Connectomics: Beyond Biological Cartography

Understanding where 100+ billion roads lead and what they influence.

Anastasija Petrovic
16 min readFeb 18, 2021

You, your joys and sorrows, your memories and your ambitions, your sense of personal identity and your free will are in fact no more than the behaviour of a vast assembly of nerve cells and their associated molecules. — Claude Shannon, the father of information theory.

As a kid, every time I would drive down a highway, I would keep track of which exits my car had already passed, but it wasn’t an efficient way of mapping my route. I would drive by many highways, and they all led somewhere, but I never was sure where they lead.

How can we become efficient biological cartographers? More specifically, how do we become more efficient neuroanatomy-based cartographers? All the tiny nerve cells in the 1.5kg mass you hold in your head lead somewhere. Whether they control emotional intelligence or chemical regulation, they are interwoven in who you and I are.

Early Neuroscience: Neuron Doctrine & Modern Day Neurotechnology

Many philosophers like to think humans are machines. Beautiful machines, unique machines, but we are also physical entities. The brain, and the heart, and the muscle, and the bones are physical machines.

The brain is a unique entity, but in the end, it is still a machine. A neuroscientist needs to understand the machine in physical terms. Neuroscientists need to be able to map this entity physically.

The most incomprehensible thing about the world is that it is at all comprehensible. — Claude Shannon

This means that we have tools, our brain, for example, to understand things. So it comes down to understanding what the route to understanding the brain is. What is the route? What is the foundation?

So, 3.5 billion years ago, life started on Earth, and we became later on and very, very recently began to study our brain systematically.

Image Source: pmarinus_180.jpg

Three and a half billion years ago, there was this little bacteria. Later on, recently, 5 million years ago, fish came into the earth. Then, more sophisticated, more complex entities came. Then 200,000 years ago came mammals, and then primates. So we, the Homo Sapiens Sapiens, are populating the world. Seven billion brains inhabiting one planet.

That’s pretty mind-boggling (see what I did there).

We have been creating art for about 30,000 to 60,000 years. With the same brain, we developed language, wrote language and now we study various languages in school. We created other things. We create science as we know it today, very systematic studying, mathematical approach, and so forth.

Modern computers were created very recently; 100 years old or so. We have been trying to understand our own brain using our own brain with our own tools that we developed to understand the brain. Tongue twister!

We need a diagram to progress further down this roadmap. Connectomics studies that road map. Before we head into the network tracking, let’s take a look at the connections and what they are.

Simplified: Neurons, Synapses and Axons

After you do go down from a highway to an exit, there are smaller connecting roads that help build these large structures. This is the same case in biology, specifically neuroscience. Nerve cells constitute other parts that contribute to everyday function.

After Camillo Golgi tried staining the brain’s elements to understand them better, he concluded that the brain is a system, but it has individual elements. This was called the neuron doctrine.

Four years later, the term neuron was coined. Therefore before 120 years ago, there were no neurons, so to speak. Through this naming process and the characterization of the nervous system, Charles Sherrington came up with and coined the word synapse.

A neuron was understood as a cell from this name, but the synapse was the connector/connection between neurons. Rather, the synapse is the tiny pocket of space between two cells where signals can be exchanged to communicate. Thousands of synapses can share a unique neuron.

So when we look at this interesting tissue below our skull, we can characterize regions. We can speak about different regions' functions, but we can zoom into the brain.

You’ll see a cumbersome, very intense network of neurons, a jungle of components, sitting within each other. One on top of the other, intermingled like a jungle of trees. And this is what we need to understand, how all this neuron jungle generates all that we know about, feelings, emotions and much more. This is what the neuron doctrine is.

The neuron doctrine is the universally accepted concept that the nervous system is made up of discrete individual cells, the neurons, supported by astrocytes and by other glial cells. -Santiago Ramón y Cajal.

Beyond the Neuron Doctrine: How does a neuron work?

In neuroscience, the relevant points in space are the inside and the outside of a cell, which are separated by a membrane that is impermeable to charged particles. Ions cannot flow across this membrane without the help of channels or pumps. Ions are for reference atoms that have an excess (one or more) of positive or negative charges.

Ions can move through membrane channels and form a charge difference between these two compartments, resulting in a potential (or voltage)across the membrane. The impermeability of the membrane allows this voltage to be maintained. This is similar to the build-up of charge across a capacitor in an electrical circuit.

