Cocaine Dependency and restricted learning

Substantial work (NasifFJetal2005a, NasifFJetal2005b , DongYetal2005HuXT2004, Marinellietal2006) has shown that repeated cocaine administration changes the intrinsic excitability of prefrontal cortical (PFC) neurons (in rats), by altering the expression of ion channels. It downregulates voltage-gated K+ channels, and increases membrane excitability in principal (excitatory) PFC neurons.

An important consequence of this result is the following: by restricting expression levels of major ion channels, the capacity of the neuron to undergo intrinsic plasticity (IP) is limited, and therefore its learning or storage capacity is reduced.

Why is IP important?

It is often assumed that the “amount” of information that can be stored by the whole neuron is restricted compared to each of its synapses, and therefore IP cannot have a large role in neural computation. This view is based on a number of assumptions, namely (a) that IP is only expressed by a single parameter such as a firing threshold or a bit value indicating internal calcium release, (b) that IP could be replaced by a “bias term” for each neuron, essentially another parameter on a par with its synaptic parameters and trainable along with these (c) at most, that this bias term is multiplicative, not additive like synaptic parameters, but still just one learnable parameter and (d) that synapses are independently trainable, on the basis of associative activation, without a requirement of the whole neuron to undergo plasticity. Since the biology of intrinsic excitability and plasticity is very complex, there are very many aspects of it, which could be relevant in a neural circuit (or tissue) and it is challenging to extract plausible components which could be most significant for IP – it is certainly a fruitful area for further study.

In our latest paper we challenge mostly (d), i.e. we advocate a model, where IP implies localist SP (synaptic plasticity), and therefore the occurrence of SP is tied to the occurrence of IP in a neuron. In this sense the whole neuron extends control of plasticity over its synapses, in this particular model, over its dendritic synapses. It is well-known that some neurons, such as in dentate gyrus, exhibit primarily presynaptic plasticity, i.e. control over axonal synapses (mossy fiber contacts onto hippocampal CA3 neurons), but we have not focused on this question concerning cortex from the biological point of view. In any case, if this model captures an important generalization, then cocaine dependency leads to reduced IP, and, as a consequence reduced SP, at a principal neuron’s site. If the neuron is reduced in its ability to learn, i.e. to adjust its voltage-gated K+ channels, such that it operates with heightened membrane excitability, then its dendritic synapses should also be restricted in their capacity to learn (for instance to undergo LTD).

As a matter of fact, a more recent paper (Otisetal2018) shows that if we block intrinsic excitability during recall in a specific area of the PFC (prelimbic PFC), memories encoded in this area are actually prevented from becoming activated.

Why a large cortex?

mouse

If we compare a small mouse cortex with a large human cortex, the connectivity per neuron is approximately the same (10^4/neuron SchuezPalm1989). So why did humans add so many neurons, and why did the connectivity remain constant? For the latter question we may conjecture that a maximal size is already reached in the mouse. Our superior human cognitive skills thus rest on the increased number of neurons in cortex, which means the number of modules (cortical microcolumns) went up, not the synaptic connectivity as such.

Soft coded Synapses

A new preprint by Filipovicetal2009* shows that striatal projection neurons (MSNs) receive different amounts of input, dependent on whether they are D2-modulated, and part of the indirect pathway, or D1-modulated, and part of the direct pathway. In particular membrane fluctuations are higher in the D1-modulated neurons (mostly at higher frequencies): they receive both more inhibitory and excitatory input. This also means that they are activated faster.

The open question is: what drives the difference in input? Do they have stronger synapses or more synapses? If the distribution of synaptic strength is indeed a universal, they could have stronger synapses overall (different peak of the distribution), or more synapses (area under the curve).

Assuming that synapses adapt to the level of input they receive, having stronger synapses would be equivalent to being connected to higher frequency neurons; but there would be a difference in terms of fluctuations of input. Weak synapses have low fluctuations of input, while strong synapses, assuming they are sent out from neurons with a higher frequency range, have larger fluctuations in input to the postsynaptic neuron.

It is also possible that the effect results from a higher amount of correlation in synaptic input to D1-modulated neurons than D2-modulated neurons. However, since correlations are an adaptive feature in neural processing, it would be unusual to have an overall higher level of correlation to one of two similar neuronal groups: it would be difficult to maintain concurrently with fluctuations in correlation which are meaningful to processing (attention).

