INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Electrical coupling is a general property of the developing (Pienado et al. 1993; Walton and Navarrete 1991) and adult CNS (Galarreta and Hestrin 1999; Gibson et al. 1999; Kandler and Katz 1995), where it tends to enhance and synchronize the activity of coupled neurons. The efficacy of electrical coupling may be altered by both ontogenetic and modulatory processes. For example, several studies have demonstrated that gap junctions are abundant early in development and then decline during subsequent maturation (Kandler and Katz 1995; Pienado et al. 1993). In the adult CNS, moreover, the strength of electrical coupling between neurons may be substantially altered by various transmitters or hormones (Baldridge et al. 1998; Hatton and Yang 1996; Johnson et al. 1993). Such alterations, either in the expression of gap junctions or via their modulation, have potentially important functional implications for neuronal network operation. However, although electrical coupling has been studied extensively at the level of cell-to-cell communication within a given network (Fukuda and Kosaka 2000; Gibson et al. 1999; Graubard and Hartline 1987; Tamas et al. 2000), little is known about its role in the interaction between different functional networks during ontogeny.

To address this problem we have explored the potential role of electrical coupling in the maturation of neural networks in the lobster stomatogastric nervous system (STNS). In the adult animal, this system controls rhythmic food-processing movements of the foregut organized in three different regional behaviors. The underlying motor patterns are generated by three discrete networks that consist of endogenous oscillators interconnected by graded inhibitory synapses (Harris-Warrick et al. 1992; Selverston and Moulins 1987) and that operate at completely different cycle frequencies (Casasnovas and Meyrand 1995; Meyrand et al. 1991). By contrast, in the lobster embryo the same population of STNS neurons generates a coordinated activity organized in a single motor pattern (Casasnovas and Meyrand 1995; Fénelon et al. 1998; Le Feuvre et al. 1999). However, recent in vitro experiments have shown that adult-like network properties are already embedded in this embryonic network but are continuously masked by an unknown mechanism (Le Feuvre et al. 1999). Since electrical coupling is prevalent in the embryonic nervous system then decreases during ontogeny (Kandler and Katz 1995; Pienado et al. 1993), we have explored the possibility that diminishing gap junction coupling may be responsible for the developmental emergence of adult STNS networks.

To address this issue we have used a mathematical model to perform the reverse experiment in which electrical coupling is introduced within and between three adult-like model STNS networks. The model networks generated antiphasic oscillations due to endogenous oscillatory properties of individual cells and reciprocal inhibition within each network. Each model cell consisted of a generalized van der Pol relaxation oscillator. Since spikes are not necessary for the generation of membrane oscillations and STNS motor patterns (Raper 1979), model membrane potential oscillation was produced without spikes. A network constructed by connecting such model cells via instantaneous graded synaptic transmission captures essential features of the biological STNS network (Rowat and Selverston 1993). Gap junctions were modeled as giving currents proportional to the differences in voltage of any two coupled cells.

We find that the addition of widespread electrical coupling into the STNS model can unify the activity of all cells belonging to the different networks into a single multiphasic pattern. Concomitant with this network reorganization is a dramatic decrease in the oscillation amplitude of all neurons. Importantly, both phenomena are reminiscent of the activity of the single STNS embryonic network. Thus our data suggest that rather than a progressive maturation of cellular and synaptic properties within a given network, a gradual reduction of electrical coupling strength may account for the emergence of preexisting adult network properties during ontogenesis.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Dissections and electrophysiological study of the STNS of the lobster Homarus gammarus were performed as previously reported in the adult (Meyrand et al. 1994) and in the embryo (Casasnovas and Meyrand 1995).

In our simulation analyses, a single-cell model was used that was a modified relaxation oscillator generating membrane potential oscillations by slow (I_slow) and fast (I_fast) voltage-dependent membrane current (Rowat and Selverston 1993). When incorporated into a network, the model neuron also contained synaptic (I_syn) and electrical junction (I_ej) currents. This dimensionless model was written in two differential equations:

1) A total current conservation
where  was cell membrane potential and _m was membrane time constant;

2) A slow current activation
where _S was the time constant and _S the steady-state conductance of the slow current. Fast current, combined from a leak and fast voltage-dependent currents, was n-shaped to a degree determined by 1  _f corresponding to the slope of the instantaneous current-voltage (I-V) curve at the origin, as given by I_fast =   tanh (_f).

