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Reaction to neural signatures through excitatory synapses in central pattern generator models
ARTICLE IN PRESS
Neurocomputing 70 (2007) 1797–1801 www.elsevier.com/locate/neucom
Reaction to neural signatures through excitatory synapses in central pattern generator models Roberto Latorre, Francisco de Borja Rodrı´ guez, Pablo Varona Grupo de Neurocomputacio´n Biolo´gica (GNB), Dpto. de Ingenierı´a Informa´tica, Escuela Polite´cnica Superior, Universidad Auto´noma de Madrid, 28049 Madrid, Spain Available online 3 November 2006
Abstract The activity of central pattern generator (CPG) neurons is processed by several different readers: neurons within the same CPG, neurons in other interconnected CPGs and muscles. Taking this into account, it is not surprising that CPG neurons may use different codes in their activity. In this paper, we study the capability of a CPG model to react to neural signatures through excitatory synapses. Neural signatures are cell-specific intraburst spike timings within their spiking–bursting activity. These fingerprints are encoded in the activity of the cells in addition to the information provided by their slow wave rhythm and phase relationships. The results shown in this paper suggest that neural signatures can be a mechanism to induce fast changes in the rhythm generated by a CPG through excitatory synapses. r 2006 Elsevier B.V. All rights reserved. Keywords: Spiking–bursting activity; Interspike intervals (ISI); Multicoding
1. Introduction A traditional view in neuroscience is that the information arriving through one channel, i.e. a synapse, is encoded through a single code in the signal, e.g. the rate or the precise timing of the incoming events. However, the need for several simultaneous codes seems to be apparent when one takes into account that, in general, cells receive many inputs from different neurons and send their output to different neurons too. Not all the neural readers have to be interested in the same aspect of the signal, specially when we talk about multifunctional networks. Bursting activity is particularly suitable to study the presence of multicoding signals, since it involves the presence of at least two different time scales that can serve to encode distinct informational aspects. However, bursts are traditionally considered as unitary events, and only recently there has been some attention to assess the specific role of the spiking Corresponding author.
E-mail addresses: [email protected] (R. Latorre), [email protected] (F. de Borja Rodrı´ guez), [email protected] (P. Varona). 0925-2312/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.neucom.2006.10.059
activity in bursting neurons [7,6,9,16]. The role of burst firing has been discussed in the context of many different neural systems. Depending on the particular system under study, bursts are interpreted for example as pathological states [15], as a very reliable mechanism for transmitting information [13], or as an essential means to induce plasticity [17]. Bursting activity is often observed in central pattern generators (CPGs), relative simple neural networks for the production of motor rhythms. CPGs are multifunctional circuits highly specialized to produce rhythmic sequences to control movements that must be repeated in time. A recent finding makes CPG bursting activity a good model to study multicoding strategies in the nervous system: in vitro experiments have revealed that the neurons of the pyloric CPG of the lobster have a cell-specific intraburst interspike interval (ISI) distributions [22,23], i.e. a neural signature. Our previous modeling results show that neural signatures can influence the pyloric CPG rhythm generation [11]. We have previously studied the ability of model neural networks to recognize different ISI neural signatures, sensitively adapting their responses to input with distinct spike timings [12]. Our results support the idea that CPG
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networks with bursting activity could use the specific temporal structure of their fast dynamics, in addition to the phase and frequency of the slow wave, as an information encoding mechanism. In the pyloric CPG of the stomatogastric ganglion of the lobster the signature generation coexists with the triphasic rhythm produced by this CPG [22]. Thus, bursting can be part of a multifunctional coding mechanism that makes use of some or all of the following features: (i) the particular frequency, duration and phase of the slow wave; (ii) the signature that identifies the emitter neuron or contextualizes its information; (iii) the information provided by additional spikes in the burst. Systems could read this multiple encoding selectively or globally. CPG neurons are typically connected through recurrent inhibitory connections. Many connections between different CPGs are also inhibitory. For this reason in all our previous studies [10,20,11,12] we have built biologically inspired CPGs with different neuron models, but always connected through graded inhibitory chemical synapses. Graded synapses release neurotransmitters at a threshold close to the resting potential, and thus before the action potentials [4]. However, excitatory connections are also present as inputs to known CPGs, e.g. the gastric CPG of crustacean [21], or as feedback from the muscles. Here we have built a network model of two CPGs to study the ability of neurons connected with non-graded excitatory synapses (spike mediated transmitter release) to react to the neural signature of a given input signal. Our results suggest that neural signatures can also have an important functional role in neural networks with excitatory synapses.
