Rhythmic Pattern Generation in Invertebrates
Abstract and Keywords
This chapter begins by defining central pattern generators (CPGs) and proceeds to focus on one of their core components, the timing circuit. After arguing why invertebrate CPGs are particularly useful for the study of neuronal circuit operation in general, the bulk of the chapter then describes basic mechanisms of CPG operation at the cellular, synaptic, and network levels, and how different CPGs combine these mechanisms in various ways. Finally, the chapter takes a semihistorical perspective to discuss whether or not the study of invertebrate CPGs has seen its prime and what it has contributed—and may continue to offer—to a wider understanding of neuronal circuits in general.
The neuronal circuits that generate the rhythmic motor commands underlying periodic behaviors in invertebrates, including walking, crawling, swimming, and rhythmic digestive movements, are called central pattern generators (CPGs) (Grillner & Zangger, 1975), and they are arguably the best studied, and best understood, class of neuronal circuits. This claim applies both in terms of experimental investigation of cellular, synaptic, and circuit properties, and in terms of physiologically detailed computational models of these circuits and their electrical behaviors.
CPG circuits can be described as multilevel systems, whose core components include (1) a rhythm generator or oscillator (also called CPG timer) that produces the basic rhythmic activity independent of rhythmic input from higher centers or rhythmic sensory feedback, (2) a pattern formation layer that receives input from the CPG timer and produces temporal activation patterns for individual muscles without retroactively affecting the CPG timer, and (3) an output layer containing motoneurons that actually activate muscles (Fig. 15.1). For a review of this multilevel structure, and how sensory feedback can influence it at several levels, see Prochazka and Yakovenko (2007). Note, however, that this separation into several layers, while conceptually useful, does not necessarily correspond to a strict separation of neurons into distinct layers. For example, in many CPGs, especially invertebrate CPGs, motoneurons can also participate in the patterning network and even in the timing network (Selverston, 2010).
This chapter will primarily focus on invertebrate CPG timing circuits, because the pattern formation layers and output circuits for several key invertebrate CPGs are discussed in detail in other chapters of this volume (Cattaert & Edwards, this volume; Cropper et al., this volume; Katz & Sakurai, this volume; Ritzmann & Zill, this volume).
Besides focusing on CPG timing circuits, this chapter will also ignore the role of sensory inputs and neuromodulatory inputs to the circuit, again because these are covered in other chapters (Cattaert & Edwards, this volume; Cropper et al., this volume; Katz & Sakurai, this volume; Ritzmann & Zill, this volume). This is not to say that sensory (p. 392) feedback and neuromodulation are not important in motor control—they can in fact substantially modify and sculpt CPG outputs (Chiel et al., 2009; Marder, 2012). However, sensory and modulatory inputs are usually not required for CPG circuits to develop and function properly (Marder & Rehm, 2005), suggesting that they often do not form a necessary part of rhythmic pattern-generating circuits.
Finally, this chapter will not focus on factors extrinsic to the CPG timing circuit per se, such as command neurons that can start and stop CPG operation in some systems (Edwards et al., 1999), or on connections to CPG circuits in other parts of an animal’s body, such as in segmented animals that require intersegmental coordination for proper motor control. Examples of extrinsic factors and intersegmental coordination mechanisms are described in two other chapters (Cattaert & Edwards, this volume; Cropper et al., this volume).
Having thus narrowed the focus of this chapter to core CPG timing circuits, subsequent sections will outline basic principles of CPG timing circuit operation, will argue why invertebrate CPGs are highly suitable for the study of these mechanisms, will ask whether the study of invertebrate CPGs has passed its heyday, and will address whether and how lessons learned from invertebrate circuits generalize to larger circuits such as those found in vertebrates.
Why Study Invertebrate Central Pattern Generators?
In a scientific climate that increasingly emphasizes research that is likely to have short-term or at least mid-term clinical relevance for humans, what is the value of basic research into the operational mechanisms and principles of invertebrate CPGs? This question becomes even more apparent if one realizes that while vertebrate CPGs usually comprise thousands of neurons, invertebrate CPGs often contain just a handful of cells—so how do invertebrate and vertebrate CPGs compare?
