Analysis of the signals generated by networks of ... - Semantic Scholar
Biosensors & Bioelectronics 13 (1998) 601–612
Analysis of the signals generated by networks of neurons coupled to planar arrays of microtransducers in simulated experiments M. Bove, S. Martinoia, G. Verreschi, M. Giugliano, M. Grattarola
*
Bioelectronics and Neurobioengineering Group, Department of Biophysical and Electronic Engineering, University of Genoa, Via Opera Pia 11a, I-16145, Genoa, Italy Received 29 October 1997; accepted 5 March 1998
Abstract Planar microelectrode arrays can be used to characterize the dynamics of networks of neurons reconstituted in vitro. In this paper simulations related to experiments of the electrical activity recording by means of planar arrays of microtransducers coupled to networks of neurons are described. First a detailed model of single and synaptically connected neurons is given, appropriate to computer simulate the action potentials of neuronal populations. Then ‘realistic’ signals are generated. These signals are intended to reproduce, both in shape and intensity, those recorded by a microelectrode array. Typical experimental conditions are considered, and a detailed analysis given, of the bioelectronic coupling and of its influence on the shape of the recorded signals. Finally, simulated experiments dealing with dorsal root ganglia neurons are described and analysed in comparison with experimental results reported in the literature and obtained in our own laboratory. The effectiveness of the planar microelectrode technique is briefly discussed. 1998 Elsevier Science S.A. All rights reserved. Keywords: In vitro networks of neurons; Planar microelectrode arrays; Neuron–electrode junction; Synaptic connections; Neuronal network dynamics; Simulated neuronal networks; Multi-signal processing tools
1. Introduction One of the main goals of neuroscience research is the understanding of the functional rules governing the behaviour of microcircuits in the vertebrate nervous system. Recent advances in cell and organotypic neuronal cultures allows the experimenter to create in vitro networks of neurons that represent rudimentary approximations of such microcircuits (Bulloch and Syed, 1992; Ga¨hwiler et al., 1997). Moreover, the electrophysiological technique based on the use of planar microelectrode arrays (Gross, 1979; Gross et al., 1985) can be used to characterize the dynamics of such networks (Maeda et al., 1995, Canepari et al., 1997). As a result, nowadays the neuroscience community has access to an increasing amount of long term multichannel recordings, obtained by in vitro coup-
* Corresponding author. Tel.: + 39-10-3532761; Fax: + 39-103532133; E-mail:[email protected]
ling networks of neurons to arrays of substrate planar microelectrodes. Elementary neurocomputational rules are hidden inside these long-term multichannel recordings and a powerful tool to decipher them is provided by the extensive use of simulated experiments, along a scientific tradition already well developed in several branches of physics (Amit, 1989). Specific simulated experiments will be described in the following: first, a detailed model of single and synaptically connected neurons will be described, appropriate computer simulate the action potentials of neuronal populations. Then ‘realistic’ signals will be generated. These signals are intended to reproduce, both in shape and intensity, those recorded by a microelectrode array. Typical experimental conditions will be considered and a detailed analysis will be given, of the bioelectronic coupling and of its influence on the shape of the recorded signals. Finally, simulated experiments dealing with dorsal root ganglia (DRG) neurons will be described and analysed in comparison with experimental results reported in the literature and obtained in our own laboratory.
0956-5663/98/$—see front matter 1998 Elsevier Science S.A. All rights reserved. PII: S 0 9 5 6 - 5 6 6 3 ( 9 8 ) 0 0 0 1 5 - 3
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2. Methods In this section simulation tools are described that form the basis of the simulated experiments analysed in the Result section. We introduce here four tools, namely: 1. Two sets of differential equations to describe the generation of action potentials in Hodgkin–Huxley-type compartmental and bursting point-neurons. 2. A kinetic scheme to introduce chemical synapses into our model. 3. An equivalent circuit description of the coupling between one electrode and a few neurons, to simulate the signal trasduction operated by a planar microelectrode. 4. Signal processing algorithms selected to analyse planar electrode multichannel recordings and to characterize neural network dynamics. 2.1. Compartmental neuron A compartmental model of neurons is needed to characterize properly the neuron-to-electrode junction. The compartmental approach allows the simulation of the action potential propagation along arborised neurons, which is one of the main features to be taken into account in the neuron–electrode junction simulations (Grattarola and Martinoia, 1993). The model is based on the discretization of a neuron into isopotential compartments which have the same electrical properties (Segev et al., 1989). Various detailed neuronal models have been proposed in literature. They are based on already existing simulation programs or use ad hoc developed programs (De Schutter, 1989; Hines, 1989; Manor et al., 1991). On the basis of previous experience (Bove et al., 1994), we use here an alternative method based on the definition of electrical equivalent circuit models describing the different functional parts of a neuron, to be solved by using the electrical circuit analysis program SPICE (SPICE3F5 version) (Storace et al., 1997).
The equation used to describe the temporal evolution of the membrane potential is the following: CmdVi = dt
冘
Isyn,i,j − INa,i − IK,i − ICa,i − IKCa, − ICl,i i
J⫽i
(1) where Vi is the membrane potential of the neuron i; Cm = 1F/cm2 is the capacitance per unit area of the membrane; INa,i and IK,i are the sodium and potassium currents responsible for the action potential generation; ICa,i and IKCa, are the calcium current and the potassium i
current depending on calcium responsible for the generation of bursts of action potential; ICl,i is the chloride current; Isyn,i,j represents the ionic current generated by each presynaptic neuron j connected to neuron i. The effects of ionic fluctuations, both in the microenviroment surrounding a cultured neuron and in the channels kinetics, were also considered in the neuronal model. These effects were modelled by making the neuronal membrane potentials float in a Gaussian way around the resting potential. Thus, the neurons increased or decreased their sensibility to an external stimulus (e.g. local synaptic input) with time in a random fashion. Consequently, neurons could show a spontaneous activity (Chow and White, 1996). 2.3. Network of synaptically connected neurons A minimal two-state Markov model of a chemical synapse has been proposed in literature (Destexhe et al., 1994). The use of such a kinetic model to describe postsynaptic dynamics is a very effective and realistic alternative to the use of stereotyped waveforms (e.g. ␣functions), for the description of changes of the conductance of chemically-gated ionic channels. Synaptic interactions between the neurons of a network were modelled by a kinetic scheme for the binding of neurotransmitters to postsynaptic receptors. The fraction of postsynaptic receptors in the open state, m, obeyed the equation
2.2. Bursting point neuron The following model will be used in the results of Section 3 to simulate the behaviour of a network of DRG neurons. The functional state (i.e. resting/firing) of neurons, modelled by a single compartment of 1000 m2 for each neuron, is described by a set of differential equations based on a modification of the Hodgkin and Huxley (1952) model. The calcium current and the potassium current depending on calcium are added to the original model in order to obtain a model neuron showing both beating and bursting behaviours (Epstein and Marder, 1990; Bove et al., 1997).