2. Neuron and network models To model the individual behavior of each neuron we have used the conductance-based Liu et al. stomatogastric neuron model [14] adapting the channel conductances values as described in [12]. The model has eight membrane currents: a fast sodium current ðI Na Þ, a fast and a slow transient calcium current (I CaT and I CaS ), a fast transient potassium current ðI A Þ, a calcium-dependent potassium current ðI KCa Þ, a delayed rectifier potassium current ðI Kd Þ, a hyperpolarization-activated inward current ðI H Þ, a voltage-independent leak current ðI leak Þ; and an intracellular calcium buffer. We have built a generic CPG network model that comprises two subcircuits (see bottom panel Fig. 1): (i) a signature emitter CPG (neurons I, M, E 1 , E 2 ) that generates bursting signals which contain neural signatures; and (ii) a signature reader CPG (neurons R, N 1 , N 2 , N 3 ) that receives these signals. Both are biological inspired CPGs, but none models a specific network. As CPGs the emitter and reader subcircuits generate slow wave rhythms. Neurons E 1 and E 2 of the emitter CPG can generate different neural signatures (S1 and S 2 , respectively—see Fig. 2) with the same slow wave properties. Table 1 shows the values of the maximal conductances used for each neuron of the model. The whole circuit has three different kinds of connections: electrical (represented by resistors in Fig. 1), fast inhibitory chemical synapses between neurons of the same CPG (open circles) and excitatory chemical synapses
Fig. 1. Reaction of the reader CPG to the arrival of two different signatures S1 and S2 . The only difference between the signals generated by E 1 and E 2 is their ISI distributions (see Fig. 2). Resistors indicate gap junctions. Filled circles represent excitatory synapses, open circles mean inhibitory synapses.
ARTICLE IN PRESS R. Latorre et al. / Neurocomputing 70 (2007) 1797–1801
60 50
S1
25
I2FS
S2
1799
ISIs
S1 S2
20
40 15 30 10 20 5
10
0
0 SPIKE #2 SPIKE #3 SPIKE #4 SPIKE #5
ISI #1
ISI #2
ISI #3
ISI #4
Fig. 2. Left panel: bar plot of the mean time interval from each action potential to the first spike (I2FS) for the signatures S1 and S2 generated by neurons E 1 and E 2 of the emitter CPG. Right panel: bar plot of the average ISI distributions. Units are ms. Note that error bars are so small that they can hardly be seen. These plots illustrate the difference between signature S1 and S2 . Burst duration is the same for both signals. Thus, the only difference seen by the R neuron of the reader CPG is the interspike interval distribution.
Table 1 Values of the maximal conductances for the different ionic channels used to model the neurons in the circuit depicted in Fig. 1 gNa
gCaT
gCaS
gA
gKCa
Signature emitter CPG M and I neurons E 1 neuron E 2 neuron
100.0 178.0 48.6
3.0 2.0 1.5
4.0 3.0 3.0
28.8 10.9 10.5
90.6 7.4 44.3
Signature reader CPG R neuron N 1 , N 2 and N 3 neurons
200.0 125.0
0.0 1.69
4.0 4.0
10.0 29.0
10.0 10.0
gKd
gH
gleak
26.4 55.0 41.0
0.01 0.0 0.0
0.01 0.02 0.02
125.0 55.0
0.08 0.02
0.08 0.04
Units are ms=cm2 .
between neurons of different CPGs (filled circles). Equations used to model each kind of connection are:
Gap junctions: I syn ¼ gelecPre_Post ðV Post V Pre Þ.
Fast inhibitory chemical synapses [3]: I syn ¼
(1)
gFastPre_Post ðV Post E syn Þ . 1:0 þ expðsðV Fast V Pre ÞÞ
(2)
Excitatory synapses (see [2]): I syn ¼ r gsyn ðV Post V syn Þ,
(3)
where r gives the fraction of the open channels in the postsynaptic neuron and it is given by dr dx ¼ asyn xð1 rÞ bsyn r; ¼ aðf ðV Pre Þ xÞ, dt dt f ðV Þ ¼ s=ð1 þ expððV yÞ=TÞÞ.
