Vertebrate brain theory

ISBN 978-3-00-064888-5

Monograph of Dr. rer. nat. Andreas Heinrich Malczan

3.18  The imprinting algorithm in early Pontocerebellum

In the original Pontocerebellum there was exactly one Purkinje cell per cortex cluster, which received the signals of the time-sensitive difference mapping of the global mean value from the assigned cortex cluster from the nucleus ruber. This signal reached the signal neurons of the associated cortex cluster via back projection and led to a certain pre-excitation.

With the increase in the number of class 5 cortical signal neurons and the enlargement of cortical clusters, the mean signal of a cortex cluster became increasingly higher frequency. The striosome system impressed signal pauses on it. The tetanic excitation resulted in a permanent change in the synaptic coupling strength between the active parallel fibres and the Purkinje cells, the active star cells and the active basket cells. As a result, the output behaviour of the neurons of the nucleus dentatus changed. The previous balance between the excitation strength of the Purkinje cells and the excitation strength of the dentate neurons was disturbed, leaving a residual signal that was beneficial to the living being.

We hypothesize a more complex form of LTP and LTD in the pontocerebellum, which leads to the fact that an output neuron of the nucleus dentatus reacts significantly stronger to a certain signal constellation. We call this signal constellation the imprinting signal. The process of LTD and LTP is called imprinting.

The embossing signal originates from a cluster group of the cortex and may consist of two partial signals:

-         The inner signal si from the inner cluster of a cluster group.

-         The external signal sA from the external clusters of this cluster group.

The internal signal must not be the zero signal; a sufficient subset of the cortex neurons from the internal cluster must be active. It forms the basis for the signal average.

The associated mean signal ends via the climbing fiber at the Purkinje cell of a cerebellum inner cluster.

The internal signal Si ends at excitatory parallel fibres of the Purkinje cell of the Cerebellum internal cluster.

The external signal SA ends at inhibiting star and basket cells of the same cerebellum inner cluster.

If the output neuron of the nucleus dentatus is to react more strongly to the complex signal S = Si + SA, the Purkinje cell of the inner cluster must be less excited by these signals.

This would require the following:

-        The internal signal is applied to parallel fibers whose synaptic coupling is reduced by the tetanic climbing fiber signal, for example from coupling value 1 to coupling value ½. Thus the Purkinje cell is less excited by the internal signal.

-         The external signal is due to the star and basket cells, which inhibit the Purkinje cell in the sense of a lateral inhibition. The synaptic coupling strength to the Purkinje cell may have the value 1. Through the effect of the tetanic excitation by the climbing fiber signal, the synaptic coupling between the star or basket cells to the Purkinje cell is strengthened, e.g. from 1 to 2. Thus, the Purkinje cell is more strongly inhibited by the external signal.

-         Since the tetanic climbing fiber signal also terminates at the output neuron of the dentate nucleus, the synaptic coupling between the active moss fibers of the complex signal and the dentate neurons is (probably) also increased, e.g. from 1 to 2, thus generally making the output signal stronger.

Thus, these three effects overlap and cause the excitatory output neuron in the nucleus dentatus to react much more strongly to exactly this complex signal than before imprinting, because the output neurons are excited more strongly and inhibited less.

If the embossing signal occurs again later, the response is much stronger. We call the embossing signal after the embossing a self-signal of the Purkinje cell.

Theorem of recognition of self-signals by the dentate neurons

By imprinting by LTD and LTP, the imprinting signal of a cortical cluster group becomes the intrinsic signal of the Purkinje cell of the associated cerebellum cluster. After imprinting, this cell reacts to the repeated occurrence of its own signal with significantly reduced inhibition of the excitatory output neuron in the nucleus dentatus, so that its output to the own signal is significantly stronger. This enables the Pontocerebellum to learn exactly one imprinting signal in each cluster and to recognize it later. The recognition output reaches the pontocerebellum.

Each Purkinje cell can therefore learn exactly one imprinting signal together with its output neuron in the nucleus dentatus and store it as its own signal by permanently and permanently changing the synaptic coupling strengths for this complex signal. In this respect, the synapses of the involved interneurons of the cerebellum are the material locations where the signal storage occurs.

However, it should be remembered that any sufficiently strong but arbitrary combination of an inner and an outer signal always generates a sufficiently strong cortical mean signal, which would strongly excite the Purkinje cell of the inner cluster via the nucleus olivaris. This would result in a new imprint for this new signal combination. This could be repeated at will and would destroy any learning effect. Overall, the Purkinje cell reacted to all complex signals with stronger output as long as they linked an inner cluster component with an outer cluster component. And only such signals should be recognized as complex signals in the future.