Synaptic current was modeled as
where w was maximal synaptic conductance, f(_pre) = (1 + e^4pre)¹ determined a fraction of postsynaptic channels open due to graded transmitter release, _pre was the potential of the presynaptic cell, and E_post was the synaptic reversal potential. Gaussian noise (t), restricted to a very low amplitude, was introduced to synaptic transmission to make cells of identical membrane and synaptic properties slightly different; otherwise a transition from synchronous to antiphase oscillations during a decrease in g did not occur. I_ej was modeled as described in the text. In the experiment shown in Fig. 8, networks were constructed from Burster C neurons (Epstein and Marder 1990). Network cells differed in their values of Ca²⁺ and Ca²⁺-activated K⁺ conductances and in the rate of accumulation of free Ca²⁺, all of which were larger in the fast than in the slow network. Synaptic current was modeled as I_syn = g_synS(_pre)(  _syn) (Skinner et al. 1994), where S(_pre) = 0.5(1 + tanh [(_{pre  thresh})/_slope)]), _syn = 80 mV, _thresh = 40 mV, and _slope = 15 mV. Simulations were run using the software XPPAUT by B. Ermentrout.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Motor patterns generated by the adult and embryonic lobster STNS

In adult H. gammarus, the isolated STNS generates three spontaneous motor patterns (gastric, esophageal, and pyloric rhythms) with different cycle frequencies (Fig. 1A). The fastest rhythm (cycle period 1-2 s) is expressed by the pyloric network while the esophageal and gastric networks generate rhythms of intermediate (4-6 s) and slow (10-15 s) periods, respectively. By contrast, in the embryo the same neuronal population (Fénelon et al. 1998) generates coordinated activity organized in a single motor pattern that drives target muscles at the same cycle frequency but with different phases (Fig. 1B) (Casasnovas and Meyrand 1995; Le Feuvre et al. 1999). In addition to these different temporal relations in the adult and embryonic STNS rhythms, the amplitude of oscillations in individual embryonic neurons is significantly lower than in their adult counterparts. This is evident in Fig. 1C, where the same pyloric cell type, the lateral pyloric (LP) neuron was recorded intrasomatically in the adult and embryonic STNS. In both cases the cells express membrane potential oscillations underlying bursts of spikes. However, the amplitude of oscillations in the adult neuron is considerably greater than in the LP cell of the embryo. Moreover, a significant difference in oscillation amplitude between embryonic and adult cells appears to be a general feature of the STNS neuronal population (see also Casasnovas and Meyrand 1995) as seen in Fig. 1D, which shows amplitude distributions of a variety of embryonic and adult neurons recorded from the pyloric and gastric networks in the stomatogastric ganglion [mean ± SE amplitude of oscillation; adult, 34.9 ± 10.6 mV (n = 58 neurons); embryo, 6.5 ± 3.7 mV (n = 41 neurons)].

View larger version (37K): [in this window] [in a new window]   Fig. 1. Rhythmic activity of stomatogastric nervous system (STNS) motor networks in adult and embryonic lobster, Homarus gammarus. A: different spontaneous rhythms recorded extracellularly and simultaneously in vitro from motoneurons innervating pyloric (Pyl), esophageal (Oeso), and gastric (Gast) muscles in adult. Pyloric activity recorded from the pyloric dilator nerve, esophageal activity from the ventral posterior esophageal nerve, gastric activity from the anterior gastric nerve. B: single multiphase rhythm recorded intracellularly in stage E98% embryo from pyloric, esophageal, and gastric muscles. C: large-amplitude membrane potential oscillations underlie bursting in an adult pyloric lateral pyloric (LP) neuron, while in the embryo, the same neuron type expresses small membrane potential oscillations. Maximal hyperpolarized levels are indicated. D: pooled amplitudes of spontaneous membrane oscillations in gastric and pyloric neurons in adult and embryo. In both the adult and embryo, the amplitude of oscillations were measured from 58 and 41 cells, respectively, from 25 embryonic and 25 adult stomatogastric. The amplitudes were measured from the lowest membrane potential level to the peak of the slow wave. Horizontal bars: 1 s. Vertical bars: 10 mV.

Effects of altering internetwork electrical coupling in a STNS model

To test the hypothesis that electrical coupling may be involved in masking adult-like network properties in the embryonic STNS, we interconnected three separate model networks, each consisting of two mutually inhibitory oscillatory neurons, through gap junction coupling (see METHODS). Each neuron was coupled through the same junction conductance g to all other neurons except its network partner (Fig. 2A). Membrane and synaptic parameters were initially set to the same values in all cells except the slow current, which determined the different intrinsic frequencies of the networks (Fig. 2B, left).

