Neuro-IT Cerebellar Modeling Workshop.
University of Antwerp, CDE, promotiezaal
December 5-6, 2005
Abstacts
Purkinje cells as neural integrators: A hypothesis.
Reinoud Maex
Theoretical Neurobiology
University of Antwerp (UA)
Universiteitsplein 1B-2610 Antwerp.
The present hypothesis starts from a striking, although up to now incomplete, similarity between the structure of the cerebellar cortex and a neural network designed by Robinson and co-workers for the computation of eye position from eye velocity signals. More particularly, if sagittal pairs of Purkinje cells would reciprocally inhibit each other, then Purkinje cells are predicted to act as a temporal integrator of their (on-beam) parallel-fiber input, owing, in conjunction, to their high spontaneous activity and the off-beam inhibition they receive from interneurons. In contrast, the input from the ascending axon segment of granule cells could pass unintegrated if this axon would make fewer synapses on interneurons. LTD of the parallel-fiber synapses would control the balance between integrated and unintegrated output, and determine, along with the strength of the reciprocal inhibition, the correlation time of simple spikes. Finally, synchronous activity of climbing fibers in the sagittal plane would reset the integration process.
Decorrelation control: A candidate for the cerebellar algorithm?
Paul Dean and John Porrill
Centre for Signal Processing in Neuroimaging and Systems Neuroscience
Department of Psychology
University of Sheffield, U.K.
Models of the cerebellar algorithm need to satisfy both biological and computational constraints. We have focussed on the latter, by simulating calibration of the vestibulo-ocular reflex (VOR) using linearised dynamics, an adaptive filter to represent cerebellar cortex, and a standard covariance learning rule. The simulations have addressed the following issues.
- How could the cerebellum learn correct motor commands, given it receives sensory not motor error signals? The covariance learning rule can be used to decorrelate motor commands from sensory error (Dean, Porrill, & Stone, 2002; Porrill, Dean, & Stone, 2004). It thus overcomes a potentially very serious problem for Marr-Albus type models, without resorting to complex and possibly unworkable schemes such as feedback error learning. The architectural feature required for decorrelation control is that a copy of motor commands be sent to the flocculus. Such recurrent architecture appears to be a very common feature of cerebellar connectivity.
- Why does VOR calibration require a site of plasticity outside cerebellar cortex? The basic problem with the VOR is that the putative error signal of retinal slip is delayed by ~100 ms, leading to unstable learning above ~2.5 Hz. The simplest way of achieving accurate VOR performance up to 25 Hz is to use cerebellar cortical output as a teaching signal for the brainstem, where a value related to VOR gain can be stored (Dean & Porrill, 2004). This mechanism depends upon the viscoelastic properties of the oculomotor plant for its efficacy.
- Why are most synapses between parallel fibres (PF) and Purkinje cells (PC) silent? The covariance learning rule at PF/PC synapses means that, given additive noise on PFs, learnt synaptic weights are proportional to root mean square PF signal and inversely proportional to mean square PF noise (Porrill & Dean, 2005). This minimises the contribution of PF noise to errors in PC output. As a consequence PFs carrying noise alone have their synaptic weights driven to zero. The evidence that 80-85% of synapses are in fact silent (Isope & Barbour, 2002) suggests that a high proportion of PFÕs carrying information irrelevant to the task of any given PC.
This computational approach, inasmuch as it solves important control problems, is likely to be of interest to e.g. robotics even if biologically mistaken. However, for understanding the actual cerebellum biological fidelity is of course crucial. Can the biological and computational approaches meet?
References:
- Dean, P., & Porrill, J. (2004). Plant compensation in vestibulo-ocular reflex (vor): Computational analysis points to multiple sites of plasticity. In 2004 abstract viewer/itinerary planner (Prog. No. 989.2). Washington, DC: Society for Neuroscience.
- Dean, P., Porrill, J., & Stone, J. V. (2002). Decorrelation control by the cerebellum achieves oculomotor plant compensation in simulated vestibulo-ocular reflex. Proceedings of the Royal Society of London, Series B, 269(1503), 1895-1904.
- Isope, P., & Barbour, B. (2002). Properties of unitary granule cell -> purkinje cell synapses in adult rat cerebellar slices. Journal of Neuroscience, 22(22), 9668-9678.
