Motor-pattern-generatingnetworksin invertebrates:modeling our way towardunderstanding Ronald L. Calabrese and Erik De Schutter

Motor-pattern-generating networks in invertebrates have been the objects of intensive study to determine the origin and modulation of rhythmic neural activity. In some pattern generators, intrinsically bursting neurons drive activity throughout the network. In most pattern generators, however, rhythmicity arises from the interplay between intrinsic membrane properties and synaptic interaction. Reciprocal inhibitory synapses between neurons are thought to be crucial for generating oscillation in these networks, but a fundamental understanding of how such network oscillators work remains elusive. Progress towards this goal has come from attempts to combine computational modeling approaches with conventional physiological analysis. The motor-pattern-generating networks of some invertebrates have become models for understanding how rhythmic motor patterns that underlie behaviors ranging from breathing to walking are generated, coordinated and modulated 1. What has emerged from the study of these systems is the realization that these oscillatory networks are not simple. The rhythmic activity of such networks results from a complex interplay of synaptic interactions and intrinsic membrane properties 2, many of which can be modulated 3. Nevertheless, persistent experimental analysis with dogged attention to detail has pointed toward mechanisms that initiate and sustain oscillation in these systems. These studies in turn illuminate the search for similar mechanisms in more complex and less accessible pattern-generating circuits of vertebrates. As exciting as these insights have been, they have been limited by the ability of the experimentalist to assimilate the details and arrive at a synthetic understanding. Computer modeling is proving particularly rewarding in this regard. The pyloric network of the crustacean stomatogastric ganglion, which controls rhythmic movements of the foregut, has been particularly well studied. This network, which consists predominantly of motor neurons, produces a stable three-phase rhythm of motor discharge. The single interneuron AB possesses intrinsic membrane properties that cause it to burst rhythmically, and thus drive oscillatory activity in the entire network 4. The synaptic interactions of the interneuron AB with the motor neurons, together with the membrane properties of those neurons, produce the three-phase motor pattern, and restrict the frequency range and duty cycle over which interneuron AB operates 5. Modeling studies by Abbott and co-workers 6'7 contributed significantly to understanding how electrical coupling between neurons regulates the firing frequency and burst duration of interneuron AB. In many pattern-generating networks, including the swimming s and heartbeat 9'1° networks of the leech (Hirudo medicinalis), the swimming network of the pelagic mollusk (Clione limacina) 11, the feeding network of the fresh-water snail (Lymnaea stagnalis) r~, TINS, Vol. 15, No. 11, 1992

and the gastric network of the crustacean stomatogastric ganglion 13, no intrinsically bursting neurons are found. The neurons in these 'network oscillators' often possess membrane properties that are thought to be important in rhythm generation. Particular attention has been paid to plateau potentials and sag potentials in rhythm-generating neurons 1°. Plateau potentials are sustained depolarizing potentials that are triggered by brief depolarization and can be terminated by brief hyperpolarizations. Often the membrane currents that generate these plateaux are substantially inactivated at rest, and a period of hyperpolarization is necessary before a plateau can be triggered, either by depolarization or release from hyperpolarization. Such plateaux may account for the often observed phenomenon of post-inhibitory rebound. Sag potentials are slow depolarizations that are activated by prolonged' periods of inhibition or hyperpolarizing shifts in membrane potential. They are produced by hyperpolarization-activated inward current, lh, similar to the vertebrate cardiac pacemaker current If (Ref. 14). Unlike other depolarizing potentials, which are regenerative, sag potentials move the membrane potentials into the range where they are deactivated. In network oscillators, synaptic interaction is necessary for oscillatory activity. Historical precedent 15, experimental analysis l°'n, theoretical considerations ~6 and conventional wisdom have pointed to reciprocal inhibitory synaptic interactions between neurons or groups of neurons as being crucial to the operation of these networks. 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 oscillation. Progress is being made, however, in several preparations. For example, Clione swims continuously with its wing-like parapodia, and its isolated pedal ganglia produce alternating bursts in presumptive swim motor neurons, which elevate and depress the parapodia ~7. In the ganglion, two antagonistic populations of identified premotor interneurons form reciprocal inhibitory synapses ls-21. These populations produce alternating single plateaulike potentials of up to 150 ms in duration that drive the motor neuron bursts 19 21. All of the interneurons show strong post-inhibitory rebound 11'19'2~, and at least some of them can produce regular trains of the plateau-like potentials when isolated from the ganglion 22. Rebound, however, is thought to be primarily responsible for the alternating pattern of activity which the reciprocally inhibitory populations produce. More progress can be made when physiological studies are combined with modeling studies 23. In the remainder of this review, we will use our own physiological and modeling studies to illustrate the value of this dual approach in understanding how such oscillations are produced in a pattern-generating

