# The gigabit machine

There are plenty of amazing things about the brain but one of the most mind boggling is that it can be coded by a genome of only 3 billion base pairs or 6 gigabits.  If we consider a brain with about $10^{11}$ neurons each receiving something like $10^4$ inputs (i.e. synapses), then we’re talking about something on the order of $10^{15}$ parameters to set.   Hence the genome does not carry enough information to set every connection.  I had an amusing senior moment on the train ride from Edinburgh to London after the Mathematical Neuroscience workshop with Peter Latham, where I took the log of $10^{15}$ and ended up with about 50 bits of information to specify the brain.  Peter had a good laugh at my expense and we’ve now dubbed the double log of the entropy as the number of “super bits”.  My confusion stemmed from the fact that I had only accounted for the amount of information needed to identify a neuron and that amounts to about 50 to 100 bits of information.  For example, if each neuron could secrete any combination of 50 different neurotrophic factors and expressed any combination of 50 different receptors then each neuron would have enough information to connect to any other specific neuron. However, that would not say   which combination of genes are expressed in a given neuron, which is what is necessary to specify all the connections. Thus, one would only need about 100 bits to be able to connect up a random brain but would need $10^{15}$ bits to specify each connection.

So, the brain has about 50 super bits or $10^{15}$ real bits of potential information and yet we start with about $10^9$ bits.  Hence, if we believe that the connections in the brain do matter then almost all of them must be set by the inputs the brain receives throughout its life.  If we take something like $10^6$ bits per second of information entering our brains (which is probably an overestimate as we will see) then that gives something on the order of $10^{13}$ bits of information per year.  Multiply that by a human lifespan and we can fill the brain.  However, this $10^6$ bits of information per second just counts the number of spikes entering from the sensory systems.  The amount of actual information used is probably lower and the amount of information that we acquire through “active” learning such as reading, lessons, advice and so forth is even smaller.  However you want to slice it, it seems like most of the connections in the brain are set by things that are independent of genetics and controlled environmental variables such as schooling and parental guidance.

This means that either most of the connections don’t matter or that there are very high correlations between them.  My guess is that it is some of both. There are crucially important connections and correlations and there are a lot of connections that are random.  However, this randomness could be important to the functioning of the brain.  It could form the initial conditions for learning or provide the initial guess for solving a problem.  This also puts constraints on the genetic contribution to brain function given that genes probably mostly influence the machinery of the brain like myelination, synaptic time scales, and ion channels rather than connectivity.  Hence, any disease related to connectivity could be influenced by many possible genes with overlapping effects.  For example,  a variation in threshold for inducing plasticity of synapses, a population imbalance between excitatory and inhibitory cells, or a difference in density of ion channels could all lead to an effective differently connected brain.