Introduction

Carbachol is poorly absorbed through the gastrointestinal tract and never crosses the blood-brain barrier. Carbachol is a parasympathomimetic compound that stimulates both nicotinic and muscarinic receptors1, 2. Carbachol, a cholinergic agonist, induces rhythmic oscillations in pyramidal neurons in the CA1 and CA3 hippocampal areas through the activation of class I interneurons using multiple collaterals. GABA-A (γ amino butyric acid-A) receptors are essential in keeping the carbachol oscillations' repeatability3. Another study claimed that glutamatergic neurons' afferent fibers are responsible for the class I interneurons' rhythmic excitation4.

One study used carbachol as a muscarinic receptor agonist to activate three different oscillation types in the CA3 region in rat hippocampal slices. It stimulated synchronous discharges (called carbachol-delta) using low concentrations (4–;13 μmol/L), while higher concentrations (13–60 μmol/L) activated a very distinctive oscillation patterns (called carbachol-theta)5. Researchers have shown that, carbachol, when applied between 8–25 μmol/L, can also activate spontaneous γ oscillation episodes again in the CA3 area of hippocampal slices5, 6, 7, which is mediated by the activation of GABA-A and AMPA (α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid) receptors8. Furthermore, carbachol is proven to induce β-oscillations in the hippocampal slices9. A recent study that characterizes carbachol oscillation's pharmacological and cellular features in the rat hippocampal slice suggested that the oscillations in CA1 area need the CA3 region's synaptic propagation for initiating the carbachol oscillations10, 11.

Carbachol also induces 40 Hz oscillations in the slices taken from hippocampal CA3 region. The oscillatory electrical activity can be observed as a response to many different stimuli in the CA3 region's pyramidal cells of the hippocampal slice. Carbachol oscillations have similar frequencies with these oscillations, called “θ-rhythm” in vivo. A successful in vitro model of those oscillations should show similar cell-cell interactions as in vivo structures11, 12.

Traub et al has suggested that, in many epilepsy models, the features of carbachol oscillations are akin to the epileptiform bursts than to the θ-rhythm13. Scanziani et al stated that carbachol oscillations in the CA3 region's neurons in the hippocampus exhibited a more controlled behavior than other sites of epileptiform bursting. This could be because the glutamate release by the muscarinic receptors on the CA3 nerves is partially suppressed14.

Nicotinic acetylcholine receptors (nAChRs) are a group of ligand-gated ion channels that play an important role in many of the brain's cognitive functions15. Alzheimer's disease (AD) is a neurological disorder that progressively destroys cognitive function. At the cell level, cholinergic neurotransmission deficits such as decrease in ACh (acetylcholine) release and choline acetyltransferase activity, and cholinergic neuron loss in the basal forebrain occur early in AD, leading to cognitive impairment16. Other distinctive characteristics of AD are intracellular neurofibrillary tangles made of tau protein and extracellular neuritic plaques made of the β-amyloid peptide (A-Beta1-42)16. Pettit et al investigated A-Beta1-42's role on nAChR currents in the rat hippocampal slice, since this is the brain's primary area for cognitive tasks. Nicotinic currents stimulated by the local photolysis of caged-carbachol are blocked by A-Beta1-42 binding to nAChRs17. These researchers further explored that this inhibition is applied by the peptide fragment that includes amino acid residues 12-28, by the A-Beta12-28 part of the A-Beta1-4218.

Liu and Wu further suggested that soluble A-Beta is more associated with cognitive decline in AD patients than insoluble fibril deposits, which has been also confirmed by the studies in APP transgenic mouse models19. Goto et al showed that carbachol reduced the field excitatory postsynaptic potentials (fEPSPs) in the hippocampal CA1 region in both wild-type and transgenic mice at 5 μmol/L concentration20. Auerbach and Segal reported similar results, suggesting that reduced field EPSPs were because of presynaptic muscarinic acetylcholine receptor stimulation in rat hippocampus with the effect of carbachol in micromolar concentrations21.