An additional observation is that dopamine depletion reduces the difference between D2- and D1-modulated MSNs. Since membrane fluctuations are due to differences of synaptic input (AMPA and GABA-A driven), but there is only conflicting evidence that D1 receptors modulate these receptors (except NMDA receptors), one would postulate a presynaptic effect. So, possibly the effect is located at indirect pathway, D2-modulated neurons, which receive less input when dopamine is present, and adjust to a lower level of synaptic input. (Alternatively, reduction of D1 activation could result in less NMDA/ AMPA, more GABA-A, i.e. less synaptic input in a D1 dopamine-dependent way.) In the dopamine depleted mouse, both pathways would receive approximately similar input.   Under this hypothesis, it is not primarily differences in structural plasticity which result in different synaptic input levels, but instead a “soft-coded” (dopamine-coded)  difference, which depends on dopamine levels and is realized by presynaptic/postsynaptic dopamine receptors. Further results will clarify this question.

*Thanks to Marko Filipovic for his input. The interpretations are my own.

Heavy-tailed distributions and hierarchical cell assemblies

In earlier work, we meticulously documented the distribution of synaptic weights and the gain (or activation function) in many different brain areas. We found a remarkable consistency of heavy-tailed, specifically lognormal, distributions for firing rates, synaptic weights and gains (Scheler2017).

Why are biological neural networks heavy-tailed (lognormal)?

Cell assemblies: Lognormal networks support models of a hierarchically organized cell assembly (ensembles). Individual neurons can activate or suppress a whole cell assembly if they are the strongest neuron or directly connect to the strongest neurons (TeramaeJetal2012).
Storage: Sparse strong synapses store stable information and provide a backbone of information processing. More frequent weak synapses are more flexible and add changeable detail to the backbone. Heavy-tailed distributions allow a hierarchy of stability and importance.
Time delay of activation is reduced because strong synapses activate quickly a whole assembly (IyerRetal2013). This reduces the initial response time, which is dependent on the synaptic and intrinsic distribution. Heavy-tailed distributions activate fastest.
Noise response: Under additional input, noise or patterned, the pattern stability of the existing ensemble is higher (IyerRetal2013, see also KirstCetal2016). This is a side effect of integration of all computations within a cell assembly.

Why hierarchical computations in a neural network?

Calculations which depend on interactions between many discrete points (N-body problems, Barnes and Hut 1986), such as particle-particle methods, where every point depends on all others, lead to an O(N^2) calculation. If we supplant this by hierarchical methods, and combine information from multiple points, we can reduce the computational complexity to O(N log N) or O(N).

Since biological neural networks are not feedforward but connect in both forward and backward directions, they have a different structure from ANNs (artificial neural networks) – they consist of hierarchically organised ensembles with few wide-range excitability ‘hub’ neurons and many ‘leaf’ neurons with low connectivity and small-range excitability. Patterns are stored in these ensembles, and get accessed by a fit to an incoming pattern that could be expressed by low mutual information as a measure of similarity. Patterns are modified by similar access patterns, but typically only in their weak connections (else the accessing pattern would not fit).

Egocentric representations for general input

The individual neuron’s state need not be determined only by the inputs received.

(a). It may additionally be seeded with a probability for adaptation that is distributed wrt the graph properties of the neuron (like betweenness centrality, choke points etc.), as well as the neuron’s current intrinsic excitability (IE) (which are related). This seeded probability would correspond to a sensitivity of the neuron to the representation that is produced by the subnetwork. The input representation is transformed by the properties of the subnetwork.

(b). Another way to influence neurons independent of their input is to link them together. This can be done by simulating of neuromodulators (NMs) which influence adaptivity for a subset of neurons within the network. There are then neurons which are linked together and increase or turn on their adaptivity because they share the same NM receptors. Different sets of neurons can become activated and increase their adaptivity, whenever a sufficient level of a NM is reached. An additional learning task is then to identify suitable sets of neurons. For instance, neurons may encode aspects of the input representation that result from additional, i.e. attentional, signals co-occuring with the input.

