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Neural firing rates are thought to represent values which code information. There are drawbacks with using biophysical events to represent numbers. (1) Rate code (like any sequence) is inherently slow to read. (2) At short intervals, the code becomes unintelligible biophysical noise. (3) Transmission times. The vital contribution of the cerebellum to skilled execution and coordination of movements requires precision timing. We present a theory supported by modeling that the output cell group of the cerebellar network is a practical solution to timing problems. In this role, it converts irregularly-patterned firing of Purkinje cells into an effectively instantaneous rate received by output cells, transforms the rate into linear analog modulation of output cell firing, synchronizes firing between output cells, and compensates for lag caused by extracerebellar transmission times. The cerebellum is widely connected to the midbrain and the cerebral cortex and involved in cognitive functions. Modular network wiring suggests that the cerebellum may perform the same computation on input from all sources regardless of where it is from. If so, and the deep cerebellar nuclei make the same contribution to the role of the cerebellum in other functions, an understanding of motor function would also provide insight into the substrate of cognitive functions.

We present a theory of the inner layer of the cerebellar cortex, the granular layer, where the main excitatory input to the cerebellum is received. We ask how input signals are converted into an internal code and what form that has. While there is a computational element, and the ideas are quantified with a computer simulation, the approach is primarily evidence-led and aimed at experimenters rather than the computational community. Network models are often simplified to provide a noiseless medium for sophisticated computations. We propose, with evidence, the reverse: physiology is highly adapted to provide a noiseless medium for straightforward computations. We find that input data are converted to a hyper low-resolution internal code. Information is coded in the joint activity of large cell groups and therefore has minimum spatial dimensions—the dimensions of a code group. The conversion exploits statistical effects of random sampling. Code group dimensions are an effect of topography, cell morphologies and granular layer architecture. The activity of a code group is the smallest unit of information but not the smallest unit of code—the same information is coded in any random sample of signals. Code in this form is unexpectedly wasteful—there is a huge sacrifice of resolution—but may be a solution to fundamental problems involved in the biological representation of information.

This paper presents a model of learning by the cerebellar circuit. In the traditional and dominant learning model, training teaches finely graded parallel fibre synaptic weights which modify transmission to Purkinje cells and to interneurons that inhibit Purkinje cells. Following training, input in a learned pattern drives a training-modified response. The function is that the naive response to input rates is displaced by a learned one, trained under external supervision. In the proposed model, there is no weight-controlled graduated balance of excitation and inhibition of Purkinje cells. Instead, the balance has two functional states—a switch—at synaptic, whole cell and microzone level. The paper is in two parts. The first is a detailed physiological argument for the synaptic learning function. The second uses the function in a computational simulation of pattern memory. Against expectation, this generates a predictable outcome from input chaos (real-world variables). Training always forces synaptic weights away from the middle and towards the limits of the range, causing them to polarise, so that transmission is either robust or blocked. All conditions teach the same outcome, such that all learned patterns receive the same, rather than a bespoke, effect on transmission. In this model, the function of learning is gating—that is, to select patterns that trigger output merely, and not to modify output. The outcome is memory-operated gate activation which operates a two-state balance of weight-controlled transmission. Group activity of parallel fibres also simultaneously contains a second code contained in collective rates, which varies independently of the pattern code. A two-state response to the pattern code allows faithful, and graduated, control of Purkinje cell firing by the rate code, at gated times.

This paper presents a model of rate coding in the cerebellar cortex. The pathway of input to output of the cerebellum forms an anatomically repeating, functionally modular network, whose basic wiring is preserved across vertebrate taxa. Each network is bisected centrally by a functionally defined cell group, a microzone, which forms part of the cerebellar circuit. Input to a network may be from tens of thousands of concurrently active mossy fibres. The model claims to quantify the conversion of input rates into the code received by a microzone. Recoding on entry converts input rates into an internal code which is homogenised in the functional equivalent of an imaginary plane, occupied by the centrally positioned microzone. Homogenised means the code exists in any random sample of parallel fibre signals over a minimum number. The nature of the code and the regimented architecture of the cerebellar cortex mean that the threshold can be represented by space so that the threshold can be met by the physical dimensions of the Purkinje cell dendritic arbour and planar interneuron networks. As a result, the whole population of a microzone receives the same code. This is part of a mechanism which orchestrates functionally indivisible behaviour of the cerebellar circuit and is necessary for coordinated control of the output cells of the circuit. In this model, fine control of Purkinje cells is by input rates to the system and not by learning so that it is in conflict with the for-years-dominant supervised learning model.