gelecE 1 _E 2 ¼ 0:095 ms, gelecE 2 _M ¼ gelecE 1 _M ¼ 0:105 ms, 0:169 ms and gelecE 2 _E 1 ¼ 0:095 ms. Parameters used for inhibitory synapses in the emitter CPG are: gFastI_M ¼ 0:178 ms, gFastM_I ¼ 0:381 ms, E syn ¼ 50:0 mV, V Fast ¼ 30:0 mV and s ¼ 1:0 mV1 . Parameters used for inhibitory synapses in the signature reader CPG are: gFastN 1 _R ¼ 0:238 ms, gFastN 1 _N 2 ¼ 0:258 ms, gFastN 1 _N 3 ¼ 0:308 ms, gFastN 2 _N 1 ¼ 0:306 ms, gFastN 2 _N 3 ¼ 0:378 ms, gFastN 3 _N 1 ¼ 0:292 ms, gFastN 3 _N 2 ¼ 0:117 ms, gFastR_N 1 ¼ 0:228 ms, gFastR_N 2 ¼ 0:168 ms, gFastR_N 3 ¼ 0:399 ms, E syn ¼ 50:0 mV, V Fast ¼ 30:0 mV and s ¼ 1:0 mV1 . Finally, parameters used for excitatory synapses are: V syn ¼ 0:0 mV, asyn ¼ 1:1 ms1 mM1 , bsyn ¼ 0:5 ms1 , a ¼ 5:0 ms1 , s ¼ 2:84 mM, y ¼ 0:0 mV and T ¼ 5 ms. The values of gsyn for each excitatory connection are discussed in the next section. 3. Results
ð4Þ
Parameters used in our simulations for gap junctions in the emitter CPG are: gelecM_E 1 ¼ 0:105 ms, gelecM_E 2 ¼ 0:169 ms,
While producing a stable biphasic rhythm (I and M cells), the emitter CPG generates two different signatures: one signature ðS1 Þ is generated by the E 1 neuron and the other ðS 2 Þ is produced by E 2 . These cells are electrically coupled between themselves and also to the pacemaker
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neuron ðMÞ of the CPG (see Fig. 1). Signals with different signatures are propagated as input to the reader CPG through the excitatory chemical synapses. The mechanism used to modulate the influence of these signatures on the reader neuron is to switch the dominant conductance of the synapses between the E neurons and the R cell (thick lines in the circuits of this figure represent gsyn ¼ 0:03 ms, thin lines gsyn ¼ 0:001 ms). Thus, the only difference between the spiking–bursting signals produced by E 1 and E 2 is the ISI distribution (see Fig. 2) since their slow depolarizing waves are synchronized because of the electrical coupling and they have the same number of spikes per burst. The reader neuron ðRÞ adapts its behavior to the signature read at a given time. The behavior of the R neuron instantaneously changes after the arrival of a signal with the same slow wave properties but with a different signature. The spiking activity of the R neuron has a higher frequency with S 2 than with S 1 . The change in the behavior of the R neuron is propagated to the rest of neurons of the reader CPG (N 1 , N 2 , N 3 ). When this CPG reads signature S 1 , it produces a triphasic rhythm with firing sequence N 2 2N 1 2N 3 . With signature S 2 , the N 3 neuron becomes silent, and the CPG produces a biphasic rhythm with firing sequence N 2 2N 1 (illustrated with dark squares in Fig. 1). Note that the adaptation of the complete reader circuit is slower than that for the R neuron due to the propagation through the inhibitory synapses. The synaptic currents from the emitters are the origin for the different behaviors displayed by the R cell in the signature reader CPG. The integration of these currents with the ongoing intracellular dynamics of the reader neurons determines the characteristics of the response. As we have studied for the inhibitory synapses [12], the kinetics of most ionic channels of the model can affect the response to a signal with a particular spike distribution. 4. Discussion The results of our simulations show that incoming neural signatures through excitatory synapses can be important for the CPG behavior and for the communication between different circuits. The fast reaction to different signatures suggests that they could be involved in control mechanisms of multifunctional networks that can take advantage of the multiple coding in the spiking–bursting signals. We have observed that with graded inhibitory connections there exists a delay in the adaptation of the reader to the input signature that can defer the reaction to the next burst [12]. Excitatory synapses are more effective in changing the properties of the reader circuits, since they can induce a faster change in the rhythm of the reader circuit. The results in this paper can be easily reproduced with different parameter values. Similar results were obtained using Komendantov–Kononenko conductance-based neurons [8] and the same network topologies (not shown), which point out the generality of the results.