(c). Finally, both E and I neurons are known to consist of morphologically and genetically distinct types. This opens up additional ways of creating heterogeneous networks from these neuron types and have distinct adaptation rules for them. Some of the neurons may not even be adaptive, or barely adaptive, while others may be adaptive only once, (write once, read-only), or be capable only of upregulation, until they have received their limit. (This applies to synaptic and intrinsic adaptation). Certain neurons may have to follow the idea of unlimited adaptation in both directions in order to make such models viable.

Similar variants in neuron behavior are known from technical applications of ANNs: hyperparameters that link individual parameters into groups (‘weight sharing’) have been used, terms like ‘bypassing’ mean that some neurons do not adjust, only transmit, and ‘gating’ means that neurons may regulate the extent of transmission of a signal (cf. LSTM, ScardapaneSetal2018). Separately, the model ADAM (or ADAMW) has been proposed which computes adaptive learning rates for each neuron and achieves fast convergence.

A neuron-centric biological network model (‘neuronal automaton’) offers a systematic approach to such differences in adaptation. As suggested, biological neurons have different capacities for adaptation and this may extend to their synaptic connections as well. The model would allow to learn different activation functions and different adaptivity for each neuron, helped by linking neurons into groups and using fixed genetic types in the setup of the network. In each specific case the input is represented by the structural and functional constraints of the network and therefore transformed into an internal, egocentric representation.

Memory and the Volatility of Spines

Memory has a physical presence in the brain, but there are no elements which permanently code for it.

Memory is located – among other places – in dendritic spines. Spines are being increased during learning and they carry stimulus or task-specific information. Ablation of spines destroys this information (Hayashi-Takagi A2015). Astrocytes have filopodia which are also extended and retracted and make contact with neuronal synapses. The presence of memory in the spine fits to a neuron-centric view: Spine protrusion and retraction are guided by cellular programs. A strict causality such that x synaptic inputs cause a new spine is not necessarily true, as a matter of fact highly conditional principles of spine formation or dissolution could hold, where the internal state of the neuron and the neuron’s history matters. The rules for spine formation need not be identical to the rules for synapse formation and weight updating (which depend on at least two neurons making contact).

A spine needs to be there for a synapse to exist (in spiny neurons), but once it is there, clearly not all synapses are alike. They differ in the amount of AMPA presence and integration, and other receptors/ion channels as well. For instance, Sk-channels serve to block off a synapse from further change, and may be regarded as a form of overwrite protection. Therefore, the existence or lack of a spine is the first-order adaptation in a spiny neuron, the second-order adaptation involves the synapses themselves.

However, spines are also subject to high variability, on the order of several hours to a few days. Some elements may have very long persistence, months in the mouse, but they are few. MongilloGetal2017 point out the fragility of the synapse and the dendritic spine in pyramidal neurons and ask what this means for the physical basis of memory. Given what we know about neural networks, for memory to be permanent, is it necessary that the same spines remain? Learning allows to operate with many random elements, but memory has prima facie no need for volatility.

It is most likely that memory is a secondary, ’emergent’ property of volatile and highly adaptive structures. From this perspective it is sufficient to keep the information alive, among the information-carrying units, which will recreate it in some form.

The argument is that the information is redundantly coded. So if part of the coding is missing, the rest still carries enough information to inform the system, which recruits new parts to carry the information. The information is never lost, because not all synapses, spines, neurons are degraded at the same time, and because internal reentrant processing keeps the information alive and recreates new redundant parts at the same time as other parts are lost. It is a dynamic cycling of information. There are difficulties, if synapses are supposed to carry the whole information. The main difficulty is: if all patterns at all times are being stored in synaptic values, without undue interference, and with all the complex processes of memory, forgetting, retrieval, reconsolidation etc., can this be fitted to a situation, where the response to a simple visual stimulus already involves 30-40% of the cortical area where there is processing going on? I have no quantitative model for this. I think the model only works if we use all the multiple, redundant forms of plasticity that the neuron possesses: internal states, intrinsic properties, synaptic and morphological properties, axonal growth, presynaptic plasticity.

