Maximum entropy models provide functional connectivity estimates in neural networks

Abstract

Tools to estimate brain connectivity offer the potential to enhance our understanding of brain functioning. The behavior of neuronal networks, including functional connectivity and induced connectivity changes by external stimuli, can be studied using models of cultured neurons. Cultured neurons tend to be active in groups, and pairs of neurons are said to be functionally connected when their firing patterns show significant synchronicity. Methods to infer functional connections are often based on pair-wise cross-correlation between activity patterns of (small groups of) neurons. However, these methods are not very sensitive to detect inhibitory connections, and they were not designed for use during stimulation. Maximum Entropy (MaxEnt) models may provide a conceptually different method to infer functional connectivity. They have the potential benefit to estimate functional connectivity during stimulation, and to infer excitatory as well as inhibitory connections. MaxEnt models do not involve pairwise comparison, but aim to capture probability distributions of sets of neurons that are synchronously active in discrete time bins. We used electrophysiological recordings from in vitro neuronal cultures on micro electrode arrays to investigate the ability of MaxEnt models to infer functional connectivity. Connectivity estimates provided by MaxEnt models correlated well with those obtained by conditional firing probabilities (CFP), an established cross-correlation based method. In addition, stimulus-induced connectivity changes were detected by MaxEnt models, and were of the same magnitude as those detected by CFP. Thus, MaxEnt models provide a potentially powerful new tool to study functional connectivity in neuronal networks.

The potential of in vitro neuronal networks cultured on micro electrode arrays for biomedical research

“…Synaptic plasticity phenomena such as long-term potentiation (LTP) and long-term depression (LTD) are reflected by changes (i.e. increase or decrease, in both spontaneous and evoked response to later electrical stimuli) [143,[169][170][171][172][173][174][175][176]. In the work of Jäckel et al, HD-MEA technology was combined with patch-clamp enabling to deliver electrical stimuli at a microsecond resolution to specific neurons, and to identify the contributions of individual presynaptic synapses to postsynaptic potentials [143].…”

“…Frequently, indeed, results obtained from rodent neuronal networks on MEAs have been confirmed by following works based on hiPSCs-derived neuronal networks, or by in vivo observations. This is the case, for instance, of studies investigating synaptic plasticity phenomena [143,[169][170][171][172][173][174][175][176] and neuromodulation of neuronal activity [187][188][189][190][191][192][193], screening neurotoxic compounds [203][204][205][206][207], and characterizing the phenotype of certain neurological disorders [225,227,[243][244][245]. In all these cases, rodent neuronal cultures still represent the most rapid, economical, and accessible way to gain valuable insights about the human brain, in both physiology and pathology.…”

The role of NMDA receptors in memory and prediction in cultured neural networks

“…Acquired analogue signals were band-pass filtered (2 nd order Butterworth 0.1 -6 kHz) before sampling [17,34]. Action potentials were detected whenever recorded voltages exceeded a threshold, set at 5.5 times the estimated root-mean-square noise level (ranging 3 -5 µV).…”

“…Connection strengths between neurons can be determined in patch clamp experiments [13], but this approach reveals only one, or at the best a few, connection strengths at a time. In past decades, micro electrode arrays (MEAs) have been used to record activity from networks of cultured neurons [14], and recorded activity patterns can be used to infer functional connectivity and study memory [15][16][17]. We will use the term 'connectivity' throughout the current work to refer to functional connectivity.…”

“…Connection strengths between neurons can be determined in patch clamp experiments [13], but this approach reveals only one, or at the best a few, connection strengths at a time. In past decades, micro electrode arrays (MEAs) have been used to record activity from networks of cultured neurons [14], and recorded activity patterns can be used to infer functional connectivity and study memory [15][16][17].Connectivity and activity in neuronal networks mutually affect each other. The finding that input deprived networks develop quasi stable activity patterns [18,19] and connectivity [20] suggests that activity and connectivity are in equilibrium [21].…”