The presence of precise timings in the spiking activity of different neurons has been reported in several vertebrate and invertebrate neural systems, e.g. see [18,1,19,5]. Although we have restricted our study to spiking–bursting CPG models, neural signatures can be a general mechanism present in other neural networks to contextualize or discriminate neural information. The existence of cellular mechanisms to identify specific neural signals, and the study of information processing based on this identification have been neglected in the context of theoretical approaches to the nervous system. Information processing based on the identification of neural signatures can be a powerful strategy for neural systems to enhance the capacity and performance of these networks. Acknowledgments Work supported by Fundacio´n BBVA, MEC TIN200404363-C03-03, and MEC BFU-2006-07902/BFI. References [1] Z. Chi, D. Margoliash, Temporal precision and temporal drift in brain and behavior of zebra finch song, Neuron 32 (2001) 899–910. [2] A. Destexhe, Z.F. Mainen, T.J. Sejnowski, An efficient method for computing synaptic conductances based on kinetic model of receptor binding, Neural Comput. 6 (1994) 14–18. [3] J. Golowasch, M. Casey, L.F. Abbott, E. Marder, Network stability from activity-dependent regulation of neuronal conductances, Neural Comput. 11 (1999) 1079–1096. [4] R.M. Harris-Warrick, E. Marder, A.I. Selverston, M. Moulins, Dynamic Biological Networks: The Stomatogastric Nervous System, MIT Press, Cambridge, MA, 1992. [5] J.D. Hunter, J.G. Milton, Amplitude and frequency dependence of spike timing: implications for dynamic regulation, J. Neurophysiol. 90 (2003) 387–394. [6] E. Izhikevich, N.S. Desai, E.C. Walcott, F.C. Hoppensteadt, Bursts as a unit of neural information: selective communication via resonance, Trends Neurosci. 26 (3) (2003) 161–167. [7] A. Kepecs, J. Lisman, Information enconding and computation with spikes and bursts, Network: Comput. Neural Syst. 14 (2003) 103–118. [8] A.O. Komendantov, N.I. Kononenko, Deterministic chaos in mathematical model of pacemaker activity in bursting neurons of snail, helix pomatia, J. Theor. Biol. 183 (1996) 219–230. [9] R. Krahe, F. Gabbiani, Burst firing in sensory systems, Nature Rev. Neurosci. 5 (2004) 13–24. [10] R. Latorre, F.B. Rodrı´ guez, P. Varona, Characterization of triphasic rhythms in central pattern generators (I): interspike interval analysis, Lect. Notes Comput. Sci. 2415 (2002) 160–166. [11] R. Latorre, F.B. Rodrı´ guez, P. Varona, Effect of individual spiking activity on rhythm generation of central pattern generators, Neurocomputing 58–60 (2004) 535–540. [12] R. Latorre, F.B. Rodrı´ guez, P. Varona, Neural signatures: multiple coding in spiking bursting cells, Biol. Cybern. 95 (2006) 169–183. [13] J.E. Lisman, Busts as a unit of neural information: making unreliable synapses reliable, Trends Neurosci. 20 (1997) 38–43. [14] A. Liu, J. Golowasch, E. Marder, F. Abbott, A model neuron with activity-dependent conductances regulated by multiple calcium sensor, J. Neurosci. 18 (1998) 2309–2320. [15] D.A. McCormick, D. Contreras, On the cellular and network bases of epileptic seizures, Annu. Rev. Physiol. 63 (2001) 815–846. [16] A.M. Oswald, M.J. Chacron, B. Dorion, J. Bastian, L. Maler, Parallel processing of sensory input by bursts and isolated spikes, J. Neurosci. 24 (2004) 4351–4362.
ARTICLE IN PRESS R. Latorre et al. / Neurocomputing 70 (2007) 1797–1801 [17] F.G. Pike, R.M. Meredith, A.W.A. Olding, O. Paulsen, J. Physiol. (London) 518 (1999) 571–576. [18] P. Reinagel, R.C. Reid, Temporal coding of visual information in the thalamus, J. Neurosci. 20 (2000) 5392–5400. [19] P. Reinagel, R.C. Reid, Precise firing events are conserved across neurons, J. Neurosci. 22 (16) (2002) 6837–6841. [20] F.B. Rodrı´ guez, R. Latorre, P. Varona, Characterization of triphasic rhythms in central pattern generators (II): burst information analysis, Lect. Notes Comput. Sci. 2415 (2002) 167–173. [21] A.I. Selverston, M. Moulins, The Crustacean Stomatogastric System: A Model for the Study of Central Nervous System, Springer, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1987. [22] A. Szu¨cs, R.D. Pinto, M.I. Rabinovich, H.D.I. Abarbanel, A.I. Selverston, Synaptic modulation of the interspike interval signatures of bursting pyloric neurons, J. Neurophysiol. 89 (2003) 1363–1377. [23] A. Szu¨cs, H.D.I. Abarbanel, M.I. Rabinovich, A.I. Selverston, Dopamine modulation of spike dynamics in bursting neurons, Eur. J. Neurosci. 2 (2005) 763–772. Roberto Latorre received his degree in Computer Science in 2000 from Universidad Autonoma de Madrid. He is member of the Grupo de Neurocomputacio´n Biologica (GNB) of the Escuela Polite´cnica Superior, Universidad Auto´noma de Madrid, where he is pursuing his Ph.D. He uses computational approaches to study information processing in CPGs. Since 2002 he is professor asociado at the Escuela Politecnica Superior, Universidad Autonoma de Madrid.
1801
Francisco de Borja Rodriguez received his degree in Applied Physics in 1992 and the Ph.D. in Computer Science in 1999 from Universidad Autonoma de Madrid. He then worked at the Nijmegen University in Holland and the Institute for Nonlinear Science, University of California, San Diego. Since 2002 he is professor titular at the Escuela Polite´cnica Superior, Universidad Autonoma de Madrid.
Pablo Varona received his degree in Theoretical Physics in 1992 and the Ph.D. in Computer Science in 1997 from Universidad Autonoma de Madrid. He was a postdoc and later an assistant research scientist at the Institute for Nonlinear Science, University of California, San Diego. Since 2002 he is professor titular at the Escuela Politecnica Superior, Universidad Autonoma de Madrid.