© 1992, Elsevier Science PublishersLtd, (UK)

Ronald L. Ca/abresets at the Dept of Biology, Emory University, Atlanta, GA 30322, USA,and Erik De Schutteris at the Division of Biolo~, California Institute of Technology, Pasadena, CA 91125, USA.

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HN(L,4) 15 mV 3s Fig. 1. Synaptic connectivity of heart motor neurons (HE) and heart interneurons (HN). (A) Circuit diagram showing the inhibitory synaptic connections from identified HN interneurons to HE motor neurons. (B) Circuit diagram showing the inhibitory synaptic connections among all the identified HN interneurons. Neurons with the same input and output connections are grouped together. (C) Circuit diagram showing inhibitory synaptic connections among the HN interneurons of the beat-timing oscillator. HN cells of the first and second ganglia are functionally equivalent and are lumped together. The HN(1) and HN(2) neurons receive their synaptic inputs on, and initiate action potentials in, processes located in the third and fourth ganglia (G3 and G4; open squares). In all the circuit diagrams, large open circles represent neurons (each identified by the number of its ganglion) and the lines represent major neurites or axons. Small filled circles represent inhibitory chemical synapses. (D) Simultaneous intracellular recordings showing the normal rhythmic activity of two reciprocally inhibitory HN interneurons and a HE motor neuron postsynaptic to one of them in an isolated nerve cord preparation. Broken lines indicate a membrane potential of - 5 0 mV. Heart interneurons are indexed by body side and ganglion number from cell HN(L,1 ) to cell HN(R,7). HE motor neurons are similarly indexed.

network. We have found that complex interactions between synaptic inhibition and particular voltagegated membrane currents produce oscillation. The leech heartbeat Rhythmic constrictions of bilateral longitudinal blood vessels with muscular walls propel blood through the circulatory system of the leech, Hirudo (see Refs 9, 10). The constrictions of these heart tubes are paced and coordinated by a rhythmically active central pattern generator through bilateral segmental heart (HE) motor neurons that provide excitatory drive to heart muscle fibers. The pattern generator consists of a network of seven bilateral pairs of heart (HN) interneurons, one pair of which is located in each of the first seven segmental ganglia 440