View larger version (38K): [in this window] [in a new window]   Fig. 2. Effects of electrical coupling between 3 model oscillatory networks. A: schematic representation of the model system studied. Each network is constructed with identical neurons linked by reciprocal inhibition of the same strength (black dots). Bars between the cells on the right indicate pattern of gap junction coupling. B: a large step coupling (g = 0.45 at arrow) transforms independent rhythms into damped synchronized activity. C: cell traces as in B on slower time scale and superimposed on the same baseline level. Stepwise coupling increase (g, 0 to 0.5; g, steps = 0.05) gradually dampens oscillations until rhythm unification occurs at g = 0.45 (left arrow). Reducing coupling (g, 0.5 to 0) unmasks different network frequencies at g = 0.3 (right arrow) and thereafter oscillation amplitudes increase. In B and C, m = 0.1666, S = 5, Af = 1, Epost = 4, f = 2 for all cells, S = 1.8, 4, 10 for slow, moderate, and fast oscillators, respectively. Synaptic strength w = 0.2.

When electrical coupling was set to zero (g = 0, Fig. 2B), the model networks expressed basic features of adult STNS output consisting of three independent rhythms with different frequencies (cf. Fig. 1A) and strict alternation between members of each network. Introduction of strong coupling between these networks (from g = 0 to g = 0.45) produced three dramatic changes in their activity (Fig. 2B, right). First, the oscillation amplitude in all neurons was abruptly decreased by ~90%. Second, neuronal oscillations within each network switched from alternation to synchrony. Third, the different network rhythms became unified into a single synchronous rhythm. The evolution of these rhythm alterations and the damping of oscillations is illustrated in Fig. 2C, where all voltage traces as in Fig. 2B are superimposed on the same baseline at a slower time scale. Here a stepwise increase, then decrease, in coupling strength (g = 0.1) produced a gradual and reversible change in oscillation amplitude of all cells. A switch between different (shaded areas) and unified (unshaded area) rhythms occurred when coupling reached critical values (Fig. 2C, see arrows).

To explore the robustness of the above phenomena, we tested the response of the model to an alteration in the strength of intra-network inhibition that remained equally distributed among the networks (Fig. 3). In contrast to the experiment presented in Fig. 2C, where we observed the dynamic alterations of the activity pattern in response to changing g, here we tested the behavior of the system after it reached steady state. When no inhibition was present in the system (w = 0) and neurons were set to oscillate in anti-phase within each network, increasing g led quickly to rhythm synchronization (transition from shaded to unshaded areas) that was accompanied by a slight decrease in oscillation amplitude (solid lines). The more inhibition was introduced into the system, the more it resisted the synchronizing influence of electrical coupling. Indeed, as inhibitory strength w was increased (Fig. 3A, w = 0.15, 0.2), network synchronization occurred at progressively higher coupling strengths and with a correspondingly larger decrease in oscillation amplitude before final rhythm synchrony occurred. If inhibition was too strong (Fig. 3A, w = 0.3), increasing g now failed to produce network unification with synchrony and, instead, led to a complete collapse of activity. In this state, however, a single rhythm appeared when neuronal oscillatory capability was strengthened by increasing the fast conductance value (not shown).

View larger version (37K): [in this window] [in a new window]   Fig. 3. Evolution of oscillation amplitude and frequency as a function of electrical coupling strength for different levels of intranetwork inhibition. A: mean oscillation amplitude vs. g in similar experiment as in Fig. 2C, for different indicated synaptic strengths (w). Shaded areas indicate multiple rhythms, whereas unshaded areas indicate single rhythmic activity. Note at w = 0.3, no synchronization occurred. Data from moderate frequency network calculated from 100 time units simulation. B: with increasing g, 3 different network periods (shaded area) gradually converge onto a common value (unshaded area), which is similar for different inhibitory strengths (horizontal bar; wmin= 0.0, wmax = 0.2). This phenomenon is reversible. Cell parameters as in Fig. 2.

The damping of oscillations was accompanied by a change in cycle period of all three networks until they converged onto a common value as illustrated for w = 0.15 (Fig. 3B). The period of the synchronized rhythm was very weakly dependent on the strength of inhibition and decreased slightly with increasing w, as indicated by the upper (w = 0.0) and lower (w = 0.2) limits within the horizontal shaded area in Fig. 3B.

It is noteworthy finally that some hysteresis accompanied these changes in electrical coupling. This was due not only to experimental procedure (i.e., a stepwise change in coupling strength before the system had reached steady state; Fig. 2C), but also when a steady-state behavior was being tested (Fig. 3B). This in turn suggests that over a certain range of electrical coupling, a bi-stability may occur where both different or synchronized rhythms can provide a stable solution.