A stronger output response to complex signals was apparently so beneficial to the vertebrate that it led to an increase in the number of Purkinje cells.

The more Purkinje cells were present in the Pontocerebellum, the more complex signals it could learn if the imprinting algorithm was refined a little bit more. Therefore, in the course of evolution, a process occurred that was to lead to an increase in the number of Purkinje cells. To do this, it was only necessary that each climbing fibre axon arriving in the Pontocerebellum - whose growth direction was the same as that of the moss fibres - contacted several Purkinje cells lying one behind the other. The moss fibres in the hippocampus exhibit a similar behaviour: They contact a large number of granule cells of the hippocampus. The sequential nature of the contacts is important. We refer to this type of divergent distribution of a signal to several signal receivers as sequential divergence.

Theorem of the increase of Purkinje cells contacted by a climbing fiber

In the course of evolution, a climbing fibre contacted several Purkinje cells by sequential divergence, their number slowly increasing in the evolutionary series.

The Purkinje cells in question inevitably received the same input as the individual Purkinje cell before. The imprinting algorithm was also identical, so that these Purkinje groups all initially learned the same imprinting signal. However, this changed with the appearance of the Golgi cells.

How can the development of golgi cells be explained? Whose descendants are they?

Even between the class 6 signal neurons in the cortex, there has been lateral inhibition since time immemorial to enhance contrast in the output. The mean class 6 neurons transferred this cluster competition to the class 5 neurons of the clusters. This neuronal competition between the clusters was taken over by the moss fibres and passed on to the granule cells. Therefore, granule cells belonging to one cerebellum cluster inhibited the granule cells of the neighbouring clusters. The necessary interneurons can be interpreted as descendants of the inhibitory interneurons of the cerebellum cortex, which realized the cluster inhibition.

Theorem of the golgi cells as inhibitory interneurons

Golgi cells are descendants of the inhibitory interneurons of the cerebellum bark, moss fiber neurons are the descendants of the cortical signal neurons. Grain cells are descendants of the moss fiber neurons.

Lateral inhibition between cortical signals in the moss fibre system is achieved by inhibitory interneurons, whose derivatives in the granule cell system are the golgi cells.

The moss fibre input of one cluster excited the golgi cells, which in turn docked with their axons to the dendrites of the granule cells of the neighbouring clusters and inhibited them if they were self-excited. This is how the mutual inhibition of the clusters was realized in the Pontocerebellum. In the spinocerebellum and in the vestibulocerebellum there was an analogous development. However, in the pontocerebellum, this algorithm enabled the prevention of so-called multiple imprinting. This is explained in the following text.

The number of golgi cells is slightly smaller than that of Purkinje cells. We assume here as an example that there are three Purkinje cells per golgi cell.

Golgi cells are excited by the climbing fibre signal and inhibited by Purkinje cells. The climbing fiber signal is the average value of the cluster signals, and these excite the golgi cells.

As an example, we consider a group of three Purkinje cells arranged one behind the other, which are contacted by the same climbing fibre one after the other. As a fourth neuron, the climbing fiber may contact a Golgi cell. The further course of the climbing fiber may not be of interest at first.

We assume that the three Purkinje cells are imprinted with an imprint signal S1. Because of their identical output, they might activate exactly one common output neuron in the nucleus dentatus. Thus, there is only one common output neuron in the nucleus dentatus for these three Purkinje cells. So for each imprinted signal there are two reserve Purkinje cells, if one fails, the circuit remains functional. Only the failure of all three Purkinje cells leads to the loss of the learned signal.

Theorem of the Purkinj groups as a security reserve of the Pontocerebellum

Purkinj groups each end with a golgi cell and are activated by the same climbing fibre. They are embossed identically. Their output converges to the same dentate neuron. This signals the recognition of the embossed own signal to the cortex.

Each Golgi cell is synaptically connected to the climbing fiber which contacts the Purkinje cells in front of it. During imprinting, this climbing fibre with its strong climbing fibre signal also activates the Golgi cell, which is strongly excited and interrupts the signal flow to the granule cells. Thus, the following Purkinje cells receive less strong parallel fiber signals, because a whole population of parallel fibers is virtually pinched off. Strictly speaking, the signals of the foreign clusters are pinched off. Thus, the three Purkinje cells in front of the Golgi cell reach the embossing threshold earlier, their LTD and LTP lead to embossing with a time lag. During the pause in the oscillation of the climbing fibre signals, they are the first to recognise the applied embossing signal, as it has become their own signal. The loss of inhibition leads to a strong output signal of the corresponding neuron in the nucleus dentatus.