(Fig. 1A). The synaptic connections among the interneurons and from the interneurons to the motor neurons are inhibitory (Fig. 1B). The four anteriormost pairs of heart interneurons constitute an oscillator that provides heartbeat timing24 (Fig. 1C), while the others are involved in intersegmental coordination of the motor neurons. Two loci of oscillation occur within the beat-timing oscillator in the third and fourth segmental ganglia of the nerve cord, where the heart interneurons form reciprocally inhibitory connections across the midline25 (Fig. 1D). Heart interneurons of the first and second segmental ganglia coordinate these segmental oscillators so that the third and fourth heart interneurons on the same side fire together 26. The normal activity cycle of each heart interneuron of these reciprocally inhibitory pairs consists of an active burst phase, during which it inhibits its contralateral partner, and an inhibitory phase, during which firing is suppressed by synaptic inhibition from the contralateral partner (Fig. 1D). Understanding the mechanisms that cause transition between these two phases is fundamental to understanding the origin of oscillation in the system. Isolation of the third or fourth segmental ganglia does not fundamentally alter the oscillation of these reciprocally inhibitory pairs of heart interneurons 25. This preparation provides an opportunity to investigate the ionic and synaptic mechanisms that promote oscillation in a two-cell reciprocally inhibitory network, which can be interpreted in the larger context of a behaviorally relevant neural network. Both synaptic interactions and voltage-gated membrane currents contribute to produce oscillation The synaptic interaction between reciprocally inhibitory heart interneurons consists of a strong graded component in addition to spike-mediated synaptic transmission 27'28. Both these components are blocked by bicuculline methiodide, and bath application of bicuculline reversibly halts oscillation of a reciprocally inhibitory pair of heart interneurons 29 (Fig. 2). This finding demonstrates that synaptic interaction is essential for oscillation in heart interneurons. Other experiments using voltage- and currentclamp techniques point to voltage-gated currents that are similarly important for oscillation. A hyperpolarization-activated inward current (Ih) appears to be crucial in pacing oscillation (Fig. 3), apparently because it promotes escape from inhibition and transition to the burst phase 3°'31. (A similar current, If, paces activity in the vertebrate heart14.) This current can be assayed as a depolarizing 'sag' in membrane potential that occurs when heart interneurons are hyperpolarized with injected current (Figs 3B, D, F). Blockade of this current with external Cs ÷ reversibly halts oscillation 3° (Figs 3A, C, E). Lowthreshold Ca2+ currents [Icas (slowly inactivating) and ICaF (rapidly inactivating)] underlie graded transmission and promote burst formation by sustaining prolonged depolarized plateaux 27. Three different K ÷ currents have been identified in heart interneurons 32, and two of these are modulated by the endogenous neuropeptide FMRFamide 33, which can alter the cycle period of the heart interneuron oscillation 32. TINS, VoL 15, No. 11, 1992

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Perturbation experiments have identified the transition from the inhibitory to the burst phase as being the critical timing transition in the activity cycle of the heart interneurons 1°,27. Apparently, the inhibited cell escapes from the inhibitory influence of the active cell during this transition. It is unclear, however, whether this transition results from the build-up of inward current (e.g. Ih) in the inhibited cell that overcomes the inhibition, or from a waning of the inhibitory influence of the active cell when graded transmission declines as the low-threshold Ca2+ currents inactivate. The myriad synaptic and voltage-gated currents that interact through membrane potential and internal Ca2+ concentration make it difficult to differentiate between these possibilities or to identify other crucial interactions that control this transition.

Interactions between lh, low-threshold Ca 2 + currents and graded synaptic transmission are crucial for oscillation We wanted to examine the respective roles of the graded synaptic inhibition and the hyperpolarizationactivated inward current (Ih) in controlling the transition between the inhibitory and the burst phase in a reciprocally inhibitory pair of heart interneurons. We decided to build a one-compartment model of a heart interneuron which included all identified ionic currents34, 35. TINS, Vol. 15, No. 11, 1992

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30 mV 2.5 nA 3s Fig. 3. Importance of voltage-gated membrane currents for oscillation in heart interneurons, Effect of blocking Ih with Cs + on the oscillatory activity of the reciprocally inhibitory HN interneurons of an isolated third ganglion. (A,C,E) Spontaneous activity; (B, D, F,) voltage responses to a prolonged hyperpolarizing current pulse used to assay lb. Bottom trace below each right-hand panel is a current monitor. (A) Normal alternating oscillations in leech safine. (B) Injection of a hyperpolarizing current pulse into the HN(R,3) neuron elicited the normal depolarizing sag. A plateau potential after the current pulse caused strong inhibition of the contralateral HN neuron [HN(L,3)]. (C) Tonic activity in HN cells 15 min after application of safine containing Cs + (4 raM) to block lb. (D) Injection of a hyperpolarizing current pulse revealed the complete block of the depolarizing sag; however, a normal plateau at the end of the pulse still occurred. (EL(F) Normal oscillation and recovery of the depolarizing sag after washing the ganglion with normal saline 3°. 441