Neurocomputing 70 (2007) 1797–1801 www.elsevier.com/locate/neucom
Reaction to neural signatures through excitatory synapses in central pattern generator models Roberto Latorre, Francisco de Borja Rodrı´ guez, Pablo Varona Grupo de Neurocomputacio´n Biolo´gica (GNB), Dpto. de Ingenierı´a Informa´tica, Escuela Polite´cnica Superior, Universidad Auto´noma de Madrid, 28049 Madrid, Spain Available online 3 November 2006
Abstract The activity of central pattern generator (CPG) neurons is processed by several different readers: neurons within the same CPG, neurons in other interconnected CPGs and muscles. Taking this into account, it is not surprising that CPG neurons may use different codes in their activity. In this paper, we study the capability of a CPG model to react to neural signatures through excitatory synapses. Neural signatures are cell-specific intraburst spike timings within their spiking–bursting activity. These fingerprints are encoded in the activity of the cells in addition to the information provided by their slow wave rhythm and phase relationships. The results shown in this paper suggest that neural signatures can be a mechanism to induce fast changes in the rhythm generated by a CPG through excitatory synapses. r 2006 Elsevier B.V. All rights reserved. Keywords: Spiking–bursting activity; Interspike intervals (ISI); Multicoding
1. Introduction A traditional view in neuroscience is that the information arriving through one channel, i.e. a synapse, is encoded through a single code in the signal, e.g. the rate or the precise timing of the incoming events. However, the need for several simultaneous codes seems to be apparent when one takes into account that, in general, cells receive many inputs from different neurons and send their output to different neurons too. Not all the neural readers have to be interested in the same aspect of the signal, specially when we talk about multifunctional networks. Bursting activity is particularly suitable to study the presence of multicoding signals, since it involves the presence of at least two different time scales that can serve to encode distinct informational aspects. However, bursts are traditionally considered as unitary events, and only recently there has been some attention to assess the specific role of the spiking Corresponding author.
E-mail addresses: [email protected] (R. Latorre), [email protected] (F. de Borja Rodrı´ guez), [email protected] (P. Varona). 0925-2312/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.neucom.2006.10.059
activity in bursting neurons [7,6,9,16]. The role of burst firing has been discussed in the context of many different neural systems. Depending on the particular system under study, bursts are interpreted for example as pathological states [15], as a very reliable mechanism for transmitting information [13], or as an essential means to induce plasticity [17]. Bursting activity is often observed in central pattern generators (CPGs), relative simple neural networks for the production of motor rhythms. CPGs are multifunctional circuits highly specialized to produce rhythmic sequences to control movements that must be repeated in time. A recent finding makes CPG bursting activity a good model to study multicoding strategies in the nervous system: in vitro experiments have revealed that the neurons of the pyloric CPG of the lobster have a cell-specific intraburst interspike interval (ISI) distributions [22,23], i.e. a neural signature. Our previous modeling results show that neural signatures can influence the pyloric CPG rhythm generation [11]. We have previously studied the ability of model neural networks to recognize different ISI neural signatures, sensitively adapting their responses to input with distinct spike timings [12]. Our results support the idea that CPG
ARTICLE IN PRESS 1798
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networks with bursting activity could use the specific temporal structure of their fast dynamics, in addition to the phase and frequency of the slow wave, as an information encoding mechanism. In the pyloric CPG of the stomatogastric ganglion of the lobster the signature generation coexists with the triphasic rhythm produced by this CPG [22]. Thus, bursting can be part of a multifunctional coding mechanism that makes use of some or all of the following features: (i) the particular frequency, duration and phase of the slow wave; (ii) the signature that identifies the emitter neuron or contextualizes its information; (iii) the information provided by additional spikes in the burst. Systems could read this multiple encoding selectively or globally. CPG neurons are typically connected through recurrent inhibitory connections. Many connections between different CPGs are also inhibitory. For this reason in all our previous studies [10,20,11,12] we have built biologically inspired CPGs with different neuron models, but always connected through graded inhibitory chemical synapses. Graded synapses release neurotransmitters at a threshold close to the resting potential, and thus before the action potentials [4]. However, excitatory connections are also present as inputs to known CPGs, e.g. the gastric CPG of crustacean [21], or as feedback from the muscles. Here we have built a network model of two CPGs to study the ability of neurons connected with non-graded excitatory synapses (spike mediated transmitter release) to react to the neural signature of a given input signal. Our results suggest that neural signatures can also have an important functional role in neural networks with excitatory synapses.
