Summary

In this essay I attempt a top-down description of the information content in engrams. I focus on the structure that most plausibly mediates rapid electrochemical flow across brain regions to recall memories stored in engrams: the connectome. The connectome is a vague term. In order to make the discussion more precise, I consider different possible levels of detail that could be used to describe or measure the connectome, which contain increasing detail: the adjacency connectome, the cell membrane connectome, the ultrastructural feature connectome, the epigenetic-annotated connectome, and the biomolecule-annotated connectome. I consider evidence that each level could be sufficient to describe engrams, such that more precise levels of detail would not be necessary. While there is some possibility that a higher level of detail could sufficiently describe engrams, I describe why I think that, most likely, the level of detail required will be the biomolecule-annotated connectome. A key area of uncertainty is what degree of biomolecule annotation will be required to sufficiently describe connectomes – on the spectrum from a sparse to a rich degree of biomolecule annotation. The amount of biomolecule annotation required depends in part on how much mutual information there is in the biomolecular networks that are relevant to engram maintenance.

During life, the connectome is not static

I use the word “connectome” to refer to the structural microscale connectome, as opposed to the mesoscale or macroscale connectome (Sporns, 2016). One important aspect of the connectome to be cognizant of is that it is not a static structure. The connectome is constantly being remodeled as a result of one’s experiences and may drift over time. Every time one recalls a memory, there is evidence that the associated engram is re-consolidated in an altered structural form (Chen et al., 2020). The memory itself may also be altered during the retrieval process (as cited in (Josselyn et al., 2017)). Yet, the fact that the connectome changes all the time does not mean that a snapshot of the connectome at any given time is not sufficient for engrams. It just means that the information contained in an engram is not necessarily an accurate representation of what happened in the world when it was initially formed. This is merely a restatement of the well-known fallibility of memory. Slight changes in the connectome are perfectly consistent with ordinary survival.

Top down approach: structural information for engrams coded in the connectome

A wealth of evidence suggests engrams are encoded in neural structures distributed across the brain (Ryan et al., 2021). More specifically, it seems to be the distributed activity of neuronal ensembles communicating through the connectome that instantiate long-term memory recall (Tonegawa et al., 2015) (Kim et al., 2020).

Beyond long-term memory recall alone, there is a lot of evidence that the class of memory systems that includes declarative memories is encoded via neural connectivity patterns. For example, see (Martin et al., 2000) and the studies described at https://aspirationalneuroscience.org/.

Based on this experimental evidence and the spatiotemporal criterion, it is a central claim of these essays that there is no set of structures in the brain other than electrochemical information flow through the connectome that could operate on a spatiotemporal scale sufficiently fast to allow for rapid long-term memory recall.

The Brain Preservation Foundation (BPF)’s prize was for a procedure that could be shown to preserve the connectome across an animal brain with a method that would allow long-term storage of at least 100 years. Unfortunately, the use of the word “connectome” in brain preservation has led to communication difficulties for the past decade. Because it is such an amorphous word, it’s easy to straw person the proposal for brain preservation as life extension by saying that the connectome is not enough. For example, Sam Gershman does so in a conversation with Live Science about the company Nectome, claiming that “You need to know the synaptic strengths, if they’re excitatory/inhibitory, various time constants, what neuromodulators are present, the dynamical state of dendritic spines. And that’s all assuming that memories are even stored at synapses!”

The core idea of the BPF’s prize was not just connectivity, but connectivity alongside sufficient molecular information. As Ken Hayworth’s 2011 prize proposal stated (Kenneth Hayworth, 2011):

We now understand that the true measure of success should be that a procedure preserves the structural connectivity of the neuronal circuits of the brain along with enough molecular level information necessary to infer the functional properties of the neurons and their synaptic connections.

But as Gershman’s quote shows, that has not always gotten across. Arguably, it may be better to speak of preserving something like “morphomolecular maps” that explicitly contain both the morphologic information of abstract structural features (e.g., the connectome) as well as their biomolecular constituents. I hope to rescue the term connectome from some of its linguistic imprecision by specifying different possible levels of detail to describe the connectome. This way, we can communicate more precisely about what we mean.

Here are the levels of detail to I’ve come up with to conceptualize the connectome:

Level Description
Adjacency connectome Adjacency matrix, with or without weights
Cell membrane connectome 3D map of cell membrane locations of brain cells
Ultrastructural feature connectome As above, + intracellular/extracellular features visible on ultrastructure
Epigenetic-annotated connectome As above, + nuclear gene expression/epigenetic information
Biomolecule-annotated connectome As above, + detailed biomolecule distribution information across the connectome

For each level of the connectome, I will consider what it is, what kind of synaptic properties could be estimated based on it, and consider the evidence that mapping this level of detail might be sufficient to describe engrams.