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All ionic currents were measured in the soma 28'3°'32, but many of the voltage-gated currents are primarily localized to the neuritic arbor, the axon, or both, and synaptic inputs are restricted to Membrane potential (right cell) 40 mV neuritic branches. We assumed that our experimental kinetic data 4s probably measured currents in both the soma and the proximal J neurite, and that they are applicable for the whole neuron. There are no data available about the Fast Ca2+-current (left cell) actual distribution or density of these channels or about Ca 2+ gradients throughout the cell. 400 pA Slow Ca2+-current (left cell) These limitations determined our choice to a one-compartment 4s model (equivalent to a big soma), _ II despite the fact that we had available detailed morphological reconIn (left cell) structions of heart interneurons. _..,J'.,.............................. ,,,, Using a morphologically more complex model would have introduced too many unmeasured Synaptic conductance (right cell) model parameters and offered little advantage, because, in any case, comparisons of the model must be made with soma recordings. The two simulated intracellular 100 nS recordings and the amplitude of some of the currents during two 4S cycles of oscillation are shown in Fig. 4. Simulated oscillations in a pair of heart intemeurons. Membrane potential is shown in both Fig. 4 (compare with Fig. 1D). cells. Note that the synaptic conductance in the right cell is controlled by Ca2+ influx (Ca 2+ Such current records can only be concentration) in the left cell (and vice versa). Most of the Ca 2+ influx comes from slow Ca 2+ produced by simulation. There is current, Icas. The contribution of the fast Ca 2+ current, ICaF,is small. The role of lcaF in oscillation is no experimental method that to depolarize the inhibited cell fast enough, despite lingering synaptic inhibition, so that Icas does would allow us to measure these not inactivate too much during the transition to the burst phase. The small blip of ICaFthat occurs currents during normal oscillations. during the transition to the inactive state results from the rapid deinactivation and subsequent The model reproduces the period activation of IC,F as the cell is inhibited by its contralateral partner. The role of Ih is explained in the and the envelope of the bursts text. In this and the following figure, the model neurons had a total membrane capacitance of well, but not all details are repro5001~F and a total leak conductance of 4.5nS. duced. The cells tend to fire too fast during the bursts, the transition between inhibitory and burst We also developed a computational description of phases is very sharp (i.e. there is no overlap in graded synapfic inhibition that could interact with the spiking), and individual spike-evoked IPSPs are too voltage-gated currents in our model35. This com- small. Most of these problems could be caused by an ponent of our model is based on voltage-clamp inadequate description of the fast Na + current, which experiments, in which presynapfic Ca 2+ currents has not been measured in the heart interneurons. We were measured in one heart interneuron while post- also suspect, however, that the model of graded synaptic currents were measured in the other cell of synaptic release does not capture events during fast the reciprocally inhibitory pair. Because neither the changes in membrane potential well, and preliminary dynamics of Ca2+ build-up and removal, nor the data indicate that a high-threshold Ca2+ current may control of transmitter release by Ca 2+ in presynaptic underlie spike-mediated transmission by heart interterminals of heart interneurons is understood, we neurons. made the simplest possible ad hoc description of Ca2+ Some interesting conclusions can be drawn from dynamics and transmitter release. This description Fig. 4. The two Ca 2+ currents behave completely relates the influx of Ca2+ from /CaS and Ica~ to differently: ICaF is only active during the transition to synaptic transmitter release by computing an effective the burst phase, while Icas never inactivates compresynaptic Ca2+ concentration. The removal of pletely during the active phase; Icas also never presynapfic Ca2+ was described by a voltage- and deinactivates completely during the inhibitory phase. Ca2+ concentration-dependent mechanism, and trans- Additionally, at the time of the transition, there is still mitter release depended on the third power of the some inhibitory current present while ]h is already effective Ca2+ concentration. With this description, deactivating. Unfortunately, this simulation does not our model was able to simulate accurately our voltage- allow us to determine whether the transition is caused clamp data aS. by the active or inhibited cell because all currents that