Network potential (NP) as a representation of network activity

We next sought an explanation for these damping and unifying effects of electrical coupling between different oscillatory networks. Initially, consider two distinct entities, a single neuron a and a single network N that consists of n cells. Let neuron a be uniformly coupled through conductance g to each of n cells of network N. The junction current between a and N is then given by

(1)

where _a is the membrane potential of a and ₁, ₂, ... , _n are the network cell membrane potentials. Equation 1 can be written as

(2)

which gives

(3)

Equation 3 thus describes the junction current of neuron a coupled through conductance ng to the mean membrane potential of all cells in network N. We will call this variable "Network Potential" (NP) as it is a dynamic image of the activity of all the cells of network N that interact with cell a. Thereby

(4)

As seen in Fig. 4, the global operation of a given neural network is encoded in its NP. For instance, consider two model neurons that oscillate in phase opposition due to reciprocal synaptic inhibition. When w is set to 0, the voltage traces are perfectly symmetrical, and the NP generated is thus a tonic signal situated at mid-amplitude of oscillation (see arrows Fig. 4A). This is due to the fact that in our model oscillatory cell, voltage traces situated above and below level  = 0 (which is the resting potential of the cell and a mid-line of membrane potential oscillation) are mirror images. Therefore for two cells that oscillate in anti-phase, the mean value of their membrane potentials is  = 0. However, for w > 0, the NP now becomes a small-amplitude phasic signal due to a slight asymmetry caused by synaptic inhibition within each half cycle (Fig. 4B). NP is also shaped by other network properties, as for example, when the oscillatory capability of one neuron is weakened (Fig. 4C) or a third cell is added to the network (Fig. 4D).

View larger version (30K): [in this window] [in a new window]   Fig. 4. Generation of different Network Potentials (NPs). A and B: 2 identical oscillatory neurons interconnected by inhibitory synapses of identical strength (w). A: for w = 0 a tonic NP is generated. B: for w = 0.2 the network generates a small amplitude phasic NP with a frequency twice as high as the inherent frequency of the network. C and D: asymmetry in cell membrane properties due to an increase of fast current conductance in one cell (C) or an increase in cell number (D) leads to large amplitude NPs with different shapes. Arrows indicate equivalent potential levels (V = 0) for all traces. In A-D, f = 2 except f = 0 in neuron a in C; S = 10; in A, w = 0; B and C, w = 0.2; in D, wa, wb = 0.1, wc = 0.2. Other parameters as in Fig. 2.

With this understanding, we then examined how the NPs generated by two networks A and B are involved in their electrical interaction. Again networks A and B consisted of two model cells a/b and c/d, respectively, which were linked by reciprocal inhibition within each network while any two cells belonging to different networks were coupled via electrical conductance g (Fig. 5A). The coupling current i_a between cell a and cells c and d of network B (Fig. 5B) is given by

(5)

Thereby

(6)

where, according to Eqs. 3 and 4, NP_B = (_c + _d)/2. Equation 6 describes the interaction between cell a, represented by its potential _a, and network B, represented by its potential NP_B (Fig. 5C). If we now add the contribution of cell b to the internetwork communication (Fig. 5D), which is described by the current
then the total current I between A and B is given by

(7)

which leads to

(8)

Equation 8 thus describes the electrical relationship between networks A and B through the interaction of their network potentials NP_A and NP_B, respectively (Fig. 5E). Similarly, the total junction current I, through which any two networks A and B, coupled in an "all-to-all" fashion, communicate, is given by

(9)

where G = n_An_Bg is the internetwork coupling strength, n_A, n_B, and NP_A, NP_B are numbers of cells and NPs of A and B, respectively.

View larger version (21K): [in this window] [in a new window]   Fig. 5. Modeling NP. A: cells belonging to reciprocally inhibitory networks A and B are coupled in an "all-to-all" fashion via identical coupling strength g. B: a sub-circuit of the model presented in A consisting of single cell a and network B. a, c, and d are membrane potentials of cell a, c, and d, respectively. Note anti-phase oscillations in network B. C: cell a "senses" network B through the latter's Network Potential NPB, which represents the mean membrane potential of network members c and d. The interaction between a and NPB is mediated by electrical coupling of the strength 2g. D: cell b interacts with network B in a similar fashion as cell a. E: the activity of network A is represented by its Network Potential NPA (similar to the construction of NPB in C), which now interacts with NPB via coupling strength 4g.

Equation 9 is also valid for nonuniform coupling. In this case

(10)

where a₁, a₂, ... , a_n specify the proportion of internetwork coupling G provided by individual network cells (a_i = 1/n for i = 1, 2, ... , n in the case of uniform coupling).

