Networks of cortical neurons were grown over multi electrode arrays to enable simultaneous measu-rement of action potentials from 60 electrodes. All possible pairs of electrodes (i,j) were tested for syn-chronized activity. We calculated conditional firing probability (CFPi,j[τ]) as the probability of an action potential at electrode j at t=τ, given that a spike was detected at i at t=0. If a CFPi,j[τ] distribution clearly deviated from flat, electrodes i and j were considered related. A function was fitted to each CFP-curve to obtain parameters for strength and delay. In young cultures the set of identified relationships changed rather quickly. At 16 days in vitro (DIV) 50% of the set changed within one day. Beyond 25 DIV this set stabilized: during a period of a week more than 50% of the set remained intact. Most individual relationships developed rather gradually. Moreover, beyond 25 DIV relational strength appeared quite stable during periods of ≈ 10 hours, with coefficients of variation (100×SD/mean) of ≈ 25% on average. CFP analysis provides a robust method to describe the stable underlying probabilistic structure of highly varying spontaneous activity in cultured cortical networks. It may offer a suitable basis for plasticity studies, in which induced changes should exceed spontaneous fluctuations. CFP analysis is likely to describe the network in sufficient detail to detect subtle changes in individual relationships. Analysis of data continuously recorded for ≈ 6 weeks, showed that highest stability is reached after ≈ 25 DIV, suggesting the 4th and 5th week as a suitable period for plasticity studies.\ud
\u

le Feber, Jakob

Ramakers, Ger

Rutten, Wim

Stegenga, J.

Stett, A

van Pelt, Jaap

Wolters, Pieter

English

Networks of cortical neurons were grown over multi electrode arrays to enable simultaneous measu-rement of action potentials from 60 electrodes. All possible pairs of electrodes (i,j) were tested for syn-chronized activity. We calculated conditional firing probability (CFPi,j[τ]) as the probability of an action potential at electrode j at t=τ, given that a spike was detected at i at t=0. If a CFPi,j[τ] distribution clearly deviated from flat, electrodes i and j were considered related. A function was fitted to each CFP-curve to obtain parameters for strength and delay. In young cultures the set of identified relationships changed rather quickly. At 16 days in vitro (DIV) 50% of the set changed within one day. Beyond 25 DIV this set stabilized: during a period of a week more than 50% of the set remained intact. Most individual relationships developed rather gradually. Moreover, beyond 25 DIV relational strength appeared quite stable during periods of ≈ 10 hours, with coefficients of variation (100×SD/mean) of ≈ 25% on average. CFP analysis provides a robust method to describe the stable underlying probabilistic structure of highly varying spontaneous activity in cultured cortical networks. It may offer a suitable basis for plasticity studies, in which induced changes should exceed spontaneous fluctuations. CFP analysis is likely to describe the network in sufficient detail to detect subtle changes in individual relationships. Analysis of data continuously recorded for ≈ 6 weeks, showed that highest stability is reached after ≈ 25 DIV, suggesting the 4th and 5th week as a suitable period for plasticity studies