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could be involved are active during the transition. Simulating the effects of partially blocking Ih (Fig. 5) has given us a better idea of what happens. Decreasing the maximum conductance of lh causes the burst period to increase and vice versa (Figs 5A, B). At least two mechanisms are involved in this process. The most intuitive effect is the slower repolarization of the inhibited cell because we are blocking an inward current, which will delay the transition to the burst phase. The second mechanism is more complex because it shows how the two parts of the burst cycle can interact. The inhibited cell will hyperpolarize to more negative values during the inhibitory phase if less Ih is present. Consequently Icas is more completely deinactivated (Fig. 5C), so that in the next part of the cycle, when the cell becomes active, more Ic,s will flow inside the neuron. This increased Icas will cause a larger Ca2+ build-up, more transmitter release, and thus a longer inhibition of the other cell of the pair. These simulations also suggest that the transition to the burst phase is controlled by the inhibited cell, and that this cell in turn forces the transition to the inhibitory phase in the other neuron when it enters its burst and begins to inhibit its partner. The synaptic conductance at the

time of the transition declines progressively with the amount of Ih block (Fig. 5C). This observation means that transitions can occur at different levels of inhibition. A transition occurs when the inward currents in the inhibited cell (at these membrane potentials, Ih and ICaF) are big enough to overcome the inhibition. The model has allowed us to dissect the interactions between the different currents during oscillation and to determine the role of the inhibited cell in causing the transition to the burst phase. It also suggests new experiments that will allow further refinement of the model. The relation between slow Ca2÷ deinactivation and synaptic current, suggested by the simulations of Ih blockade, has not yet been examined experimentally. We also need to examine the relation between Ca 2+ currents and spike-evoked [PSPs more fully. This interaction between experiment and simulation shows the importance of realistic modeling for all neurophysiologists. F u t u r e u s e s of o u r model Wang and Rinze137 have provided a theoretical framework for understanding how reciprocally inhibitory neurons oscillate. The neurons in their model

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Fig. 5. Simulated effect of varying Ih on oscillation. The simulations always started with a 'normal' amount of hconductance (due to Ih), which yields an oscillation with a period of 11 s, then the h-conductance was suddenly increased (+ %) or decreased ( - %); (an exception was the 100% block that was applied over I s). (A) Membrane potential in a reciprocally inhibitory pair of heart interneurons during partial (-50%, left panel) and complete ( - 100%, right panel) block of In. When complete block is applied as shown, bursting of the inhibited cell is interrupted and replaced by bilateral tonic firing (compare with Fig. 3). Partial block of Ih causes slowing of the oscillation. (B) Reintion between the percentage increase or decrease (block) of the h-conductance and burst period. The pair of cells do not oscillate at periods shorter than 8 £ (C) 5ynaptic and Ca 2+ conductances at the beginning of the transition from inhibition to bursting (when Vm crosses - 5 0 m Y ) versus h-conductance. There is no relation between the Ca 2+ conductance and the synaptic conductance because only values for the same cell are plotted (Ca 2+ conductance will, through transmitter release, affect synaptic conductance in the other cell of the pair). The transition occurs at the same level of Ca2+ conductance, regardless of the amount of h-conductance present. The synaptic conductance at the transition changes because with more Ih the inhibited cell will have enough inward current to overcome higher levels of synaptic current. The inactivation of leas, which varies between 0 and 1, is also plotted using the left ordinate scale. It increases when the h-conductance is reduced, as discussed in the text. The inactivation level of Ic, s at the transition to the burst phase is an important factor in the increase of burst period with decreasing h-conductance.