dm = ␣[T](1 − m) − m dt
(2)
where [T] is the concentration of neurotransmitter in the synapse, and ␣ and  are the forward and backward binding rates, respectively. The neurotransmitter is released in a pulse (1 ms duration, 1 mM amplitude) when a presynaptic spike occurs. The synaptic currents are modelled by Isyn = gsynm(V − Esyn)
(3)
where gsyn is the maximal synaptic conductance. V and
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Fig. 1. Sketch of the coupling between a compartimentalized microelectrode and neurons. Rseal is the sealing resistance referred to a single cell; Rspread is the spreading resistance referred to one of the four compartments into which the microelectrode is split. The four compartments are connected by metallic resistances (Rmt) and the output signal is connected to an ideal amplifier. Rel and Cel are the equivalent capacitance and resistance of the electrolyte–microelectrode compartment interface.
Esyn are the membrane and synaptic reversal potentials, respectively. An useful feature of this modeling approach is that the synaptic events are represented by equations with the same structure as the Hodgkin and Huxley equations. Simulated experiments dealing with DRG neurons were performed by using networks consisting of twenty bursting point neurons, chemically connected in a random way, as explained in the Section 3.
2.4. Circuit model formulation of the coupling between an electrode and a few neurons The coupling strength beween a neuron and a planar microtransducer is a very critical parameter in determining the ‘quality’ (shape and amplitude) of a recorded signal. Equivalent circuits describing the interface between a neuron and a microtransducer have been already proposed in literature (Regehr et al., 1988;
Fig. 2. Sketch of the topography of the idealized network of neurons coupled to the microelectrode. All the neurons of the network were simulated by using a three-compartment model (see neuron 5 in detail). IHH represents the sum of the sodium and potassium currents related to Hodgkin and Huxley model equations; Rl and Vl are the leakage resistance and the leakage ion equilibrium potential, respectively; Cm is the cell membrane capacitance; Ri denotes the cytoplasmatic resistance connecting two adjacent compartments.
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Fromherz et al., 1991, 1993; Grattarola and Martinoia, 1993, Bove et al., 1995). They consisted of circuits describing the neuron-microtranducer coupling with a one-to-one correspondence. Unfortunately, this condition is very difficult to satisfy experimentally. Usually a few neurons (soma or neurites) are coupled to a single electrode and the recorded signal is a combination of signals coming from different neurons (Gross and Kowalski, 1991; Maeda et al., 1995). For this reason, we developed a circuit model able to take into account the presence of several neurons coupled to a single electrode in order to understand better the signal transduction operated by a microelectrode in a ‘realistic’ experimental condition (Gross and Kowalski, 1991; Maeda et al., 1995; Bove et al., 1997). A schematic of the circuit model representing the neurons-to-microelectrode junction is shown in Fig. 1. The microelectrode is split into compartments in order to follow the topography of the network and to take into account different coupling conditions between different portions of the electrode and the adhering neurons. The portions of the microelectrode are modelled by means
of RC parallel circuits (Rel, Cel) and they are connected together by small resistors (Rmt) which model the low resistivity of the metallic layer. The neurons-microtransducer coupling conditions are modelled by means of sealing resistances (Rseal) whose values depend on the distances between neurons and microelectrode and on the percentage of microelectrode area covered by the cells. Finally spreading resistances (Rspread) are used to connect the neurons-network to the appropriate portion of the microelectrode. 2.5. Multi-signal processing algorithms In this Section a description is given of the multi-signal processing algorithms used to analyse the signals resulting from simulated experiments. 2.5.1. Pre-processing technique A peak detection procedure is used to obtain the spike coordinates (i.e. occurrence and duration time and voltage amplitude). These coordinates then allow us to calculate the interspike interval, ISI, defined as the time
Fig. 3. (a) Simulated signals of the electrically connected neurons of the idealized network (gap junction conductance Gj = 10 000 pS) coupled to the microelectrode with different coupling strenghts (Rseal2 = 2M⍀; Rseal4 = 10M⍀; Rseal6 = 10M⍀; Rseal8 = 2M⍀). (b) Simulated signals of the electrically connected neurons of the idealized network in which neurons 5 and 9 were disconnected.
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Fig. 4. Simulation results of a recording from a local network characterized by (a) fast excitatory synapses (␣ = 3 ms−1 mM−1;  = 1 ms−1; Esyn = 30 mV; gsyn = 1 nS); (b) slow excitatory synapses (␣ = 1ms−1 mM−1;  = 0.1 ms−1; Esyn = 30 mV; gsyn = 2 nS).
interval between two successive spikes, to be used for the characterization of single neuron activity. A statistical analysis is performed as a pre-processing phase to extract the following parameters: mean firing rate (MFR) which can evidence possible changes in the bursting frequency as a function of synaptic strength, raw signal root mean square (RMS), noise band amplitude and ISI variance. 2.5.2. Identification and evaluation of bursting activity The different activities (periodic action potential bursting, not synchronized firing) of single neurons in a network were identified on the basis of the ISI variance. This algorithm processed the ISI data and calculated the variance, the difference between the maximum and minimum of the ISI data, and a ‘bin’ coefficient to estimate the bursting activity (Grattarola et al., 1997). Another relevant tool for bursting activity evaluation is the auto-correlation of the neuronal signals. This algorithm is able to extract the maximum information about the distribution of bursts. A transformation from a stochastic process (raw signals) to a renewal process, based on the ISI data, was performed allowing us to simplify the auto-correlation procedure (Papoulis, 1989).