Balanced Inhibition/Excitation (2) – The I/E ratio

Some time ago, I suggested that the theoretical view on balanced inhibition/excitation (in cortex and cortical models) is probably flawed. I suggested that we have a loose regulation instead, where inhibition and excitation can fluctuate independently.

The I/E balance stems from the idea that the single pyramidal neuron should receive approximately equal strength of inhibition and excitation, in spite of the fact that only 10-20% of neurons in cortex are inhibitory (Destexhe2003, more on that below). Experimental measurements have shown that this conjecture is approximately correct, i.e. inhibitory neurons make stronger contacts, or their influence is stronger relative to excitatory inputs.

The E-I balance in terms of synaptic drive onto a single pyramidal neuron is an instance of antagonistic regulation which allows gear-shifting of inputs, and in this case, allows very strong inputs to be downshifted by inhibition to a weaker effect on the membrane potential. What is the advantage of such a scheme? Strong signals are less prone to noise and uncertainty than weak signals. Weak signals are filtered out by the inhibitory drive. Strong signals allow unequivocal signal transmission, whether excitatory synaptic input, (or phasic increases of dopamine levels, in other contexts), which are then gear-shifted down by antagonistic reception. There may also be a temporal sequence: a strong signal is followed by a negative signal to restrict its time course and reduce impact. In the case of somatic inhibition following dendritic excitation the fine temporal structure could work together with the antagonistic gear-shifting exactly for this goal. Okun and Lampl, 2008 have actually shown that inhibition follows excitation by several milliseconds.

But what are the implications for an E/I network, such as cortex?

Here is an experimental result:

During both task and delay, mediodorsal thalamic (MD) neurons have 30-50% raised firing rates, fast-spiking (FS) inhibitory cortical neurons have likewise 40-60% raised firing rates, but excitatory (regular-spiking, RS) cortical neurons are unaltered. Thus there is an intervention possible, by external input from MD, probably directly to FS neurons, which does not affect RS neuron rate at all (fig. a and c, SchmittLIetal2017)

Untitled 1

Mediodorsal thalamic stimulation raises inhibition, but leaves excitation unchanged.

At the same time, in this experiment, the E-E connectivity is raised (probably by some form of short-term synaptic potentiation), such that E neurons receive more input, which is counteracted by more inhibition. (cf. also Hamilton, L2013). The balance on the level of the single neuron would be kept, but the network exhibits only loose regulation of the I/E ratio: unilateral increase of inhibition.

There are several studies which show that it is possible to raise inhibition and thus enhance cognition, for instance in the mPFC of CNTNAP2 (neurexin, a cell adhesion protein) deficient mice, which have abnormally raised excitation, and altered social behavior (SelimbeyogluAetal2017, cf. Foss-FeigJ2017 for an overview). Also, inhibition is necessary to allow critical period learning – which is hypothesized to be due to a switch from internally generated spontaneous activity to external sensory perception (ToyoizumiT2013) – in line with our suggestion that the gear-shifting effect of locally balanced I/E allows only strong signals to drive excitation and spiking and filters weak, internally generated signals.

 

Balanced Inhibition-Excitation

Another idea that I consider ill-conceived is the notion that neural networks need to have balanced inhibition-excitation. This means that with every rise (or fall) of overall excitation of the network, inhibition has to closely match it.

On the one hand, this looks like a truism: excitation activates inhibitory neurons and therefore larger excitation means larger inhibition, which reduces excitation. However, the idea in the present form stems from neural modeling: conventional neural networks with their uniform neurons and dispersed connectivity easily either stop spiking because of a lack of activity, or spike at very high rates and ‘fill up’ the whole network to capacity. It is difficult to tune them to the space in-between, and difficult to keep them in this space. Therefore it was postulated that biological neural networks face the same problem and that here also excitation and inhibition need to be closely matched.

First of all inhibition is not simple. Inhibitory-inhibitory interactions make the simplistic explanation unrealistic, and the many different types of inhibitory neurons that have evolved again make it difficult to implement the balanced inhibition-excitation concept.

Secondly, more evolved and realistic neural networks do not face the tuning problem, they are resilient even with larger and smaller differences between inhibition and excitation.