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are rudimentary, containing a synaptic conductance that is a sigmoidal function of the presynaptic memhrane potential with a set threshold and instantaneous kinetics, a constant leak conductance, and a voltagegated post-inhibitory rebound conductance (gpir). The gpir is derived from a quantitative model of a T-type Ca2+ current in thalamic neurons38; it activates rapidly and inactivates slowly, and is strongly inactivated at rest so that 'hyperpolarization of sufficient duration and amplitude is required to deinactivate' gpir to produce 'rebound excitation after removal of hyperpolarization'. The authors note that an h-conductance (i.e. due to Ih) 'would have an expression similar to' gpir, and thus their model should be relevant to oscillators that employ an h-conductance. Wang and Rinze137 recognize two fundamentally different modes of oscillation, 'release' and 'escape'. In the release mode, the inactivation ofgpir erodes the depolarized or active phase of a neuron so that it falls below the threshold for synaptic transmission, and consequently its partner is released from inhibition and rebounds into the active depolarized state. By simply increasing gpir, the escape mode can be realized. In the escape mode, once gpi~ becomes deinactivated by the hyperpolarization associated with inhibition, it activates and overcomes the synaptic current so that the neuron escapes into the active phase. In the release mode, the transition from the inactive state to the active state is controlled by the active presynaptic neuron, and the period of the oscillation is critically dependent on the threshold for synaptic transmission since the threshold determines the fraction of time during rebound in which the neuron can inhibit its partner. In the escape mode, the transition from the inactive state to the active state is controlled by the inactive postsynaptic neuron, and the period of the oscillation is relatively insensitive to the synaptic threshold. Rather, the inhibitory phase of the cycle, which is half the cycle period due to oscillator symmetry, should be equal to the time it takes for gpir to deinactivate and subsequently activate sufficiently to overcome the inhibition. Given our experimental and modeling results, it seems certain that the heart interneuron oscillator operates in the escape mode; whenever Ih is sufficiently activated to overcome the synaptic current, a transition from the inactive state to the active state occurs. In the heart interneurons and in our model, gpir is represented by three conductances, gh, gcaF and gcas, with differing activation ranges and inactivation properties. It will now be interesting to explore how the relative amplitudes of these three conductances influence the mode of bursting observed in the model. Moreover, our more realistic model of synaptic transmission, which has Ca2+-dependent amplitude and kinetics rather than simple sigmoidal voltage dependence with instantaneous kinetics, should allow us to explore not only the importance of threshold in determining cycle period but how the kinetics of synaptic inhibition influence the fundamental operation of the oscillator. Recently, Tierney and Harris-Warrick 39 provided pharmacological evidence indicating that the transient outward current IA is an important regulator of cycle period in the pyloric network of the crustacean stomatogastric ganglion. Thus far, we have not explored the role of outward currents in regulating 444

burst production and cycle period using our model. This exploration should prove particularly informative because outward currents are the target of modulation by FMRFamide in the heart interneurons32. It is also interesting to note that the Clione swim oscillator appears to operate in the release mode. Perhaps this mode is more suited to the operational frequency range of this oscillator, which is some ten times faster than the leech heartbeat oscillator. This hypothesis can be explored by determining the parameter changes necessary to force our model into this frequency range and ascertaining the mode of bursting produced. Thus, our own scientific evolution has progressed from detailed physiological analysis, through computer simulation, to a more theoretical understanding of the operation of biological oscillators.

