User:Jbpassot/Cerebellar models and theory

Cerebellar models and theories

Introduction
The cerebellum presents a striking feature: all along the cerebellar cortex, the connection layout of its neural constituents is remarkably uniform, thus suggesting that the cerebellum processes information using unified computational principles. In 1967, John C. Eccles, Masao Ito, and Janos Szentágothai depicted this regular cerebellar circuitry in the manuscript “The Cerebellum as a Neuronal machine”. This book stimulated discussions on the operational mechanisms of the neural structure, and, a few years later, David Marr (1969) and James Albus(1971) independently published theoretical models of the cerebellar circuitry which intended to explain its machinelike function with some unified principles. These neurocomputational works have helped to better understand its precise role in classical conditioning, motor learning and voluntary movements. Furthermore, many predictions made from these studies have later been verified experimentally, re-enforcing the importance of a computational approach (see for example ).

This article review the most influential theoretical works and modeling studies describing the computational rules driving cerebellar functions.

The classical model
Most of the existing models are based on the presumed adaptive role of the cerebellum and derived from the conceptualization work made in parallel by Marr D and James Albus, published respectively in 1969 and 1971.

Ten years later, Ito and Kano discovered a heterosynaptic long-term depression at parallel fibers-Purkinje cell's (PF-PC) synapses , validating experimentally the existence of a plasticity predicted by both Albus and Marr's models. The main difference between the Marr and Albus theories is that Marr assumed that climbing fiber activity would cause parallel fiber synapses to be strengthened, whereas Albus proposed that they would be weakened. Consequently, the resulting theoretical system is often referred as the Marr-Albus-Ito model.

The theory, in its simple form, can be summarized in four fundamental points:
 * 1) Mossy fibers signals convey contextual sensorimotor information. They drive the firing of granule cells, which optimally recode the input signal, and in turn excite Purkinje cells.
 * 2) Neurons of the inferior olive encode an error signal and target the Purkinje cell through the climbing fiber.
 * 3) The convergence of both the contextual signal and the error signal to a Purkinje cell leads to a diminution of the efficacy of PF-PC synapses.
 * 4) A diminution of the strength of PF-PC synapses leads to an augmentation of the activity of the cerebellar nuclei targeted by the Purkinje cells, and to the emergence of a response adapted to the contextual information.

The granular layer optimally re-encode the input signal.
According to the theory, the granular layer re-encodes optimally the sensorimotor signals arising from mossy fibers. This optimal encoding is supposed to minimize destructing interferences between learning tasks, and optimize neuronal resources by evicting redundancies. Such a recoding is supposed to convey a contextual representation to the Purkinje cells that simplifies the integration of information, hence facilitating learning. It has been proposed that a sparse coding –- i.e. a code where each information is encoded by only a few neuronal units -- at the level of parallel fibers would provide such properties : a sparse coding increases the amount of information conveyed by a single spike; conversely reduces the amount of energy needed to transmit a signal, and therefore maximizes the efficacy of the information transfer. Some experimental data and theoretical arguments support a sparse coding at the level of parallel fibers.

First, the huge amount of granular cells ($$10^{10}$$ – $$10^{11}$$) provides the neuronal resources to sparsely encode many contexts; then, LTD and LTP at mossy fiber-granule cell synapses and backward inhibition of Golgi favors such an encoding. Golgi cells are supposed to play an important role in the formation of a sparse code in the granular layer by inhibiting a large field of granular cells. This retroactive loop would functionally regulate the activity of the granular cells, and also limit noise. Third, most of PF-PC synapses are silent. Finally, a Purkinje cell only needs a few conjointly active parallel fibers to be activated.

Purkinje cells integrate the information.
In the Marr-Albus-Ito theory, the Purkinje cell is considered as the central element of the cerebellar microcomplex. Each Purkinje cell can integrate a huge amount of information. According to Brunel, by considering only two computational states (active and inactive), a Purkinje cell could classify in two sets as much as 5 ko of information. This massive processing power is due to the particular architecture of the cell (a very large dendritic tree) and the high number of parallel fibers that project onto it ($$\approx$$ 200,000 in humans). In this sense, a Purkinje cell is often considered as a perceptron: a simple and abstract neuronal network capable of linear associations.

The climbing fiber conveys a teaching signal.
The theory postulates that the strength of each PF-PC connection is plastic and that the climbing fiber drives the adaptation process by sending a teaching signal. Evidence of this supervised learning has been discovered experimentally by Ito in 1982, thus giving credit to the theory. Also, in order to reverse learning and protect synapses from saturation, the theory postulates an homosynaptic LTP at PF-PC synapses. This was also validated experimentally.

Applications and open questions.
The Marr-Albus-Ito model has been applied to a wide range of tasks in motor learning, ranging from ocular reflexes (VOR, OKR and OFR), classical conditioning and voluntary movements. In the VOR adaptation and the eyeblink conditioning, the conditioned stimulus reaches the granular layer via the mossy fibers and targets the Purkinje cells by means of the parallel fibers, whereas the information from the unconditioned stimulus reaches the cerebellum through the climbing fibers. In the two paradigms, the arrangement of the neuronal circuitry fits well the modifiable path scheme described by the theory. In voluntary movements, the Marr-Albus-Ito model has been used to explain coordination and the fine tuning of movements. It has also been proposed that the cerebellum may replace reflex control with predictive control (during a navigation task) using such an adaptation scheme. Furthermore, the standard scheme accounts for a possible role of the cerebellum in higher level functions and the formation of internal models for mental actions <ref. The theory also gains credits with exper- imental data and thanks to many theoretical supports

However, the standard model can not account for all experimental observations, and other models based on a different set of hypothesis have accurately described unexplained phenomenons. First, the role of the climbing fiber remains controversial (see  ). Although the predominant view given by the Marr-Albus-Ito theory proposes that the axon of the inferior olive acts as a teacher and drives synaptic plasticity, another view suggests that the inferior olive might provide a timing signal to the targeted Purkinje cells. The main line of evidence of this theory relies on the synchronization that has been ob- served in vitro in olivary neurons. Second, the classical theory does not take into consideration most plasticity sites that have been reported so far. While some of these plasticities integrate well with the standard theory (for example the synaptic plasticity between mossy fibers and granular cells could provide an optimal sparse encoding of the input signal) other plasticity sites still need a consistent explanation on their possible functions.

Third, the postulated adaptive role of a long term depression between parallel fibers and Purkinje cells (PF-PC LTD) is still debated. Very recent findings suggest that PF-PC LTD is not essential for cerebellar motor learning. Fourth, anatomical and neurophysiological properties of the cellular substrates are still not fully understood. For example, the bistability of the Purkinje cell caused by the climbing fiber’s discharge is not reported by the classical model. Furthermore, the functional role of some neural sub- strates (e.g., the differentiation of inhibitory interneurons), and the com- putational properties of some connections (e.g., Purkinje cell’s axon collateral, inferior olive- cerebellar nuclei connections, ascending segment of the granule cell’s axon) are still a matter of debate.

Finally, although the Marr-Albus-Ito model can explain simple motor learnings, other models also inspired from the biological properties of the cerebellar microcircuitry have successfully explained such adaptation processes and finely reproduced neurophysiological properties of the cerebellar substrates.

These discrepancies are highlighted in the next subsection, in which the neurocomputational works related to the study of VOR adaptation and eyeblink conditioning are presented.