Physiological signals have a wide variety of forms. To describe them, traditional feature measures typically extract amplitude and frequency information. This makes comparison of signals which have different bandwidths difficult22. In addition, such measures do not allow comparison within subject groups, as the absolute frequency of rhythms may differ from person to person, and may depend on other factors such as patient sex and age. Hence, additional analysis methods are needed to be developed. When visually inspecting signals, one of the first impressions is their “complexity.” In the present study, we have analyzed the complexity and the dynamics of carbachol-induced neuronal oscillations in the hippocampal CA1 area in both WT and 3xTg AD mice with 5- and 10-month old ages by utilizing the Lempel-Ziv (LZ) method.

Materials and methods

Hippocampal slice preparation

Hippocampal slices were prepared from 5- and 10 month-old mice that were sacrificed in accordance with Institutional Animal Welfare Committee guidelines, as previously described23, 24. After isoflurane-induced anesthesia, brain tissue was quickly removed and bathed in cold (4 °C) artificial cerebrospinal fluid (ACSF) containing (in mmol/L): 135 NaCl, 3 KCl, 16 NaHCO3, 1 MgCl2, 1.25 NaH2PO4, 2 CaCl2, and 10 glucose, bubbled with 95% O2–5% CO2 (carbogen). This specific ACSF composition was chosen because it has been successfully used in previous γ oscillation studies25, 26, 27, 28. Using a vibratome (Vibroslice 725 M, WPI, Sarasota, FL, USA), several 400-μm transverse coronal sections containing the dorsal hippocampus were cut, transferred to a holding chamber and were incubated at room temperature (22±1 °C) for at least 60 min in ACSF prior to recording. Next, one slice was transferred to a liquid-air interface chamber (Fine Science Tools Inc, Foster City, CA, USA) and was suspended on a nylon net at the liquid-air interface in a bath of continuously dripping ACSF (2–2.5 mL/min) bubbled with carbogen. Humidified carbogen was passed along the upper surface of the slice and bath temperature was regulated by a feedback circuit accurate to 0.5±0.2 °C. Baseline temperature was 34±1 °C. Carbachol (CCh) was the chemical used in this study and was purchased from Sigma.

Electrophysiological recordings

Standard extracellular field potential recordings were performed from the hippocampal CA1 cell layer using borosilicate glass micropipettes pulled to a 1 mm tip diameter and filled with 2 mol/L NaCl23, 24. Recordings were made using an Axoclamp-2B amplifier (Axon Instruments Inc, Union City, CA, USA). CCh was applied continuously during recording period. The CCh was dissolved in ACSF, and the drug solution was dripped at the same rate into the bath as drug-free ACSF (2–2.5 mL/min). Washout was accomplished by switching from the dripping solution containing the drug to the drug-free ACSF. The drug application's effects were observed 20–60 min after perfusion.

Data acquisition and analysis

Data were acquired by pClamp 9 via an Axon Digidata 1322 (Axon Instruments, Inc, Union City, CA, USA) interface board set to a 10 kHz sampling frequency, filtered in Clampex 9.0 using an 8-pole Bessel filter and a 1-kHz low-pass filter, and stored on hard media for subsequent off-line analysis. The induced response's power in the frequency spectrum was calculated off-line using Fast Fourier Transform (FFT) in Clampfit software 9.0 (Axon Instruments). Statistical comparisons of results were performed using Origin 5.0 (Microcal Software, Inc, Northampton, MA). Spike counting was performed off-line using Clampfit by setting a threshold of 3 times baseline noise. Prior to having the program count the number of spikes, those above threshold were manually confirmed. Waveforms having an interspike interval (ISI) under 12.5 ms (frequency greater than 80 Hz) were excluded. Also, no further spikes were considered after two or more consecutive ISIs over 33.3 ms had been identified.