Selected references 1 Getting, P. A. (1988) in Neural Control of Rhythmic Movements in Vertebrates (Cohen, A. H., Rossignol, S. and Grillner, S., eds), pp. 101-128, J. Wiley & Sons 2 Getting, P. A. (1989) Annu. Rev. Neurosci. 12, 184-204 3 Harris-Warrick, R. M. and Marder, E. (1991) Annu. Rev. Neurosci. 14, 39-57 4 Selverston, A. I. and Moulins, M. (1987) The Crustacean Stomatogastric System, Springer-Verlag 5 Hooper, S. L. and Marder, E. (1987) J. Neurosci. 7, 2097-2112 6 Kepler, T., Marder, E. and Abbott, L. F. (1990) Science 6, 83-85 7 Abbott, L. F., Marder, E. and Hooper, S. L. (1991) Neur. Comput. 3, 487-492 8 Friesen, W. O. (1989) in Cellular and Neuronal Oscillators (Jacklet, J. W., ed.), pp. 269-316, Marcel Dekker 9 Calabrese, R. L. and Peterson, E. (1983) in Neural Origin of Rhythmic Movements (Roberts, A. and Roberts, B., eds), pp. 195-221, Symposium Soc. Exp. Biol. XXXVII 10 Calabrese, R. L., Angstadt, J. D. and Arbas, E. A. (1989) in Perspectives in Neural Systems and Behavior (Carew, T. J. and Kelley, D., eds), pp. 33-50, Alan R. Liss 11 Satterlie, R. A. (1989)in Cellular and Neuronal Oscillators (Jacklet, J. W., ed.), pp. 151-172, Marcel Dekker 12 Benjamin, P. R. and Elliott, C. J. H. (1989) in Cellular and Neuronal Oscillators (Jacklet, J. W., ed.), pp. 173-214, Marcel Dekker 13 Selverston, A. I. (1989) in Cellular and Neuronal Oscillators (Jacklet, J. W., ed.), pp. 339-370, Marcel Dekker 14 DiFrancesco, D. and Noble, D. (1989) in Cellular and Neuronal Oscillators (Jacklet, J. W., ed.), pp. 31-58, Marcel Dekker 15 Graham-Brown, T. (1911) Prec. R. Soc. London Ser. B 84, 308-319 16 Perkel, D. H. and Mulloney, B. (1974) Science 185, 181-183 17 Arshavsky, Y. I., Beloozerova, I. N., Orlovsky, G. N., Panchin, Y. V. and Pavlova, G. A. (1985) Exp. Brain Res. 58, 255-262 18 Arshavsky, Y. I., Betoozerova, I. N., Orlovsky, G. N., Panchin, Y. V. and PavIova, G. A. (1985) Exp. Brain Res. 58, 263-272 19 Arshavsky, Y. I., Beloozerova, I. N., Orlovsky, G. N., Panchin, Y. V. and PavIova, G. A. (1985) Exp. Brain Res. 58, 273-284 20 Arshavsky, Y. I., Beloozerova, I. N., Orlovsky, G. N., Panchin, Y. V. and Pavlova, G. A. (1985) Exp. Brain Res. 58, 285-293 21 Satteflie, R. A. (1985) Science 229, 402-404 22 Arshavsky, Y. I. etal. (1986) Exp. Brain Res. 63, 106-112 23 Mulloney, B. and Perkel, D. H. (1988) in Neural Control of Rhythmic Movements in Vertebrates (Cohen, A. H., Rossignol, S. and Grillner, S., eds), pp. 415-453, J. Wiley & Sons 24 Peterson, E. L. and Calabrese, R. L. (1982) J. Neurophysiol. 47, 256-271 25 Peterson, E. (1983)J. Neurophysiol. 49, 611-626 26 Peterson, E. (1983) J. Neurophysiol. 49, 627-638 27 Arbas, E. A. and Calabrese, R. L. (1987) J. Neurosci. 7, 3953-3960 28 Angstadt, J. D. and Calabrese, R. L. (1991) J. Neurosci. 11, 746-759 29 Schmidt, J. and Calabrese, R. L. J. Exp. Biol. (in press) 30 Angstadt, J. D. and Calabrese, R. L. (1989) J. Neurosci. 9, 2846-2857 TINS, Vol. 15, No. 11, 1992

31 Arbas, E. A. and Calabrese, R. L. (1987) J. NeuroscL 7, 3945-3952 32 Simon, T. W., Opdyke, C. A. and Calabrese, R. L. (1992) J. Neurosci. 12,525-537 33 Evans, B. D. and Calabrese, R. L. (1991) Peptides 12, 897-908 34 De Schutter, E. (1989) Comput. Biol. A4ed. 19, 71-81 35 De Schutter, E., Angstaclt, J. D, and Calabrese, R. L.

J. Neurophysiol. (in press) 36 Hodgkin, A. L. and Huxley, A. F. (1952) J. Physiol. 117, 500-544 37 Wang, X-J. and Rinzel, J. (1992) J. Neural Comp. 4, 84-97 38 Wang, X-J., Rinzel, J. and Rogawski, M. A. (1992) J. Neurophysiol. 66, 839-850 39 Tierney, A. J. and Harris-Warrick, R. M. (1992) J. Neurophysiol. 67, 599-609