As an example of this, in investigating the Drosophila hemibrain connectome, (Scheffer et al., 2020) analyzes different levels of the connectome: compartment maps, neuron skeletons, connectivity graphs, and adjacency matrices. Here they show some of the ways that they represent their connectome data:

Connectome data formats; (Scheffer et al., 2020)

As another example, here is a figure from (Morgan et al., 2017) describing different levels of connectome representation:

Connectome data organizations; Source: (Morgan et al., 2017)

As you can see, the first figure from (Scheffer et al., 2020) describes how raw electron microscopy data can be processed in different ways, which produces different types of connectome data that is useful to different types of users. The second figure from (Morgan et al., 2017) shows how connectome data can have its dimensionality reduced, for example, to a representation of the connectome between different cell types. Both of these can be thought of as different levels of detail to describe connectome data.

Adjacency connectome

In one of two 2005 publications to independently coin the term “connectome,” Hagmann defined the connectome as a graph in which “each neuron is represented by a labeled vertex and its connections with a set of weighted and oriented edges” (Hagmann, 2005). Specifying connectivity data between neurons is therefore the first and perhaps the most literal definition of a connectome, in the -omics sense of capturing the totality of the connections within a nervous system. I would call Hagmann’s definition an adjacency connectome with weights and directions.

Representing a subnetwork of the C elegans connectome as a graph: neurons as nodes, synaptic connections as edges; (Arnatkevic̆iūtė et al., 2018)

There are different possible ways to measure the adjacency connectome. Investigators could use a viral tracing approach that spreads across chemical synapses. This has been used to produce an adjacency connectome in a local brain region (Rossi et al., 2020). However, this viral tracing method would not necessarily allow counting the number of synaptic connections between neurons. One could also use electron microscopy and then use dimension reduction techniques to only focus on the synaptic connections (Lichtman et al., 2014). A true adjacency connectome would contain not only chemical synapses but also electrical ones, which are not as widely studied as chemical synapses but clearly play a major role in rapid electrochemical ion flow (Alcamí et al., 2019). Capturing electrical synapses would likely require electron microscopy measurements with a resolution of 2 nm or below (Marc et al., 2014).

It’s important to point out that Hagmann’s definition of the connectome, and indeed most definitions of the connectome, focus on connections between neurons. However, this focus is incomplete. Other cell types also participate in rapid electrochemical ion flow between cells, such as oligodendrocyte precursor cells and oligodendrocytes (Yamazaki et al., 2019). The strength of synaptic connections is likely also dependent on other cells nearby a synapse, such as astrocytes. In a complete adjacency connectome, non-neuronal cells would also need to be included.

Related to this, my personal feeling is that sometimes there is an excessive focus on neurons in the neuroscience literature. A lot of this may come from the bias of historically influential neuroscientists, such as Santiago Ramón y Cajal, who called non-neurons “glue” (thus: glia, which is Greek for glue) and considered them uninteresting. Regardless of the reason, a possible bias towards neurons is important to recognize and be cautious about.

Synaptic properties estimate: To distinguish the adjacency connectome from the next level of description, I will define synaptic weights in the adjacency connectome level solely based on counting the number of connections between cells.

While the adjacency connectome may seem like a coarse level of description, it’s important to point out that measuring the connections between cells is certainly not a trivial task. It has been estimated that there are 10^16 synapses in the brain, just considering neurons alone (DeFelipe et al., 2016). Assigning those connections to their origin cells also requires one to either identify a unique label for each cell or to trace back the origin cell of the process from which the synapse branches.

Sufficiency for describing engrams: It is hard to imagine being able to describe engrams in brain tissue without being able to infer the connections between cells. Communication between cells is the fundamental unit of information transmission in the brain. There is a reason that many neuroscientists such as Joseph LeDoux have pinned the majority of information about our sense of self on our set of synapses (LeDoux, 2003).

At the same time, the adjacency connectome alone seems not to be sufficient for engram storage. First, evidence from C. elegans suggests that simply counting the number of synaptic connections between two neurons is not a good predictor of the functional strength between those neurons (Yemini et al., 2021). This data point suggests that the adjacency connectome, even when connections are assigned weights via counting the number of synapses between neurons, is insufficient as a measure of connection strength.

Another form of information that the adjacency connectome will lose is the timing with which signals are sent and received by cells in the nervous system, which is dependent on the speed with which electrochemical signals propagate within and between cells. This, in turn, depends on the relative distances between connections, which is lost when reducing the connectome to an adjacency matrix level of description.