Lempel-Ziv complexity

Synaptic connections between CA1 and CA3 neurons trigger the neural oscillations induced by carbachol, resulting in rhythmic excitation of CA1 region. Thus, the rhythmic activity we recorded from hippocampal neurons arise from complex feedback networks and non-linear interconnections that are characteristic for such physiological systems. We used the Lempel-Ziv (LZ) complexity estimator to analyze our recordings. Traditional analysis techniques (eg Fourier, power spectra) can't capture neural oscillations dynamics. Thus we used the LZ complexity, which quantifies the new pattern generation rate along given sequences of symbols, as a measure of the oscillation complexity (regularity)29, 30, 31, 32. LZ complexity is similar to information theoretic methods such as entropy31 and can cope with discrete-time symbolic sequences. The use of symbolic representations of time series data is particularly favored when low amplitude noise hampered the data. Thus, we transformed the neural signals into finite sequences in the symbolic space, which was perfectly suitable because of the particularities of our recordings. Each sample in the time domain was assigned a symbol and the total number of unique symbols forms the sequence's alphabet. Since the data was composed of long series of field events (spikes) in the extracellular recordings, that form the oscillation response of the neurons when presented with the cholinergic agonist carbachol, we used a binary alphabet. The time axis was divided into discrete bins. The field events were detected using an amplitude threshold and each time the threshold was crossed, we placed a “1” in the respective bin of the symbolic representation of our signals. For all bins with values below the threshold were assigned as “0”32.

Our signal x(n) was formally converted into a binary sequence S=s(1), s(2), ... , s(n) where:

where T is the threshold, in our case 2·σ(x(n)), where σ denotes the standard deviation of the signal32.

When computing the LZ complexity, the sequence S is parsed from left to right and a complexity counter c(n) is increased whenever a new subsequence (distinct word) is encountered. The algorithm followed is: (a) Let S(i,j) denote a substring of S that starts at position i and ends at position j, where i<j, S(i,j)=sisi+1sj and when i > j, S(i,j)={}. The vocabulary of the sequence S, V(S), is the set of all unique substrings (words) S(i,j) of S. (b) The parsing procedure starts by comparing a substring S(i,j) to the vocabulary that is comprised of all substrings of S up to j–1, that is V(S(1,j–1)). If S(i,j) is present in V(S(1,j–1)) then update S(i,j) and V(S(1,j–1)) to S(i,j+1) V(S(1,j)), respectively and repeat the previous check. If the substring is absent, place a dot after S(j) to indicate the end of a new component, update S(i,j) and V(S(1,j–1)) to S(j+1,j+1) and V(S(1,j)), respectively and the process continues. The whole parsing operation begins at S(1,1) and continues until j=n, the total length of the binary sequence30.

For example, the sequence S=1011110100010 is parsed as 1·0·11·110·100·010. Therefore, the vocabulary of S is 6. Similarly, a sequence S=0001101001000101 would be parsed as 0·001·10·100·1000·101, and hence yield a vocabulary sized 6 (see29 for details).

The LZ complexity is defined as the total number of words in the decomposition, c(n). The normalized LZ complexity is defined as:

More details on the LZ method and its implementation are given elsewhere29.

Results

The bath application of carbachol (100 μmol/L) generated extracellularly recorded field events (oscillations), which were recorded for at least 60 min. The oscillations presented three distinct pattern types, one consisting of individual field events that were grouped into regularly spaced bursts with high firing rate (>3 Hz), second, with long-lasting periods of continuous low firing rate activity with relatively constant frequency (<1 Hz), and third one is a mixture of the continuous firing with burst. The bursting-type patterns are typically referred to as carbachol oscillations and can be recorded in either S pyramidale or S radiatum33. The carbachol oscillations may represent population spikes fired synchronously from multiple pyramidal cells23, 24, 33.