NARCIS 

Cultured cortical networks described by conditional firing probabilities

University of Twente Research Information

 ISBN XXX 5th Int. Meeting on Substrate-Integrated Microelectrodes, 2006 1 Cultured cortical networks described by conditional firing probabilities Joost le Feber1*, Wim Rutten1, Jan Stegenga1, Pieter Wolters2, Ger Ramakers2, Jaap van Pelt2 1  Biomedical Signal and Systems Group, Department of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, the Netherlands 2  Netherlands Institute for Neurosciences, Meibergdreef 33, 1105 AZ, Amsterdam, the Netherlands  *  Corresponding author. E-mail address: j.lefeber@utwente.nl Abstract Networks of cortical neurons were grown over multi electrode arrays to enable simultaneous measu-rement of action potentials from 60 electrodes. All possible pairs of electrodes (i,j) were tested for syn-chronized activity. We calculated conditional firing probability (CFPi,j[τ]) as the probability of an action potential at electrode j at t=τ, given that a spike was detected at i at t=0. If a CFPi,j[τ] distribution clearly deviated from flat, electrodes i and j were considered related. A function was fitted to each CFP-curve to obtain parameters for strength and delay.  In young cultures the set of identified relationships changed rather quickly. At 16 days in vitro (DIV) 50% of the set changed within one day. Beyond 25 DIV this set stabilized: during a period of a week more than 50% of the set remained intact. Most individual relationships developed rather gradually. Moreover, beyond 25 DIV relational strength appeared quite stable during periods of ≈ 10 hours, with coefficients of variation (100×SD/mean) of ≈ 25% on average.  CFP analysis provides a robust method to describe the stable underlying probabilistic structure of highly varying spontaneous activity in cultured cortical networks. It may offer a suitable basis for plasticity studies, in which induced changes should exceed spontaneous fluctuations. CFP analysis is likely to describe the network in sufficient detail to detect subtle changes in individual relationships.  Analysis of data continuously recorded for ≈ 6 weeks, showed that highest stability is reached after ≈ 25 DIV, suggesting the 4th and 5th week as a suitable period for plasticity studies.  1 Introduction To demonstrate learning or memory in cultured neu-ronal networks one needs to monitor connections between neurons. Most learning studies used elec-trical stimulation to induce connectivity changes in networks [1, 2]. One of the problems is that sponta-neous network activity may mask, or even cancel out induced alterations [3]. Networks may be characterized by ‘functional con-nections’ between pairs of electrodes: abstract rep-resentations of possibly parallel neuronal pathways between attached neurons [4, 5]. Various techniques have been developed to identify such connections, most of which are based on or related to cross-correlation analysis [4-6]. We developed a method to describe functional connections between all pairs of active electrodes in neuronal networks. The method estimates conditional firing probabilities to calculate parameters for strength and delay in rela-tionships between electrodes.  These relationships will serve to provide a stable underlying probabilis-tic structure in widely varying patterns of spontane-ous activity, which may facilitate demonstration of learning or memory. 2  Methods Networks of cortical neurons (cells obtained from 9 fetal or newborn Wistar rats) were grown over multi electrode arrays to enable simultaneous measure-ment of action potentials from 60 electrodes. All possible pairs of electrodes (i,j) were tested for syn-chronized activity. We calculated the conditional firing probability (CFPi,j[τ]) as the incidence of an action potential at electrode j at delay τ (0 ≤ τ ≤ 500 ms) after a spike at electrode i, divided by the total number of action potentials at i.  To analyze the measured signals, binary arrays Xi were constructed with as many data points as the sampled signals; Xi[n] = 1 at a detected action po-tential and Xi[n] = 0 elsewhere.  The number of action potentials at electrode i that is followed by a spike at j with a delay τ (Nfollow i,j[τ]) is now calculated as:    (1) Equation 1 holds because it is applied to binary ar-rays Xi,j, with Xi,j[n] ∈  {0,1} for all n. CFP[τ] can ∑ +⋅= ][][][, ττ tXtXN jijifollow   ISBN XXXX 2 5th Int. Meeting on Substrate-Integrated Microelectrodes, 2006 be calculated by dividing Nfollow[τ] by the total num-ber of action potentials at electrode i ( Ni):           It may be noted that CFPi,j[τ] is a measure related to cross-correlation (Ri,j[τ]):      If CFPi,j[τ] showed a distribution that clearly devi-ated from flat, electrodes i and j were considered related. Figure 1 shows an example.           Equation 4 was fitted to the shape of the CFP curve.      (4)   Mi,j and Ti,j were interpreted as measures for strength and delay of the relationships. We con-structed 2 matrices M and T, containing all parame-ters Mi,j and Ti,j  to describe the whole network.  We investigated the stability of the set of relationships in a network and the stability of strength and delay of individual relationships.  