How a Memory May Be a Number and an Organism May Be Digitally Controlled:

Considerations of a Systems Analyst
Peeking at the Inner Machinery of Long-Term Memory

Cesare Marchetti
International Institute for Applied Systems Analysis
Laxenburg Austria

Abstract

Among the various types of memory that may exist I single out for study the long-term one. I apply techniques of systems analysis to produce a credible and self-consistent picture of the process, taking hints from the immense amount of experimental work in the field. Papers connected in one way or another to the problem of long-term memory may number 100,000.
I put to work in appropriately complex tasks three actors that did not seem yet to have found the complex role they deserve, spike trains, kinase II, and dendritic spines. With their integration, everything seems to fall into place, not a proof, but certainly a good omen. I hope I elevate a few keywords and provide a theoretical context for new experiments, if some attention is raised by this work.
I hypothesize that spike trains are digital signals (binary numbers) that activate digitally codable gates. These gates take the form of kinase II molecules which are capable to assume a very large number of configurations. I further hypothesize that kinase II is in fact a counter that can be preset to a given number by a spike train and later activated by spike trains carrying a number with appropriate coding . The process of memory can then be described as four steps:

1) coding of kinase II into a certain configuration corresponding to a number presented in synchrony with an event, e.g., by a central clock via a spike train;
2) conservation of a certain amount of the coded kinase II into a dendritic spine;
3) activation of this kinase II with a spike train carrying the appropriate number; and
4) squirting of Ca2+ from the spine into the dendritic space, activating the synapse. The Ca2+ is produced in the spine by the action of the kinase on associated calmodulin (CaMKII complex)

In summary, the physical seat of long-term memory is in the spines that cover the surface of each dendrite by the hundreds, each spine holding kinase II counters that, in a sense, freeze the reference number of an event. A set of spines, eg a million, that hold counters set on the same number define the neuronal topography of the event.

A recall is the repetition of an event, through the reactivation of a sufficient number of neural circuits that participated to it.. The mechanism delineated is capable of synchronous reactivation of the set of synapses that participated in a given event just by a recall on the coded kinases II through a spike train with the appropriate code number.

If sufficient family resemblance exists between kinase II and kinases C in general, one may speculate that kinases C, which mediate action in a vast number of events, may too be activated by similar procedures. This view would offer the exciting perspective of a central controller dispatching its orders all over the organism in digital form, a virtual Morse Code of life.

Introduction

Long-term memory stores an immense amount of information that biological machinery retrieves almost instantly and, in the good cases, with crystal clarity even tens of years after the event. A satisfactory account of the machinery for storage and retrieval has remained elusive. The crux of the problem has been lack of specificity in the permanent coding of an event.

Consider that a recall is not shorthand for an event. Rather, it is the repetition of the event by a representative number of neurons that originally participated in it. These neurons constitute an extremely complex web of interconnections, based principally on their thin branches, the dendrites, which plug into other neurons through nonlinear switches, the synapses. A recall then requires the simultaneous switching on of thousands of synapses by a signal of some sort that travels through the brain.

Because a given synapse may have participated in many different events, a specific coding for each event must be preserved in all of them to reset specifically that particular circuit. The current consensus on the mechanism most explored for long-term memory, synaptic potentiation, meaning that a past event makes a synapse easier to open, cannot be correct, because it lacks this necessary specificity.

By general consensus, three actors, spike trains, kinase II, and dendritic spines, appear important in the operation of the long term memory system because they always appear participating and knockout mutants show evident deficits. But their functions in the memory process are yet insufficiently clarified. Here I put them together to work, to reach the specificity needed for synchronized synapse opening and more generally for a theory of long-term memory.

The basic tool I will use to reach my conclusions is the Occam's Razor of Darwinian theory. In short, a complex machinery cannot survive for long the ablation of stochastic evolution if it is not fully and proficiently employed.

On spike trains

The first actor is the spike train, a brief sequence of voltage pulses or action potentials lasting altogether tens of milliseconds. Inside the train the pulses are precisely positioned into time slots, where a pulse may be present or not (Fig.1). The irregular distribution of pulses shown in the figure is more apparent than real, since the discovery that the pulses fall precisely into individual time slots having a width of the order of a millisecond.