2.5.3. Identification and evaluation of synchronized activity In order to identify and evaluate the synchronization of the activity among the neurons of a network, we assumed the neuronal signals as a stochastic random process. This assumption allowed us to process the data with the formula related to the cross-correlation function Rxy(), which gives information about the similarity between two signals as a function of the time lag . Rxy() = E{x(t)y(t − )}
(4)
As already effected in the auto-correlation algorithm, a transformation of the signals from a discrete random process into a renewal process based on the ISI data was carried out (Papoulis, 1989) in order to better interpret the signals.
3. Results In this Section we first predict the shape of signals recorded by a few planar microelectrodes as a function of the number of neurons coupled to them by using the
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3.1. Shape of the recorded signals
Fig. 5. Sketch of the three electrodes coupled to a network of chemically connected neurons.
compartmental circuit models simulated with SPICE3F5. Then, the appearence of synchronized bursting is detected in a network of simulated DRG neurons coupled to a planar microelectrode array under different conditions of the chemical microenvironment.
Fig. 2 shows an example of an idealized small network of neurons coupled to a planar microelectrode. This network connection scheme was used in the simulations for both electrically connected neurons and synaptically connected neurons. The dimensions of the electrode were 60 m × 60 m and the area of the three-compartment neurons was about 2800 m2. The compartment modelling approach was used to define the area of the neuron coupled to the microelectrode. For each coupled neuron a sealing resistance Rseali was defined. The developed computer simulations can be used to interpret the shape of actual recorded signals as a function of the coupling parameters (Rseal and Rspread) and of the synaptic transmission. 3.1.1. Signal trasduction by an electrode coupled to electrically connected neurons Electrical synaptic transmission is characterized by the absence of synaptic delay. Thus, the propagation of the signal between a neuron and its neighbourhood neu-
Fig. 6. Simulation results of the membrane potential and of the signal transduction operated by the three microelectrodes in the isolated neurons condition. (a) neuron n1 and microelectrode El1; (b) neurons n2, n3 and n4 and microelectrode El2; (c) neurons n5 and n6 and microelectrode El3.
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Changes in the shape of the signals transduced by the microelectrode were observed as a consequence of changes in the topography of the network, as shown in Fig. 3b, in which neurons 5 and 9 were disconnected.
Fig. 6.
Continued.
rons is immediate. In such conditions the synaptic transmission is modulated by the gap junction conductance (Gj) only, which allows a bidirectional transmission of the signal. Fig. 3a shows simulated signals when the neurons of the network were connected with Gj = 10 000 pS and they were coupled to the microelectrode with different coupling strenghts (Rseal2 = 2 M⍀; Rseal4 = 10 M⍀; Rseal6 = 10 M⍀; Rseal8 = 2 M⍀). The choice to define two different values for the coupling resistance refered to two different conditions of coupling to the electrode of the neurons 2, 4, 6 and 8 (completely and partially coupled) (Fig. 2) and the values defined for the simulations were obtained by the literature (Grattarola and Martinoia, 1993; Bove et al., 1995). As shown by Fig. 3, a large signal was obtained, resembling the third time derivative of an action potential (Grattarola and Martinoia, 1993). This result suggests that the absence of delay in the propagation of the action potential is transduced into a single large signal by the microelectrode. Similar signals were obtained, experimentally, by recording the electrical activity of populations of chick embryo cardiac cells, which are known to be connected by electrical synapses (Martinoia et al., 1993; Grattarola et al., 1995).
3.1.2. Signal trasduction by an electrode coupled to chemically connected neurons The same network was also analysed by connecting the neurons with excitatory chemical synapses. Chemical synapses are characterized by a synaptic delay of about 1 ms between the arrival of an impulse in the presynaptic terminal and the appearance of an electrical potential in the postsynaptic neuron. The delay is due to the time taken by the terminal to release the neurotransmitter. The release operation is modulated by different parameters such as the concentration of neurotransmitter in the synapse, the forward (␣) and backward () binding rates and the duration of neurotransmitter release. As shown in the Section 2, these parameters are present in our model and can be changed during the simulation phase. Only excitatory synapses were considered in the simulations, since they are known to be responsible for the generation of synchronized activity patterns (Robinson et al., 1993) and we were interested in simulating the recording operated by a microelectrode in the case of synchronized signals of neurons coupled to it. Fig. 4a shows a recording from the network characterized by fast excitatory synapses (␣ = 3 ms−1 mM−1;  = 1 ms−1; Esyn = 30 mV; gsyn = 1 nS). The coupling parameters were the same utilized in the electrically connected network. As indicated by Fig. 4a, there are several signals having a small amplitude when compared with those of Fig. 3, and with different shape. New small separated signals referring to single neuronal units were observed by replacing the fast excitatory synapses with slow excitatory synapses (␣ = 1 ms−1 mM−1;  = 0.1 ms−1; Esyn = 30 mV; gsyn = 2 nS) (Fig. 4b). These results suggest that the presence of synaptic delay makes the microelectrode able to record signals coming from different neuronal units coupled to it. 3.1.3. Three electrodes coupled to a network of chemically connected neurons The simulated experimental situation is shown in Fig. 5. In the simulations, three different network conditions were considered, namely: 쐌 isolated neurons condition; 쐌 locally connected neurons condition; 쐌 global connection condition. Fig. 6a, b and c shows the membrane potential of the neurons 1–6 and the signal transduction operated by the three microelectrodes in the isolated neurons condition, respectively. Uncorrelated small signals coming from different single units are observed. An increasing of the
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Fig. 7. Simulation results of the membrane potentials and of the signal transduction operated by two microelectrodes in the locally connected neurons condition. (a) neurons n2, n3 and n4 and microelectrode El2; (b) neurons n5 and n6 and microelectrode El3.
Fig. 8. Simulation results of the membrane potential and of the signal transduction operated by the three microelectrodes in the global connection condition.
