connectivity matrices hardly differ between baseline chunks, and if there was no significant drift. We calculated EDs between all possible pairs of chunks within baseline, and averaged them to determine the magnitude of spontaneous baseline connectivity fluctuations: ED. To visualize possible drift, we calculated the EDs between the first baseline chunk and all other baseline chunks, and determined the slope (the average increase per unit of time) (see figure 2). This analysis showed that the last chunk of baseline was representative of all chunks in baseline, and could be used to evaluate connectivity changes following electrical stimulation.

Figure 2. Calculation of Euclidean distances (ED). Top panel (a): visual representation of Euclidean distance computation in memory experiments. Black vertical lines indicate the division of spontaneous activity recordings into chunks, which were used to calculate connectivity matrices M. Red dashed arrows indicate Euclidean distance calculation between chunks of activity after stimulation at a specific electrode and the last baseline chunk obtained before the first stimulation at that electrode. Black circles indicate final averaging to obtain for each spontaneous activity period. Bottom panels indicate spontaneous connectivity drift in baseline recordings. Panel (b): example of connectivity drift during baseline in one culture (slope ). Graph shows distances of all chunks from the first chunk. Drift was estimated as the slope of a linear fit, and averaged across cultures. Panel (c) shows mean drift during baseline, the last period of spontaneous activity before stimulation at electrode B, and the last one before return to electrode A. Error bars represents SEM.

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Next, we computed EDs between the last chunk of baseline and each chunk contained in the (5) spontaneous periods that followed stimulation of electrode A. These distances are referred to as ED. This procedure was repeated for electrode B, but now the last chunk before the first stimulation at electrode B was used as baseline. Similarly, after return to electrode A, the last chunk before the first (second round) stimulation at electrode A was used as baseline (see figure 2). In the computation we considered only the nonzero elements of the M matrices. These analyses were applied to both controls and APV experimental data.

2.4.2. Network excitability

Network excitability, defined as the average network response to a spike in one neuron, was calculated using single pulse resposnse (SPRs) as developed in [56]. This allows estimation of the average response at electrode j to a single spike at electrode i under widely varying dynamic regimes. The computation of SPRs requires deconvolving the auto-correlation of electrode i from CFP. Also in this case spontaneous recordings were subdivided in blocks of 213 recorded spikes. SPR strengths of all pairs of active electrodes were calculated for each period of spontaneous activity in both control and APV groups, and averaged to obtain a measure of network excitability.

2.4.3. Quantification of prediction and short-term memory

We first verified that networks remained responsive to stimulation throughout experiments (see the appendix, figure S2). We used mutual information to quantify prediction [27, 35]. Mutual information estimates how much one signal reduces the uncertainty of another one, and is computed as the sum of the entropy of both signals minus the joint entropy [57]. Then we first binarized the recorded neural activity (X) in bins of 100 ms by setting if electrode i recorded activity in that time bin, and if not. The same binarization was applied to the stimulation signal (S). After binarizing the activity X and the stimulation signal S , for each hour, we calculated MI between S and X, with X shifted in time by Δt ms (Δt = n bins ×100 ms, with ). Negative shifts reveal short-term memory, as quantified by MI:

where and represent the unshifted stimulation signal and the time-shifted binarized activity. Activity was shifted forward up until a maximum of 2 s. Positive shifts are used to quantify prediction by computing :

Consequently from equations (1) and (2) and are functions of the shift Δt. We applied this analysis to the APV prediction experiments and compared our results to control experiments obtained in earlier work [35]. In APV experiments, stimulus responses significantly decreased after 13 h (see appendix, figure S2). Therefore, we took into account only the first 10 h of stimulation (instead of all 20 h) for APV as well as control cultures.

2.4.4. Relationship between prediction and short-term memory

To study possible effects of APV on the relationship between short-term memory and prediction we analyzed the area under the curve (AUC) of () and () for each analyzed hour, for each experiment (see equations (S3) and (S4) appendix) [35]. Then we plotted against , and fitted a linear equation to determine the slope and offset of the relation, and the correlation coefficient. Finally, we investigated whether and how slope and offset changed during the considered 10 h of stimulation.