Fig.1 - Click per ingrandire

That spike trains represent numbers, presumably in binary notation, is well accepted. If we visualize the slots containing a pulse as 1's and the slots with no pulse as 0's the spike train appears as a straight binary digit. The function of these numbers roaming the cortex remains however mysterious. One hypothesis is that they serve to make calculations, but how and where has not been convincingly specified.

The precise patterning of spike trains contradicts the assumption in memory research that exact timing of nerve impulses in the brain does not matter much. A popular view has been that each neuron's message is carried in the average number of electrical impulses it sent to its neighbors over a set period. Neurons then collect impulses from connected neighbors and integrate them over a period of time, and fire when the "leaky bucket" fills.

A modern and controversial view is that the timing of the pulses carries information, either intrinsically or in relation to the timing of other spike trains. Softky (National Institutes of Health, Bethesda MD) appears one of the most enthusiastic and articulate propagators of the idea that these sequences encode binary digits and are used by the brain to perform its internal calculations.

Softky (1994, 1995, 1996) extensively and convincingly demonstrate that a digital system of computation in the brain would be vastly superior to an analogue system. However, he has yet to show how the brain performs its calculations using the pulse trains. Supporters of the (quasi) analogue theory of computation also did not go far in decoding the actual computing procedures of the brain.

That the spike trains are likely to carry messages (a number for coding or decoding a counter is a message) is shown by the fact that in the sensory system of insects (locusts, to mention a well-studied case) the brain input from the olfactory sensors comes in form of spike trains.

To a given "simple" odor, call it rose or turpentine, always corresponds the same spike train. One simple odor, one typical spike train. In our scheme, if the spike train can open the appropriate set of counters corresponding, e.g., to the circuits that fired during the first experience of a rose, then every time the spike train arrives that memory of rose scent will be reenacted by reopening the appropriate neuronal circuits. Even in the human brain it is known that the memory of odors is extremely stable in time which may call for fixed patterns in the connected spike trains.

The sense of olfaction may be somehow peculiar in the brains of mammals that started their careers as small nocturnal sniffing creatures. However, the general similarity of a neuronal process across species, even genera, makes it improbable that olfaction operates on different basic principles.

The eye also communicates to the brain via spike trains. Here the input is more variegated, and it is hard to reach the point simplicity of a single odor. Moreover, one cannot expect that a given visual image is already in store, to be seen as a memory when the signal reaches the brain. However, many experiments show the same spike train output for the same input.

Among the most illuminating current explorations of the function of spike trains are those carried out on sensory discrimination in insects (MacLeod et al., 1998). Here oscillatory synchronized activity in the early olfactory system seems needed for fine odor discrimination and enables the encoding of information about a stimulus in spike times relative to the oscillatory clock. The fact that downstream neurons show odor responses whose specificity is degraded when their inputs are desynchronized shows that the timing carries the message.

Identifying how the chemical representing the odor stimulates the production of the spike train is also important and doesn't seem to have been searched yet. Although we are still far from this explanation, it is interesting to observe that a single projection neuron responded to three different odors with three distinct temporal patterns.

Such phenomena burden the integrate-and-switch theory that has dominated the interpretation of the functioning of the brain. If neurons integrate, the previous information coded in the precise timing of the spikes would be lost. Much research done on the statistical properties of spike trains may thus be misdirected. The statistical properties of the digits from Wall Street tickers do not carry much information about the workings of the stock exchange.

The most interesting feature of the spike trains is that each neuron reproduces exactly the same pattern of impulses with accuracy better than a millisecond. However, this might be only the icing on the neural cake. To use signals effectively from the ears or from electric sensors to locate their prey, owls, bats, and electric fishes must make time discriminations precise to the microsecond and better.They show the potential and perhaps the limits.For these animals precise timing is a premise for survival, so that all the tricks of the trade must have been set in place through evolutionary tinkering.

Here I add a general consideration: spike trains are well-conserved in animals having a nervous system, be they human, mouse, or locust. All the details are conserved, e.g., the precise location of the spikes in a time slot reference system. Spike trains must thus be central to brain operation. Certainly a spike train is central if it is the way a neural event becomes digitized, that is, the way a memory becomes a number.

Thus, I hypothesize that spike trains are digital signals that activate digitally coded gates by coding them into a certain configuration and decoding them into readiness for action. These gates take the form of kinase II molecules, the second important actor in my model of the functioning of long term memory.