Finally, there are a number of experimental findings showing that it is possible to tune inhibition in the absence of tuning excitation. In a coupled negative feedback model this simply means that the equilibrium values change. But some excitatory neurons may evolve strong activity without directly increasing their own inhibition. Inhibition needs not to be uniformly coupled to excitation, if a network can tolerate fairly large fluctuations in excitation.

Ubiquitous interneurons may still be responsible for guarding lower and upper levels of excitation (‘range-control’). This range may still be variably positioned.

In the next post I want to discuss an interesting form of regulation of inhibitory neurons, which also does not fit well  with the concept of balanced inhibition-excitation.

 

Dopamine and Neuromodulation

Some time ago, I suggested that equating dopamine with reward learning was a bad idea. Why?
First of all, because it is a myopic view of the role of neuromodulation in the brain, (and also in invertebrate animals). There are at least 4 centrally released neuromodulators, they all act on G-protein-coupled receptors (some not exclusively), and they all have effects on neural processing as well as memory. Furthermore there are myriad neuromodulators which are locally  released, and which have similar effects, all acting through different receptors, but on the same internal pathways, activating G-proteins.

Reward learning means that reward increases dopamine release, and that increased dopamine availability will increase synaptic plasticity.

That was always simplistic and like any half-truth misleading.

Any neuromodulator is variable in its release properties. This results from the activity of its NM-producing neurons, such as in locus ceruleus, dorsal raphe, VTA, medulla etc., which receive input, including from each other, and secondly from control of axonal and presynaptic release, which is independent of the central signal. So there is local modulation of release. Given a signal which increases e.g. firing in the VTA, we still need to know which target areas are at the present time responsive, and at which synapses precisely the signal is directed. It depends on the local state of the network, how the global signal is interpreted.

Secondly, the activation of G-protein coupled receptors is definitely an important ingredient in activating the intracellular pathways that are necessary for the expression of plasticity. Roughly, a concurrent activation of calcium and cAMP/PKA (within 10s or so) has been found to be supportive or necessary of inducing synaptic plasticity. However, dopamine, like the other centrally released neuromodulators, acts through antagonistic receptors, increasing or decreasing PKA, increasing or reducing plasticity. It is again local computation which will decide the outcome of NM signaling at each site.

So, is there a take-home message, rivaling the simplicity of dopamine=reward?

NMs alter representations (=thought) and memorize them (=memory) but the interpretation is flexible at local sites (=learn and re-learn).

Dopamine alters thought and memory in a way that can be learned and re-learned.

Back in 1995 I came up with the idea of analysing neuromodulators like dopamine as a method of introducing global parameters into neural networks, which were considered at the time to admit only local, distributed computations. It seemed to me then, as now, that the capacity for global control of huge brain areas (serotonergic, cholinergic, dopaminergic and noradrenergic systems), was really what set neuromodulation apart from the neurotransmitters glutamate and GABA. There is no need to single out dopamine as the one central signal, which induces simple increases in its target areas, when in reality changes happen through antagonistic receptors, and there are many central signals.  Also, the concept of hedonistic reward is badly defined and essentially restricted to Pavlovian conditioning for animals and addiction in humans.

Since the only known global parameter in neural networks at the time occurred in reinforcement learning, some people created a match, using dopamine as the missing global reinforcement signal (Schultz W, Dayan P, Montague PR. A neural substrate of prediction and reward. Science. 1997). That could not work, because reinforcement learning requires proper discounting within a decision tree. But the idea stuck. Ever since I have been upset at this primitive oversimplification. Bad ideas in neuroscience.

Scheler, G and Fellous, J-M: Dopamine modulation of prefrontal delay activity- reverberatory activity and sharpness of tuning curves.  Neurocomputing, 2001.

Scheler, G. and Schumann, J: Presynaptic modulation as fast synaptic switching: state-dependent modulation of task performance. Proceedings of the International Joint Conference on Neural Networks 2003, Volume: 1. DOI: 10.1109/IJCNN.2003.1223347

Bad Ideas in Neuoscience

balanced excitation inhibition

dopamine=reward learning

hidden layers

explaining attention by top-down and bottom-up processes

I should collect some more. Why are they bad? Because they are half-truths. There is “something” right about these ideas, but as scientific concepts, the way they are currently defined, I think they are wrong. Need to be replaced.