It is important to note that the NP as defined by Eq. 10 is a representation of a given network in terms of a particular distribution of its electrical coupling with another network. For an all-to-all uniform coupling, this variable is equivalent to the mean value of the membrane potential of all cells belonging to a given network, as in Eqs. 4-9. However, in a general case the contribution to NP of individual network members may be different (i.e., a_i, i = 1; n in Eq. 10 may be different). Thus a given network may be represented by different NPs in its interaction with different networks, depending on the distribution of electrical coupling with these networks.

Electrical interaction between one cell and a network

To investigate the essential mechanism underlying the damping and unifying effects of electrical coupling, we first analyzed the sub-circuit of the model illustrated in Fig. 5, containing single cell a with membrane potential _a and network B, built of two reciprocally inhibitory oscillators that generates potential NP_B (Fig. 6A). As seen by Eq. 6, with increasing coupling g, the coupling current will equalize the potentials _a and NP_B. Assume now that network B is solely a receiver of the potential _a of cell a, without any reciprocal influence (Fig. 6A). Therefore as _a is not affected by this interaction, NP_B will be gradually sculpted into _a's own waveform (compare a and NP_B traces in Fig. 6A). These modifications in NP_B reflect the alterations in the intranetwork coordination that is changed from anti-phasic oscillation to full synchrony (see traces c and d in Fig. 6A). It must be noted that the weaker the reciprocal inhibition within the network, the lower is the coupling strength at which synchrony can be imposed on network B members by cell a.

View larger version (25K): [in this window] [in a new window]   Fig. 6. Interaction between a single cell and a network. A: assuming cell a influences network B without reciprocal interaction. Increasing g (from g = 0 to 1.2) results in a gradual unification of NPB with a (cf. 2 top traces). As a result, NPB amplitude increases significantly, reflecting the increased level of synchronization between cells c and d of network B. B: assuming network B influences cell a unidirectionally. Due to a low amplitude of NPB, cell a undergoes a significant damping of oscillation amplitude (cf. top traces for g = 0, 0.3, 0.6) as a result of unification of a with NPB. C: when reciprocal interaction is permitted, both damping and synchronization of all cells occur as a final state with increasing g (right panel). At intermediate coupling strength, rhythm unification with patterned activity, instead of full synchrony, occurs (middle panel). In A-C, f = 2, s = 1.8 in a, s = 5 in c and d, wc, wd = 0.2. Other parameters as in Fig. 2.

In a reverse case of such unidirectional influence, where network B now affects cell a, _a will be gradually modified into the form of NP_B (Fig. 6B). Since the network potential of two oscillatory cells is a low-amplitude signal situated close to the mid-line of their oscillations (i.e., toward  = 0, see Fig. 4B), the major effect of this NP_B influence on cell a will be a significant damping of its oscillation (Fig. 6B). A decrease in the oscillation amplitude of cell a as a function of the strength of electrical coupling can be estimated by assuming NP = 0. Such an approximation is also applicable in the case when a cell is electrically coupled to a large population of cells oscillating at very different phases (see APPENDIX).

In a final step, we allowed for a reciprocal influence between cell a and network B. In this case the two previously described effects of electrical coupling, i.e., damping and synchronization, are present together (Fig. 6C). Thus with increasing g the system reaches the state where all cells oscillate in synchrony and with diminished amplitudes. However, the damping effect is not as strong as in the case of a unidirectional influence between network B and cell a (Fig. 6B), since NP_B now increases in amplitude due to the synchronization of network B members imposed by cell a. Significantly, unified patterns with multiple phases may be expressed at moderate coupling strengths (Fig. 6C, middle panel). In this case, the rhythm of cells a, c, and d are already unified, whereas cells c and d, due to their reciprocal inhibition are not yet fully synchronized. It is important to reemphasize here that we use the term unification with pattern, and not synchronization, to describe this new organization of neuronal activity into a common cycle frequency. In such unified rhythms, individual cells can still exhibit multiphasic coordination without full synchronization, as in the case of the motor pattern expressed by the embryonic STNS network (Fig. 1B) (see also Casasnovas and Meyrand 1995).

Until now we have examined the effect of electrical coupling between a single cell and a given network in which reciprocal inhibition generates antiphasic activity. In these conditions, whereas the oscillatory cell expresses a large-amplitude signal, the network generates a low-amplitude NP. As a result of increasing g, therefore the potential of cell a will be damped while the NP will be enhanced (see unification of _a and NP_B through the coupling current, Eq. 6). This corresponds to a change from anti-phasic to synchronous coordination of network members. The capacity to enhance the amplitude of NP through electrical coupling and thereby increase the level of synchrony within the network is dependent on the strength of intranetwork inhibitory connectivity, which acts in opposition to electrical coupling.