On kinase II

Kinase II belongs to the ubiquitous class of kinases, important in managing all sort of processes inside an organism. Kinase II is a modular molecule made up of a set of subunits. In the brain it may constitute up to 30% of the proteins in the space near the synapse, and with a " smoking gun" argument, researchers saw it as the molecule of memory.It is normally associated with calmodulin and is coded then as CaMKII

Kanaseki et al. (1991) published excellent observations of kinase II by electron microscopy. The molecule is bulky, so that the images come out quite clear (Fig.1). A set of more or less identical modules, 8, 10, or 12, arranged in the form of a rosette, make up kinase II.

Each module has the form of a dumbbell, with a small ball and a large one. The small balls coalesce around a central hole and the large ones spread out. Each module can phosphorylate at three sites. This phosphorylation and its stability depend on the state of neighboring components.

With my background in physics, when I first saw the molecule in Kanaseki's pictures, I could not resist thinking that kinase II must be a counter of some sort. The interaction between the components provides the ratcheting mechanism (e.g., through sequential phosphorylation) that may make it possible to exploit its large capacity for different configurations. This capacity depends on how the counter is operated. Coomber (1998b) in a paper presented by J. Lisman of Brandeis, a great supporter of CaMKII as a memory molecule, calculates 1012 possible configurations for the 10-unit version of kinaseII that seems most common in the brain.

Such a complex machine, probably present in all nervous systems and highly conserved, would certainly be evolutionarily degraded if its full potential were not central to the functioning of the brain. In spite of this elementary consideration, researchers who came to the idea that kinase II may be a switch have never gone much beyond the hypothesis that it is a binary switch (Lisman, 1994; Matsushita et al., 1995), or a frequency detector (Hanson et al., 1994), or a recorder of Ca2+ transients spacings (Dosemeci and Albers, 1996).

Coomber, bringing skills in computers and informatics, best analyzed kinase II in physical and functional terms and cleverly dug into the gears of the machine (Coomber, 1998). Coomber did not spell out the word counter, though he may well have thought of it, perhaps deferring to his neuroscience colleagues who see kinase II as a binary switch, perhaps a graded one. A possible definition if one can accept one trillion grades.

To use its configurational potential of 1012 states (for the 10-subunit molecule), kinase II can only be a counter with 1012 positions or so. The conservation argument is in my opinion a fairly hard proof for this hypothesis although other hypotheses might be possible. Experimentation is here necessary.

Obviously one has to test the counter with appropriate signals for inputs and outputs. If my hypothesis is correct, sophisticated time structures such as spike trains should do that work. Experiments have been tried applying oscillatory signals at constant frequency. These experiments may imitate too roughly what happens in the brain, so the reactions, if any, are mixed and confused.

Kinase II usually operates in connection with a cofactor, calmodulin, which appears to be a universal calcium carrier. It normally holds 4 calcium atoms. Calcium (Ca2+) is the universal signal for action in biological systems Ion pumps keep it in low concentration in the cytoplasm, so that a squirt of Ca2+ is interpreted by cellular machinery as a signal to operate, contracting a muscle, opening a synapse, or reading DNA. As said the association of kinase II and calmodulin is usually coded as CaM KII. I kept them separate as the quintessential information processing seems to be concentrated in the kinaseII structure.

One could worry that kinase counters have only 1012 positions (in Coomber's conceptual scheme), so that one trillion events would saturate the system. However, as Kanaseki reports, kinase II molecules tend to coalesce in clusters. This may owe to the electron microscopy preparation or not. In the last image of Fig.1, two kinase II molecules appear to be interconnected. If this visual appearance corresponds to a functional connectivity, then their joint capacity would jump to an ample 1024 positions, requiring perhaps a "doublet" of spike trains to open the two in sequence.

In sum, my second and central hypothesis for the functioning of memory is that kinase II is a counter that can be preset to a given number (configuration) and later reactivated. More specifically, a spike train representing a digital number sets kinase II into one of its 1012 states and, carrying the same number, re-activates it in terms of Ca2+ metabolism.

On dendritic spines

The nervous system appears as an extremely complex web of connected machinery, the neurons. Already in 1873 Camillo Golgi with his selective silver staining could stare at this marvel of finer and finer wiring and connection points.