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amplitude of the signals transduced by the three electrodes is observed when the neurons covering each microelectrode were connected, in a local way, by means of fast excitatory synapses (Fig. 7a and b). This is due to a partial and local synchronization among the neurons covering the same microelectrode. The coupling parameters were the same utilized in the electrically connected network. Fig. 8 shows the simulation results related to the case in which the groups of neurons coupled to the different microelectrodes were connected together by means of fast excitatory synapses, according to the scheme of Fig. 5. Attempts of local and global synchronization can be observed. 3.2. Simulated experiments dealing with DRG neurons In this Section an example of simulated experiment dealing with dorsal root ganglia (DRG) neurons is described and analysed in comparison with experimental results reported in the literature and obtained in our own laboratory. On the basis of the previous considerations of the signal transduction operated by a planar microelectrode and in order to appropriately simulate the output signals resulting from experiments utilising microelectrode arrays, the action potentials generated by the bursting point neuron model should be ‘corrupted’ into extracellularly recorded signals. In order to simplify the model, a one-to-one correspondence between neuron and electrode was chosen and the signals resulting from the model were filtered according to the constraints defined
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by the equivalent circuit of the neuron-to-electrode coupling impedance (Bove et al., 1995, 1997). Moreover, in order to make the simulated signals more realistic, they were also ‘corrupted’ by a Johnson noise, which represents the primary source of noise affecting the measurement (i.e. neuron–electrode interface) (Regehr et al., 1988). Synchronization as a function of the synaptic strength seems to be the main feature to be tracked in a multielectrode experiment. Several experiments based on the in vitro coupling of neurons to planar microelectrodes arrays suggest that synchronization of activity in networks of neurons can be considered as one of the elementary features at the basis of neurocomputation. This feature seems to be of relevance in the development of the nervous system (Meister et al., 1994; Goodman and Shatz, 1993; Kamioka et al., 1996) and it has been shown to happen in the form of synchronized bursting in in vitro neuronal networks generated by mammalian cortical and spinal cord neurons (Gross and Kowalski, 1991; Robinson et al., 1993; Maeda et al., 1995; Canepari et al., 1997). For this reason, only excitatory synapses were considered in our simulations, since they are responsible for the generation of synchronized activity patterns (Robinson et al., 1993; Maeda et al., 1995). Twenty bursting point neurons were randomly connected to form a network, so as to simulate an in vitro experiment dealing with microelectrode array recordings. Electrical activity in single neurons was driven by fluctuations in the membrane potentials, as described in the Section 2. During each simulation, the strength of the random
Fig. 9. Simulated responses of a neuron (arbitrarily chosen) of twenty neurons randomly connected in the five synaptic connection conditions.
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synaptic connections was initially set at zero and then allowed to increase in the sequence: 0, 0.05 ns, 0.1 ns, 1 ns and 3 ns. Fig. 9 shows a simulation result for one (arbitrarily chosen) of the twenty neurons belonging the network in the five synaptic connection conditions. The low synaptic connection is intended to simulate experimental situations in which the network is in an early stage of development and only few synapses are formed, or experimental situations in which an agent which reduces the network excitatory synaptic transmission, such as Mg + + , was added to the solution. It should be noted that in both simulation phases the neurons of the network do not appreciably influence each other and the network dynamics is dominated by a spontaneous and not synchronized firing activity. This activity is characterized by low values of the bursting evaluation parameter, of the cross-correlation coefficent and of the auto-correlation function (Fig. 10). The effect of an increase of the synaptic conductance
value on the network dynamics results into a transition towards a synchronized bursting state. This situation should simulate an experimental culture where the concentration of a reinforcing agent of the excitatory synaptic transmission was increased and/or the concentration of an inhibiting agent was decreased. This transition (see phase C in Fig. 9) is characterized by a relevant change in the bursting evaluation parameter (Fig. 10a) and by the appearance of a peak in the auto-correlation function (Fig. 10b). This peak supplies information concerning the interspike interval inside the burst. The maximum cross-correlation value is obtained for the higher synaptic connection condition (Fig. 10a). On the whole, the transition from a low synaptic connectivity to medium/high one is well identified by the changes in the bursting evaluation parameter and in the shape of the auto-correlation function. Bursting synchronization among the neurons of the network is well identified by the cross-correlation coefficient. Changes in the burst pattern as a function of a further
Fig. 10. (a) Bursting evaluation parameter and cross-correlation coefficient; (b) auto-correlation function evaluated for the different simulation phases (A corresponds to gsyn = 0.05 ns; B corresponds to gsyn = 0.05 nS; C corresponds to gsyn = 0.1 nS; D corresponds to gsyn = 1 nS; E corresponds to gsyn = 3 nS).
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increase in the synaptic strength could be observed for gsyn = 3 nS. As Fig. 9 (phase E) shows, this further increase in the synaptic strength results in an increase in burst duration, the number of spikes in a burst and the time lag between two bursts (interburts interval). These features are characterized by a decreasing of the peak value of the auto-correlation function corresponding to the presence of bursts with a variable number of spikes which occur with different timing.
4. Discussion and conclusions The vertebrate nervous system is made of thousands of millions of neurons, organized into a vast number of microcircuits. The technique of planar electrode arrays (PEA) gives for the first time the opportunity to study collective behaviours of in vitro constituted networks that somehow mimic some basic properties of in vivo neural circuits. This new fact, in turn, opens the door to the extensive use of simulated experiments, thus placing neuroscience research into a new perspective. As pointed out in Amit (1997), a simulated network is at the same time both a theoretical construct and also an empirical specimen on which simulation experiments can be performed to characterize its response, and then compared with real experiments, based on PEAs. The result is a continous positive feedback between simulated and real experiments. Our paper aimed at giving two specific contributions towards the improvement of such a feedback, namely: (a) A systematic analysis of the PEA-operated signal transduction under simulated situations resembling those described in the literature. (b) The generation of multichannel signals and of related processing algorithms appropriately tuned to reproduce experimental data and to suggest new experiments. Our simulations confirm the appropriteness of PEAbased measurements to track the time evolution of the dynamics of networks of neurons. Furthermore, they point out that, under experimental conditions in which a number of neurons is likely to cover a single electrode, the recorded signal represents a complex convolution of single neuron electrical activity which should be carefully analysed by means of appropriate software tools. We foresee that simulated experiments will become soon a standard tool in neuroscience research.
Acknowledgements Work supported by the Italian Ministry for University and Scientific and Technological Research (MURST), by
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the EU BIOMED 2 Programme (NESTING, Contract No. BMH4-CT97-2723) and by the University of Genoa.