We recorded data from 72 hippocampal slices taken from eight wild-type (WT) and six 3xTg AD mice aged 5 and 10 months (n=5 for the 5-month aged WT group, n=3 for the 10-month aged WT group, n=3 for both the 5- and 10- month aged 3xTg groups). We generally observed more burst-type activity in the young age group (5 months) and in the wild-type (WT) mice, when compared to old (10 months) and 3xTg AD mouse counterparts. Figure 1 shows typical traces of the two neural activity patterns that were recorded from a 5 months old WT (A and B) or 3xTg AD (C and D) mouse, respectively. Figure 2 presents the corresponding raw traces from WT (A and B) and 3xTg AD (C and D) mouse at 10 months age. Bursting duration ranged generally from 5 to 10 s. The system transitioned between the two states (of continuous and burst-type activity), with neural activity of highly irregular firing rate lasting 2–3 min. This transition might be a stage during which the neural activity undergoes reorganization, reflected by the corresponding random patterns of oscillation. Figure 3 presents typical transitional neural activity traces from a 5 month-old (panels A and C) and a 10 month-old mouse (panels B and D), respectively. The left side panels correspond to WT and the right side panels to the 3xTg AD mouse. We observed no neural activity during the control experiments (no drug applied).

Figure 1
figure 1

Typical recordings from two 5 months old mice: Wild-Type (A and B) and Transgenic (C and D). A and C: Continuous type activity of very low firing rate. B and D: regularly spaced burst formations of higher firing rate (>3 Hz).

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Figure 2
figure 2

Typical recordings from two 10 months old mice: Wild-Type (A and B) and Transgenic (C and D). A and C: Continuous type activity of very low firing rate. B and D: regularly spaced burst formations of higher firing rate (>3 Hz).

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Figure 3
figure 3

Typical recordings during transition from continuous to burst type neural activity: Wild-Type (A and B) and Transgenic (C and D). A and C: 5-month-old mouse. B and D: 10- month-old mouse.

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We further analyzed the carbachol's effects on the complexity of the hippocampal oscillations in WT and 3xTg AD mice using the LZ estimator. For this analysis, the segments of 1 min were taken during the continuous-type activity from records exhibiting more than 3 min of relatively constant firing rate (as shown in Figure 1 and 2, panels A and C). We also selected 5 consecutive bursts from each recording exhibiting bursting type activity.

The procedure was repeated for both age groups in WT and 3xTg AD mice. As shown in Figure 4, the complexity values of continuous-type neural activity segments were similar when comparing WT and 3xTg AD mice. The old age group's values were slightly (but immaterially) smaller than the young group. However, when examining the burst-type activity's complexity (Figure 5), the patterns changed dramatically. The difference in the WT case is lower but still significant (P<0.01). The complexity values for the 3xTg AD mice were decreased with a drastic drop in the case of the 10-month-old age group (significant, with P<0.001).

Figure 4
figure 4

Complexity values for continuous type neural activity. Values correspond to complexity averages (±SEM) of 1 min long recording segments taken from each of the 14 mice (nWT_10 months=nWT_5months=34, nTG_10 months=nTG_5 months=28).

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Figure 5
figure 5

Complexity values for burst-type neural activity. Values correspond to complexity averages (±SEM) of 5 consecutive bursts taken for each of the 14 mice (nWT_10 months=nWT_5 months=45 and nTG_10 months =nTG_5 months= 20). cP<0.01.

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Figure 6 shows the complexity values of 1 min long signal segments during transition phase. The differences between the complexities of young and old age group are irrelevant for both WT and 3xTg AD mice.

Figure 6
figure 6

Complexity values for transitional neural activity. Values correspond to complexity averages (±SEM) of 1 min long recording segments taken from each of the 14 mice (nWT_10 months=nWT_5 months=12 and nTG_10 months=nTG_5 months=18).

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Discussion

In the present study, we proposed a novel nonlinear dynamical analysis method based on the LZ complexity method to analyze hippocampal oscillations induced by acute carbachol exposure on hippocampal slices in WT and 3xTg AD mice. By using this mathematic analysis, we are able to quantitatively distinguish three patterns from hippocampal neuronal oscillations. These patterns may reflect different status of neuronal network synchronization. More importantly, the analysis using the non-linear mathematic model (LZ complexity estimator) demonstrates that only burst pattern exhibits significant impairment in 3xTg AD mice and this impairment is likely age-dependent.