In the cerebellum, granule cells make parallel fibre contact on (and excite) Golgi cells and Golgi cells inhibit granule cells, forming an open feedback loop. Parallel fibres excite Golgi cells synaptically, each making a single contact. Golgi cells inhibit granule cells in a structure called a glomerulus almost exclusively by GABA spillover acting through extrasynaptic GABA A receptors. Golgi cells are connected dendritically by gap junctions. It has long been suspected that feedback contributes to homeostatic regulation of parallel fibre signals activity, causing the fraction of the population that are active to be maintained at a low level. We present a detailed neurophysiological and computationally-rendered model of functionally grouped Golgi cells which can infer the density of parallel fibre signals activity and convert it into proportional modulation of inhibition of granule cells. The conversion is unlearned and not actively computed; rather, output is simply the computational effect of cell morphology and network architecture. Unexpectedly, the conversion becomes more precise at low density, suggesting that self-regulation is attracted to sparse code, because it is stable. A computational function of gap junctions may not be confined to the cerebellum.

The attempt to understand the cerebellum has been dominated for years by supervised learning models. The central idea is that a learning algorithm modifies transmission strength at repeatedly co-active synapses, creating memories stored as finely calibrated synaptic weights. As a result, Purkinje cells, usually the de facto output cells of these models, acquire a modified response to input in a remembered pattern. This paper proposes an alternative model of pattern memory in which the function of a match is permissive, allowing but not driving output, and accordingly controlling the timing of output but not the rate of firing by Purkinje cells. Learning does not result in graded synaptic weights. There is no supervised learning algorithm or memory of individual patterns, which, like graded weights, are unnecessary to explain the evidence. Instead, patterns are classed as simply either known or not, at the level of input to a functional population of 100s of Purkinje cells (a microzone). The standard is strict. If only a handful of Purkinje cells receive a mismatch output of the whole circuit is blocked. Only if there is a full and accurate match are projection neurons in deep nuclei, which carry the output of most circuits, released from default inhibitory restraint. Purkinje cell firing at those times is a linear function of input rates. There is no effect of modification of synaptic transmission except to either allow or block output.

The cerebellum is a large brain structure. Most of the mass and volume of the cerebellum is made up by the cerebellar cortex. The outer layer of the cerebellar cortex is divided functionally into long, thin strips called microzones. We argue that the cerebellar microzone computation is the aggregate of simple unit computations and a passive effect of anatomy, unaided and unlearned, which we recreate in silico. This is likely to polarise opinion. In the traditional view, data processing by the cerebellum (stated very briefly) is the effect of learned synaptic changes. However, this has become difficult to reconcile with evidence that rate information is linearly conserved in cerebellar signalling. We present an alternative interpretation of cell morphologies and network architecture in the light of linear communication. Parallel fibre synaptic memory has a supporting role in the network computation.

Climbing fibers, connecting the inferior olive and Purkinje cells, form the nervous system's strongest neural connection. These fibers activate after critical events like motor errors or anticipation of rewards, leading to bursts of excitatory postsynaptic potentials (EPSPs) in Purkinje cells. The number of EPSPs is a crucial variable when the brain is learning a new motor skill. Yet, we do not know what determines the number of EPSPs. Here, we measured the effect of nucleo-olivary stimulation on periorbital elicited climbing fiber responses through in-vivo intracellular Purkinje cell recordings in decerebrated ferrets. The results show that while nucleo-olivary stimulation decreased the probability of a response occurring at all, it did not reduce the number of EPSPs. The results suggest that nucleo-olivary stimulation does not influence the number of EPSPs in climbing fiber bursts.

For most brain regions the only realistic approach to theory is a top down, systems view because the evidence is too sparse to 'join the dots'. For a number of reasons the cerebellum is probably the best-suited large brain structure to take a different, evidence-based approach. That is the approach here, combining evidence of anatomy, electrophysiology, molecular biology and behavioural conditioning studies with mathematical and computational modelling, to build a model of the way the cerebellum derives output from input. Modelling is used to test predictions and to generate hypothetical data not available with current experimental techniques, which feed back into the model. This allows modelled behaviour of different parts of the circuit to be tested against evidence of other parts. The focus is on circuits involved in control of axial and limb movements, although parts of an explanation are likely to be portable to other circuits (because cerebellar circuit wiring is modular). An important part of the proposals is that the functions of pattern recognition and output coding are separate. It is a function of recoding in the granular layer to turn input variables into independent (and fewer) internal variables. Independence means they can be used in different functions without mutual interference of the execution of those functions with each other. Pattern recognition determines which circuits have output and when, but does not code output. Instead, the response to a known pattern following training is permissive, creating a time window in which output cells are controlled ad hoc by internally generated information about movement. Recoding in the granular layer, as well as having a long-suspected role in pattern detection, also has a role in control of output rates, by turning (what is from a cerebellar view) an arbitrary range and frequency distribution of input rates into a narrow range of granule cell rates with a fixed bandwidth and a frequency distribution with a fixed shape, so that the only functional variable of internal signals traffic at the scale of input to a Purkinje cell is the adjustable range.

Though the major European Union member states all have research and Bolar exemptions in their patent laws, the scope and effect differs considerably from country to country. The strength and economic importance of patent protection in the pharmaceutical and biotech industries in Europe is discussed.