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Analysis of the signals generated by networks of neurons coupled to planar arrays of microtransducers in simulated experiments M. Bove, S. Martinoia, G. Verreschi, M. Giugliano, M. Grattarola
*
Bioelectronics and Neurobioengineering Group, Department of Biophysical and Electronic Engineering, University of Genoa, Via Opera Pia 11a, I-16145, Genoa, Italy Received 29 October 1997; accepted 5 March 1998
Abstract Planar microelectrode arrays can be used to characterize the dynamics of networks of neurons reconstituted in vitro. In this paper simulations related to experiments of the electrical activity recording by means of planar arrays of microtransducers coupled to networks of neurons are described. First a detailed model of single and synaptically connected neurons is given, appropriate to computer simulate the action potentials of neuronal populations. Then ‘realistic’ signals are generated. These signals are intended to reproduce, both in shape and intensity, those recorded by a microelectrode array. Typical experimental conditions are considered, and a detailed analysis given, of the bioelectronic coupling and of its influence on the shape of the recorded signals. Finally, simulated experiments dealing with dorsal root ganglia neurons are described and analysed in comparison with experimental results reported in the literature and obtained in our own laboratory. The effectiveness of the planar microelectrode technique is briefly discussed. 1998 Elsevier Science S.A. All rights reserved. Keywords: In vitro networks of neurons; Planar microelectrode arrays; Neuron–electrode junction; Synaptic connections; Neuronal network dynamics; Simulated neuronal networks; Multi-signal processing tools
1. Introduction One of the main goals of neuroscience research is the understanding of the functional rules governing the behaviour of microcircuits in the vertebrate nervous system. Recent advances in cell and organotypic neuronal cultures allows the experimenter to create in vitro networks of neurons that represent rudimentary approximations of such microcircuits (Bulloch and Syed, 1992; Ga¨hwiler et al., 1997). Moreover, the electrophysiological technique based on the use of planar microelectrode arrays (Gross, 1979; Gross et al., 1985) can be used to characterize the dynamics of such networks (Maeda et al., 1995, Canepari et al., 1997). As a result, nowadays the neuroscience community has access to an increasing amount of long term multichannel recordings, obtained by in vitro coup-
* Corresponding author. Tel.: + 39-10-3532761; Fax: + 39-103532133; E-mail:[email protected]
ling networks of neurons to arrays of substrate planar microelectrodes. Elementary neurocomputational rules are hidden inside these long-term multichannel recordings and a powerful tool to decipher them is provided by the extensive use of simulated experiments, along a scientific tradition already well developed in several branches of physics (Amit, 1989). Specific simulated experiments will be described in the following: first, a detailed model of single and synaptically connected neurons will be described, appropriate computer simulate the action potentials of neuronal populations. Then ‘realistic’ signals will be generated. These signals are intended to reproduce, both in shape and intensity, those recorded by a microelectrode array. Typical experimental conditions will be considered and a detailed analysis will be given, of the bioelectronic coupling and of its influence on the shape of the recorded signals. Finally, simulated experiments dealing with dorsal root ganglia (DRG) neurons will be described and analysed in comparison with experimental results reported in the literature and obtained in our own laboratory.
0956-5663/98/$—see front matter 1998 Elsevier Science S.A. All rights reserved. PII: S 0 9 5 6 - 5 6 6 3 ( 9 8 ) 0 0 0 1 5 - 3
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2. Methods In this section simulation tools are described that form the basis of the simulated experiments analysed in the Result section. We introduce here four tools, namely: 1. Two sets of differential equations to describe the generation of action potentials in Hodgkin–Huxley-type compartmental and bursting point-neurons. 2. A kinetic scheme to introduce chemical synapses into our model. 3. An equivalent circuit description of the coupling between one electrode and a few neurons, to simulate the signal trasduction operated by a planar microelectrode. 4. Signal processing algorithms selected to analyse planar electrode multichannel recordings and to characterize neural network dynamics. 2.1. Compartmental neuron A compartmental model of neurons is needed to characterize properly the neuron-to-electrode junction. The compartmental approach allows the simulation of the action potential propagation along arborised neurons, which is one of the main features to be taken into account in the neuron–electrode junction simulations (Grattarola and Martinoia, 1993). The model is based on the discretization of a neuron into isopotential compartments which have the same electrical properties (Segev et al., 1989). Various detailed neuronal models have been proposed in literature. They are based on already existing simulation programs or use ad hoc developed programs (De Schutter, 1989; Hines, 1989; Manor et al., 1991). On the basis of previous experience (Bove et al., 1994), we use here an alternative method based on the definition of electrical equivalent circuit models describing the different functional parts of a neuron, to be solved by using the electrical circuit analysis program SPICE (SPICE3F5 version) (Storace et al., 1997).
The equation used to describe the temporal evolution of the membrane potential is the following: CmdVi = dt
冘
Isyn,i,j − INa,i − IK,i − ICa,i − IKCa, − ICl,i i
J⫽i
(1) where Vi is the membrane potential of the neuron i; Cm = 1F/cm2 is the capacitance per unit area of the membrane; INa,i and IK,i are the sodium and potassium currents responsible for the action potential generation; ICa,i and IKCa, are the calcium current and the potassium i
current depending on calcium responsible for the generation of bursts of action potential; ICl,i is the chloride current; Isyn,i,j represents the ionic current generated by each presynaptic neuron j connected to neuron i. The effects of ionic fluctuations, both in the microenviroment surrounding a cultured neuron and in the channels kinetics, were also considered in the neuronal model. These effects were modelled by making the neuronal membrane potentials float in a Gaussian way around the resting potential. Thus, the neurons increased or decreased their sensibility to an external stimulus (e.g. local synaptic input) with time in a random fashion. Consequently, neurons could show a spontaneous activity (Chow and White, 1996). 2.3. Network of synaptically connected neurons A minimal two-state Markov model of a chemical synapse has been proposed in literature (Destexhe et al., 1994). The use of such a kinetic model to describe postsynaptic dynamics is a very effective and realistic alternative to the use of stereotyped waveforms (e.g. ␣functions), for the description of changes of the conductance of chemically-gated ionic channels. Synaptic interactions between the neurons of a network were modelled by a kinetic scheme for the binding of neurotransmitters to postsynaptic receptors. The fraction of postsynaptic receptors in the open state, m, obeyed the equation
2.2. Bursting point neuron The following model will be used in the results of Section 3 to simulate the behaviour of a network of DRG neurons. The functional state (i.e. resting/firing) of neurons, modelled by a single compartment of 1000 m2 for each neuron, is described by a set of differential equations based on a modification of the Hodgkin and Huxley (1952) model. The calcium current and the potassium current depending on calcium are added to the original model in order to obtain a model neuron showing both beating and bursting behaviours (Epstein and Marder, 1990; Bove et al., 1997).
