A simplified model of the connectome

Following the thinking process of a “typical neuroscientist”, we construct the model with the following assumptions:

  • Signals pass in a stepwise manner from one neuron to another through the synapses. So target neurons multiple synaptic hops away are reached later than those one synaptic hop away.

  • Excitation and inhibition take the same time to propagate (that is, one step).

  • The activation of a neuron ranges from “not active at all” (0) to “somewhat active” (0~1), to “as active as it can be” (1).

Unlike a “typical neuroscientist”, we also make the following assumptions:

  • Neurons are “points”. That is, we disregard synapse location, ion channel composition, cable radius etc..

  • We disregard neuromodulation for now (unless you know what a specific instance of neuromodulation should do, in which case you could either model by modifying the connection weights, or ask me to incorporate some new features in the package (yy432[at]cam.ac.uk)).

With these assumptions, we construct the following model, aiming to provide “connectome-based hypotheses” for your circuit of interest:

Simplified model

Panel A shows the implementation: all neurons are in each layer. Signed weights between adjacent layers are defined by the connectome. Each layer is therefore like a timepoint.

User can define a set of source neurons (blue/brown circles) which could be e.g. input to the central brain (sensory neurons, visual projection neurons, ascending neurons). External input is provided by activating the source neurons (brown / Panel B). The network is silent before any external input is fed in.

Panel C shows the activation function of each neuron: the (signed) weighted sum of the upstream neurons’ activity (x) is passed into a Rectified Linear Unit (ReLU()), scaled by excitability, and then passed into tanh(), to keep the activation of each neuron between 0 and 1.

An example implementation can be found here, which uses the MultilayeredNetwork().

Comparison with “effective connectivity”

Pros

  • nonlinearity (i.e. the curvature in panel C) - a bit more similar to real neurons;

  • users can see directly the response from a user-defined input pattern (panel B);

  • cheaper to compute than “effective connectivity”;

  • neuron activation don’t diminish with the increase in layers / time points, which does happen for “effective connectivity” calculation;

  • almost forces users to not cherry pick neurons/connections for interpretation in the densely-connected connectome.

Cons

  • a bit more complicated;

Plasticity

The connectivity in the connectome between some neurons, e.g. ring neurons and compass neurons, is only a scaffold for, instead of a direct reflection of, functional connectivity (Fisher et al. 2022). We therefore implemented (third-party-dependent) change in weights (“plasticity”), based also on the activation similarity of two groups of neurons (change_model_weights()).