Cell membrane connectome

In the 1980s, Sydney Brenner and colleagues collected numerous electron microscopy images of the nematode C. elegans. From these images, they worked out how the 302 neurons in this organism made the approximately 7600 connections to one another. This data set contains not only the presence or absence of connections between neurons, but also the relative location of their cell bodies and neuronal processes. This has been described as the first nervous system-wide connectome (DeWeerdt, 2019). Brenner’s connectome was combined as a mosaic of nervous systems from several different individual C. elegans (White et al., 1986). If we instead imagine that it came from just one specific organism and contained cells other than just neurons, then in our framework, I would call this a cell membrane connectome. I find it helpful to break down the cell membrane connectome into four components.

Another historical reason the cell membrane connectome level is relevant is that some electron microscopy stains allow for the detection of the extracellular space or cell surface, but not the detection of intracellular details (Helmstaedter et al., 2008).

The cell membrane connectome maps cell membrane locations in 3d space; (Greene et al., 2016)

The first component of the cell membrane connectome is an outline of the location of cell membranes in three-dimensional space. This map would capture many different types of abstract structural features, such as cell body volume distribution, neurite branching, the arrangement of cell processes into bundles, and the locations of chemical and electrical synapses.

Several non-neuronal cell types, such as astrocytes, may not be strictly required for approximating rapid ion flow across brain regions. However, astrocytes help to establish the baseline ion concentrations. So if the ion distributions were lost, as they almost certainly would be in a preserved brain, then the location of these non-neuronal cell membranes would also need to be preserved to be able to infer the baseline ion distribution. Given the contribution of numerous cell types to baseline ion and small molecule distributions, it is likely that it would be necessary to be able to infer at least the approximate location of nearly all the cells in the brain. However, as discussed in a previous essay, the baseline distribution of ions in the brain likely need not be exact to capture the information content of engrams.

How precisely the cell membrane shape would need to be preserved and measured is an open question. Cell membrane shapes are in constant fluctuation in vivo. Cell membranes undergo slow fluctuations (~10 seconds) that are relatively large in size (100 nm-10 um) and occur primarily as a result of actin cytoskeleton rearrangements (Biswas et al., 2017). Because of the presence of a substantial amount of fluctuation in the cell membrane shape, there is good reason to think that the precise nanometer cell membrane contour may be relatively unstable during life and therefore unlikely to be a unique store of long-term engram information, based on the longevity criterion.

The second component of the cell membrane connectome is the thickness of cell membranes. Cell membranes in the brain have an average thickness of around 4 nm (Ingólfsson et al., 2017). The thickness or width of plasma membranes tells us about the electrochemical resistance of the membrane. All things equal, cell membranes that are thicker have higher resistance to ion flow. For example, the diameter of the myelin sheath around an axon can clearly affect the speed of rapid ion flow through that axon, and in turn can play an important role in mediating plasticity of cognitive functions (Fields, 2015).

The third component of the cell membrane connectome is the extracellular space. Ions do not just flow inside of cells. It is the change in ion concentration between the extracellular space and intracellular space that leads to voltage-dependent alterations in ion channels and allows for the propagation of neural information flow.

One example of the importance of the extracellular space in rapid ion flow is ephaptic coupling. As a result of ephaptic coupling, an action potential in one cell process can alter the ion flow and electrical field properties in nearby cell processes via the extracellular space, even if there is no synapse between these processes. The more extracellular space there is between two cellular processes, the less likely ephaptic transmission is to occur between them (Anastassiou et al., 2011). It has been suggested that changing the properties of the extracellular space can therefore lead to changes in the electrical synchronization of neurons and the likelihood of epileptiform activity (Hochman, 2012).

The amount of space between the presynaptic and postsynaptic cells at a chemical synapse is a particularly important type of extracellular space. This synaptic cleft space is likely more stable than other forms of extracellular space because it is maintained in part by trans-synaptic adhesion proteins (Kinney et al., 2013).

However, the extracellular space likely does not need to be preserved very precisely to retain engram information. It is not very stable during life, as it is subject to changes due to osmolar concentration and local movements of motile cells such as microglia. It is also highly altered in perturbations of the brain that have otherwise been found to not destroy engrams. For example, sleep or induction of anesthesia both lead to significant changes in the volume of extracellular space (Ding et al., 2016), yet engrams are robust to both of these perturbations.

The fourth component of the cell membrane connectome is morphology-based estimates of cell types. Different neuron types, such as pyramidal cells, interneurons, Purkinje cells, and granule cells, each have different shapes of their cell processes, so it is feasible to classify cells into each of these types to a certain degree of accuracy on the basis of their morphology (Luczak, 2010). Cell types also have characteristic connectivity patterns to other cell types that can be used to aid in their classification (Jiang et al., 2015) (Motta et al., 2019). Classifying cells based on these types of morphologic information has been done in the Drosophila olfactory connectome, leveraging prior information about cell types collected from the literature (Schlegel et al., 2021).

