The Effect of Signaling Latencies and Node Refractory States on the Dynamics of Networks

Abstract

We describe the construction and theoretical analysis of a framework derived from canonical neurophysiological principles that model the competing dynamics of incident signals into nodes along directed edges in a network. The framework describes the dynamics between the offset in the latencies of propagating signals, which reflect the geometry of the edges and conduction velocities, and the internal refractory dynamics and processing times of the downstream node receiving the signals. This framework naturally extends to the construction of a perceptron model that takes into account such dynamic geometric considerations. We first describe the model in detail, culminating with the model of a geometric dynamic perceptron. We then derive upper and lower bounds for a notion of optimal efficient signaling between vertex pairs based on the structure of the framework. Efficient signaling in the context of the framework we develop here means that there needs to be a temporal match between the arrival time of the signals relative to how quickly nodes can internally process signals. These bounds reflect numerical constraints on the compensation of the timing of signaling events of upstream nodes attempting to activate downstream nodes they connect into that preserve this notion of efficiency. When a mismatch between signal arrival times and the internal states of activated nodes occurs, it can cause a break down in the signaling dynamics of the network. In contrast to essentially all the current state of the art in machine learning, this work provides a theoretical foundation for machine learning and intelligence architectures based on the timing of node activations and their abilities to respond, rather than necessary changes in synaptic weights. At the same time, the theoretical ideas we developed are guiding the discovery of experimentally testable new structure-function principles in the biological brain.

Super-selective reconstruction of causal and direct connectivity with application toin-vitroiPSC neuronal networks

“…Importantly, spatio-temporal information is implicitly contained in the estimated connectivity and delay map too; we expect therefore that, when used in combination with novel computational methodologies [66,58,67], our method will help reveal more fundamental network properties crucial to the understanding of the relationships between network topology, dynamic signaling and network functions in healthy and disease models.…”

Understanding the Human Brain using Brain Organoids and a Structure-Function Theory

“…Competitive-refractory dynamics model As a second example, we (G.S.) recently described the construction and theoretical analysis of a framework (competitive-refractory dynamics model) derived from the canonical neurophysiological principles of spatial and temporal summation [19]. Like the Hodgkin Huxley model, the dependency of the model on the fundamental structurefunction constraint is explicit in its construction and equations.…”

“…The effects of the structure-function constraint can be seen in experimental results through analyses that make use of the competitive-refractory dynamics model. We have shown in numerical simulations that network dynamics can completely break down in geometric networks (such as biological neural networks) if there is a mismatch in the refraction ratio [5,19]. In numerical simulation experiments, we stimulated a geometric network of 100 neurons for 500 ms with a depolarizing current and then observed the effects of modifying the refraction ratio ( Figure 2).…”

“…The mean of the median ratio distribution had a value of 1.01 with 49 neurons (86 % of the entire data set) within one standard deviation. The theoretically derived ideal for efficient signaling in a geometric network is unity (see the refraction ratio theorem in [19]). (D) Distribution of the refraction ratio for the entire data set (same data shown in panel B) but with x-axis extending out to the full range of values in order to show the few outliers (indicated by the red arrows).…”

Computing temporal sequences associated with dynamic patterns on the C. elegans connectome

“…We first simulated the plausible dynamics resulting from the known C. elegans connectome [25,31,18] using a recent model and theoretical study we published that computes the dynamics of neurobiological networks by focusing on how local interactions among connected neurons give rise to the global dynamics in an emergent way, independent of the biophysical or molecular details of the cells themselves [58]. This framework was derived from a theoretical abstraction of the canonical principles of spatial and temporal summation in biological neurons.…”