Arguably, it is precisely the fact that invertebrate CPGs contain few and often large neurons that makes these circuits such ideal experimental testbeds. In addition to the small number and large size of many invertebrate CPG neurons, another major advantage is that many of them are “identifiable” neurons (Hudson & Prinz, 2010), meaning that the same individual neuron can be identified from animal to animal based on its stereotyped electrical activity, its synaptic connections, its projections through motor nerves (Harris-Warrick et al., 1992), and sometimes even its exact location within the nervous system or ganglion (Bucher et al., 2007).
Does this seeming simplicity of invertebrate CPG circuits mean that we cannot glean insights into general CPG operation from them? Many experts would disagree, arguing that while invertebrate CPG networks may be small, they are not simple at all (Calabrese & De Schutter, 1992). Ignoring the wealth of experimental data and insights obtained from invertebrate CPGs over decades by many labs would therefore constitute a major setback to our understanding of pattern generation in a multitude of systems, and to neuroscience as a whole (Selverston, 2010).
Increasingly, in cellular and circuit neuroscience, computational modeling is becoming a powerful tool to complement experimental investigation of the principles underlying signal generation and processing in neuronal networks. In this respect, too, the exceptional features of invertebrate CPGs—small numbers of experimentally accessible neurons, stereotyped outputs, and so on—are a major boon, because they make physiologically realistic computational modeling more feasible than in most other systems. As one expert puts it, “of all the circuits (p. 393) that have been examined thus far, only small invertebrate CPGs have come close to having enough data at the cellular level to model reasonably accurately” (Selverston, 2010, p. 2330).
Basic Principles of Central Pattern Generator Operation
An increasingly popular concept and recent focus of much of neuroscience is the “connectome,” which comes with the notion that operational principles, memories, and the ability of brains to learn and adapt to the environment reside primarily in the synaptic connectivity between individual neurons and between brain regions (http://www.scholarpedia.org/article/Connectome, and references therein). In contrast, decades of work in invertebrate CPG circuits and many other systems indicate that although understanding the connectome is certainly necessary for understanding brain function, it is not by itself sufficient (Bargmann & Marder, 2013). Furthermore, complex, dynamic, and often counterintuitive interactions between electrical and chemical synaptic connections can additionally complicate our understanding of network dynamics based on the connectome alone (Marder et al., 2017).
Rather, CPGs have taught us that functional network activity arises from a complex interplay of synaptic and cellular properties, and that both are relevant for proper circuit function (Marder & Calabrese, 1996). The following paragraphs will describe several ubiquitous rhythm-generating mechanisms that rely mainly on cell-intrinsic properties, mainly on synaptic connectivity, or on the tight interplay of both. For further reference, a relatively comprehensive compendium of all three types of rhythm generating mechanisms—cell-based, network-based, or hybrids of both—is provided in Selverston (2010).
Perhaps the conceptually simplest way in which CPGs can generate rhythmic oscillatory activity is through the use of endogenous oscillators. These are individual neurons that generate rhythmic spiking or, more commonly, bursting electrical activity even in synaptic isolation, meaning that the oscillation is generated by the neuron itself rather than arising from the interaction of multiple neurons in a network. Cell-intrinsic properties can allow an isolated neuron to be an endogenous burster, that is, to generate rhythmic trains of action potentials separated by intervals of hyperpolarization and silence even in the absence of rhythmic inputs. Cellular properties that allow for such endogenous bursting typically involve the interaction of a fast dynamic process that underlies spiking activity during the burst, and a slower mechanism that switches the neuron between the spiking phase that constitutes a burst of action potentials, and the quiescent interburst interval. Figure 15.2 illustrates several classes of mechanisms that combine a fast and a slow process in this manner to produce cell-intrinsic oscillations. To describe just one example in more detail, refer to the bottom right circular diagram in the figure. During fast spiking generated by sodium and fast potassium currents, voltage-gated calcium channels flux calcium into the cell during every spike, leading to a gradual buildup of calcium during the burst that in turn activates calcium-dependent potassium (KCa) channels, which eventually hyperpolarize the neuron and terminate the fast spiking activity. During the resulting quiescent phase, calcium is slowly buffered back to normal levels, which causes the KCa channels to close, allowing the neuron to depolarize and enter its next burst of rapid spiking.