The reason that estimating cell types is important is that much of the variation in electrophysiologic properties between cells is likely present at the level of the cell type. This is especially true for large mammalian nervous systems such as the human brain, which is generally thought to have many more cells than cell types, as opposed to some insect nervous systems, such as C. elegans, which have uniquely defined neurons (Yemini et al., 2021). Our goal with a cell or neuron typing system is to predict the properties of how ions flow through cells. These properties include the levels and locations of biomolecules that affect membrane electrical conductance properties, such as ion channels, neurotransmitters, and neurotransmitter receptors.

It is unclear whether a cell type definition based on membrane morphology alone could ever be sufficient to predict electrophysiology to a sufficient degree to describe engrams, although to me it feels unlikely. There are so many different patterns of biomolecule distribution that can occur in different cells that seem to mediate variability in electrophysiologic function, and I doubt that they are all adequately correlated with membrane morphology to make that alone a sufficient channel of inference.

Synaptic properties estimate: There are multiple types of synaptic properties – a synapse doesn’t just have one “weight.” For example, at chemical synapses, we can consider the probability of neurotransmitter release, the speed of neurotransmitter release, and the strength of effect on the electrochemical potential of the postsynaptic cell. It is unclear to what extent these properties might be inferable from the cell membrane connectome.

A key aspect of synaptic properties is the size of the pre- and postsynaptic membranes, which have been found to vary in size up to 40-fold (Jarrell et al., 2012). The size of these cell membranes is sometimes used as a proxy of the functional strength, or “weight,” of the synaptic connection. The original connectome of C. elegans mapped by Brenner and colleagues in the 1980s did not have detailed synaptic weight information. Synaptic sizes were only mapped for the first time in 2012, for both electrical and chemical synapses (Jarrell et al., 2012). The size of the cell membranes at chemical synapses has been found to correlate well with the number of neurotransmitter receptors (Kasai et al., 2003). However, to the extent that there is not a perfect correlation between the abstract structural features visible on imaging and the actual biomolecules present at the synapse, the cell membrane connectome level would be unable to detect the discordance. Another problem is that, without synaptic vesicles, it can be challenging to identify whether two opposed cell membranes contain a chemical synapse at all.

Sufficiency for describing engrams: It is likely that information derived from the cell membrane connectome can account for much of the variation in electrochemical signaling and synapse properties relevant to long-term memory recall – but almost certainly not all of the variation, as will be discussed in the more detailed levels of the connectome.

Sebastian Seung’s 2010 TED talk was provocatively titled “I am my connectome” (Seung, 2010). Seung’s subsequent 2012 book expanded upon this theme (Seung, 2012). From our definition of the different levels of connectome description, Seung primarily described the level of the cell membrane connectome to be the key component of information necessary for personal identity. In a later chapter of Seung’s book, he clarified the level of detail further to specify that they were referring to this level of connectome detail in addition to models of cell types, which he called the “connectome plus”. Seung’s book stirred up considerable debate within the neuroscience community, including by those who critiqued it for focusing on too narrow of a level of detail. For example, it is unknown whether the resolution of cell typing achievable via information in the cell membrane connectome will be sufficient to adequately predict how ions flow through each of the cells.

One can imagine an argument such as “we have already had the connectome of C. elegans for decades, and yet we still cannot simulate it to accurately predict physiology and behavior, so clearly the connectome is not sufficient for engram information.” To which, the obvious responses would be that (a) Brenner et al’s original connectome, even when considered as a type of cell membrane connectome, was coarse and did not include important information such as synapse sizes; (b) the cell membrane connectome alone is clearly insufficient for whole brain emulation, which would also require detailed models of how different cells actually operate; and (c) the cell membrane connectome may not be a sufficient level of detail to describe engrams. So, from this perspective, it is utterly unsurprising that we have not yet been able to model the properties of C. elegans in silico in a detailed way. This property of our current technology is certainly not dispositive of the amount of information present in the cell membrane connectome.

Ultrastructural feature connectome

Clearly, cells are not monoliths. They contain cytoskeletal elements, organelles, and condensates that divide up the cytoplasm into different compartments. We can consider these components of cells to be abstract structural features, each made up of numerous different types of biomolecules. The extracellular space also contains abstract structural features, such as the extracellular matrix and perineuronal nets.

Because the connectome is currently typically measured with electron microscopy and nonspecific stains (Morgan et al., 2017), one important level of connectome detail that we can consider is the level that includes not only cell membrane information, but also information about all of the cellular details that can be visualized under the electron microscope, such as the endoplasmic reticulum, ribosomes, or microtubules (Heinrich et al., 2021). One can imagine this as the cell membrane connectome in addition to abstract ultrastructural features, which I will call the ultrastructural feature connectome.