Simulations of cerebellar motor learning: computational analysis of plasticity at the mossy fiber to deep nucleus synapse

Abstract

We question the widely accepted assumption that a molecular mechanism for long-term expression of synaptic plasticity is sufficient to explain the persistence of memories. Instead, we show that learning and memory require that these cellular mechanisms be correctly integrated within the architecture of the neural circuit. To illustrate this general conclusion, our studies are based on the well characterized synaptic organization of the cerebellum and its relationship to a simple form of motor learning. Using computer simulations of cerebellar-mediated eyelid conditioning, we examine the ability of three forms of plasticity at mossy fiber synapses in the cerebellar nucleus to contribute to learning and memory storage. Results suggest that when the simulation is exposed to reasonable patterns of "background" cerebellar activity, only one of these three rules allows for the retention of memories. When plasticity at the mossy fiber synapse is controlled by nucleus or climbing fiber activity, the circuit is unable to retain memories because of interactions within the network that produce spontaneous drift of synaptic strength. In contrast, a plasticity rule controlled by the activity of the Purkinje cell allows for a memory trace that is resistant to ongoing activity in the circuit. These results suggest specific constraints for theories of cerebellar motor learning and have general implications regarding the mechanisms that may contribute to the persistence of memories.

Fig. 1.

Simulations are based on the connectivity of the cerebellar-olivary system and its relationship to eyelid conditioning. While the interpositus nucleus ( NUC ) transmits the entire output of the cerebellum, two major excitatory afferents convey stimuli to the cerebellum. The mossy fiber afferent ( Mossy ) influences cerebellar output through direct excitatory connections onto the nuclei cells ( mf → nuc synapses) and through a more indirect projection onto a very large number of granule cells ( Granule ) that ultimately results in modulation of nuclei cells by Purkinje neurons ( PURK ). Granule cells affect Purkinje cell activity through connections to inhibitory interneurons known as basket and stellate cells ( B/S ) and through a large number of direct excitatory synapses ( gr → Pkj synapses) onto the Purkinje cell. In sharp contrast to this vastly diverging input, each Purkinje cell receives synaptic connections from a single climbing fiber ( CF ), which also contacts the output cells of the cerebellar nuclei. Evidence indicates that conditioned stimuli such as tones are conveyed to the cerebellum via mossy fibers, the reinforcing air puff is conveyed via climbing fibers, and paired presentation of these stimuli leads to the expression of a conditioned eyelid response through increases in nucleus activity. This correspondence permits a simple representation of eyelid conditioning with a computer simulation of the cerebellum. Increases in simulated nucleus cell output during the conditioned stimulus are taken as a measure of the conditioned response. Presentation of the conditioned stimulus is emulated by altering the background activities of the mossy fibers and granule cells, whereas a transient excitatory input to the climbing fiber simulates the reinforcing puff. With these inputs determined, the remainder of the circuit is simulated with stochastic neurons (Materials and Methods). The simulations also implement the well characterized climbing fiber-dependent plasticity at the excitatory gr → Pkj synapses and plasticity at the mf → nuc synapses controlled by one of three signals: nucleus cell activity, climbing fiber activity, or Purkinje cell activity.

Fig. 2.

A representation of the well characterized, activity-dependent plasticity at the gr → Pkj synapses in the cerebellar cortex, and three possible cellular rules for plasticity at mf → nuc synapses. Black symbols indicate that the cell is active, and gray symbols denote inactivity. Conditions for increasing the strength of synapses ( LTP ) are shown in the left column, whereas the right column shows the signals that lead to the induction of LTD . a , Activity-dependent plasticity at gr → Pkj synapses in the cerebellar cortex is controlled by climbing fiber inputs. These gr → Pkj synapses undergo LTP when active in the absence of a climbing fiber input and undergo LTD when active in the presence of a climbing fiber input. b1 , With a Hebbian rule, active mf → nuc synapses undergo LTD when the nucleus cell is quiet and undergo LTP during periods of nucleus cell activity. b2 , With a climbing fiber-dependent rule, mf → nuc synapses that are active in the absence of a climbing fiber input to the nucleus cell undergo LTD and undergo LTP when the climbing fiber fires. b3 , A Purkinje cell-dependent rule assumes that active mf → nuc synapses undergo LTD during periods of Purkinje inhibition of the nucleus and LTP during decreases in this inhibition.

