Abstract
Determining the structure of a network is of central importance to understanding its function in both neuroscience and applied mathematics. However, recovering the structural connectivity of neuronal networks remains a fundamental challenge both theoretically and experimentally. While neuronal networks operate in certain dynamical regimes, which may influence their connectivity reconstruction, there is widespread experimental evidence of a balanced neuronal operating state in which strong excitatory and inhibitory inputs are dynamically adjusted such that neuronal voltages primarily remain near resting potential. Utilizing the dynamics of model neurons in such a balanced regime in conjunction with the ubiquitous sparse connectivity structure of neuronal networks, we develop a compressive sensing theoretical framework for efficiently reconstructing network connections by measuring individual neuronal activity in response to a relatively small ensemble of random stimuli injected over a short time scale. By tuning the network dynamical regime, we determine that the highest fidelity reconstructions are achievable in the balanced state. We hypothesize the balanced dynamics observed in vivo may therefore be a result of evolutionary selection for optimal information encoding and expect the methodology developed to be generalizable for alternative model networks as well as experimental paradigms.
Highlights
Addressing the current theoretical and experimental difficulties in measuring the structural connectivity in large neuronal networks, we show that the high degree of sparsity in network connections makes it feasible to accurately reconstruct network connectivity from a relatively small number of measurements of evoked neuronal activity via Compressive sensing (CS) theory
We hypothesize that evolution may have fine-tuned much of the cortical network connectivity to optimize both the encoding of sensory inputs as well as local connectivity based on balanced network dynamics
It is important to note that while the compressive sensing theory leveraged in this work is well-suited for the reconstruction of sparse signals, the reconstruction of densely-connected neuronal networks in the brain with potentially strongly correlated dynamics remains a challenging area for future investigation (Wang et al, 2011a; Markov et al, 2013; Yang et al, 2017)
Summary
The connectivity of neuronal networks is fundamental for establishing the link between brain structure and function (Boccaletti et al, 2006; Stevenson et al, 2008; Gomez-Rodriguez et al, 2012); recovering the structural connectivity in neuronal networks is still a challenging problem both theoretically and experimentally (Salinas and Sejnowski, 2001; Song et al, 2005; Friston, 2011; Kleinfeld et al, 2011; Bargmann and Marder, 2013). Network Reconstruction in Balanced Dynamics mathematical approaches for recovering network connectivity based on measured neuronal activity, such as Granger causality, information theory, and Bayesian analysis, typically demand linear dynamics or long observation times (Aertsen et al, 1989; Sporns et al, 2004; Timme, 2007; Eldawlatly et al, 2010; Friston, 2011; Hutchison et al, 2013; Zhou et al, 2013b, 2014; Goñi et al, 2014) Is it possible to achieve the successful reconstruction of network connectivity from the measurement of individual non-linear neuronal dynamics within a short time scale?. In the case of realistic neuronal networks, their non-linear dynamics in time pose a major conceptual difficulty, in isolating the impact of direct network connections on recorded activity from the effects of indirect neuronal interactions and the external drive
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