dm = ␣[T](1 − m) − m dt
(2)
where [T] is the concentration of neurotransmitter in the synapse, and ␣ and  are the forward and backward binding rates, respectively. The neurotransmitter is released in a pulse (1 ms duration, 1 mM amplitude) when a presynaptic spike occurs. The synaptic currents are modelled by Isyn = gsynm(V − Esyn)
(3)
where gsyn is the maximal synaptic conductance. V and
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Fig. 1. Sketch of the coupling between a compartimentalized microelectrode and neurons. Rseal is the sealing resistance referred to a single cell; Rspread is the spreading resistance referred to one of the four compartments into which the microelectrode is split. The four compartments are connected by metallic resistances (Rmt) and the output signal is connected to an ideal amplifier. Rel and Cel are the equivalent capacitance and resistance of the electrolyte–microelectrode compartment interface.
Esyn are the membrane and synaptic reversal potentials, respectively. An useful feature of this modeling approach is that the synaptic events are represented by equations with the same structure as the Hodgkin and Huxley equations. Simulated experiments dealing with DRG neurons were performed by using networks consisting of twenty bursting point neurons, chemically connected in a random way, as explained in the Section 3.
2.4. Circuit model formulation of the coupling between an electrode and a few neurons The coupling strength beween a neuron and a planar microtransducer is a very critical parameter in determining the ‘quality’ (shape and amplitude) of a recorded signal. Equivalent circuits describing the interface between a neuron and a microtransducer have been already proposed in literature (Regehr et al., 1988;
Fig. 2. Sketch of the topography of the idealized network of neurons coupled to the microelectrode. All the neurons of the network were simulated by using a three-compartment model (see neuron 5 in detail). IHH represents the sum of the sodium and potassium currents related to Hodgkin and Huxley model equations; Rl and Vl are the leakage resistance and the leakage ion equilibrium potential, respectively; Cm is the cell membrane capacitance; Ri denotes the cytoplasmatic resistance connecting two adjacent compartments.
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Fromherz et al., 1991, 1993; Grattarola and Martinoia, 1993, Bove et al., 1995). They consisted of circuits describing the neuron-microtranducer coupling with a one-to-one correspondence. Unfortunately, this condition is very difficult to satisfy experimentally. Usually a few neurons (soma or neurites) are coupled to a single electrode and the recorded signal is a combination of signals coming from different neurons (Gross and Kowalski, 1991; Maeda et al., 1995). For this reason, we developed a circuit model able to take into account the presence of several neurons coupled to a single electrode in order to understand better the signal transduction operated by a microelectrode in a ‘realistic’ experimental condition (Gross and Kowalski, 1991; Maeda et al., 1995; Bove et al., 1997). A schematic of the circuit model representing the neurons-to-microelectrode junction is shown in Fig. 1. The microelectrode is split into compartments in order to follow the topography of the network and to take into account different coupling conditions between different portions of the electrode and the adhering neurons. The portions of the microelectrode are modelled by means
of RC parallel circuits (Rel, Cel) and they are connected together by small resistors (Rmt) which model the low resistivity of the metallic layer. The neurons-microtransducer coupling conditions are modelled by means of sealing resistances (Rseal) whose values depend on the distances between neurons and microelectrode and on the percentage of microelectrode area covered by the cells. Finally spreading resistances (Rspread) are used to connect the neurons-network to the appropriate portion of the microelectrode. 2.5. Multi-signal processing algorithms In this Section a description is given of the multi-signal processing algorithms used to analyse the signals resulting from simulated experiments. 2.5.1. Pre-processing technique A peak detection procedure is used to obtain the spike coordinates (i.e. occurrence and duration time and voltage amplitude). These coordinates then allow us to calculate the interspike interval, ISI, defined as the time
Fig. 3. (a) Simulated signals of the electrically connected neurons of the idealized network (gap junction conductance Gj = 10 000 pS) coupled to the microelectrode with different coupling strenghts (Rseal2 = 2M⍀; Rseal4 = 10M⍀; Rseal6 = 10M⍀; Rseal8 = 2M⍀). (b) Simulated signals of the electrically connected neurons of the idealized network in which neurons 5 and 9 were disconnected.
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Fig. 4. Simulation results of a recording from a local network characterized by (a) fast excitatory synapses (␣ = 3 ms−1 mM−1;  = 1 ms−1; Esyn = 30 mV; gsyn = 1 nS); (b) slow excitatory synapses (␣ = 1ms−1 mM−1;  = 0.1 ms−1; Esyn = 30 mV; gsyn = 2 nS).
interval between two successive spikes, to be used for the characterization of single neuron activity. A statistical analysis is performed as a pre-processing phase to extract the following parameters: mean firing rate (MFR) which can evidence possible changes in the bursting frequency as a function of synaptic strength, raw signal root mean square (RMS), noise band amplitude and ISI variance. 2.5.2. Identification and evaluation of bursting activity The different activities (periodic action potential bursting, not synchronized firing) of single neurons in a network were identified on the basis of the ISI variance. This algorithm processed the ISI data and calculated the variance, the difference between the maximum and minimum of the ISI data, and a ‘bin’ coefficient to estimate the bursting activity (Grattarola et al., 1997). Another relevant tool for bursting activity evaluation is the auto-correlation of the neuronal signals. This algorithm is able to extract the maximum information about the distribution of bursts. A transformation from a stochastic process (raw signals) to a renewal process, based on the ISI data, was performed allowing us to simplify the auto-correlation procedure (Papoulis, 1989).