Endogenously oscillating individual neurons provide a relatively simple and robust mechanism to generate reliable oscillations in a CPG. But this same robustness can also make endogenous oscillators hard to control if the CPG needs to be able to initiate and terminate oscillations or control oscillation frequency over broad ranges to accommodate variable environmental conditions and behavioral requirements (Marder & Bucher, 2001).
An alternative pattern-generating circuit structure that overcomes some of these controllability issues relies on circuit components that are not in themselves oscillatory, but give rise to oscillations through mutual inhibition. In many circuits that rely on mutual inhibition for pattern generation, inhibitory synapses occur between circuit components that—directly or through downstream motoneurons—control antagonistic muscles. Mutual inhibition can thus help ensure that antagonistic muscles, such as flexors and extensors of the same limb, are not counterproductively activated simultaneously. An additional advantage of inhibition versus excitation in CPGs, and in their core timing circuits, is that inhibition promotes more stable and accurately phase-locked activity in the circuit components (F. H. Sieling et al., 2009; Szucs et al., 2009). Given these beneficial effects of inhibition for CPG circuit function and reliability, it is thus not surprising that while electrical and excitatory chemical synapses can occur in CPGs, inhibitory synapses are the most ubiquitous form of synaptic interaction within pattern-generating circuits. (p. 394)
The particular circuit configuration where mutual inhibition between two neurons or groups of neurons leads to a periodic alternation in their spiking or bursting activity is called a “half-center oscillator,” or HCO (Cropper & Weiss, 1996). Such oscillatory structures coordinate the activity of antagonistic muscles that control the same limb (as mentioned earlier), but they can also coordinate left-right or dorsal-ventral movements in locomotor CPGs. Mechanisms of oscillation in HCOs have been extensively studied.
A useful distinction that helps conceptualize different coordination principles at work in HCOs, and in other types of CPGs, is that of escape versus release mechanisms, a distinction introduced in Wang and Rinzel (1992) on the basis of theoretical studies of a reduced HCO computational model. In the release mechanism, the spontaneous termination of a spike or burst of spikes in one half of the HCO leads to the cessation of the inhibition imposed by that neuron on the other half of the HCO, which thereby gets released from inhibition. The characteristics of an alternating oscillatory pattern generated through the release mechanism sensitively depend on the temporal dynamics of the inhibitory synapses involved, that is, how soon after termination of the presynaptic spike or burst the inhibition of the postsynaptic partner ends.
In contrast, the escape mechanism depends more heavily on the cellular properties of the HCO components than on the synaptic dynamics. In the escape scenario, each half of the HCO is endowed with a slow cellular postinhibitor rebound (PIR) mechanism (for example, a hyperpolarization-activated (p. 395) inward current with slow dynamics) that gradually activates during synaptic inhibition of the cell, until it is strong enough to counteract the inhibition and allow the postsynaptic neuron to “escape” from inhibition and generate its next spike or burst. The classes of burst mechanisms provided in Figure 15.3 contain components of both escape-like and release-like mechanisms.
This dichotomy of escape and release mechanisms illustrates that the oscillatory behavior of a CPG can be heavily influenced by cellular as well as synaptic properties (Calabrese & De Schutter, 1992)—this confirms that the connectome, while necessary, is not sufficient to explain circuit function, whether in invertebrate CPGs or other systems (Marder & Calabrese, 1996; Bargmann & Marder, 2013).
Beyond PIR properties and cell-endogenous oscillations, other cellular characteristics often found in CPG neurons, and conducive to rhythm generation, include plateau potentials, bistability, and spike rate adaptation (Fig. 15.3), as reviewed in more detail in Marder and Bucher (2001).