Electrical interaction between two networks: effect of heterogeneity

The phenomena described above concerning the communication between a single cell and a network are also expressed in the interactions between two networks in which the neurons are linked by inhibitory synapses. As demonstrated in Fig. 7A, uncoupled networks A and B generate different NPs (Fig. 7A, left, top 2 traces) due to their different inherent cycle frequencies. The amplitude of the NPs is low because of the lack of heterogeneity in the networks that are built of identical cells, interconnected by synapses of identical strengths (cf. Fig. 4B). As coupling is introduced, each cell becomes influenced by the NP of the neighboring network as described above. This produced damping of oscillation amplitude in each cell (compare cells a-d from left to right panels in Fig. 7A). Additionally, changes in coordination within each network occurred: at intermediate g the network rhythms expressed 1:2 coordination (middle panel, Fig. 7A), whereas for large g the rhythms became unified (right panel, Fig. 7A). These changes in coordination were accompanied by a gradual unification of the two NPs as described by Eq. 9.

View larger version (27K): [in this window] [in a new window]   Fig. 7. Networks communicate through their NPs. A-C: 2 uncoupled networks generate independent NPs (left, top 2 traces). With increasing g (0, 0.4, 0.8), interacting NPs become unified and entrain the entire neuronal population into a single, fully synchronized rhythm (right panel, neuron traces). A: if the cells in both networks are interconnected by identical synapses and NPs are of low amplitude, rhythm unification occurs together with synchronization of neurons only for g = 0.8. B: weakening synaptic strength in network A results in rhythm unification, cells a and b being synchronized for g = 0.4, while cells c and d continue to oscillate in anti-phase. C: with intranetwork heterogeneity in synaptic strength, networks generate large-amplitude NPs. As a consequence, multiphasic unification of both networks occurs at g = 0.4. Note eventual damping of activity (at g = 0.8) is weak (B), moderate (A), or complete (C), depending on the strength of inhibition in the system. In A-C, f = 2, S = 1.8 in a and b, S = 5 in c and d. In A, wa-d = 0.2; in B, wa, wb = 0.1, wc, wd = 0.2; in C, wb, wd = 0.05, wa, wc = 0.3. Other parameters as in Fig. 2.

To test the effect of heterogeneity on the behavior of this system, we first weakened the synaptic strength within network A (Fig. 7B). Such an alteration reduced the resistance of network A to the synchronizing influence of incoming NP_B. As a consequence, cells a and b belonging to network A now became fully synchronized at intermediate coupling strength (g = 0.4, Fig. 7B). Thereby, the amplitude of NP_A was significantly enhanced, providing a strong signal that entrained network B and reduced the damping effect on this network. However, since reciprocal inhibition in network B is stronger than in network A, the cells c and d were still not yet fully synchronized (see middle panel, Fig. 7B). Thus in contrast with the previous case (Fig. 7A), the cells now expressed a unified rhythm with multiple phases at the moderate coupling strength (g = 0.4). At higher coupling strength (g = 0.8), the cells within each network expressed fully synchronized coordination as previously, but with a relatively high oscillation amplitude. This was due to the reduced amount of inhibition within the system (compare A and B in Fig. 7).

Second, we introduced intranetwork heterogeneity in the strength of synaptic inhibition in both networks (Fig. 7C). These changes enlarged the amplitude of corresponding NPs (compare 2 top traces in Fig. 7, A-C, left panels) and thereby reinforced the entraining effect of a given NP on the members of the other network. Thus the network rhythms already became unified at moderate coupling strengths, with individual cells still expressing out-of-phase coordination maintained by inhibitory coupling (middle panel, Fig. 7C). A further increase in g now led to a complete collapse of oscillations. This was again due to the presence of strong inhibition in the system (compare Fig. 7, C and B; see also DISCUSSION).

Thus we have shown that the unified rhythm can express different temporal patterns. With increasing g, the system always attains full synchrony (see right panels in Fig. 7, A and B) or collapse (see right panel in Fig. 7C), depending on the strength of inhibitory connections within the networks (see also Fig. 3A). However, at intermediate g patterned rhythm unification may occur before either of these final states is reached (see middle panels, Fig. 7, C and D). The necessary condition for such multi-phasic unification is that the incoming NP is sufficiently large to entrain the neighboring network members to its own frequency, whereas the reciprocal inhibition prevents them from reaching full synchrony.

The generality of the phenomenon described above was further tested by experiments with more complex neuron models containing five conductances (Epstein and Marder 1990). Here again as for the simpler neuron model used above, increasing coupling led to damping of oscillations and network unification with multiple phases (Fig. 8). Interestingly, in this model where neurons generate fast spikes, introducing electrical coupling can result in damping of oscillation amplitude below spike generation threshold. Nonetheless, the unified multiphasic patterns of slow membrane potential oscillations still occur.

