Setting network states via the dynamics of action potential generation
To understand neural computation and the dynamics in the brain, we usually focus on the connectivity among neurons. In contrast, the properties of single neurons are often thought to be negligible, at least as far as the activity of networks is concerned. In this talk, I will contradict this notion and demonstrate how the biophysics of action-potential generation can have a decisive impact on network behaviour. Our recent theoretical work shows that, among regularly firing neurons, the somewhat unattended homoclinic type (characterized by a spike onset via a saddle homoclinic orbit bifurcation) particularly stands out: First, spikes of this type foster specific network states - synchronization in inhibitory and splayed-out/frustrated states in excitatory networks. Second, homoclinic spikes can easily be induced by changes in a variety of physiological parameters (like temperature, extracellular potassium, or dendritic morphology). As a consequence, such parameter changes can even induce switches in network states, solely based on a modification of cellular voltage dynamics. I will provide first experimental evidence and discuss functional consequences of homoclinic spikes for the design of efficient pattern-generating motor circuits in insects as well as for mammalian pathologies like febrile seizures. Our analysis predicts an interesting role for homoclinic action potentials as an integral part of brain dynamics in both health and disease.
Population coding in the cerebellum: a machine learning perspective
The cerebellum resembles a feedforward, three-layer network of neurons in which the “hidden layer” consists of Purkinje cells (P-cells) and the output layer consists of deep cerebellar nucleus (DCN) neurons. In this analogy, the output of each DCN neuron is a prediction that is compared with the actual observation, resulting in an error signal that originates in the inferior olive. Efficient learning requires that the error signal reach the DCN neurons, as well as the P-cells that project onto them. However, this basic rule of learning is violated in the cerebellum: the olivary projections to the DCN are weak, particularly in adulthood. Instead, an extraordinarily strong signal is sent from the olive to the P-cells, producing complex spikes. Curiously, P-cells are grouped into small populations that converge onto single DCN neurons. Why are the P-cells organized in this way, and what is the membership criterion of each population? Here, I apply elementary mathematics from machine learning and consider the fact that P-cells that form a population exhibit a special property: they can synchronize their complex spikes, which in turn suppress activity of DCN neuron they project to. Thus complex spikes cannot only act as a teaching signal for a P-cell, but through complex spike synchrony, a P-cell population may act as a surrogate teacher for the DCN neuron that produced the erroneous output. It appears that grouping of P-cells into small populations that share a preference for error satisfies a critical requirement of efficient learning: providing error information to the output layer neuron (DCN) that was responsible for the error, as well as the hidden layer neurons (P-cells) that contributed to it. This population coding may account for several remarkable features of behavior during learning, including multiple timescales, protection from erasure, and spontaneous recovery of memory.
From single cell to population coding during defensive behaviors in prefrontal circuits
Coping with threatening situations requires both identifying stimuli predicting danger and selecting adaptive behavioral responses in order to survive. The dorso medial prefrontal cortex (dmPFC) is a critical structure involved in the regulation of threat-related behaviour, yet it is still largely unclear how threat-predicting stimuli and defensive behaviours are associated within prefrontal networks in order to successfully drive adaptive responses. Over the past years, we used a combination we used a combination of extracellular recordings, neuronal decoding approaches, and state of the art optogenetic manipulations to identify key neuronal elements and mechanisms controlling defensive fear responses. I will present an overview of our recent work ranging from analyses of dedicated neuronal types and oscillatory and synchronization mechanisms to artificial intelligence approaches used to decode the activity or large population of neurons. Ultimately these analyses allowed the identification of high dimensional representations of defensive behavior unfolding within prefrontal networks.
NMC4 Short Talk: Synchronization in the Connectome: Metastable oscillatory modes emerge from interactions in the brain spacetime network
The brain exhibits a rich repertoire of oscillatory patterns organized in space, time and frequency. However, despite ever more-detailed characterizations of spectrally-resolved network patterns, the principles governing oscillatory activity at the system-level remain unclear. Here, we propose that the transient emergence of spatially organized brain rhythms are signatures of weakly stable synchronization between subsets of brain areas, naturally occurring at reduced collective frequencies due to the presence of time delays. To test this mechanism, we build a reduced network model representing interactions between local neuronal populations (with damped oscillatory response at 40Hz) coupled in the human neuroanatomical network. Following theoretical predictions, weakly stable cluster synchronization drives a rich repertoire of short-lived (or metastable) oscillatory modes, whose frequency inversely depends on the number of units, the strength of coupling and the propagation times. Despite the significant degree of reduction, we find a range of model parameters where the frequencies of collective oscillations fall in the range of typical brain rhythms, leading to an optimal fit of the power spectra of magnetoencephalographic signals from 89 heathy individuals. These findings provide a mechanistic scenario for the spontaneous emergence of frequency-specific long-range phase-coupling observed in magneto- and electroencephalographic signals as signatures of resonant modes emerging in the space-time structure of the Connectome, reinforcing the importance of incorporating realistic time delays in network models of oscillatory brain activity.
Metachronal waves in swarms of nematode Turbatrix aceti
There is a recent surge of interest in the behavior of active particles that can at the same time align their direction of movement and synchronize their oscillations, known as swarmalators. While analytical and numerical models of such systems are now abundant, no real-life examples have been shown to date. I will present an experimental investigation of the collective motion of the nematode Turbatrix aceti, which self-propel by body undulation. I will show that under favorable conditions these nematodes can synchronize their body oscillations, forming striking traveling metachronal waves which, similar to the case of beating cilia, produce strong fluid flows. I will demonstrate that the location and strength of this collective state can be controlled through the shape of the confining structure; in our case the contact angle of a droplet. This opens a way for producing controlled work such as on-demand flows or displacement of objects. I will illustrate this by a practical example: showing that the force generated by the collectively moving nematodes is sufficient to change the mode of evaporation of fluid droplets, by counteracting the surface-tension force, which allow us to estimate its strength.
Designing temporal networks that synchronize under resource constraints
Being fundamentally a non-equilibrium process, synchronization comes with unavoidable energy costs and has to be maintained under the constraint of limited resources. Such resource constraints are often reflected as a finite coupling budget available in a network to facilitate interaction and communication. In this talk, I will show that introducing temporal variation in the network structure can lead to efficient synchronization even when stable synchrony is impossible in any static network under the given budget. Our strategy is based on an open-loop control scheme and alludes to a fundamental advantage of temporal networks. Whether this advantage of temporality can be utilized in the brain is an interesting open question.
A neuronal model for learning to keep a rhythmic beat
When listening to music, we typically lock onto and move to a beat (1-6 Hz). Behavioral studies on such synchronization (Repp 2005) abound, yet the neural mechanisms remain poorly understood. Some models hypothesize an array of self-sustaining entrainable neural oscillators that resonate when forced with rhythmic stimuli (Large et al. 2010). In contrast, our formulation focuses on event time estimation and plasticity: a neuronal beat generator that adapts its intrinsic frequency and phase to match the extermal rhythm. The model quickly learns new rhythms, within a few cycles as found in human behavior. When the stimulus is removed the beat generator continues to produce the learned rhythm in accordance with a synchronization continuation task.