- Porrill, J., & Dean, P. (2005). Computational consequences of parallel-fibre noise in decorrelation-control algorithm for cerebellar calibration of the VOR. In 2005 abstract viewer/itinerary planner (Prog. No. 986.6). Washington, DC: Society for Neuroscience.
- Porrill, J., Dean, P., & Stone, J. V. (2004). Recurrent cerebellar architecture solves the motor error problem. Proceedings of the Royal Society of London, Series B, 271, 789-796.
Toward the functional unit of the cerebellum: a theoretical approach.
G. Chauvet.
The determination of the functional unit is major for : (i) interpreting the main function of the cerebellum, i.e. the coordination of movement, and (ii) making artificial neuromimetic circuits that simulate this function.
However, the rigorous definition of a functional unit needs a theoretical framework in which the mathematical coherence is satisfied.
In this presentation, I show that the above main function of the sensorimotor system may be interpreted in the framework of the mathematical theory of integrative physiology (MTIP)(Chauvet 2005). The essential concepts will be first recalled before to show why the domain of Purkinje composed of the Purkinje unit and deep nucleus cells could be a good candidate for the functional unit of the cerebellum.
More specifically, the Purkinje domain is the local circuit composed of one or several Purkinje cells and its associated cells (the Purkinje unit) associated with the deep cerebellar nuclei. This is supported by the following arguments:
- The definition of a Purkinje unit is geometrical as well as functional. A set of Purkinje units corresponds to a micro-zone (Ito 1984), although it should be noted that the definition of the micro-zone is not based on mathematical criteria.
- The stability of the function, which takes into account the internal dynamics due to the time-lag in the propagation within the unit and between two units (Chauvet and Chauvet 1995), determines the conditions for the definition of the structural unit.
- Variational learning rules (VLRs) (Chauvet 1995), deduced from neural learning rules, apply to Purkinje units and govern the coordination of movement through excitatory and inhibitory interactions between the units. The hypothesis of synaptic plasticity, applied to granular cells, reveals a wide range of learning behaviour. The same learning rules probably apply during the developmental period as well as in adult life to ensure the convergence of signals carried by the climbing fibers of the cerebellar cortex.
- The coupling between units increases the overall stability of the system in agreement with the general theory (Chauvet 1993).
All these statements will be discussed from an anatomical and physiological point of view.
References:
- Chauvet GA. 1993. Hierarchical functional organization of formal biological systems: a dynamical approach. I. An increase of complexity by self-association increases the domain of stability of a biological system. Phil Trans Roy Soc London B 339:425-444.
- Chauvet GA. 1995. On associative motor learning by the cerebellar cortex: from Purkinje unit to network with variational learning rules. Math Biosci 126:41-79.
- Chauvet GA. 2005. The use of representation and formalism in a theoretical approach to integrative neuroscience. Journal of Integrative Neuroscience 4(3):291-312.
- Chauvet P, Chauvet GA. 1995. Mathematical conditions for adaptive control in Marr's model of the sensorimotor system. Neural Networks 8(5):693-706.
- Ito M. 1984. The Cerebellum and Neural Control. New York: Raven Press.
A model of the sensory and motor components of classical conditioning.
Paul F.M.J. Verschure
Institute of Neuroinformatics,
University & ETH Zurich, Switzerland.
The cerebellum is known to play a central role in the conditioning of discrete motor responses such as the eye blink reflex. However, the conditioned stimuli to which it acquires a conditioned response are in turn learned by structures outside of the cerebellum, i.e. the cortex, amygdala and or hippocampus. Acquisition of the representation of an auditory CS, for instance, appears to involve the rearrangement of the tuning properties of neurons in the primary auditory cortex leading to an enhance population response to the CS. It is believed that learning in the cerebellum requires the long-term depression of the parallel fiber to Purkinje cell (pf-Pu) synapse and that this learning mechanism is based on the notion of a stimulus trace, for instance expressed in local synaptic calcium dynamics. An important question is how the sensory and motor learning components of conditioning are interfaced. For instance, it is not clear what the effect is of the enhanced cortical response to a CS on the cerebellar CS trace of the pf-Pu synapse, i.e. the requirements of cerebellar LTD could be violated by the sensory learning of the cortex. Here we show in an anatomically and physiologically constrained simulation study of both the cerebellar and the extra cerebellar components, i.e. cerebral cortex, of classical conditioning that the interfacing of these two complementary learning systems requires a particular gating mechanism that appears consistent with the physiology of the granule cells.