Voltage is a relative measurement, and neuroscientists always use the outside of the cell as the ‘ground’ or reference point to measure the voltage across the membrane. For example, if the inside of the cell is 50 mV more negative compared to the outside of the cell, we would report the voltage as –50 mV.

Neurons can send signals through the use of electricity, and we see that neurons themselves are electrically charged. Specifically, neurons' lipid membrane separates solutions of charged particles, such as K+ (Potassium) and Na+ (Sodium) ions, and this separation creates a difference in potential energy across the lipid membrane. In neurons that are not sending or receiving signals, this potential difference is called the ‘resting potential.’

If we look at a typical neuron, we can see that it has a variety of parts — a cell body, or soma, that houses the cell’s nucleus and a variety of cellular machinery. Extending out from the cell body are fine processes called “axons” and “dendrites.” All of these parts' outer surface is made up of a bilayer of lipid molecules that partition the inside of the cell from the outside. This is called the “cell membrane.”

Image Source: ba4196a3ef1255b9cdaa9308fdcfbcbb.jpg

Resting Potential: Baseline Communication

Even when the cell is at rest, it’s not electrically neutral. If you measure the voltage — the difference in electrical potential energy across this membrane between the inside and the outside of a living neuron — you’ll see a small but important voltage called the “membrane potential.”

If we measure the potential difference between the inside and outside of a neuron at rest, we measure a voltage of about negative 70 millivolts. Voltage is a relative quantity. It is also referred to as the resting potential of neurons without depolarization.

Diffusive and electrostatic forces guide ion movement through membrane channels, and the movement of these ions can change the membrane potential. For example, ions include K+. This change in concentrations of ions impacts the amount of bioelectricity in a neuron.

Variable to the voltage of intercellular vs extracellular areas, the bioelectric quantity is dependable. This is overall referred to as the membrane (the border between the outside and the inside of the cell) potential. Note: these charges travel through ion channels present in the membrane. You are designed to power neurons!

Another way of seeing this fundamental concept of neurons and the way they work is like a lever, the measuring tool. Depending on how you move the liquids from one side to the other, a measurement is given. The same is thought of the amount of + or — forces inside or outside a neuron.

This process helps keep the neurons in your brain working and keeping the connections running. Neurons communicate with each other using rapid changes in their membrane potentials. These fast changes are called ‘action potentials’ and can be sent down an axon in order to send an electrical signal from one neuron to the next.

Action Potential: Positive Communication

Another crucial way neurons function is through the action potential. An action potential is a way a neuron sends information down an axon away from the cell. Neuroscientists refer to this process as the “spike” as well. We can see this in the graph below. The action potential is a rapid increase in the electrical activity created by a depolarizing activity. Depolarization in action potential is when a cell’s membrane has an increase in positive charge.

Image Source:

Three scientists, with the last names Goldman, Hodgkin and Katz, came up with a calculation for calculating action potential in a neuron incorporating our key players, Potassium (K+), Sodium (Na+) and Chlorine (Cl-). This equation is a key step to understanding how the connections between our brain work, and as big of a mouthful it is, it’s crucial to building an understanding of neuron connections. Let’s define the variables:

Goldman-Hodgkin-Katz Equation Formula

Vm = the cell’s membrane potential. At times this value can equal zero due to equitable amounts of + & — charges.

R= universal gas constant (8.314 J.K-1.mol-1).

T= temperature in Kelvin (K = °C + 273.15).

F= Faraday’s constant (96485 C.mol-1).

PK, PNa and PCl = relative membrane permeability (how fast an ion can diffuse/spread) of each ion.

[K+]o + [K+]i = concentration of K+ in the extracellular (o) + intracellular (i) fluid.

[Na+]o + [Na+]i = concentration of Na+ in the extracellular (o) + intracellular (i) fluid.

[Cl-]o + [Cl-]i = concentration of Cl- in the extracellular (o) + intracellular (i) fluid.

That’s the general idea behind the functionality of neurons and the way they connect to other neurons. But the action and resting potential formulas differ due to the different types of neurons.

Classification: Types of Neurons

Image Source:

For bioelectric purposes and reading time, we’ll be looking at only, emphasis on only four types of neurons.

Type 1: Unipolar Neurons

This is a type of neuron through which only one process called a neurite extends from the cell body. The neurite also then branches out from the axons and dendrites. This type of neuron is usually found in invertebrates like insects.

Type 2: Bipolar Neurons

This is a type of neuron which has two extensions (one axon and one dendrite). Many bipolar cells are advanced sense-transmission sensory neurons. Due to this, they are part of pathways for smell, sight, taste, hearing, touch, balance and proprioception.