To asses the stability of the set of relationships, we divided long term recordings into data blocks with a fixed number of action potentials (33000) and we calculated M matrices for each data block. All non-zero elements in M represented an identified rela-tionship. Similarity between two data blocks (Si) was calculated as the number of relationships that were found in both blocks, divided by the product of the number of relationships in data block A and data block B. To obtain a balanced expression the denominator was squared. Finally, we took the square root of this fraction:    Consecutively, we calculated similarity indices be-tween each possible reference block and all data blocks. Three examples of thus obtained curves are shown in Figure 2. All curves showed a maximum at the location of the reference block, and decreased in both directions. We defined int50 as the interval around a reference block with >50% of the set of relations intact. Figure 2B shows the development over time of the length of this interval. Additionally, we grouped the data blocks into series of 15 consecutive blocks. For all relationships that were found in more than 50% of the blocks in a se-ries, we calculated the coefficients of variation (100×SD/mean) of Mi,j and Ti,j.   00.00120 500        jijijijiji offsetwTMCFP ,2,,,,)(1)( +−+= ττsec5000][][][][ ,, mtXtXtXNNCFPtitjiifollowjiji ≤<+⋅==∑∑τττ (2)Fig. 1. Example of a conditional firing probability curve, calcula-ted using Equation 2. Fitting Equation 4 yields maximum CFP(Mi,j=4.5·10-3) and delay until this maximum (Ti,j=29ms). Means ± SD of 10 consecutive values from 0.5 ms bins are shown, data wasrecorded at 10 DIV. The maximum probability may seem extreme-ly small. However, this is the  probability to record a spike in a 0.5ms interval. In the above figure, the probability to record a spike atelectrode j within 50 ms after an action potential at electrode i canbe estimated as  ≈ 2×50×0.004=0.4. { } { }{ } { }0000 2≠⋅≠≠≠=BABAMMMMSiIFig. 2.  Development of similarity indices. A: typical example of a long term recording, divided into 772 data blocks. Successively, similarity indices (Si, Eq. 5) were calculated for all blocks, using three reference blocks: 16 DIV (Δ), 27 DIV (○), and 35 DIV (□). Similar graphs were constructed using all other data blocks as a reference. Curves were smoothed using a 5th order moving avera-ge filter (not shown). Then, we determined Int50: the duration of the interval around each reference point, in which 50% of the set of relations remained intact (Si remained above 0.5). For each culture Int50 was averaged per day. B: Averaged graph for all cultures. Standard deviations refer to differences between cultu-res. Beyond 35 DIV, in two or more cultures the 50% intact inter-val could not be determined because the end of the long term re-cording was reached before Si dropped below 0.5. The increase beyond 25 DIV was significant (ANOVA, p<0.01).  (5)∑=+=Ntjiji tXtXNR1, ][][1][ ττ  (3) 03691 21 57 1 4 2 1 2 8 3 5 4 2A B Time [DIV] Int50 [days] Si Int50 0.001.007 14 21 28 35 42Conditional firing probability Ti,j τ [ms] 0.006 Mi,j  5th Int. Meeting on Substrate-Integrated Microelectrodes, 2006 3 In each series these coefficients of variation were averaged to obtain a measure for stability in that se-ries: CVM and CVT.  3  Results CFP curves The vast majority of the non-flat relationships in all 9 cultures could be adequately described by Equati-on 4. Relationships differed widely in both strength and delay. Mi,j ranged from 6·10-6 to 6.8·10-2 (appro-ximately following a negative exponential distribu-tion and averaging (1.0±1.1)·10-3). We found Ti,j va-lues between 0 and 250 ms, more than 98% of which were below 100ms. Figure 1 shows an e-xample. Stability Long term recordings from four cultures were in-vestigated for stability. In young cultures the set of identified relationships changed rather quickly. At 16 days in vitro (DIV) 50% of the set changed within one day on average. Beyond 25 DIV this set stabilized: during a period of a week more than 50% of the set remained unchanged (See Figure 2B).                                  Most individual relationships showed a rather grad-ual development on a time scale of days, Figure 3 shows two examples. Moreover, beyond 25 DIV relational strength appeared quite stable during measurement series of 15 data blocks (≈ 10 hours), with coefficients of variation around 25% on aver-age (see Figure 4).                                 CVM was calculated from the set of relations that were found in at least 50% of the data blocks in a series. The size of this set averaged 54% of the total number of relationships that could be analysed.  CVT showed much larger values than CVM, often more than 100%. CVT also tended to decrease with aging of the culture, but this decrease was not sig-nificant.  