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Kawato

and Hiroaki Gomi

Although one particular model of the cerebellum, as proposed by Marr and Albus, provides a formal framework for understanding how heterosynaptic plasticity of Purkinje cells might be used .for motor learning, the physiological details remain largely an enigma. Developments in computational neuroscience and artificial neural networks applied to real control problems are essential to understand fully how workspace errors associated with movement performances can be converted into motor-command errors, and how these errors can then be used as one kind of synaptic input by motor-learning algorithms that are based on biologically plausible rules involving heterosynaptic plastic@. These developments, as well as recent advances in the study of cellular mechanisms of synaptic plasticity, form the basis for the detailed computational models of cerebellar motor learning that have been proposed. These models provide hints toward resolving a long-standing controversy in the oculomotor literature regarding the sites of adaptive changes in the vestibuloocular reflex (VOR) and the optokinetic eye movement response (OKR), and suggest new experiments to elucidate general mechanisms of sensory motor learning. The problem of controlling goal-directed limb movements can be partitioned conceptually into a set of information-processing subprocesses; trajectory planning, coordinate transformation from extracorporal space to intrinsic body coordinates and motor command generation. These subprocesses are required to translate the spatial characteristics of the target or goal of the movement into an appropriate pattern of muscle activations 1'2. However, fast, smooth and coordinated movements cannot be realized by just feedback control alone because, in biological motor control systems, the delays associated with feedback loops are long and the feedback gains are low. Thus, internal predictive models of the motor apparatus need to be utilized in the course of these computations3. The internal models in the brain must be acquired through motor learning in order to accommodate the changes that occur with the growth of controlled objects such as hands, legs and torso, as well as with the unpredictable variability of the external world. Where in the brain are internal models of the motor apparatus likely to be stored? First, the locus should exhibit a remarkable adaptive capability, which is essential for acquisition and continuous update of internal models of the motor apparatus. A number of physiological studies4'~ have suggested that the cerTINS, Vol. 15, No. 11, 1992

ebeUum may play important functional roles in motor Mitsuo Kawato and learning, and demonstrated remarkable synaptic Hiroaki Gomi are at plasticity in the cerebellar cortex. Second, biological the A TRHuman objects of motor control by the brain, such as arms, Information speech articulators and the torso, possess many ProcessingResearch degrees of freedom and complicated nonlinear Laboratories, Kyoto 619-02, Japan; dynamics. Correspondingly, the neural internal Mitsuo Kawato is also models should receive a broad range of sensory inputs associatedwith the and possess a capacity high enough to approximate Laboratory of complex dynamics. Extensive sensory signals carried ParallelOistributed by mossy fiber inputs and an enormous number of Processing,Research granule cells in the cerebeUar cortex seem to fulfillthe Institute for Electronic above prerequisites for internal models. Finally, the Science, Hokkaido cerebellar symptoms usually known as the 'triad' of University, Sapporo, hypotonia, hypermetria and intention tremor 6 could Hokkaido 060, Japan. be understood as a degraded performance when motor control is forced to rely solely on negative feedback after the internal models are destroyed, cannot be updated, or both. Precise, fast and coordinated movements can be executed if accurate internal models of the motor apparatus can be used during trajectory planning, coordinate transformation and motor control; a pure feedback control, involving long feedback delays and small gains, can attain only a poor performance in these computations and usually leads to oscillatory instability for forced fast movements. It is clear that internal models are essential for normal motor coordination; the question that must now be asked is how might these internal models be acquired in the cerebellum through motor learning? Supervised motor learning of internal models Controlled objects in biological movement can generally be described as multi-variable nonlinear dynamic systems whose inputs are muscle tensions, joint torques or firing rates of the nerve fibers that innervate muscles, and whose outputs are muscle lengths, joint angles or the position of the hand, for example, in Cartesian coordinates. Thus, the direction of information flow in the controlled objects is from the motor commands to the movement trajectory. Following robotics jargon, we state that this direction of the information flow is forward, and the opposite direction, inverse. Accordingly, internal models of the motor system can be divided into two types: forward models and inverse models. By 'forward model' we mean a neural representation of the transformation from motor commands to the resultant behavior of the controlled object. In other words, a forward model is just a simple model of the controlled object, and can be used as its substitute. If the actual motor command given to the motor

© 1992, ElsevierSciencePublishersLtd, (UK

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Motor-pattern-generating networks in invertebrates: modeling our way toward understanding.

Motor-pattern-generating networks in invertebrates have been the objects of intensive study to determine the origin and modulation of rhythmic neural ...
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