2. Neuron and network models To model the individual behavior of each neuron we have used the conductance-based Liu et al. stomatogastric neuron model [14] adapting the channel conductances values as described in [12]. The model has eight membrane currents: a fast sodium current ðI Na Þ, a fast and a slow transient calcium current (I CaT and I CaS ), a fast transient potassium current ðI A Þ, a calcium-dependent potassium current ðI KCa Þ, a delayed rectifier potassium current ðI Kd Þ, a hyperpolarization-activated inward current ðI H Þ, a voltage-independent leak current ðI leak Þ; and an intracellular calcium buffer. We have built a generic CPG network model that comprises two subcircuits (see bottom panel Fig. 1): (i) a signature emitter CPG (neurons I, M, E 1 , E 2 ) that generates bursting signals which contain neural signatures; and (ii) a signature reader CPG (neurons R, N 1 , N 2 , N 3 ) that receives these signals. Both are biological inspired CPGs, but none models a specific network. As CPGs the emitter and reader subcircuits generate slow wave rhythms. Neurons E 1 and E 2 of the emitter CPG can generate different neural signatures (S1 and S 2 , respectively—see Fig. 2) with the same slow wave properties. Table 1 shows the values of the maximal conductances used for each neuron of the model. The whole circuit has three different kinds of connections: electrical (represented by resistors in Fig. 1), fast inhibitory chemical synapses between neurons of the same CPG (open circles) and excitatory chemical synapses
Fig. 1. Reaction of the reader CPG to the arrival of two different signatures S1 and S2 . The only difference between the signals generated by E 1 and E 2 is their ISI distributions (see Fig. 2). Resistors indicate gap junctions. Filled circles represent excitatory synapses, open circles mean inhibitory synapses.
ARTICLE IN PRESS R. Latorre et al. / Neurocomputing 70 (2007) 1797–1801
60 50
S1
25
I2FS
S2
1799
ISIs
S1 S2
20
40 15 30 10 20 5
10
0
0 SPIKE #2 SPIKE #3 SPIKE #4 SPIKE #5
ISI #1
ISI #2
ISI #3
ISI #4
Fig. 2. Left panel: bar plot of the mean time interval from each action potential to the first spike (I2FS) for the signatures S1 and S2 generated by neurons E 1 and E 2 of the emitter CPG. Right panel: bar plot of the average ISI distributions. Units are ms. Note that error bars are so small that they can hardly be seen. These plots illustrate the difference between signature S1 and S2 . Burst duration is the same for both signals. Thus, the only difference seen by the R neuron of the reader CPG is the interspike interval distribution.
Table 1 Values of the maximal conductances for the different ionic channels used to model the neurons in the circuit depicted in Fig. 1 gNa
gCaT
gCaS
gA
gKCa
Signature emitter CPG M and I neurons E 1 neuron E 2 neuron
100.0 178.0 48.6
3.0 2.0 1.5
4.0 3.0 3.0
28.8 10.9 10.5
90.6 7.4 44.3
Signature reader CPG R neuron N 1 , N 2 and N 3 neurons
200.0 125.0
0.0 1.69
4.0 4.0
10.0 29.0
10.0 10.0
gKd
gH
gleak
26.4 55.0 41.0
0.01 0.0 0.0
0.01 0.02 0.02
125.0 55.0
0.08 0.02
0.08 0.04
Units are ms=cm2 .
between neurons of different CPGs (filled circles). Equations used to model each kind of connection are:
Gap junctions: I syn ¼ gelecPre_Post ðV Post V Pre Þ.
Fast inhibitory chemical synapses [3]: I syn ¼
(1)
gFastPre_Post ðV Post E syn Þ . 1:0 þ expðsðV Fast V Pre ÞÞ
(2)
Excitatory synapses (see [2]): I syn ¼ r gsyn ðV Post V syn Þ,
(3)
where r gives the fraction of the open channels in the postsynaptic neuron and it is given by dr dx ¼ asyn xð1 rÞ bsyn r; ¼ aðf ðV Pre Þ xÞ, dt dt f ðV Þ ¼ s=ð1 þ expððV yÞ=TÞÞ.