In practice, whether a given CPG relies on intrinsic oscillators or on network mechanisms can at times be difficult to determine experimentally because of confounds such as invasive recording (p. 396) techniques that can actually alter the biophysical properties of the neurons that are being recorded from (Marder et al., 2005). One example of this phenomenon concerns the leech heartbeat rhythm generator, which consists of two interneurons mutually inhibiting each other in a half-center configuration and which generates a pattern of alternating bursts. Historically, it was thought that the neurons themselves were not intrinsic bursters, because applying synaptic blockers while recording intracellularly from the neurons with sharp electrodes caused a transition from bursting to tonic spiking in these neurons. This led to the conclusion that the leech heartbeat timing circuit relies on network-level mechanisms—rather than cell-autonomous mechanisms—to produce rhythmic bursting (Schmidt & Calabrese, 1992). However, revisiting the oscillation mechanism in this circuit with less invasive extracellular recording techniques revealed that the synaptically isolated cells were in fact endogenous bursters. The transition to tonic spiking upon synaptic isolation that had been observed earlier turned out to be an experimental artifact caused by membrane damage and leak inadvertently introduced with the invasive intracellular recording (Cymbalyuk et al., 2002). Pattern generation in the leech heartbeat system therefore does rely, at least in part, on cell-based mechanisms.
Most CPGs likely employ a combination of cellular and synaptic properties to reliably generate rhythmic oscillations. One circuit that has clearly been demonstrated to use both mechanisms is the pyloric pattern-generating circuit of the crustacean stomatogastric ganglion. At its core, the pyloric circuit contains a pacemaker kernel comprised of one anterior burster (AB) neuron tightly electrically coupled to two pyloric dilator (PD) neurons, with all three cells bursting in synchrony during the ongoing pyloric rhythm (Harris-Warrick et al., 1992). This pacemaker kernel rhythmically inhibits two types of follower neurons, a single lateral pyloric (LP) neuron and six to eight electrically coupled pyloric constrictor (PY) neurons. The LP and the PY neurons are not endogenous bursters, but burst in rebound from the inhibition they receive from the AB/PD pacemaker kernel—hence the term “follower neurons.” LP and the PYs also mutually inhibit each other, and the circuit produces a triphasic rhythm with the sequence AB/PD-LP-PY (Harris-Warrick et al., 1992). Careful analysis of the synapses from AB/PD onto LP and onto the PYs, and the rebound properties of LP and of the PYs, showed that both cellular and synaptic properties help ensure the correct AB/PD-LP-PY burst sequence. At the cellular level, LP has faster rebound properties than the PYs have. At the synaptic level, the AB/PD-to-LP inhibition has faster dynamics than the AB/PD-to-PY inhibition. Together, this combination of cellular and synaptic features synergistically ensures reliable generation of a physiologically functional pyloric rhythm (Eisen & Marder, 1982, 1984).
These are just a few examples that illustrate how the experimental accessibility and small number of identified neurons found in invertebrate CPGs allow the demonstration of fundamental principles of circuit operation. As described earlier, one conclusion is that CPGs have evolved to employ multiple mechanisms to promote robust and reliable pattern generation, which is often vital for the animal’s survival.
Are We Done With Invertebrate Central Pattern Generators?
Reviewing invertebrate central pattern generators, Calabrese and De Schutter (1992, p. 439) lamented that “a fundamental understanding of how such network oscillators work remains elusive,” and that “it is clear that both reciprocal inhibition and intrinsic membrane properties are important, but there remains no comprehensive understanding of how these two features interact to produce oscillations.” The elusiveness of such a fundamental understanding may well arise from the fact that there may not be a unique principle that explains all CPGs, let alone larger or more complex oscillatory circuits (Selverston, 2010). Examining more and previously unexplored invertebrate CPGs may only further illustrate circuit diversity rather than revealing a unique organizational principle of pattern generation. In keeping with this notion, few new invertebrate CPGs are currently being brought forward to be explored. Selverston speculates that we “may have seen the era of invertebrate circuit chasing come and go” (Selverston, 2010, p. 2343). Are we done with invertebrate CPGs?