View larger version (25K): [in this window] [in a new window]   Fig. 8. Interaction between networks built from spiking model oscillators with 5 currents. Increasing g (0, 0.03, 0.037) results in NP unification and a damped single rhythm. Note 1:2 network coordination despite 1:1 NP coordination for g = 0.03. Synaptic conductance (in mmho/cm2) gsyn(a), gsyn(b) = 0.1, gsyn(c), gsyn(d) = 0.02; membrane conductance (in mmho/cm2) gCa = 0.12 in a and b, 0.18 in c and d, gKCa = 0.32 in a and b, 0.6 in c and d; electrical conductance g as indicated in B (in mmho/cm2); Ca2+ accumulation rate (in ms1)  = 0.003 in a and b, 0.005 in c and d. Other parameters as in Epstein and Marder (1990).

Effect of widespread electrical coupling in a more realistic STNS model

In a final step we tested a more realistic model of the adult STNS, which consisted of two two-neuron circuits (corresponding to esophageal and gastric network subsets) and one three-neuron network (equivalent to the pyloric network) operating at different frequencies (Harris-Warrick et al. 1992). In an approximation to the general early developmental situation where electrical coupling is widespread and nonspecific (Kandler and Katz 1995; Pienado et al. 1993; Walton and Navarrete 1991), we introduced electrical coupling within these model networks, in addition to internetwork coupling (Fig. 9A, top). Both damping and unification with multiple phases persisted under such experimental conditions (Fig. 9A, bottom). Indeed, electrical coupling between cells belonging to the same network produced additional damping of membrane potential oscillations and effectively weakened their reciprocal inhibition. This in turn facilitated the unifying influence of incoming NPs (not shown). As seen in Fig. 9B (see also simulations in Figs. 2B and 3) escape from coupling revealed three independent network rhythms corresponding to the intrinsic frequency of each circuit. Moreover, as illustrated in the simulation of Fig. 9C, these networks can be reunified, but without damping (Fig. 9C, bottom), if a number of specific internetwork electrical connections is preserved (Fig. 9C, top). In this case the single-cell activity constitutes the NP of a given network and thereby represents the network in its communication with the other networks. Importantly, since this NP signal is now of large amplitude, there is no damping effect on individual cell oscillations as in the case of widespread electrical coupling (cf. Fig. 9, A and C).

View larger version (51K): [in this window] [in a new window]   Fig. 9. Effects of modulating electrical coupling on the activity of a network ensemble. Shown are 2- and 3-cell networks and the activity patterns they produce when nonspecifically coupled (A), uncoupled (B), and specifically coupled (C). Note emergence of large-amplitude independent network oscillations from a damped single rhythm (A and B), then unification without damping (B and C). The boxes highlight the periods of the different network outputs. f = 2 except f = 1.5 in b and d, 2.5 in e, S = 1.8 in a and b, 4 in c and d, 10 in e-g; wa, wc, wgf = 0.05, wb, wd, wfe, wfg, wge = 0.2, we = 0.3. Other parameters as in Fig. 2.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

The results described here indicate that widespread electrical coupling dampens neuronal oscillations and can fuse different network outputs into a single multiphasic pattern. The fact that strong electrical coupling unifies the cycle frequencies of different oscillators comes as no surprise to any neurophysiologist. Also, despite the classical view of gap junctions as a synchronizing mechanism, it is already known that in some circumstances such coupling can actively foster asynchrony in a population of spiking cells (Chow and Kopell 2000; de Vries et al. 1998; Sherman and Rinzel 1992). Indeed, depending on spike shape/size and gap junction strength, coupled neurons can be synchronized, anti-synchronized, phase locked at any phase, or lose their ability to fire periodically (Chow and Kopell 2000). This can be understood by thinking of electrical coupling as acting as excitation or inhibition, depending on whether the electrically coupled cell partner is active in the spike phase or in the postpolarization phase, respectively. We show here that in a population of mutually inhibitory cells expressing slow membrane potential oscillations, there exists another mechanism for multiphasic unification of neuronal activity through electrical coupling. Specifically, this phenomenon is a consequence of a battle between two opposing forces: one of them a synchronizing influence of electrical coupling, and the other, mutual inhibition that tends to maintain cell activity in antiphase and thereby competes directly with the action of electrical coupling. When electrical coupling is weak, cells within each network oscillate in anti-phase due to inhibitory coupling and network rhythms are independent. When electrical coupling is strong, all cells belonging to multiple networks are forced to oscillate in phase. However, for intermediate coupling strengths, a third state may occur. In this state the network rhythms are already unified due to interaction of network potentials conveyed through electrical junctions, whereas phase differences between cells still occurs due to the presence of inhibition, which is still relatively strong in relation to electrical coupling. Importantly, moreover, this multiphasic rhythm unification occurs only if there is sufficient heterogeneity of inhibitory or electrical coupling. The opposing action of electrical and inhibitory coupling between two network cells is also not a new phenomenon, especially in the stomatogastric system (Graubard and Hartline 1987). However, the novelty of the present study has been to investigate the competition between these two types of coupling throughout a population of neurons organized in multiple inhibitory networks operating at different inherent cycle frequencies.