2.5.3. Identification and evaluation of synchronized activity In order to identify and evaluate the synchronization of the activity among the neurons of a network, we assumed the neuronal signals as a stochastic random process. This assumption allowed us to process the data with the formula related to the cross-correlation function Rxy(), which gives information about the similarity between two signals as a function of the time lag . Rxy() = E{x(t)y(t − )}
(4)
As already effected in the auto-correlation algorithm, a transformation of the signals from a discrete random process into a renewal process based on the ISI data was carried out (Papoulis, 1989) in order to better interpret the signals.
3. Results In this Section we first predict the shape of signals recorded by a few planar microelectrodes as a function of the number of neurons coupled to them by using the
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3.1. Shape of the recorded signals
Fig. 5. Sketch of the three electrodes coupled to a network of chemically connected neurons.
compartmental circuit models simulated with SPICE3F5. Then, the appearence of synchronized bursting is detected in a network of simulated DRG neurons coupled to a planar microelectrode array under different conditions of the chemical microenvironment.
Fig. 2 shows an example of an idealized small network of neurons coupled to a planar microelectrode. This network connection scheme was used in the simulations for both electrically connected neurons and synaptically connected neurons. The dimensions of the electrode were 60 m × 60 m and the area of the three-compartment neurons was about 2800 m2. The compartment modelling approach was used to define the area of the neuron coupled to the microelectrode. For each coupled neuron a sealing resistance Rseali was defined. The developed computer simulations can be used to interpret the shape of actual recorded signals as a function of the coupling parameters (Rseal and Rspread) and of the synaptic transmission. 3.1.1. Signal trasduction by an electrode coupled to electrically connected neurons Electrical synaptic transmission is characterized by the absence of synaptic delay. Thus, the propagation of the signal between a neuron and its neighbourhood neu-
Fig. 6. Simulation results of the membrane potential and of the signal transduction operated by the three microelectrodes in the isolated neurons condition. (a) neuron n1 and microelectrode El1; (b) neurons n2, n3 and n4 and microelectrode El2; (c) neurons n5 and n6 and microelectrode El3.
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Changes in the shape of the signals transduced by the microelectrode were observed as a consequence of changes in the topography of the network, as shown in Fig. 3b, in which neurons 5 and 9 were disconnected.
Fig. 6.
Continued.
rons is immediate. In such conditions the synaptic transmission is modulated by the gap junction conductance (Gj) only, which allows a bidirectional transmission of the signal. Fig. 3a shows simulated signals when the neurons of the network were connected with Gj = 10 000 pS and they were coupled to the microelectrode with different coupling strenghts (Rseal2 = 2 M⍀; Rseal4 = 10 M⍀; Rseal6 = 10 M⍀; Rseal8 = 2 M⍀). The choice to define two different values for the coupling resistance refered to two different conditions of coupling to the electrode of the neurons 2, 4, 6 and 8 (completely and partially coupled) (Fig. 2) and the values defined for the simulations were obtained by the literature (Grattarola and Martinoia, 1993; Bove et al., 1995). As shown by Fig. 3, a large signal was obtained, resembling the third time derivative of an action potential (Grattarola and Martinoia, 1993). This result suggests that the absence of delay in the propagation of the action potential is transduced into a single large signal by the microelectrode. Similar signals were obtained, experimentally, by recording the electrical activity of populations of chick embryo cardiac cells, which are known to be connected by electrical synapses (Martinoia et al., 1993; Grattarola et al., 1995).
3.1.2. Signal trasduction by an electrode coupled to chemically connected neurons The same network was also analysed by connecting the neurons with excitatory chemical synapses. Chemical synapses are characterized by a synaptic delay of about 1 ms between the arrival of an impulse in the presynaptic terminal and the appearance of an electrical potential in the postsynaptic neuron. The delay is due to the time taken by the terminal to release the neurotransmitter. The release operation is modulated by different parameters such as the concentration of neurotransmitter in the synapse, the forward (␣) and backward () binding rates and the duration of neurotransmitter release. As shown in the Section 2, these parameters are present in our model and can be changed during the simulation phase. Only excitatory synapses were considered in the simulations, since they are known to be responsible for the generation of synchronized activity patterns (Robinson et al., 1993) and we were interested in simulating the recording operated by a microelectrode in the case of synchronized signals of neurons coupled to it. Fig. 4a shows a recording from the network characterized by fast excitatory synapses (␣ = 3 ms−1 mM−1;  = 1 ms−1; Esyn = 30 mV; gsyn = 1 nS). The coupling parameters were the same utilized in the electrically connected network. As indicated by Fig. 4a, there are several signals having a small amplitude when compared with those of Fig. 3, and with different shape. New small separated signals referring to single neuronal units were observed by replacing the fast excitatory synapses with slow excitatory synapses (␣ = 1 ms−1 mM−1;  = 0.1 ms−1; Esyn = 30 mV; gsyn = 2 nS) (Fig. 4b). These results suggest that the presence of synaptic delay makes the microelectrode able to record signals coming from different neuronal units coupled to it. 3.1.3. Three electrodes coupled to a network of chemically connected neurons The simulated experimental situation is shown in Fig. 5. In the simulations, three different network conditions were considered, namely: 쐌 isolated neurons condition; 쐌 locally connected neurons condition; 쐌 global connection condition. Fig. 6a, b and c shows the membrane potential of the neurons 1–6 and the signal transduction operated by the three microelectrodes in the isolated neurons condition, respectively. Uncorrelated small signals coming from different single units are observed. An increasing of the
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Fig. 7. Simulation results of the membrane potentials and of the signal transduction operated by two microelectrodes in the locally connected neurons condition. (a) neurons n2, n3 and n4 and microelectrode El2; (b) neurons n5 and n6 and microelectrode El3.
Fig. 8. Simulation results of the membrane potential and of the signal transduction operated by the three microelectrodes in the global connection condition.