gelecE 1 _E 2 ¼ 0:095 ms, gelecE 2 _M ¼ gelecE 1 _M ¼ 0:105 ms, 0:169 ms and gelecE 2 _E 1 ¼ 0:095 ms. Parameters used for inhibitory synapses in the emitter CPG are: gFastI_M ¼ 0:178 ms, gFastM_I ¼ 0:381 ms, E syn ¼ 50:0 mV, V Fast ¼ 30:0 mV and s ¼ 1:0 mV1 . Parameters used for inhibitory synapses in the signature reader CPG are: gFastN 1 _R ¼ 0:238 ms, gFastN 1 _N 2 ¼ 0:258 ms, gFastN 1 _N 3 ¼ 0:308 ms, gFastN 2 _N 1 ¼ 0:306 ms, gFastN 2 _N 3 ¼ 0:378 ms, gFastN 3 _N 1 ¼ 0:292 ms, gFastN 3 _N 2 ¼ 0:117 ms, gFastR_N 1 ¼ 0:228 ms, gFastR_N 2 ¼ 0:168 ms, gFastR_N 3 ¼ 0:399 ms, E syn ¼ 50:0 mV, V Fast ¼ 30:0 mV and s ¼ 1:0 mV1 . Finally, parameters used for excitatory synapses are: V syn ¼ 0:0 mV, asyn ¼ 1:1 ms1 mM1 , bsyn ¼ 0:5 ms1 , a ¼ 5:0 ms1 , s ¼ 2:84 mM, y ¼ 0:0 mV and T ¼ 5 ms. The values of gsyn for each excitatory connection are discussed in the next section. 3. Results
ð4Þ
Parameters used in our simulations for gap junctions in the emitter CPG are: gelecM_E 1 ¼ 0:105 ms, gelecM_E 2 ¼ 0:169 ms,
While producing a stable biphasic rhythm (I and M cells), the emitter CPG generates two different signatures: one signature ðS1 Þ is generated by the E 1 neuron and the other ðS 2 Þ is produced by E 2 . These cells are electrically coupled between themselves and also to the pacemaker
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neuron ðMÞ of the CPG (see Fig. 1). Signals with different signatures are propagated as input to the reader CPG through the excitatory chemical synapses. The mechanism used to modulate the influence of these signatures on the reader neuron is to switch the dominant conductance of the synapses between the E neurons and the R cell (thick lines in the circuits of this figure represent gsyn ¼ 0:03 ms, thin lines gsyn ¼ 0:001 ms). Thus, the only difference between the spiking–bursting signals produced by E 1 and E 2 is the ISI distribution (see Fig. 2) since their slow depolarizing waves are synchronized because of the electrical coupling and they have the same number of spikes per burst. The reader neuron ðRÞ adapts its behavior to the signature read at a given time. The behavior of the R neuron instantaneously changes after the arrival of a signal with the same slow wave properties but with a different signature. The spiking activity of the R neuron has a higher frequency with S 2 than with S 1 . The change in the behavior of the R neuron is propagated to the rest of neurons of the reader CPG (N 1 , N 2 , N 3 ). When this CPG reads signature S 1 , it produces a triphasic rhythm with firing sequence N 2 2N 1 2N 3 . With signature S 2 , the N 3 neuron becomes silent, and the CPG produces a biphasic rhythm with firing sequence N 2 2N 1 (illustrated with dark squares in Fig. 1). Note that the adaptation of the complete reader circuit is slower than that for the R neuron due to the propagation through the inhibitory synapses. The synaptic currents from the emitters are the origin for the different behaviors displayed by the R cell in the signature reader CPG. The integration of these currents with the ongoing intracellular dynamics of the reader neurons determines the characteristics of the response. As we have studied for the inhibitory synapses [12], the kinetics of most ionic channels of the model can affect the response to a signal with a particular spike distribution. 4. Discussion The results of our simulations show that incoming neural signatures through excitatory synapses can be important for the CPG behavior and for the communication between different circuits. The fast reaction to different signatures suggests that they could be involved in control mechanisms of multifunctional networks that can take advantage of the multiple coding in the spiking–bursting signals. We have observed that with graded inhibitory connections there exists a delay in the adaptation of the reader to the input signature that can defer the reaction to the next burst [12]. Excitatory synapses are more effective in changing the properties of the reader circuits, since they can induce a faster change in the rhythm of the reader circuit. The results in this paper can be easily reproduced with different parameter values. Similar results were obtained using Komendantov–Kononenko conductance-based neurons [8] and the same network topologies (not shown), which point out the generality of the results.