Fig. 3.

Acquisition of simulated conditioned responses when a Hebbian ( a ), climbing fiber-dependent ( b ), or Purkinje-dependent ( c ) plasticity rule is implemented at mf → nuc synapses and plasticity is permitted only during the training trial. Increases in nucleus cell activity during presentation of the CS ( thick black line ) provide a measure of the conditioned response amplitude. The contributions made to the conditioned response by plasticity at gr → Pkj synapses in the cerebellar cortex ( thin black line ) and by plasticity at mf → nuc synapses in the cerebellar nucleus ( gray line ) are also shown. Consistent with existing data from eyelid conditioning and VOR adaptation, conditioned responses were produced by a combination of plasticity at these two sites.

Fig. 4.

Retention of simulated conditioned responses when plasticity rules are operational during background input activity. a , The left graph shows that the amplitude of the conditioned response decreases rapidly when either a Hebbian ( dark gray line ) or climbing fiber-dependent ( light gray line ) plasticity rule is implemented at mf → nuc synapses. In contrast, when a Purkinje-dependent rule is used ( black line ), increases in nucleus cell activity during presentation of the CS could be observed for much longer periods of time ( right graph ). b , The effects that implementing different rules for plasticity have on the persistence of memory can be further illustrated by assuming that the pattern of strengths at gr → Pkj synapses corresponds to the picture of Salvador Dali. Light pixels correspond to weak synapses, and dark pixels correspond to strong synapses. Implementing a Purkinje-dependent rule in the cerebellar nucleus drives the system to a state of equilibrium where memories are retained, because although synapses are continually changing (note that the encoded picture slowly degrades with time), they are as likely to increase in strength as they are to decrease ( top row ). In contrast, Hebbian (data not shown) or climbing fiber-dependent ( bottom row ) rules produce a spontaneous drift of synaptic strength, which ultimately results in saturation and complete loss of memory.

Fig. 5.

Properties of simulations that implement a Purkinje-dependent plasticity rule in the cerebellar nucleus. As shown in the schematic representation of the cerebellar circuitry, in these simulations the climbing fiber signal ( thick black line ) controls plasticity at gr → Pkj synapses, whereas the Purkinje cell signal ( thin black line ) controls plasticity at mf → nuc synapses. Under these conditions, simulated climbing fiber and Purkinje cell activities are self-regulated to equilibrium levels (as predicted by Eq. EA2 and A9, respectively) even when these equilibrium levels are different from each other. Although the strength of a mf → nuc or gr → Pkj synapse is modified each time the synapse is active, the bottom graph shows that at these equilibrium levels synapses are as likely to increase as they are to decrease in strength.

Fig. 6.

Properties of simulations that implement Hebbian or climbing fiber-dependent plasticity rules in the cerebellar nucleus. As shown in the schematic representation of the cerebellum, simulations that implement a climbing fiber-dependent or Hebbian rule in the nucleus automatically place both gr → Pkj and mf → nuc synapses under the control of a single signal related to the activity of the climbing fiber ( thick black line ). For the parameters used in these simulations, the level of climbing fiber activity required for equilibrium of gr → Pkj synapses is shown in the left column . The top graph in the left column shows that in simulations with plasticity at mf → nuc synapses turned off, climbing fiber activity was self-regulated to the level predicted by Equation EA2, and that at this equilibrium level the mean strength of gr → Pkj synapses remained constant ( left column, bottom graph ). Conversely, the level of simulated climbing fiber activity required for equilibrium of mf → nuc synapses is shown in the middle column . The top graph in the middle column shows that in simulations with plasticity at gr → Pkj synapses turned off, climbing fiber activity was self-regulated to the level predicted by Equation EA7, and that at this equilibrium level the mean strength of mf → nuc synapses remained constant ( middle column, bottom graph ). However, as shown in the right column , in simulations with plasticity turned on at both sites, climbing fiber activity fell between these two equilibrium levels ( top graph ), such that both sets of synapses drifted ( bottom graph ). Spontaneous drift is reduced only in simulations that use the single set of parameters that makes these two equilibrium levels (Eq. EA2 and A7) equal to each other (data not shown).