How many neurons does it take to change a lightbulb?
I’ve been reading this excellent paper by David Barack and John Krakauer, on “Two Views on the Cognitive Brain”, and it made me wonder about which mode of nervous system function might have come first. To use their terminology, the “Sherringtonian” view (named after Charles Scott Sherrington) focuses on individual neurons as the elementary units of control, computation, and cognition. In this view, neurons can be thought of as individual relays in a control circuit (such as a reflex) or as elements performing discrete logical operations, which can be combined into larger circuits to carry out more complex computations. It’s all very bottom-up, algorithmic, and mechanistic (and, indeed, provided the inspiration for artificial neuronal networks, as conceived by McCulloch and Pitts). The “Hopfieldian” view (after John Hopfield), by contrast, takes the view that more global and dynamic patterns of activity across populations of neurons are the elements encoding and representing cognitive objects.
The Sherringtonian view can be applied to simple reflex circuits and seems like the right way to describe what they are doing and how they work. (It’s certainly the traditional way). By contrast, the Hopfieldian view seems much better suited to describing the functions of larger brain regions, especially in the cerebral cortex (see figures below, from the paper). In the Hopfieldian view, the details of the firings of individual neurons are not so important – what matters are the global patterns that emerge. Barack and Krakauer propose that those kinds of dynamical population-based patterns are essential as representational vehicles for a truly cognitive internal economy of the kind we see in humans. It’s easy enough to reconcile these two views as different perspectives that apply more or less in different parts of the nervous system (meaning the human nervous system).
But a different question occurred to me in thinking about these two modes of function: which one arose first in evolution? In creatures with very simple nervous systems, do the neurons work in little Sherringtonian circuits, or did neurons in fact arise as distributed Hopfieldian networks?
It seems pretty natural, naively, to assume that population-level encoding and representation would only have evolved once nervous systems reached a certain size and complexity. That is, that nature would have started with isolated neural circuits and scaled up from there, by multiplying and combining them, resulting in some emergent properties that it then capitalised on.
And maybe that’s right. Maybe creatures with small nervous systems carry out all their information processing and other neural functions based on the activities of single neurons and the discrete transformations carried out by connections between them. And maybe the functions of each of those single neurons became functions of populations of neurons as nervous systems got bigger.
But maybe it’s completely wrong. Maybe even the simplest nervous systems actually work in Hopfieldian ways, characterised by field dynamics, with attractors and low-dimensional manifolds in collective state spaces, rather than like motherboards composed of discrete logic gates arranged in particular ways. This raises the question: how many neurons do you need to create those kinds of collective state spaces? In creatures with really simple nervous systems, do they even have enough individual elements to generate these kinds of dynamics?
That set me to wondering: what animals have the fewest neurons? A twitter query threw up lots of interesting examples. The well-studied nematode, Caenorhabditis elegans, was a popular candidate, with exactly 302 neurons in hermaphrodites (all identified, named, with developmental lineages and neuronal connections known). But all kinds of other wonderful creatures were mentioned too, several courtesy of evolutionary neuroscientist Gáspár Jékely, who knows all the weirdest and wonderfullest critters.
These include the dwarf male of the annelid polychaete species Dinophilus gyrociliatus, which has 68 neural cells, notably concentrated in two centers: its “brain” (or frontal ganglia) and its penis. This organisation apparently “accords well with the bipartite behavioral pattern, which is entirely devoted to locomotion and copulation”. Ah, the simple life!
Even simpler are the parasitic “orthonectid” annelids, which grow and divide inside various marine host species, generating male and female larvae, which are basically just motile reproductive organs. Some species, such as Rhopalura litoralis, have a dozen neurons or so, but the winners are the males of Intoshia vaiabili, which have precisely two neurons!
It doesn’t seem possible that a nervous system with only two neurons could be working by generating dynamical state spaces. Those neurons have got to be just acting as individual electrical elements, in a Sherringtonian fashion… right? You can’t have a Hopfield network with only two neurons! But how many neurons do you need to get those kinds of population dynamics? And how many did evolution start with?
Naively (I mean, really naively) you might think, since nervous systems have grown in size and complexity along many lineages, that they must have started small and simple – with only a few neural cells. Among extant species, you’ve got sponges, with no neurons, and then you’ve got things like comb jellies or cnidaria, that have neurons (quite a few, as it happens). So how many neurons did the first critter with neurons have?!?
Did evolution start with just a couple neurons and build from there? That doesn’t seem to have been the case. Examples of animals we see today with very few neurons, like those mentioned above, may actually have reduced their numbers over evolution – perhaps due to adopting a parasitic lifestyle or due to other ecological reasons that reduced the need for a complex nervous system (like their only behavior being copulation!). It seems more likely that evolution started with lots of proto-neurons, which then evolved into lots of neurons.