The presence of precise timings in the spiking activity of different neurons has been reported in several vertebrate and invertebrate neural systems, e.g. see [18,1,19,5]. Although we have restricted our study to spiking–bursting CPG models, neural signatures can be a general mechanism present in other neural networks to contextualize or discriminate neural information. The existence of cellular mechanisms to identify specific neural signals, and the study of information processing based on this identification have been neglected in the context of theoretical approaches to the nervous system. Information processing based on the identification of neural signatures can be a powerful strategy for neural systems to enhance the capacity and performance of these networks. Acknowledgments Work supported by Fundacio´n BBVA, MEC TIN200404363-C03-03, and MEC BFU-2006-07902/BFI. References [1] Z. Chi, D. Margoliash, Temporal precision and temporal drift in brain and behavior of zebra finch song, Neuron 32 (2001) 899–910. [2] A. Destexhe, Z.F. Mainen, T.J. Sejnowski, An efficient method for computing synaptic conductances based on kinetic model of receptor binding, Neural Comput. 6 (1994) 14–18. [3] J. Golowasch, M. Casey, L.F. Abbott, E. Marder, Network stability from activity-dependent regulation of neuronal conductances, Neural Comput. 11 (1999) 1079–1096. [4] R.M. Harris-Warrick, E. Marder, A.I. Selverston, M. Moulins, Dynamic Biological Networks: The Stomatogastric Nervous System, MIT Press, Cambridge, MA, 1992. [5] J.D. Hunter, J.G. Milton, Amplitude and frequency dependence of spike timing: implications for dynamic regulation, J. Neurophysiol. 90 (2003) 387–394. [6] E. Izhikevich, N.S. Desai, E.C. Walcott, F.C. Hoppensteadt, Bursts as a unit of neural information: selective communication via resonance, Trends Neurosci. 26 (3) (2003) 161–167. [7] A. Kepecs, J. Lisman, Information enconding and computation with spikes and bursts, Network: Comput. Neural Syst. 14 (2003) 103–118. [8] A.O. Komendantov, N.I. Kononenko, Deterministic chaos in mathematical model of pacemaker activity in bursting neurons of snail, helix pomatia, J. Theor. Biol. 183 (1996) 219–230. [9] R. Krahe, F. Gabbiani, Burst firing in sensory systems, Nature Rev. Neurosci. 5 (2004) 13–24. [10] R. Latorre, F.B. Rodrı´ guez, P. Varona, Characterization of triphasic rhythms in central pattern generators (I): interspike interval analysis, Lect. Notes Comput. Sci. 2415 (2002) 160–166. [11] R. Latorre, F.B. Rodrı´ guez, P. Varona, Effect of individual spiking activity on rhythm generation of central pattern generators, Neurocomputing 58–60 (2004) 535–540. [12] R. Latorre, F.B. Rodrı´ guez, P. Varona, Neural signatures: multiple coding in spiking bursting cells, Biol. Cybern. 95 (2006) 169–183. [13] J.E. Lisman, Busts as a unit of neural information: making unreliable synapses reliable, Trends Neurosci. 20 (1997) 38–43. [14] A. Liu, J. Golowasch, E. Marder, F. Abbott, A model neuron with activity-dependent conductances regulated by multiple calcium sensor, J. Neurosci. 18 (1998) 2309–2320. [15] D.A. McCormick, D. Contreras, On the cellular and network bases of epileptic seizures, Annu. Rev. Physiol. 63 (2001) 815–846. [16] A.M. Oswald, M.J. Chacron, B. Dorion, J. Bastian, L. Maler, Parallel processing of sensory input by bursts and isolated spikes, J. Neurosci. 24 (2004) 4351–4362.
ARTICLE IN PRESS R. Latorre et al. / Neurocomputing 70 (2007) 1797–1801 [17] F.G. Pike, R.M. Meredith, A.W.A. Olding, O. Paulsen, J. Physiol. (London) 518 (1999) 571–576. [18] P. Reinagel, R.C. Reid, Temporal coding of visual information in the thalamus, J. Neurosci. 20 (2000) 5392–5400. [19] P. Reinagel, R.C. Reid, Precise firing events are conserved across neurons, J. Neurosci. 22 (16) (2002) 6837–6841. [20] F.B. Rodrı´ guez, R. Latorre, P. Varona, Characterization of triphasic rhythms in central pattern generators (II): burst information analysis, Lect. Notes Comput. Sci. 2415 (2002) 167–173. [21] A.I. Selverston, M. Moulins, The Crustacean Stomatogastric System: A Model for the Study of Central Nervous System, Springer, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1987. [22] A. Szu¨cs, R.D. Pinto, M.I. Rabinovich, H.D.I. Abarbanel, A.I. Selverston, Synaptic modulation of the interspike interval signatures of bursting pyloric neurons, J. Neurophysiol. 89 (2003) 1363–1377. [23] A. Szu¨cs, H.D.I. Abarbanel, M.I. Rabinovich, A.I. Selverston, Dopamine modulation of spike dynamics in bursting neurons, Eur. J. Neurosci. 2 (2005) 763–772. Roberto Latorre received his degree in Computer Science in 2000 from Universidad Autonoma de Madrid. He is member of the Grupo de Neurocomputacio´n Biologica (GNB) of the Escuela Polite´cnica Superior, Universidad Auto´noma de Madrid, where he is pursuing his Ph.D. He uses computational approaches to study information processing in CPGs. Since 2002 he is professor asociado at the Escuela Politecnica Superior, Universidad Autonoma de Madrid.
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Francisco de Borja Rodriguez received his degree in Applied Physics in 1992 and the Ph.D. in Computer Science in 1999 from Universidad Autonoma de Madrid. He then worked at the Nijmegen University in Holland and the Institute for Nonlinear Science, University of California, San Diego. Since 2002 he is professor titular at the Escuela Polite´cnica Superior, Universidad Autonoma de Madrid.
Pablo Varona received his degree in Theoretical Physics in 1992 and the Ph.D. in Computer Science in 1997 from Universidad Autonoma de Madrid. He was a postdoc and later an assistant research scientist at the Institute for Nonlinear Science, University of California, San Diego. Since 2002 he is professor titular at the Escuela Politecnica Superior, Universidad Autonoma de Madrid.