Over the decades, the study of invertebrate CPGs has contributed important insights into mechanisms of pattern generation, and to an understanding of oscillations in neuronal circuits more broadly. In 2005, Marder et al. noted a “resurgence of interest in central pattern generators” (Marder et al., 2005). Many neuroscientists would agree that CPGs, including (or perhaps, especially) those of invertebrates, are worthy of study in their own right. Others question to what extent findings and (p. 397) conclusions from the study of invertebrate CPGs are generalizable to other, and supposedly more complex, neuronal circuits and systems. Opinions on this question have been mixed over the past decades, and are briefly reviewed in the following section.
What Invertebrate Central Pattern Generators Teach Us About Other Circuits
As stated earlier, the study of invertebrate CPGs and neuronal circuits in general is a basic research area in its own right. However, especially in a research funding climate that places increasing emphasis on translational and clinically relevant research, it is worth discussing how and to what extent CPG research has informed, and can inform, our understanding of other circuits. (Marder, 2000) states that “the early history of work on central pattern generating circuits was characterized by the hope that general principles would emerge that crossed phylogenetic boundaries” and asserts that “many principles first established in invertebrates also hold in vertebrates.” Indeed, for many years, vertebrate CPG preparations were lagging behind—and trying to catch up with—invertebrate CPG circuits, often because of technical difficulties that have since been at least partially overcome (see Marder, 2000; Marder & Rehm, 2005; Briggman & Kristan, 2008; and citations therein).
At what levels of organization do mechanisms identified in invertebrate CPGs generalize to other neuronal systems? At the neuronal level, some of the cell-intrinsic mechanisms described earlier, such as postinhibitory rebound (PIR) and plateau potentials, have been found to transfer relatively well to larger systems (Selverston, 2010), and generalize widely “in all animal groups” (Cooke, 2002).
At the circuit level, organizational principles such as the half-center oscillator structure and the importance of mutual inhibition, and some of the dynamic principles outlined earlier, are common to invertebrate CPG and vertebrate CPGs, especially spinal CPGs. Furthermore, the insight (originally from invertebrate CPGs) that anatomically similar circuits can produce similar and biologically functional rhythmic output on the basis of different cellular and synaptic properties (Prinz et al., 2003, 2004) is echoed in our growing understanding of how spinal CPGs can at least partially recover after spinal cord injury (Marder & Bucher, 2001). Going beyond pattern generation, it has been argued that even cortical circuits exhibit many anatomical, biophysical, dynamic, modulatory, and pathological similarities with CPGs, and, like CPGs, have rich internal dynamics even without rhythmic inputs. Indeed, Yuste et al. (2005, p. 477) go so far as to contemplate “the cortex as a central pattern generator.”
At a more technical level, techniques such as photoablation of individual neurons and dynamic clamp that were initially developed for the study of invertebrate CPGs are also applicable to vertebrate circuits (Nusbaum & Beenhakker, 2002), although it has been argued that such single-neuron techniques are less useful in vertebrate circuits, which usually rely on entire populations of neurons to generate functional electrical activity that in an invertebrate circuit would be generated by single or small numbers of neurons (Selverston, 2010). However, the advent of optogenetics and other genetic approaches now allows the deletion or manipulation (via hyper- or depolarization) of entire classes of neurons in vertebrate nervous systems, in essence providing vertebrate analogs to the single-neuron techniques previously pioneered in invertebrates (Marder & Rehm, 2005).
Some higher level lessons may be learned from the early “circuit breaking” efforts conducted on invertebrate CPGs and other circuits in the 1960s and 1970s. At the time, the field stepped into what some call the “connectivity trap,” that is, the notion that knowing the component neurons of a circuit and their synaptic connectivity is sufficient to fully understand the circuit and explain its function (Nusbaum & Beenhakker, 2002; Bargmann & Marder, 2013). In the invertebrate field and in many vertebrate neuronal systems it has since been well recognized that the biophysical properties of a circuit’s component neurons can be just as important for shaping circuit function as the network connectivity (Nusbaum & Beenhakker, 2002; Marder et al., 2005).