Here the inhibitory reaction of the nucleus dentatus on the nucleus olivaris comes into play. Each excitatory output neuron of the dentate nucleus activates an inhibitory projection neuron with its excitation, the axon of which pulls towards the olivaric nucleus and docks there exactly to the neuron that has generated the formative climbing fibre signal. This weakens the climbing fibre signal considerably, so that subsequent Purkinj groups are no longer imprinted with this complex signal.

The inhibiting rear projection of the nucleus dentatus to the nucleus olivaris serves to prevent multiple imprinting. Without golgi cells and without this inhibitory feedback, all Purkinj groups of a cerebellum cluster would be imprinted with the same imprinting signal.

Now, the Pontocerebellum was able to learn several different complex signals per cortex cluster using LTD and LTP, because it was possible to prevent multiple imprinting of different Purkinj groups with an identical imprinting signal.

Theorem of prevention of multiple imprinting of Purkinje cells of a cluster

Each imprinted Purkinje cell reacts to its own signal with significantly less inhibition of the assigned output neuron of the nucleus dentatus. As a result, the output neuron reacts much more strongly to this signal. It reports the recognition to the cortex and simultaneously excites a connected inhibitory output neuron, which in the nucleus olivaris inhibits the climbing fibre signal more strongly, so that it becomes low-frequency.

Thus, all other Purkinje cells connected to the same climbing fiber lack the tetanic excitation by the climbing fiber signal, which is absolutely necessary for LTD and LTP. No subsequent Purkinje cell on this climbing fiber can now be imprinted with the same complex signal. Multiple imprinting is actively prevented.

If a climbing fibre contacted several successive Purkinj groups and the golgi cells between them during its propagation in the Pontocerebellum, as many different complex signals could be learned as there were Purkinj groups.

Before that, however, each Purkinje cell of a Purkinje group had to make synaptic contact with the Golgi cell, which was at the end of the group. If an external signal was then present, each Purkinje cell of the group remained strongly excited, because only the imprinting signal could significantly minimize their excitation. With this strong excitation, it inhibited the Golgi cell at the end of the group, so that it could not stop the moss fibre signals from passing through to the parallel fibres. Therefore, the following Purkinje group received the complete input signal and, because the tetanic climbing fiber signal was active at the same time, could be imprinted with this signal. However, because the same climbing fibre signal excited the subsequent Golgi cell, subsequent Purkinj groups could not receive the moss fibre signals and therefore could not be imprinted with this signal.

The minting with new signals in the chain of Purkinj groups was carried out step by step and sequentially. The more Purkinj groups existed, the more different embossing signals they could learn.

Imprint theorem of the primitive Pontocerebellum

In the Pontocerebellum, in each cortex cluster, as many different complex signals could be learned as there were Purkinj groups connected to the climbing fibre derived from this cortex cluster.

As a reminder, the climbing fiber signal was obtained from the mean value signal of the cortex cluster and the striosome signal derived from it and distributed by sequential distribution to the Purkinj groups arranged in a row.

The sequential divergence of the climbing fiber signals may have been differently pronounced in different species. The more different complex signals a vertebrate could learn, the more specific and adapted its reactions to complex stimuli became. This gave it an advantage over other species that were not so well able to do so.

As the neurologist and cerebellum expert David Marr already suspected in [41], the cerebellum is a learning machine. However, there is a huge difference to learning systems described by neural networks. Neuronal networks learn by slowly and gradually changing the synaptic coupling strength. They need a huge amount of input and time for their learning process. In most cases, they also require correction mechanisms to ensure that desired signal patterns are recognized. Thus, input and output are compared and new, modified input is made available via correction mechanisms to bring about desired learning processes.

The cerebellum, on the other hand, learns on its own, and to learn a complex signal, it is only necessary that this complex signal is available as input for about one second. After that, the learning process for this signal is finished, from then on it is always recognized.

The extremely fast learning is achieved via the climbing fibre signal, which as a signal average in the associated cerebellum cluster causes a tetanic excitation of the learning Purkinje cell, in the result of which LTP and LTD lead to a sudden and permanent change in synaptic strength in the relevant synapses.

The climbing fiber signal is the neural write command that is used to burn the signals into the Purkinje cell in an extremely short time. Thus, the Cerebellum is a thousand times superior to theoretical neural networks and has the write command in common with ordinary computer memories. Its neural architecture corresponds to a sequential memory, in which each memory cell whose imprint signal is applied to the data lines responds with a recognition output, while the first free cell learns the next, as yet unimprinted complex signal as soon as it is applied.

A further, strong increase of Purkinje cells in the Pontocerebellum should occur in a phase that we call the second expansion phase of the Pontocerebellum. However, before that, it is necessary to analyze the parallel development in the olfactory and limbic system.

Monografie von Dr. rer. nat. Andreas Heinrich Malczan