The neural oscillations recorded from hippocampus neurons arise from complex feedback networks and non-linear interconnections, which are characteristic for physiological systems. Traditional analysis techniques (eg Fourier, power spectra) may not capture the dynamics of neural oscillations22, 34. A series of methods have been used to investigate the properties of biomedical signals, such as the Shannon entropy (ShEn), spectral entropy (SpEn), approximate entropy (ApEn), Lempel-Ziv complexity (LZ), or Higuchi fractal dimension (HFD). Ferenets et al34 provided an extensive comparison of different entropy and complexity measures using surrogate signals as well as real EEG signals34. Their study is especially interested in the sensitivity of the mentioned measures to the bandwidth of the signal spectrum and the shape of the probability density function (PDF). They showed that ShEn does not depend on signal bandwidth as could be expected from the definition of this measure. The SpEn, in contrary to ShEn, does not depend on the shape of the signal's PDF. ApEn depends on both the shape of the PDF as well as the spectral bandwidth of the signal. At sharp PDFs, ApEn behaves similarly to ShEn with respect to the shape of the PDF (given that the bandwidth is large enough). As the signal amplitude becomes more uniformly distributed, ApEn values stay constant, depending only on the spectral bandwidth. Also, the ApEn values slightly increase with increasing signal length. The behavior of LZ complexity and HFD look similar. Both parameters depend mainly on the bandwidth of the signal spectrum (less than the other measures, however) while slight dependence on the PDF can be observed mostly when the parameters controlling PDF's sharpness is small.

Additionally, Ferenets et al34 showed that while LZ complexity, ApEn, and HFD are relatively independent of the amount of data (window length), SpEn and, in some cases, ShEn, show significant trend. This comes from the fact that ShEn and SpEn both use transformation over the Shannon function. The same study concludes that methods based on the phase space background (ApEn and HFD) or pattern recurrence (LZ complexity) seems to have slight advantage in analyzing the EEG signals. Their results clearly show that the various parameters called entropy actually measure different properties of the signal. ShEn, the “classical” entropy measure, does not depend on signal spectrum while SpEn is insensitive to the amplitude distribution (which is easy to predict from the mathematical formulas defining these parameters). However, LZ complexity seems to be more suitable when dealing with finite symbol and discrete time signals, as it can be expected from its mathematical formula.

As noted by several authors, the complex feedback networks and nonlinear couplings inherent in the physiological system give rise to characteristic oscillations35, 36, 37. Nagarajan et al37 pointed out that while the system is undisputedly nonlinear, it is far from trivial whether this nonlinearity is exhibited in the external recording. The oscillations in these recordings can be either due to a nondeterministic component or a nonlinear deterministic component. Traditional techniques such as Fourier analysis fail to provide adequate information regarding the dynamics of the data. For instance, it is possible to generate two data sets, which have similar spectra but different dynamics. The search for alternate measures to quantify the dynamics has been an area of recent interest.

The use of symbolic techniques to map a time series into a sequence retaining its dynamics has been quite popular38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57. The robustness of the resulting symbolic representation to low amplitude noise is also appreciated40, 41, 42. The fundamental idea is to partition the samples in the real space into a finite sequence in the symbol space. Each sample in the original data is assigned a unique symbol and the number of distinct symbols forms the alphabet set of the sequence. The regularity of the resulting sequence is quantified using a chosen complexity measure.

The LZ complexity has been applied extensively in biomedical signal analysis as a metric to estimate the complexity of discrete-time physiologic signals, proving its robustness when over other complexity/entropy measures. For instance, LZ has been used for recognition of structural regularities42, for complexity characterization of DNA sequences45, 46, 47, to develop new methods for discovering patterns in DNA sequences by applying it to genomic sequences of Plasmodium falciparum47, and to estimate the entropy of neural discharges (spike trains)48, 49. LZ complexity has also been used to study brain function51, brain information transmission52, and EEG complexity in patients with Alzheimer's disease53, and epileptic seizures54. Other authors have used LZ complexity to study ECG dynamics55, Generally, previous work involving the application of LZ in the context of biomedical signal analysis has consisted of analyzing signals from a specific patient population or pathology, and identifying a LZ change associated with a specific condition of interest56. The fact that LZ quantifies primarily the signal bandwidth and bandwidth of the signal harmonics is relevant in biomedical signal analysis29.