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amplitude of the signals transduced by the three electrodes is observed when the neurons covering each microelectrode were connected, in a local way, by means of fast excitatory synapses (Fig. 7a and b). This is due to a partial and local synchronization among the neurons covering the same microelectrode. The coupling parameters were the same utilized in the electrically connected network. Fig. 8 shows the simulation results related to the case in which the groups of neurons coupled to the different microelectrodes were connected together by means of fast excitatory synapses, according to the scheme of Fig. 5. Attempts of local and global synchronization can be observed. 3.2. Simulated experiments dealing with DRG neurons In this Section an example of simulated experiment dealing with dorsal root ganglia (DRG) neurons is described and analysed in comparison with experimental results reported in the literature and obtained in our own laboratory. On the basis of the previous considerations of the signal transduction operated by a planar microelectrode and in order to appropriately simulate the output signals resulting from experiments utilising microelectrode arrays, the action potentials generated by the bursting point neuron model should be ‘corrupted’ into extracellularly recorded signals. In order to simplify the model, a one-to-one correspondence between neuron and electrode was chosen and the signals resulting from the model were filtered according to the constraints defined
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by the equivalent circuit of the neuron-to-electrode coupling impedance (Bove et al., 1995, 1997). Moreover, in order to make the simulated signals more realistic, they were also ‘corrupted’ by a Johnson noise, which represents the primary source of noise affecting the measurement (i.e. neuron–electrode interface) (Regehr et al., 1988). Synchronization as a function of the synaptic strength seems to be the main feature to be tracked in a multielectrode experiment. Several experiments based on the in vitro coupling of neurons to planar microelectrodes arrays suggest that synchronization of activity in networks of neurons can be considered as one of the elementary features at the basis of neurocomputation. This feature seems to be of relevance in the development of the nervous system (Meister et al., 1994; Goodman and Shatz, 1993; Kamioka et al., 1996) and it has been shown to happen in the form of synchronized bursting in in vitro neuronal networks generated by mammalian cortical and spinal cord neurons (Gross and Kowalski, 1991; Robinson et al., 1993; Maeda et al., 1995; Canepari et al., 1997). For this reason, only excitatory synapses were considered in our simulations, since they are responsible for the generation of synchronized activity patterns (Robinson et al., 1993; Maeda et al., 1995). Twenty bursting point neurons were randomly connected to form a network, so as to simulate an in vitro experiment dealing with microelectrode array recordings. Electrical activity in single neurons was driven by fluctuations in the membrane potentials, as described in the Section 2. During each simulation, the strength of the random
Fig. 9. Simulated responses of a neuron (arbitrarily chosen) of twenty neurons randomly connected in the five synaptic connection conditions.
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synaptic connections was initially set at zero and then allowed to increase in the sequence: 0, 0.05 ns, 0.1 ns, 1 ns and 3 ns. Fig. 9 shows a simulation result for one (arbitrarily chosen) of the twenty neurons belonging the network in the five synaptic connection conditions. The low synaptic connection is intended to simulate experimental situations in which the network is in an early stage of development and only few synapses are formed, or experimental situations in which an agent which reduces the network excitatory synaptic transmission, such as Mg + + , was added to the solution. It should be noted that in both simulation phases the neurons of the network do not appreciably influence each other and the network dynamics is dominated by a spontaneous and not synchronized firing activity. This activity is characterized by low values of the bursting evaluation parameter, of the cross-correlation coefficent and of the auto-correlation function (Fig. 10). The effect of an increase of the synaptic conductance
value on the network dynamics results into a transition towards a synchronized bursting state. This situation should simulate an experimental culture where the concentration of a reinforcing agent of the excitatory synaptic transmission was increased and/or the concentration of an inhibiting agent was decreased. This transition (see phase C in Fig. 9) is characterized by a relevant change in the bursting evaluation parameter (Fig. 10a) and by the appearance of a peak in the auto-correlation function (Fig. 10b). This peak supplies information concerning the interspike interval inside the burst. The maximum cross-correlation value is obtained for the higher synaptic connection condition (Fig. 10a). On the whole, the transition from a low synaptic connectivity to medium/high one is well identified by the changes in the bursting evaluation parameter and in the shape of the auto-correlation function. Bursting synchronization among the neurons of the network is well identified by the cross-correlation coefficient. Changes in the burst pattern as a function of a further
Fig. 10. (a) Bursting evaluation parameter and cross-correlation coefficient; (b) auto-correlation function evaluated for the different simulation phases (A corresponds to gsyn = 0.05 ns; B corresponds to gsyn = 0.05 nS; C corresponds to gsyn = 0.1 nS; D corresponds to gsyn = 1 nS; E corresponds to gsyn = 3 nS).
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increase in the synaptic strength could be observed for gsyn = 3 nS. As Fig. 9 (phase E) shows, this further increase in the synaptic strength results in an increase in burst duration, the number of spikes in a burst and the time lag between two bursts (interburts interval). These features are characterized by a decreasing of the peak value of the auto-correlation function corresponding to the presence of bursts with a variable number of spikes which occur with different timing.
4. Discussion and conclusions The vertebrate nervous system is made of thousands of millions of neurons, organized into a vast number of microcircuits. The technique of planar electrode arrays (PEA) gives for the first time the opportunity to study collective behaviours of in vitro constituted networks that somehow mimic some basic properties of in vivo neural circuits. This new fact, in turn, opens the door to the extensive use of simulated experiments, thus placing neuroscience research into a new perspective. As pointed out in Amit (1997), a simulated network is at the same time both a theoretical construct and also an empirical specimen on which simulation experiments can be performed to characterize its response, and then compared with real experiments, based on PEAs. The result is a continous positive feedback between simulated and real experiments. Our paper aimed at giving two specific contributions towards the improvement of such a feedback, namely: (a) A systematic analysis of the PEA-operated signal transduction under simulated situations resembling those described in the literature. (b) The generation of multichannel signals and of related processing algorithms appropriately tuned to reproduce experimental data and to suggest new experiments. Our simulations confirm the appropriteness of PEAbased measurements to track the time evolution of the dynamics of networks of neurons. Furthermore, they point out that, under experimental conditions in which a number of neurons is likely to cover a single electrode, the recorded signal represents a complex convolution of single neuron electrical activity which should be carefully analysed by means of appropriate software tools. We foresee that simulated experiments will become soon a standard tool in neuroscience research.
Acknowledgements Work supported by the Italian Ministry for University and Scientific and Technological Research (MURST), by
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the EU BIOMED 2 Programme (NESTING, Contract No. BMH4-CT97-2723) and by the University of Genoa.
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