Furthermore, invertebrate CPGs have taught us that neuronal circuits can be extremely modulatable, in the sense that they can generate quite different activity patterns depending on the neuromodulatory milieu (Selverston, 2010). This importance of neuromodulation generalizes to other invertebrate and vertebrate circuits—Nusbaum and Beenhakker (2002, p. 349) state that “it is now evident that vertebrate neurons and neural circuits are as multifunctional as their invertebrate counterparts.” This further underscores the point that circuit anatomy by itself is not sufficient for an appreciation of the complexity and rich dynamics of neuronal circuits. These are important lessons to keep in mind, if only to complement the current emphasis and focus on (p. 398) the connectome embraced by many neuroscientists (Nusbaum & Beenhakker, 2002).
One aspect in which invertebrate CPGs are less likely to provide generalizable insights that apply to other neuronal circuits is that of Hebbian-style plasticity (Hebb, 1949). By their very nature, CPGs generate relatively stereotyped and robust electrical output, and therefore rarely display the types of synaptic plasticity that are thought to underlie learning and memory in other types of circuits (Yuste et al., 2005; Selverston, 2010). That said, other (non-Hebbian) forms of plasticity are well documented in invertebrate CPGs. A prominent example is the feeding circuit in the sea hare Aplysia californica, a CPG that controls movements of the animal’s buccal mass that are involved in the ingestion and egestion of food. The feeding CPG can undergo both classical and operant conditioning (Lorenzetti et al., 2006), and these forms of conditioning can involve both cell-intrinsic (Brembs et al., 2002) and synaptic plasticity (F. Sieling et al., 2014). During operant conditioning, the circuit plastically adjusts its biophysical properties in response to contingent reinforcement of certain motor patterns over others (Nargeot et al., 1997). These adjustments rely at least in part on excitability changes in individual CPG component neurons (Brembs et al., 2002). Interestingly, the same neurons whose properties change during operant conditioning also undergo changes during classical conditioning, although those changes are slightly different in nature (Lorenzetti et al., 2006). For another form of plasticity, namely homeostatic plasticity, invertebrate CPGs have also provided insights into cellular and synaptic mechanisms that turn out to be applicable in many other neural systems (Marder & Goaillard, 2006; Turrigiano, 2012).
Despite some limitations regarding the extent to which findings from invertebrate CPGs apply to many other circuits, these classic preparations still have a role to play (Marder & Rehm, 2005), and their study can provide a roadmap to general principles of circuit operation (Marder & Bucher, 2001). They continue to be invaluable for vertebrate studies (Nusbaum & Beenhakker, 2002) and can illuminate vertebrate systems that operate on the basis of similar mechanisms (Calabrese & De Schutter, 1992). Although some opine that the heyday of invertebrate CPG studies may have come and gone (Selverston, 2010), these classic preparations still have an important role to play (Marder & Rehm, 2005).
This chapter has examined our understanding of invertebrate central pattern-generating circuits—with a special emphasis on the timing circuits that lie at their core—and has summarized some basic mechanisms of pattern generation and their potential generalizability to neuronal network operation, beyond CPGs. Reflecting the field of invertebrate CPG research, recurring themes of the chapter have been (1) the recognition that multiple mechanisms have evolved to ensure reliable CPG operation, (2) that these mechanisms go beyond synaptic connectivity and include cell-intrinsic properties as well as emergent circuit phenomena that are not understandable from the connectome or from cellular properties alone, and (3) that different circuits combine these cellular, synaptic, and circuit mechanisms in many different ways to achieve and ensure proper physiological function.
While the most basic principles of pattern generation in invertebrate circuits may have been worked out in past decades, these circuits continue to hold the potential to help further our understanding of nervous system operation in the future.