A neuron is a cell with a cell's normal attributes but with extraordinary features in terms of shape. It is made of a cell proper with a robust elongation, the axon, sometimes as long as one meter, which branches into a terminal kind bushy root, plus has a forest of thin interconnecting wires starting out from the cell body, the dendrites. Dendrites are extremely thin but with a complex infrastructure for the transfer of molecules.

The nervous system preserves its complexity even in its finest recesses. There are, for example, two internal spaces to the cell, the cytoplasmatic (the normal one for a cell) and the endoplasmatic reticulum. The endoplasmatic reticulum, which keeps and provides ions for the working of the neuron, penetrates as an independent structure the entire neuron including the dendrites, down to the final recesses, the spines, as we shall see (Fig.1).

Dendrites are very thin, in the micron range, and provide terminal and intermediate synaptic connections. A possible number for dendrites is 100,000 for a single neuron. On their surface they carry small protuberances, the spines, our third actors, so small that they escape detailed observation with optical microscopes. Well-examined however with electron microscopy, the dendritic spines have a range of shapes, from a flat waddle to a pear with a thin neck.

Dendritic spines contain all the machinery for neuronal operation, in particular CaM KII, the combination of the calcium carrier calmodulin and the gate molecule kinase II, which represents their largest protein constituent. They are also penetrated by the endoplasmatic reticulum, the universal tool bag of the neuron machinery. Because the dendritic spines are always implicated with memory, in one way or another, any "smoking gun" theory must also give them great importance in memory processes. The same holds for CaM KII, but also in this case the mechanisms of the implication have remained obscure.

It must be kept in mind that the neck that joins the spine to the dendrite, even if narrow, does not deny access of spine fluids to the body of the dendrite and vice versa. The neck may also shut out the fluid, so that the spine could be seen as a gated recess of the dendrite itself. However the descriptions of the operation of the neck are still too sketchy for this conclusion.

Dendritic spines have been quite thoroughly studied during the last twenty years with the rise of techniques that overcome the problem of their very small size. For example, two photon microscopy and laser microscopy permit views of the spines when functioning, and not only as dead specimens, as with electron microscopy. The spines are shown schematically in Fig.1.

My third hypothesis then is that the physical seat of the memory is in the spines that cover the surface of the dendrite by the hundreds, each of them holdinga pack of kinaseII counters that can "freeze" the reference number of an event by taking the corresponding configuration.

Conclusions

My leading idea has been that spike trains, kinase II, and dendritic spines are complex, widespread, and conserved systems and consequently must have a general, important, and sufficiently complex task to perform.

Spike trains and kinase II can be seen as representing numbers, large ones and of similar size, and thus I tried to make them work together numerically at full performance, by attributing to spike trains the task of carrying digital gate signals in binary form, and to kinase II the task of a digital gate that can be set and unlocked by spike trains.

Once this basic mechanism is established, if hypothetically, then the description of the functioning of memory becomes more straightforward. Remembering means re-acting an event at neuronal level, and this requires opening a large set of synapses to reactivate the original circuits that fired when the event did first happen. If the event is dubbed via a number stored in spines near these synapses in the form of coded kinase II, then the reactivation of a given set of kinase molecules carrying the same number can do the job, as the association CaM KII can liberate the Ca2+ necessary for the activation of the nearby synapse.

The coded kinase II cannot be safely left around together with a mass of kinase II molecules dozing next to the synapses. It should be better preserved in a receptacle ready for use. These receptacles exist in the form of dendritic spines, tiny, sophisticated, and conserved structures whose complex machinery would not resist evolutionary weathering if their role were not essential. These spines populate by the hundreds the wall of the dendrites, especially near the synapses, i.e., in a very strategic position.

Suppose the neck of a spine is open to the channel of the dendrite when an event occurs. The spine gathers some coded kinase II and the neck shuts tight. The coded kinase may be preserved indefinitely if metabolic processes stop at the spine itself. It can then wait for the appropriate spike train to come that will open it. When this happens, the CaM KII complex can liberate Ca2+ ions and squirt them into the dendrite where they could open the synapse.As all the synapses that participated to a given event would open in synchrony, the original circuit is then restored, and can be restored again and again.

