We are looking for a postdoctoral researcher to work on the Vidi project 'Top-down neuromodulation and bottom-up network computation, a computational study' and study the effects of neuromodulators in balanced networks. You will use cellular and behavioural data on the effects of dopamine, acetylcholine and serotonin in mouse barrel cortex gathered by our department over the past five years, to bridge the gap between single cell, network and behavioural effects. You will use the balanced network framework to study network activity under neuromodulation. In order to do this, you will develop a balanced network description of the barrel cortex, with realistic barrel cortex properties (see https://doi.org/10.1007/s12021-022-09576-5). Next, you will incorporate the cellular effects of dopamine, acetylcholine and serotonin that we have measured over the previous years (see https://doi.org/10.1093/gigascience/giy147 and https://doi.org/10.1101/2022.01.12.476007) into the network, and investigate their effects on overall network activity and behaviour. More particularly, through simulations and analytical derivations, you will research the effects of neuromodulators on the stability of the balanced state, synchrony, regularity and chaos. You will build on the single cell data, models and analysis methods available in our group, and your results will be incorporated into our group's further research to develop and validate machine learning and efficient coding models of (somatosensory) perception. We are therefore looking for a team player who can work well with our other group members and is willing to both learn from them and share their knowledge.

Timescales characterize how fast the observables change in time. In neuroscience, they can be estimated from the measured activity and can be used, for example, as a signature of the memory trace in the network. I will first discuss the inference of the timescales from the neuroscience data comprised of the short trials and introduce a new unbiased method. Then, I will apply the method to the data recorded from a local population of cortical neurons from the visual area V4. I will demonstrate that the ongoing spiking activity unfolds across at least two distinct timescales - fast and slow - and the slow timescale increases when monkeys attend to the location of the receptive field. Which models can give rise to such behavior? Random balanced networks are known for their fast timescales; thus, a change in the neurons or network properties is required to mimic the data. I will propose a set of models that can control effective timescales and demonstrate that only the model with strong recurrent interactions fits the neural data. Finally, I will discuss the timescales' relevance for behavior and cortical computations.

Neural circuits exhibit complex activity patterns, both spontaneously and in response to external stimuli. Information encoding and learning in neural circuits depend on the ability of time-varying stimuli to control spontaneous network activity. In particular, variability arising from the sensitivity to initial conditions of recurrent cortical circuits can limit the information conveyed about the sensory input. Spiking and firing rate network models can exhibit such sensitivity to initial conditions that are reflected in their dynamic entropy rate and attractor dimensionality computed from their full Lyapunov spectrum. I will show how chaos in both spiking and rate networks depends on biophysical properties of neurons and the statistics of time-varying stimuli. In spiking networks, increasing the input rate or coupling strength aids in controlling the driven target circuit, which is reflected in both a reduced trial-to-trial variability and a decreased dynamic entropy rate. With sufficiently strong input, a transition towards complete network state control occurs. Surprisingly, this transition does not coincide with the transition from chaos to stability but occurs at even larger values of external input strength. Controllability of spiking activity is facilitated when neurons in the target circuit have a sharp spike onset, thus a high speed by which neurons launch into the action potential. I will also discuss chaos and controllability in firing-rate networks in the balanced state. For these, external control of recurrent dynamics strongly depends on correlations in the input. This phenomenon was studied with a non-stationary dynamic mean-field theory that determines how the activity statistics and the largest Lyapunov exponent depend on frequency and amplitude of the input, recurrent coupling strength, and network size. This shows that uncorrelated inputs facilitate learning in balanced networks. The results highlight the potential of Lyapunov spectrum analysis as a diagnostic for machine learning applications of recurrent networks. They are also relevant in light of recent advances in optogenetics that allow for time-dependent stimulation of a select population of neurons.