Type 3: Pseudounipolar Neurons

This type of neuron has no dendrites, with the one poor axon doing both element’s jobs. This axon extends into organs as this is a sensory neuron. This form of a neuron can be found in the skin, joints and muscles, and the spinal cord.

Type 4: Multipolar Neurons

This is a type of neuron that has a single axon but multiple dendrites, specifically dendritic branches. This characteristic allows for the integration of a great deal of information from other neurons. Additionally, this is the most photographed neuron.

The units used to look at the connections in the brain are variable to environments, which are hard to study. Neuroscientists have been attempting to figure out what these roads or highway exits mean for more than 120 years. This is where connectomics comes in handy.

Defining: Connectomics in Application

Image Source:

Camillo Golgi, a giant character in the field of anatomists, worked on a staining method for mapping neural activity. He hoped to look at the brain and look at the elements that build the brain by staining its elements.

Today, his methods might seem too two-dimensional, but his staining methods helped form the formation of connectomics, The Neuron Doctrine.

Additionally, he and his partner Santiago Ramón y Cajal were awarded the Nobel Prize in Physiology or Medicine in recognition of their work on the structure of the nervous system.

Image Source: b1f8d0bb-e7fc-41d8–8c8b-644a580595a8-foundations.jpg

These drawings appeared to be an accurate look into the brain 120 years ago. You can see in the drawings the technological advancements at the time as compared to today.

Neuroscientists experienced this dye (George dye) in order to look into the elements. But they were limited to visual interpretations that were drawn. The need for the current method of studying was needed, and this is where Connectomics comes to play.

The dye didn’t stain everything since if you would stain the brain and everything would be coloured, it would become completely dark. This is because it is so packed that it’s so dense, with the jungle of nerves there. Only 1% of the cells were coloured and in a way mapped.

The project was a step forward, but it wasn’t efficient. With the progression of technology came a new way of doing this. A new kind of anatomy map based on understanding circuits, different regions of the brain through identifying connections.

Connectomics' idea is to cut very, very thin slices of the brain at the nanometer scale (10^-1000 of a meter) to detect structure. You detect structure, and then you put the slices back in a sense. You align them back one on top of the other to create a fine reconstructed resolution.

In a very small piece of the brain, in this case, you can really really see whether they touch each other or not and in that way identify synaptic contact. Think of Connectomics as a 3D puzzle.

Connectomics: Putting the Pieces Together

Image Source: 51263_2_640px.jpg

A 3D puzzle can be taken part in 3D and then and there analyzed. You take up a few pieces and try to put them together to figure out where they fit in. This way, you look at the piece (or nerve cell) in a detective-like way: looking at the individual piece and its correlation to the surrounding pieces.

Today, we are still figuring out how to reconstruct the brain, the pieces that were cut up in a 3D anatomy of the brain tissue.

So what are connectomes?

A connectome is essentially a distilled version of the biological roads I was referencing earlier. Connectomes are a comprehensive map of neural connections. It is sometimes referred to as a wiring diagram and shows molecular connections. Think of the connectome as an electrical device where axons and dendrites are wires, and neuron bodies are components.

Depending on the scientist, the term connectome may also include learning-relevant molecular states at each synaptic connection (the “synaptosome”) and any learning-relevant changes in the nucleus of each neuron (the “epigenome”).

In terms of entire brains, there can be whale connectomes, mouse connectomes and etc. We can also speak of connectomes of specific brain subsystems, such as hippocampal connectomes, thalamic connectomes, and cortical connectomes.

Connectomes Goal: C.elegans

Image Source: celeg_connectome.png

The human brain has one hundred billion neurons and some seven hundred trillion synaptic links. This network is about eleven orders of magnitude more complex than C. elegans. C.elegans have already had their connectomes mapped out. We are struggling with humans for two reasons.

First, while modern electron microscopes are efficient enough to picture the human brain’s nano-scale features, there are not enough electron microscopes to visualize the human brain's tissue. The visualization of this aspect seems impossible today. Second, the work of interpreting these images and tracing the projections emanating from each neuron is still done by humans clicking through images in real-time.

The Human Connectome Project (HCP) is a project tackling the challenge of mapping the human brain today in hopes of connecting structure to function, taking Golgi’s staining method a step further in a sense. The project has broken into HCP Young Adult Project for not fully developed brains and one for lifespans (HCP Lifespan). The HCP Lifespan project looks into the connections between neurodegenerative diseases, structure and function.