2.4.5. Efficiency of predictions

We used the predictive information bottleneck concept as shown in Lamberti et al [35] to determine whether APV affected the efficiency of prediction. This allows us to determine the minimum information about the past () necessary to make predictions on the future () (see appendix). The entire past and future were replaced by the time since the last stimulus (past; ), and the time to the next stimulus (future; ) [58]:

where denotes mutual information between and X. Prediction as quantified in experimental data under APV or control conditions was then compared to a theoretical optimum (R(D)). The theoretical optimum was obtained calculating the minimum memory required to enable a certain prediction. This resulted in a line that divides between achievable and unachievable combinations of information about the past () and the future (),

Here D corresponds to the required predictive power, R(D) is the memory necessary to reach that predictive power, is the conditional probability of neural activity given time since the last stimulus, x is a realization of the activity X, is a realization of . For both controls and APV treated cultures we computed and considering the first 10 h of stimulation only.

2.5. Statistical analysis

All analyses were performed using SPSS statistics for Windows (IBM, Inc. Chicago, IL) or Matlab (The Mathworks, Inc. Natick, MA, USA). Normality of data distribution was verified using Shapiro-Wilk tests. Effects of APV concentrations were tested with one sample t-test, in case of normality, or one sample Wilcoxon test otherwise. Significance of connectivity changes was assessed using repeated measurements ANOVA, in case of normality, or repeated measurement Friedman test otherwise. Assessment of possible effects of APV on network excitability was performed with two way repeated measurement ANOVA, with condition and time as independent variables. In both memory and prediction experiments significance of temporal differences in effectiveness of stimulation were analyzed by one way ANOVA (if normally distributed) or Kruskal–Wallis (if non-normal). In the end t-statistics measure was applied to check trends of slope and offset of the relationship between memory and prediction. P-values were considered to indicate significance.

3.1. Long-term memory

In total 12 cultures were used, first under control conditions (control experiments), and then under NMDA blockade (APV experiments). All 12 control recordings were included for analysis, and 7 of the APV experiments. In the other 5 cultures APV administration reduced network activity to such low levels that CFP analysis could not be done to estimate functional connectivity.

3.1.1. Network excitability

Network excitability was quantified by the average magnitude of SPRs during each period of spontaneous activity. There was no significant difference in network excitability between APV treated cultures and controls (see figure 3(a)); two-way repeated measures ANOVA p = 0.11), and network excitability in APV treated cultures did not significantly change during experiments (two-way repeated measures ANOVA p = 0.13). In the control group network excitability slightly decreased with time (two-way repeated measures ANOVA p = 0.045).

Figure 3. Memory formation and time course of network excitability. (a) Network excitability for the control group (orange, N = 12) and APV group (green, N = 7). APV treatment did not significantly affect network excitability (p = 0.11), and there was no significant trend over time in either group (APV p = 0.13, control p = 0.045). (b) Stimulation-induced connectivity changes the control group (orange) and APV group (green). First series of stimulation at electrode A induced connectivity changes in the control group (p = 0.002), but not in the APV group (p = 0.12). Stimulation at electrode B yielded similar effects (control p = 0.003, APV p = 0.88). Return to electrode A did not induce connectivity changes in either group (control p = 0.08, APV p = 0.61). Horizontal scales indicate the number of stimulation-and-recording cycles. Each cycle contained 10 min of stimulation followed by 1 h of recording. In both panels the red arrow indicates the addition of APV. Shaded areas show SEM, and indicate differences between experiments.

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We first computed baseline functional connectivity fluctuations () and possible drift (slope). In the networks. Baseline slopes averaged for 1st stimulation of electrode A, for electrode B, and for return to electrode A (figure 2). Figure 3(b) shows