The intensity and features of sensory stimuli are encoded in the activity of neurons in the cortex. In the visual and piriform cortices, the stimulus intensity re-scales the activity of the population without changing its selectivity for the stimulus features. The cortical representation of the stimulus is therefore intensity-invariant. This emergence of network invariant representations appears robust to local changes in synaptic strength induced by synaptic plasticity, even though: i) synaptic plasticity can potentiate or depress connections between neurons in a feature-dependent manner, and ii) in networks with balanced excitation and inhibition, synaptic plasticity determines the non-linear network behavior. In this study, we investigate the consistency of invariant representations with a variety of synaptic states in balanced networks. By using mean-field models and spiking network simulations, we show how the synaptic state controls the emergence of intensity-invariant or intensity-dependent selectivity by inducing changes in the network response to intensity. In particular, we demonstrate how facilitating synaptic states can sharpen the network selectivity while depressing states broaden it. We also show how power-law-type synapses permit the emergence of invariant network selectivity and how this plasticity can be generated by a mix of different plasticity rules. Our results explain how the physiology of individual synapses is linked to the emergence of invariant representations of sensory stimuli at the network level.

We study the dynamics of (inhibitory) balanced networks at varying (i) the level of symmetry in the synaptic connectivity; and (ii) the ariance of the synaptic efficacies (synaptic gain). We find three regimes of activity. For suitably low synaptic gain, regardless of the level of symmetry, there exists a unique stable fixed point. Using a cavity-like approach, we develop a quantitative theory that describes the statistics of the activity in this unique fixed point, and the conditions for its stability. Increasing the synaptic gain, the unique fixed point destabilizes, and the network exhibits chaotic activity for zero or negative levels of symmetry (i.e., random or antisymmetric). Instead, for positive levels of symmetry, there is multi-stability among a large number of marginally stable fixed points. In this regime, ergodicity is broken and the network exhibits non-exponential relaxational dynamics. We discuss the potential relevance of such a “glassy” phase to explain some features of cortical activity.

Neurons in the primary visual cortex (V1) encode the orientation and contrast of visual stimuli through changes in firing rate (Hubel and Wiesel, 1962). Their activity typically peaks at a preferred orientation and decays to zero at the orientations that are orthogonal to the preferred. This activity pattern is re-scaled by contrast but its shape is preserved, a phenomenon known as contrast invariance. Contrast-invariant selectivity is also observed at the population level in V1 (Carandini and Sengpiel, 2004). The mechanisms supporting the emergence of contrast-invariance at the population level remain unclear. How does the activity of different neurons with diverse orientation selectivity and non-linear contrast sensitivity combine to give rise to contrast-invariant population selectivity? Theoretical studies have shown that in the balance limit, the properties of single-neurons do not determine the population activity (van Vreeswijk and Sompolinsky, 1996). Instead, the synaptic dynamics (Mongillo et al., 2012) as well as the intracortical connectivity (Rosenbaum and Doiron, 2014) shape the population activity in balanced networks. We report that short-term plasticity can change the synaptic strength between neurons as a function of the presynaptic activity, which in turns modifies the population response to a stimulus. Thus, the same circuit can process a stimulus in different ways –linearly, sublinearly, supralinearly – depending on the properties of the synapses. We found that balanced networks with excitatory to excitatory short-term synaptic plasticity cannot be contrast-invariant. Instead, short-term plasticity modifies the network selectivity such that the tuning curves are narrower (broader) for increasing contrast if synapses are facilitating (depressing). Based on these results, we wondered whether balanced networks with plastic synapses (other than short-term) can support the emergence of contrast-invariant selectivity. Mathematically, we found that the only synaptic transformation that supports perfect contrast invariance in balanced networks is a power-law release of neurotransmitter as a function of the presynaptic firing rate (in the excitatory to excitatory and in the excitatory to inhibitory neurons). We validate this finding using spiking network simulations, where we report contrast-invariant tuning curves when synapses release the neurotransmitter following a power- law function of the presynaptic firing rate. In summary, we show that synaptic plasticity controls the type of non-linear network response to stimulus contrast and that it can be a potential mechanism mediating the emergence of contrast invariance in balanced networks with orientation-dependent connectivity. Our results therefore connect the physiology of individual synapses to the network level and may help understand the establishment of contrast-invariant selectivity.