Due to its robustness, LZ complexity has also found applications to the neural recordings. Szczepanski et al57 present three applications of LZ complexity to the analysis of spike trains: (i) estimation of the entropy, (ii) discrimination of neural responses via complexity curves and (iii) discrimination of neural responses via the number of states of the corresponding neuronal sources. Additionally, Amigo et al49 used LZ for estimating the entropy rate of spike trains and underlined that LZ is closely related to such important source properties as entropy and compression ratio, but in contrast to these, it is a property of individual sequences49.

Previous studies58, 59, 60, 61, 62 in transgenic (Tg) mice models of Alzheimer's Disease (AD) point out the presence of quite a number of beta-amyloid deposit in the hippocampus and other brain areas as well as cholinergic dysfunction and impairment in learning and memory functions. Therefore a vast amount of research has been done to make a comparison between the 7 month-old Tg and WT (wild type) mice in terms of the intracellular pathways that might be switched on/off in the hippocampal areas. One of the major pathways that have been proven to be responsive to inflammatory stimuli, environmental stress or other insults is ERK (extracellular regulated kinase)63. It has been widely accepted that activation of ERK is very closely related to memory formation64, 65, 66, 67. Since it has been shown in many systems that, ERK activation is downstream of cholinergic stimulation through both nicotinic65 and muscarinic66 receptors, a research has been done to determine whether cholinergic stimulation might activate ERK differently in the hippocampus of Tg and WT mice. Cholinergic stimulation with CCh (carbachol) has shown a strong increase in ERK activation in the CA1 (cornu ammonis area 1) pyramidal neurons of WT mice while this effect is significantly less dense in the hippocampus of Tg mice, pointing out a possible mechanism responsible for the presence of memory deficits 58 in them because of the strong connections between the ERK pathway and the cholinergic system in memory functions 68.

All these previous studies encouraged us to use this novel nonlinear dynamical analysis method, based on the LZ complexity method, to analyze hippocampal oscillations induced by acute carbachol exposure on hippocampal slices in WT and 3xTg AD mice. Our analysis demonstrated that the complexity values of continuous patterns in response to carbachol were almost the same for the 5-month old wild and transgenic mice. But, they were decreased in the 10-month old wild and transgenic mice, but these differences were not statistically significant. On the other hand, the complexity values of burst patterns were smaller for the 5-month old transgenic mice compared to those of 5-month wild mice and were significantly smaller in the 10-month wild and transgenic mice. Thus, the difference was much more drastic for the transgenic mice. Finally, the complexity values of the mixed patterns were more or less the same for the 5- and 10-month old wild and transgenic mice. The difference in the WT case is lower but still significant (P<0.01). We speculate that the reason for the drastic drop in the complexity of burst-type neural activity of TG mice is the declined cholinergic neurotransmission that has been reported in TG mouse models in several studies. This neurotransmission deterioration was shown to be caused by the formation of amyloid β–peptide deposits59, 60, 61. The even larger decrease in complexity values that we observed in our data for the older group matches with results that indicate the deterioration to be age-dependent59, 60.

Therefore, our analysis indicates that the LZ based complexity estimator is a useful tool for the characterization of the dynamical changes in hippocampal oscillations. It is well known that neuronal synchronization deficits, especially theta oscillation, are correlated to learning and memory deficit in the AD patients. As demonstrated in our mathematical analysis, such attenuation could be quantitatively represented as an impairment of burst pattern firing during exposure to CCh. Therefore, our analysis not only provides a convinced way to evaluate the nature of hippocampal neuronal oscillations, but also may open a new window to help the diagnosis of AD, to evaluate pathological status of AD and also to evaluate the effects of the medical therapy of the AD.

Author contribution

Jie WU and Kui WANG designed research; ALL the authors performed research; Metin AKAY,Andrei Dragmir and Yasemin M Akay contributed new analytical tools and reagents; Metin AKAY, Andrei Dragomir and Yasemin M Akay analyzed data; Metin Akay, Yasemin M Akay, Andrei Dragomir,and Jie Wu wrote the paper.