4  Discussion CFP analysis provides a robust method to describe the stable underlying probabilistic structure of highly varying spontaneous activity in cultured net-works of cortical neurons. The set of identified rela-tionships appeared quite stable. Furthermore, these 0204060801007 14 21 28 35 42Fig. 4. Development of the average coefficient of variation of relational strength in 4 long term recordings. A long term recor-ding was divided into data blocks. In all data blocks M matrices were determined. Next, data blocks were grouped into series of 15 consecutive blocks. For the set of relationships that were found in at least 50% of the 15 blocks in a series, means and standard deviations were calculated for all Mi,j. Then coefficients of variation (100×SD/mean) were calculated for each relation in the selected set. The figure shows mean coefficients of variation (CVM). ♦: culture I, ●: culture II, Δ: culture III, and □: culture IV. Pooled data of all cultures yielded a correlationcoefficient ρ=-0.32. This correlation was significant (p<0.01).  Time [DIV] Mean CVM [ %]  00.0310 400.0100.010 4000.0310 400.0100.010 40   Fig. 3. Examples of development of strength and delay of relati-ons throughout long term recordings. 61 relations that were found in the last 50 data blocks of long term recordings from 4 cultures were selected. The development of Mi,j (upper panels) and Ti,j (lower panels) of these relations between pairs of e-lectrodes (i,j) was traced back throughout the long term recor-ding. The figure shows examples of two basic types of develop-ment: I) shows a relation with increasing Mi,j (39% of the relati-ons); in  II) Mi,j increased first and then decreased (28%). In  the other 33%, Mi,j fluctuated around a horizontal line.   I II Time [DIV] Ti,j Mi,j    ISBN XXXX 4 5th Int. Meeting on Substrate-Integrated Microelectrodes, 2006 relationships were quite stable in terms of strength and delay on a timescale of several hours to several days, while development in strength and delay on this time scale were rather gradual.  Stability in-creased with aging of the culture. The high values of CVT were caused by relationships that had (almost) zero delay in the major part of a series, with one or a few outliers that led to a relatively large standard deviation and thus to a high CVT.  It is probable that relationships are single abstract representations of multiple pathways between elec-trodes. This was illustrated by an occasional CFP curve that showed two distinct peaks (<<1%). Our fit algorithm reduced these to a representation with a single peak and thus one strength and delay. Besides the pathways between electrodes, relation-ships were also influenced by the surrounding net-work. Many of the recorded neurons were in excita-tory loops, leading to autocorrelations with extra peaks at certain (non-zero) delays. In a linear ap-proach, it has been suggested to deconvolve the autocorrelation out of the CFP curve to obtain a ‘synaptic response function’ [7]. In this study we did not perform such a deconvolution. However, if a relationship is identified, this does indicate the exis-tence of a neuronal pathway between a pair of elec-trodes.  CFP analysis may offer a suitable basis for plasticity studies, in which induced changes should exceed spontaneous fluctuations. Furthermore, the analysis is likely to describe the network in sufficient detail to detect subtle changes in individual relationships.  Analysis of data continuously recorded for ≈ 6 weeks, showed that highest stability is reached after ≈ 25 DIV, suggesting the 4th and 5th week as a suit-able period for plasticity studies.   5  References 1. Jimbo, Y., H.P.C. Robinson, and A. Kawana, Strengthening of synchronized activity by tet-anic stimulation in cortical cultures: Applica-tion of planar electrode arrays. IEEE Trans Biomed Eng., 1998. 45(11): p. 1297-1304. 2. Shahaf, G. and S. Marom, Learning in networks of cortical neurons. J Neurosci, 2001. 21(22): p. 8782-8788. 3. Wagenaar, D.A., et al., Controlling bursting in cortical cultures with closed-loop multi-electrode stimulation. J Neurosci, 2005. 25(3): p. 680-8. 4. Aertsen, A.M.H.J. and G.L. Gerstein, Evalua-tion of neural connectivity: sensitivity of cross-correlation. Brain Res, 1985. 340: p. 341-354. 5. Melssen, W.J. and W.J.M. Epping, Detection and estimation of neural connectivity based on Crosscorrelation analysis. Biol. Cybern., 1987. 57: p. 403-414. 6. Palm, G., A.M.H.J. Aertsen, and G.L. Gerstein, On the significance of correlation among neu-ral spike trains. Biol. Cybern., 1988. 59: p. 1-11. 7. Eggermont, J.J., The correlative brain. Studies of brain function, ed. V. Braitenberg. Vol. 16. 1990, Tuebingen: Springer-Verlag. 307.  

Controlling bursting in cortical cultures with closed-loop multielectrode stimulation.

Detection and estimation of neural connectivity based on Crosscorrelation analysis.

Evaluation of neural connectivity: sensitivity of crosscorrelation. Brain Res,

Learning in networks of cortical neurons.

On the significance of correlation among neural spike trains.

Strengthening of synchronized activity by tetanic stimulation in cortical cultures: Application of planar electrode arrays.

The correlative brain. Studies of brain function,

Cultured cortical networks described by conditional firing probabilities

Abstract

Similar works

Full text

Available Versions

NARCIS

University of Twente Research Information