The other new effect of widespread electrical coupling reported here, which accompanies the unification and eventual synchronization of the population of neurons, is a gradual damping of individual neuronal oscillations. With weak coupling, the damping of neuronal oscillations results from the electrical interaction of individual cells with surrounding networks, which generate low-amplitude NPs due to a still asynchronous coordination within each network. By contrast, when cells are synchronized by strong electrical coupling, the NPs generated are of large amplitude, and there is no damping effect resulting from a single-cell-NP interaction. In this state the damping is produced by the synchrony itself. As they depolarize, individual cells will release more inhibitory transmitter as well as receiving an increased amount of inhibition from their synchronized neighbors. On the other hand, during hyperpolarized phases they are weakly inhibited or not at all (depending on the gradient of graded transmitter release as a function of voltage). If sufficiently strong, this mutual inhibitory effect can lead to a complete collapse of entire network activity.

The results described here have important implications for communication between networks in which oscillatory neurons are interconnected by synaptic inhibition. Many such networks are responsible for rhythmic motor behavior (Marder and Calabrese 1996). A possible role of electrical coupling in such systems could be to coordinate multiple network function without synchronizing the activity of their constituent elements. Moreover, since coupling efficacy is subject to ontogenetic (Kandler and Katz 1995; Pienado et al. 1993; Walton and Navarrete 1991) and/or modulatory (Baldridge et al. 1998; Hatton and Yang 1996; Johnson et al. 1993) control, then a powerful mechanism for the dynamic reorganization of multiple network operation is potentially available.

Interestingly, the transition in network interactions seen in Fig. 9, A and B, for example, strongly recalls alterations in lobster STNS network function seen during the course of development, where separate adult circuits emerge from a single embryonic network that expresses small amplitude oscillations (Casasnovas and Meyrand 1995). Moreover, recent data indicate that fundamental adult traits are already embedded in the immature STNS but are masked by some developmental mechanism (Le Feuvre et al. 1999). Our present results suggest such a mechanism: adult networks may be present in the same neuronal population early in development but are forced to express a single embryonic pattern by widespread electrical coupling.

A role for oscillation damping is still unclear. Indeed an initial concern was that the relatively small amplitude of oscillation in embryonic stomatogastric (STG) neurons simply resulted from cell damage due to microelectrode impalement. However, notwithstanding the fact that the size of these embryonic neurons, although considerably smaller than their adult counterparts, are still larger than most neurons that have been studied with intracellular recordings in the vertebrate nervous system, there is evidence suggesting that major cell injury was not responsible for the small oscillations in the STG neurons. First, comparison of intrasomatic activity with intracellular recordings from target muscles before presynaptic motorneuron impalement confirmed that all network output parameters (cycle period, burst duration, spike frequency, and phase relationships) remained unaltered. Second, soma impalement never led to tonic firing, which would be expected to occur during any generalized damage-induced membrane depolarization.

A biological role for oscillation damping therefore is that it could serve to match bioelectrical behavior with neuronal size by preventing the electrotonic invasion of large-amplitude oscillations throughout the entire structure of small embryonic neurons. Another related possibility is that in a given network assemblage, the reduction of oscillation amplitudes below spike threshold (see Fig. 8) may immediately and reversibly prevent impulse-mediated communication with other parts of the nervous system or the periphery, while any graded transmitter signaling at central synapses within the population is maintained. It is also important to realize that specific changes in coupling strength (see Fig. 9C), such as a retention of certain pathways during a developmental reduction in coupling (Spitzer 1982; Walsh et al. 1989) or their alteration by modulatory instruction in the adult nervous system (Baldridge et al. 1998; Hatton and Yang 1996; Johnson et al. 1993), may sustain multiple network unification without causing damping of neuronal oscillations.

Finally, our data point to the possibility of considering neuronal information transfer not only at the level of cell-to-cell communication, but also at the level of signaling between neuronal ensembles via synthetic representations of their activity conveyed through NPs.