The process of memory can thus be essentially described as four steps:
1) coding of kinase II into a certain configuration corresponding to a number presented in synchrony with the event, e.g., by a central clock via a spike train;
2) conservation of a certain amount of the coded kinase II into a spine;
3) activation of this kinase II and the associated calmodulin with a spike train carrying the appropriate number; and:
4) squirting of Ca2+ from the spine into the dendrite space, activating the synapse.

The common problem to all models of long term memory, how to skip molecular destruction by metabolic processes is skipped here by assigning a hypothetically protected space inside the spines. The search for the mechanism is open. The fact that Prion molecules have one configuration escaping metabolization and that they play an important role in brain and memory as knockout animals have shown might constitute a first lead for this research on metabolic sanctuaries.

Speculations

The obviously complementary problem is who and how starts the chain of events leading to a recall. I did not touch this problem because my scanning of the literature did not reveal the elements I could use even for hints.

However, evolution imposes economy and ingenuity. When a trick is invented, it will finally find its place whenever it can be used. Kinase II as a counter with 1012 positions (or whatever it may be in practice) is a sophisticated engine. It would be natural to use it also uphill, to help code the spike train that, downhill, will re-open the neuron chain related to a given event. The fact that spike trains in the olfactory system are started by a cell shows that one or more gated counters can be located in a cell and operate as starters.

This leads to the next question: Even if the information is there, how is it set properly in motion? Every child who has a microscope to observe the famous drop of water from a pond has seen protozoa swimming around and tried to tease them with tiny hairs. The astonishing fact is that these monocellular creatures behave more or less as a dog or a hen would, showing that they have computational machinery and memory. Eminent students of protozoa, such as Csaba (Csaba and Kovacs, 1986), have stated this view explicitly, but nobody seems to have tried carefully to see how the machinery works.

In terms of evolution, the cells going into the brain clearly did not shed their computing and remembering capacity, but interconnected it in a network, or more precisely a web, as each "computer" can connect up to say 100,000 other computers.

If my reasoning is correct, a single cell may hold the code of a single memory in the form of one or more molecules of coded kinase II. Obviously it would not store the memory as in the corresponding set of dendritic spines but only its code number. Because the memory of the protozoa is complex, a protozoan must also contain a whole set of coded molecules (kinase II?) that it can extract, this or that, according to an external input. Consequently it is reasonable to assume that special brain cells also may hold the code of many memories. Again in terms of evolution, research with the monocellulars could hold the key to answering the question of how this information is set in motion.

As a further thought, I observe that other kinases, kinases C, make a large and omnipresent family of actuators, mostly with a small number of component modules, e.g., three. Once the principle of the digital chain of command is established, why not extend it to the peripheral outposts? In these outposts the commands can employ a much shorter arithmetic, as they are certainly more limited in alternatives than the events in a brain and consequently the counters can have a smaller capacity, as it is the case. This outlines the picture of an organism where the management runs by numbers, fitting well the general picture where the basic mechanisms are digitalized, starting from DNA.

It would also adumbrate a system for entering into the regulatory system, e.g., for medical purposes, in a subtle way, by sending precisely coded electric signals to put this and that into operation. A PC as a pharmacy lights up my imagination.

The strength of my argument relies essentially on evolutionary necessity and the smooth meshing of the functions once spike trains, kinase II, and dendritic spines are put to work together. If I have successfully sketched the elemental gears of the long-term memory process, the empirical evidence is scant or nil and a wealth of details remain to be verified. Part of the needed information might be rescued from the tens of thousands of papers already written by re-reading them with the appropriate new filters.

However, the general clockwork of the memory process has yet to be sufficiently explored. A number theory should be created that explains association, identification of the object to be remembered, and creation of objects that did not start from the senses but rather from the "imagination". The question of an appropriate ISDN address code to precede a spike train is open.

I hope the beauty of the proposed ensemble performance of the three actors descending from the internal logic of evolving living systems provides inspiration. So might the hypothesis that all the kinases may ultimately be numerically controlled, presumably via the nervous system. After all, this view offers the exciting perspective of a central controller dispatching its orders all over the organism in digital form, a virtual Morse Code of life.

Acnowledgements

I shall thank the Sloan Foundation and NEDO of Japan for financial support and IIASA librarian Eddie Loeser for having waded me through the infinite literature on the subject.

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