Connectomics Experimentation: The Brainbow Technique

The Brainbow strategy is a technique that imitates multicoloured wires, kind of like those you see in Among Us or spy movies. This technique takes advantage of the fact that neurons can be visualized in different colours, specifically red, green and blue (RGB).

Due to the fact the neurons are represented through different colours, the neural connections can be seen. This technique requires the use of FPs (fluorescent proteins) at random concentrations. To achieve this, scientists use Cre-recombinase-mediated DNA excision and DNA inversion. Cre-recombinase is an enzyme that can either perform DNA excision or DNA inversion that has been strengthened by the Lox sites (the white triangles below).

The three sequenced colours are arranged in this method, almost like a braid with two pairs of Cre recombinase recognition sites (loxP and lox2272). Before Cre-meditated recombination, only one FP is visible, but with these recombinations, the other expressions are presented as well.

Different lox sites (loxP 1 and loxP 2) can have completely randomized results as they are incompatible. If loxP 2 is selected, it will either be kept or inverted through the DNA process. If kept, one colour would be expressed, or if inverted, the other colour of the loxP pair would be expressed. This process is the same if the loxP 1 pair is selected. It comes down to being random between DNA excision or DNA inversion.

Using the techniques above, the Brainbow Technique forms intricate neural networks with the possibility of probing into the world of 100 billion neurons.

As a result of these models, we get colour-coded connection maps. The question remains how we can analyze the data gathered.

Connectomics Analysis: Connectivity Matrixes

Image Source: celeg_connectome.png

The central goal of connectomics is to map the connections between anatomically distributed neural elements. The number of connections between these nodes (N) is N². Knowing this, we can use this to express the connectomic data. The matrix is a common way to represent the connectivity between every pair of nodes in a network in 2D.

Symmetrical Matrix (Square Matrix)

The connectivity matrix compactly explains the relationships in a pathwise direction. To build this type of connectivity matrix, C, for a brain network comprising N nodes, we construct a 2D array called a square matrix (pictured above). This square matrix comprises of N rows and N columns. Each column and row represent a unique network node. We then populate the elements of the matrix with the connectivity values that have been estimated for every pair of nodes (red and blue) to construct N x N(in black).

Following this notion, the subscripts under C are used to index each element. The first subscript (i) indexes the rows, and the second subscript (j) indexes columns.

If we have different values in the upper and lower portions of the matrix, the Cji is asymmetric. It isn’t a square matrix any longer. This represents a directed graph or a network that, through asymmetry, encodes the directions of the connections. These matrixes are also sometimes referred to as digraphs, and the great thing about them is that they can show us the influence that one network can have on another.

Pictured to the left is an example of a directed graph with weights (associated graph number that is a non-negative integer). The direction of the digraphs is pictured in the upper portion of the image and through the arrows shows neuroscientists where the connection is going.
In the introduction of this article, I explained some different neurons for this reason. To explain the differentiation in analysis methods. Connectomics aims to map the biological pathways of the mind, but they are so very different. The great thing about methods like directional graphs is that they allow us to visualize direction and, therefore, change.

Understanding the Brain: 3 Frontiers

The key thing is that we need to have dynamic measurements since these little cars driving down the highway (neurons) on the high of resting and action potentials change all the time. Different connections are sent, and the best way to keep track of them is through analysis and experimentation methods like the Brainbow Technique and the Connectivity Matrix.

Today’s three neurotechnology frontiers, optogenetics, brain-computer interfaces, and connectomics, require understanding each other. In the field of connectomics, it comes down to understanding the elements of structures and functions in the brain at a dynamic level.


  • The Neuron Doctrine is a pivotal idea in Neuroscience that established the correlation between functionality and structure in the brain.
  • Neurons communicate/work through differentiation between ion concentrations.
  • Connectomics aims to map the biological pathways of the mind.
  • The Brainbow is a technique that relies on differences in RBG to identify neural connections.
  • The Connectivity Matrix uses the values of nodes to classify data into rows and columns. When this matrix doesn’t form a square (is asymmetrical), it forms a directed network. This network visualizes the influence of one network on another.
  • To truly understand the intersection between structures and functions, it is key to dynamically keep track of networks and their influences.



Anastasija Petrovic

I’m Anastasija, a 17-year-old interested in the intersection between biotechnology and bioinformatics. I also write about mindsets and emerging technologies!