Topology of synaptic connectivity constrains neuronal stimulus representation, predicting two complementary coding strategies

Abstract

In motor-related brain regions, movement intention has been successfully decoded from in-vivo spike train by isolating a lower-dimension manifold that the high-dimensional spiking activity is constrained to. The mechanism enforcing this constraint remains unclear, although it has been hypothesized to be implemented by the connectivity of the sampled neurons. We test this idea and explore the interactions between local synaptic connectivity and its ability to encode information in a lower dimensional manifold through simulations of a detailed microcircuit model with realistic sources of noise. We confirm that even in isolation such a model can encode the identity of different stimuli in a lower-dimensional space. We then demonstrate that the reliability of the encoding depends on the connectivity between the sampled neurons by specifically sampling populations whose connectivity maximizes certain topological metrics. Finally, we developed an alternative method for determining stimulus identity from the activity of neurons by combining their spike trains with their recurrent connectivity. We found that this method performs better for sampled groups of neurons that perform worse under the classical approach, predicting the possibility of two separate encoding strategies in a single microcircuit.

An application of neighbourhoods in digraphs to the classification of binary dynamics

“…In particular, it is shown that an informed choice of neighbourhood improves classification accuracy when compared to traditional methods. Interestingly, the selection of neighbourhoods that improved performance with the technique presented in M. Reimann et al (2021) show reduced performance with the techniques presented in this article, and vice versa. In both projects a classification accuracy of nearly 90% was achievable, but with different selection parameters (see Results ).…”

“…The primary test of our methods in this paper is done on data generated by the Blue Brain Project that was also used in M. Reimann et al (2021) for signal classification by established neuroscience methodology. The data consists of eight families of neuronal stimuli that are injected in a random sequence to the digital reconstruction of the neocortical column of a young rat.…”

“…In this article we did not attempt to explain the relevance of any of the mathematical concepts we use to neuroscience, as our main aim was to discover and investigate the utility of various concepts. However, in M. Reimann et al (2021) the same dataset is studied by standard techniques of computational neuroscience combined with the ideas presented in this paper. In particular, it is shown that an informed choice of neighbourhood improves classification accuracy when compared to traditional methods.…”

Simplicial $q$-connectivity of directed graphs with applications to network analysis

“…The microcircuit also facilitates simulation of neuronal activity. Recently, various simulated activities were classified with high accuracy using feature vectors constructed from the network struc-ture [13,33]. The microcircuit is obtainable from [31].…”

“…In topological data analysis (TDA) particularly the advent of applying topological tools to questions in neuroscience has spawned interest in constructing topological spaces out of digraphs, developing computational tools for obtaining topological information, and using these to understand networks and phenomena they support. For a progression of works on these ideas, see [13,29,32,33]. Our main example of a topological space on a digraph G is the directed flag complex, which is constructed from the directed cliques of G. For example, a 2-simplex is given by an ordered sequence of vertices (v 0 , v 1 , v 2 ) whenever any ordered pair (v i , v j ), for i < j, is a directed edge in G. By construction the simplices are endowed with an inherent directionality.…”