There are a number of somewhat competing (maybe really complementary) hypotheses about when and where neurons arose, and what problems they solved for early multicellular animals. On a cellular level, most of the components that neurons use to do their jobs were already present and being used in other types of cells. This includes the machinery for regulating electrical potential across the membrane (ion channels and transporters), for coupling electrically to neighboring cells (gap junction proteins), or for communicating with other cells chemically (secretory systems and a diverse range of receptors). The real specialisation of neurons may have been their morphology – their long, branching projections that allow them to contact cells far away, bypassing intervening cells, and to connect to multiple cells at a time. In addition, their polarity – having an input side and an output side – allows them to propagate signals in a directional fashion.
These make them ideal for solving one of the main problems that arises in multicellular animals – the need to coordinate movements of all of their parts. Many simple animals have sheets of myoepithelial cells, which are electrically coupled and capable of contraction. (Not quite muscles, but muscle-like epithelia). Sponges, for example, are capable of rhythmic movements that rely on traveling waves through such sheets. What neurons give you is a more specific way to coordinate the contractions of these sheets of cells, which, in parallel, may have evolved into more discrete contractile units, i.e., muscles. One hypothesis for the early evolution of nervous systems – the “skin-brain thesis” – posits that neurons emerged as specialised cells intercalated within these myoepithelia, providing a “horizontal” coordination across the entire animal.
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| This figure and the one above reproduced from: Arendt, Detlev (2021) |
There are arguments in favour of both of these hypotheses and perhaps both functions emerged in a coordinated fashion. In both cases, it’s notable that what is posited is a “horizontal” coordinating function, rather than a “vertical” connecting function that links sensory inputs to motor outputs in some specific, reflex-like way. Neurons obviously offer the potential to make such functional couplings between particular stimuli and coordinated behavioural responses, once they are in place, but that may have been a secondarily evolving role.
What’s important for our discussion is this: in both these models, neurons emerged as new elements in a pre-existing network of non-neuronal cells. Those cells were already interconnected, often both electrically and chemically – comprising fields or populations with emergent dynamics. It’s not that neurons were added to these networks from outside – it’s more likely that some of those cells became neurons. The earliest neurons may thus have been born from and into Hopfieldian collectives.
Barack and Krakauer specifically propose population patterns as vehicles representing cognitive objects – elements they argue are necessary to explain high-level human cognition. (An argument I agree with). But perhaps the Hopfieldian model is just how neurons work, more generally. Maybe it’s how multicellular organisms work – as fields of cells, rather than discrete, machine-like components. Perhaps the Sherringtonian model, if it applies at all, reflects a derived function, an exception to this more general pattern. Or maybe it’s just an artefact of a forced perspective – an illusion of specificity created by an experimentally isolated system.
We teach neuroscience using the reflex circuit as a tidy, well-behaved, easily understandable exemplar to illustrate neural circuit function. This is potentially misleading in a number of ways. First, it emphasises an input-output function and gives an erroneous view of the nervous system as a passive, stimulus-response machine. Second, as pointed out by John Dewey, focusing on the unidirectional reflex ignores the crucial return part of the “circuit” – the action of the organism that changes the nature of the stimulus it’s receiving. And third, starting with the reflex can give the impression that such circuits are somehow the building blocks of the whole nervous system, or at least the most primitive instantiation of what can become more complex kinds of circuits. But there’s no indication that reflex circuits represent a primitive “kernel” from an evolutionary point of view.
It’s striking that the Sherringtonian approach has not succeeded in revealing the logic of the workings of even simple nervous systems or isolated subsystems. For example, the full connectome of the C. elegans nervous system has been known for decades, and all kinds of powerful tools have been applied to studying how the nervous system mediates and governs the small repertoire of behaviors that these animals display. And yet, even the simplest behaviors resist any reduction to a few discrete circuit elements, as discussed here by Cori Bargmann and Eve Marder. The capability to record activity from all the neurons in the animal, during awake behavior, is likely to change that, but this involves a move to a more global dynamical systems perspective, describing trajectories through state space, rather than discrete logical computations.
The same can be said for the well-studied lobster stomatogastric ganglion, which is clearly best thought of as a dynamical system with various possible operating regimes. And there are multiple other examples, from hydra to leeches to fruit flies to zebrafish, where these kinds of population-based, dynamical systems approaches are providing crucial insights. (All echoing pioneering work by Walter Freeman and much more recent perspectives, such as Luiz Pessoa’s new book, The Entangled Brain).
In a way, the debate between the perspectives of Sherrington and Hopfield parallels the earlier debate between Santiago Ramon y Cajal and Camillo Golgi about the nature of the nervous system. Golgi argued that neurons comprise a continuous reticulum, while Cajal contended that individual neurons were physically separated from one another and should be considered independent units. Cajal was right, of course, on an anatomical level – neurons really are discrete cellular units, rather than a cytoplasmically connected reticulum or syncytium. But perhaps Golgi was closer to the mark, from a functional sense. Maybe no neuron is an island – maybe, right from the get-go, evolutionarily speaking, neurons functioned as members of populations, fields of cells with shared dynamics, collectively traversing common state spaces.
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