Bargmann, C. I., & Marder, E. (2013). From the connectome to brain function. Nature Methods, 10(6), 483–490.Find this resource:
Brembs, B., Lorenzetti, F. D., Reyes, F. D., Baxter, D. A., & Byrne, J. H. (2002). Operant reward learning in Aplysia: Neuronal correlates and mechanisms. Science, 296(5573), 1706–1709.Find this resource:
Briggman, K. L., & Kristan, W. B. (2008). Multifunctional pattern-generating circuits. Annual Review of Neuroscience, 31, 271–294.Find this resource:
Bucher, D., Johnson, C. D., & Marder, E. (2007). Neuronal morphology and neuropil structure in the stomatogastric ganglion of the lobster, Homarus americanus. Journal of Comparative Neurology, 501(2), 185–205.Find this resource:
Calabrese, R. L., & De Schutter, E. (1992). Motor-pattern-generating networks in invertebrates—modeling our way toward understanding. Trends in Neurosciences, 15(11), 439–445.Find this resource:
Chiel, H. J., Ting, L. H., Ekeberg, O., & Hartmann, M. J. Z. (2009). The brain in its body: Motor control and sensing in a biomechanical context. Journal of Neuroscience, 29(41), 12807–12814.Find this resource:
Cooke, I. M. (2002). Reliable, responsive pacemaking and pattern generation with minimal cell numbers: The crustacean cardiac ganglion. Biological Bulletin, 202(2), 108–136.Find this resource:
Cropper, E. C., & Weiss, K. R. (1996). Synaptic mechanisms in invertebrate pattern generation. Current Opinion in Neurobiology, 6(6), 833–841.Find this resource:
Cymbalyuk, G. S., Gaudry, Q., Masino, M. A., & Calabrese, R. L. (2002). Bursting in leech heart interneurons: Cell-autonomous and network-based mechanisms. Journal of Neuroscience, 22(24), 10580–10592.Find this resource:
Edwards, D. H., Heitler, W. J., & Krasne, F. B. (1999). Fifty years of a command neuron: the neurobiology of escape (p. 399) behavior in the crayfish. Trends in Neurosciences, 22(4), 153–161.Find this resource:
Eisen, J. S., & Marder, E. (1982). Mechanisms underlying pattern generation in lobster stomatogastric ganglion as determined by selective inactivation of identified neurons. III. Synaptic connections of electrically coupled pyloric neurons. Journal of Neurophysiology, 48(6), 1392–1415.Find this resource:
Eisen, J. S., & Marder, E. (1984). A mechanism for production of phase-shifts in a pattern generator. Journal of Neurophysiology, 51(6), 1375–1393.Find this resource:
Grillner, S., & Zangger, P. (1975). How detailed is central pattern generation for locomotion. Brain Research, 88(2), 367–371.Find this resource:
Harris-Warrick, R. M., Marder, E., Selverston, A. I., & Moulins, M. (1992). Dynamic biological networks: The stomatogastric nervous system. Cambridge, MA: MIT Press.Find this resource:
Hebb, D. O. (1949). The organization of behavior: A neuropsychological theory: New York, NY: Wiley & Sons.Find this resource:
Hudson, A. E., & Prinz, A. A. (2010). Conductance ratios and cellular identity. PLoS Computational Biology, 6(7), e1000838.Find this resource:
Izhikevich, EM (2007). Dynamical systems in neuroscience: The geometry of excitability and bursting. Cambridge, MA: MIT Press.Find this resource:
Lorenzetti, F. D., Mozzachiodi, R., Baxter, D. A., & Byrne, J. H. (2006). Classical and operant conditioning differentially modify the intrinsic properties of an identified neuron. Nature Neuroscience, 9(1), 17–19.Find this resource:
Marder, E. (2000). Motor pattern generation. Current Opinion in Neurobiology, 10(6), 691–698.Find this resource:
Marder, E. (2012). Neuromodulation of neuronal circuits: Back to the future. Neuron, 76(1), 1–11.Find this resource:
Marder, E., & Bucher, D. (2001). Central pattern generators and the control of rhythmic movements. Current Biology, 11(23), R986–996.Find this resource:
Marder, E., Bucher, D., Schulz, D. J., & Taylor, A. L. (2005). Invertebrate central pattern generation moves along. Current Biology, 15(17), R685–R699.Find this resource:
Marder, E., & Calabrese, R. L. (1996). Principles of rhythmic motor pattern generation. Physiology Reviews, 76(3), 687–717.Find this resource:
Marder, E., & Goaillard, J. M. (2006). Variability, compensation and homeostasis in neuron and network function. Nature Reviews Neuroscience, 7(7), 563–574.Find this resource:
Marder, E., Gutierrez, G. J., & Nusbaum, M. P. (2017). Complicating connectomes: Electrical coupling creates parallel pathways and degenerate circuit mechanisms. Developmental Neurobiology, 77(5), 597–609.Find this resource:
Marder, E., & Rehm, K. J. (2005). Development of central pattern generating circuits. Current Opinion in Neurobiology, 15(1), 86–93.Find this resource:
Nargeot, R., Baxter, D. A., & Byrne, J. H. (1997). Contingent-dependent enhancement of rhythmic motor patterns: An in vitro analog of operant conditioning. Journal of Neuroscience, 17(21), 8093–8105.Find this resource:
Nusbaum, M. P. & Beenhakker, M. P. (2002). A small-systems approach to motor pattern generation. Nature, 417(6886), 343–350.Find this resource:
Prinz, A. A., Billimoria, C. P., & Marder, E. (2003). Alternative to hand-tuning conductance-based models: Construction and analysis of databases of model neurons. Journal of Neurophysiology, 90(6), 3998–4015.Find this resource:
Prinz, A. A., Bucher, D., & Marder, E. (2004). Similar network activity from disparate circuit parameters. Nature Neuroscience, 7(12), 1345–1352.Find this resource:
Prochazka, A., & Yakovenko, S. (2007). The neuromechanical tuning hypothesis. In P. Cisek, T. Drew, and J. F. Kalaska (Eds.), Computational neuroscience: Theoretical insights into brain function (Progress in Brain Research, 165), 255–265.Find this resource:
Schmidt, J., & Calabrese, R. L. (1992). Evidence that acetylcholine is an inhibitory transmitter of heart interneurons in the leech. Journal of Experimental Biology, 171, 329–347.Find this resource:
Selverston, A. I. (2010). Invertebrate central pattern generator circuits. Philosophical Transactions of the Royal Society B-Biological Sciences, 365(1551), 2329–2345.Find this resource:
Sieling, F., Bedecarrats, A., Simmers, J., Prinz, A. A., & Nargeot, R. (2014). Differential roles of nonsynaptic and synaptic plasticity in operant reward learning-induced compulsive behavior. Current Biology, 24(9), 941–950.Find this resource:
Sieling, F. H., Canavier, C. C., & Prinz, A. A. (2009). Predictions of phase-locking in excitatory hybrid networks: Excitation does not promote phase-locking in pattern-generating networks as reliably as inhibition. Journal of Neurophysiology, 102(1), 69–84.Find this resource:
Szucs, A., Huerta, R., Rabinovich, M. I., & Selverston, A. I. (2009). Robust microcircuit synchronization by inhibitory connections. Neuron, 61(3), 439–453.Find this resource:
Turrigiano, G. G. (2012). Homeostatic synaptic plasticity: Local and global mechanisms for stabilizing neuronal function. Cold Spring Harbor Perspectives on Biology, 4(1), a005736.Find this resource:
Wang, X. J., & Rinzel, J. (1992). Alternating and synchronous rhythms in reciprocally inhibitory model neurons. Neural Computation, 4(1), 84–97.Find this resource:
Yuste, R., MacLean, J. N., Smith, J., & Lansner, A. (2005). The cortex as a central pattern generator. Nature Reviews Neuroscience, 6(6), 477–483. (p. 400) Find this resource: