Bernstein SmartSteps 2021 | Spring Series

Thursday, April 29, 4 pm CEST

  • Gily Ginosar (Ulanovsky lab) | Weizmann Institute, Rehovot, Israel
    Locally-ordered representation of 3D space in the entorhinal cortex
  • Friedrich Schuessler (Barak lab) | Technion, Haifa, Israel
    Recurrent network dynamics lead to interference in sequential learning

Thursday, May 20, 4 pm CEST

  • Claire Meissner-Bernard (Friedrich lab) | Friedrich Miescher Institute, Basel, Switzerland
    Co-tuned, balanced excitation and inhibition in olfactory memory networks
  • Samuel Eckmann (Gjorgjieva lab) | Max Planck Institute for Brain Research, Frankfurt, Germany
    A theory for Hebbian learning in recurrent E-I networks

Thursday, June 10, 4 pm CEST

  • Paul Pfeiffer (Schreiber lab) | Humboldt University Berlin, Germany
    Capacitance clamp – artificial capacitance in biological neurons via dynamic clamp
  • Willem Wybo (Morrison lab) | Forschungszentrum Jülich, Germany
    Data-driven reduction of dendritic morphologies with preserved dendro-somatic responses

Please find the recordings of the talks here.


Locally-ordered representation of 3D space in the entorhinal cortex

Grid cells, 3D Navigation, Bats

When animals navigate on a two-dimensional (2D) surface, many neurons in the medial entorhinal cortex (MEC) are activated as the animal passes through multiple locations (‘firing fields’) arranged in a hexagonal lattice that tiles the locomotion-surface; these neurons are known as grid cells.
However, although our world is three-dimensional (3D), the 3D volumetric representation in MEC remains unknown. Here we recorded MEC cells in freely-flying bats and found several classes of spatial neurons, including 3D border cells, 3D head-direction cells, and neurons with multiple 3D firing-fields. Many of these multifield neurons were 3D grid cells, whose neighboring fields were separated by a characteristic distance – forming a local order – but these cells lacked any global lattice arrangement of their fields. Thus, while 2D grid cells form a global lattice – characterized by both local and global order – 3D grid cells exhibited only local order, thus creating a locally ordered metric for space. We modeled grid cells as emerging from pairwise interactions between fields, which yielded a hexagonal lattice in 2D and local order in 3D – thus describing both 2D and 3D grid cells using one unifying model. Together, these data and model illuminate the fundamental differences and similarities between neural codes for 3D and 2D space in the mammalian brain.

Recurrent network dynamics lead to interference in sequential learning

sequential learning, interference, recurrent neural networks

Learning in real life is often sequential: A learner first learns task A, then task B. If the tasks are related, the learner may adapt the previously learned representation instead of generating a new one from scratch. Adaptation may ease learning task B but may also decrease the performance on task A. Such interference has been observed in experimental and machine learning studies. In the latter case, it is mediated by correlations between weight updates for the different tasks. In typical applications, like image classification with feed-forward networks, these correlated weight updates can be traced back to input correlations. For many neuroscience tasks, however, networks need to not only transform the input, but also generate substantial internal dynamics.
Here we illuminate the role of internal dynamics for interference in recurrent neural networks (RNNs). We analyze RNNs trained sequentially on neuroscience tasks with gradient descent and observe forgetting even for orthogonal tasks. We find that the degree of interference changes systematically with tasks properties, especially with emphasis on input-driven over autonomously generated dynamics.
To better understand our numerical observations, we thoroughly analyze a simple model of working memory: For task A, a network is presented with an input pattern and trained to generate a fixed point aligned with this pattern. For task B, the network has to memorize a second, orthogonal pattern. Adapting an existing representation corresponds to the rotation of the fixed point in phase space, as opposed to the emergence of a new one. We show that the two modes of learning – rotation vs. new formation – are directly linked to recurrent vs. input-driven dynamics. We make this notion precise in a further simplified, analytically tractable model, where learning is restricted to a 2×2 matrix.
In our analysis of trained RNNs, we also make the surprising observation that, across different tasks, larger random initial connectivity reduces interference. Analyzing the fixed point task reveals the underlying mechanism: The random connectivity strongly accelerates the learning mode of new formation, and has less effect on rotation. The prior thus wins the race to zero loss, and interference is reduced.
Altogether, our work offers a new perspective on sequential learning in recurrent networks, and the emphasis on internally generated dynamics allows us to take the history of individual learners into account.

Co-tuned, balanced excitation and inhibition in olfactory memory networks

E/I balance, memory, olfaction

Odor memories are exceptionally robust and essential for the survival of many species. In rodents, the olfactory cortex shows features of an autoassociative memory network and plays a key role in the retrieval of olfactory memories (Meissner-Bernard et al., 2019). Interestingly, the telencephalic area Dp, the zebrafish homolog of olfactory cortex, transiently enters a state of precise balance during the presentation of an odor (Rupprecht and Friedrich, 2018). This state is characterized by large synaptic conductances (relative to the resting conductance) and by co-tuning of excitation and inhibition in odor space and in time at the level of individual neurons. Our aim is to understand how this precise synaptic balance affects memory function. For this purpose, we build a simplified, yet biologically plausible spiking neural network model of Dp using experimental observations as constraints: besides precise balance, key features of Dp dynamics include low firing rates, odor-specific population activity and a dominance of recurrent inputs from Dp neurons relative to afferent inputs from neurons in the olfactory bulb. To achieve co-tuning of excitation and inhibition, we introduce structured connectivity by increasing connection probabilities and/or strength among ensembles of excitatory and inhibitory neurons. These ensembles are therefore structural memories of activity patterns representing specific odors. They form functional inhibitory-stabilized subnetworks, as identified by the “paradoxical effect” signature (Tsodyks et al., 1997): inhibition of inhibitory “memory” neurons leads to an increase of their activity. We investigate the benefits of co-tuning for olfactory and memory processing, by comparing inhibitory-stabilized networks with and without co-tuning. We find that co-tuned excitation and inhibition improves robustness to noise, pattern completion and pattern separation. In other words, retrieval of stored information from partial or degraded sensory inputs is enhanced, which is relevant in light of the instability of the olfactory environment. Furthermore, in co-tuned networks, odor-evoked activation of stored patterns does not persist after removal of the stimulus and may therefore subserve fast pattern classification. These findings provide valuable insights into the computations performed by the olfactory cortex, and into general effects of balanced state dynamics in associative memory networks.

A theory for Hebbian learning in recurrent E-I networks

Hebbian learning, Stabilized Supralinear Network, recurrent networks, inhibition stabilized, response normalization

The Stabilized Supralinear Network is a model of recurrently connected excitatory (E) and inhibitory (I) neurons with a supralinear input-output relation. It can explain cortical computations such as response normalization and inhibitory stabilization. However, the network’s connectivity is designed by hand, based on experimental measurements. How the recurrent synaptic weights can be learned from the sensory input statistics in a biologically plausible way is unknown. Earlier theoretical work on plasticity focused on single neurons and the balance of excitation and inhibition but did not consider the simultaneous plasticity of recurrent synapses and the formation of receptive fields.
Here we present a recurrent E-I network model where all synaptic connections are simultaneously plastic, and E neurons self-stabilize by recruiting co-tuned inhibition. Motivated by experimental results, we employ a local Hebbian plasticity rule with multiplicative normalization for E and I synapses. We develop a theoretical framework that explains how plasticity enables inhibition balanced excitatory receptive fields that match experimental results. We show analytically that sufficiently strong inhibition allows neurons’ receptive fields to decorrelate and distribute themselves across the stimulus space. For strong recurrent excitation, the network becomes stabilized by inhibition, which prevents unconstrained self-excitation. In this regime, external inputs integrate sublinearly. As in the Stabilized Supralinear Network, this results in response normalization and winner-takes-all dynamics: when two competing stimuli are presented, the network response is dominated by the stronger stimulus while the weaker stimulus is suppressed.
In summary, we present a biologically plausible theoretical framework to model plasticity in fully plastic recurrent E-I networks. While the connectivity is derived from the sensory input statistics, the circuit performs meaningful computations. Our work provides a mathematical framework of plasticity in recurrent networks, which has previously only been studied numerically and can serve as the basis for a new generation of brain-inspired unsupervised machine learning algorithms.

Capacitance clamp – artificial capacitance in biological neurons via dynamic clamp

feedback, neuronal excitability, electrophyiology, dynamic clamp, computational modelling

A basic time scale in neural dynamics from single cells to the network level is the membrane time constant – set by a neuron’s input resistance and its capacitance. Interestingly, the membrane capacitance appears to be more dynamic than previously assumed with implications for neural function and pathology. Indeed, altered membrane capacitance has been observed in reaction to physiological changes like neural swelling, but also in ageing and Alzheimer’s disease. Importantly, according to theory, even small changes of the capacitance can affect neuronal signal processing, e.g. increase network synchronization or facilitate transmission of high frequencies. In experiment, robust methods to modify the capacitance of a neuron have been missing. Here, we present the capacitance clamp – an electrophysiological method for capacitance control based on an unconventional application of the dynamic clamp.
In its original form, dynamic clamp mimics additional synaptic or ionic conductances by injecting their respective currents. Whereas a conductance directly governs a current, the membrane capacitance determines how fast the voltage responds to a current. Accordingly, capacitance clamp mimics an altered capacitance by injecting a dynamic current that slows down or speeds up the voltage response (Fig 1 A). For the required dynamic current, the experimenter only has to specify the original cell and the desired target capacitance. In particular, capacitance clamp requires no detailed model of present conductances and thus can be applied in every excitable cell.
To validate the capacitance clamp, we performed numerical simulations of the protocol and applied it to modify the capacitance of cultured neurons. First, we simulated capacitance clamp in conductance based neuron models and analysed impedance and firing frequency to verify the altered capacitance. Second, in dentate gyrus granule cells from rats, we could reliably control the capacitance in a range of 75 to 200% of the original capacitance and observed pronounced changes in the shape of the action potentials: increasing the capacitance reduced after-hyperpolarization amplitudes and slowed down repolarization.
To conclude, we present a novel tool for electrophysiology: the capacitance clamp provides reliable control over the capacitance of a neuron and thereby opens a new way to study the temporal dynamics of excitable cells.

Data-driven reduction of dendritic morphologies with preserved dendrosomatic responses

dendritic computation, model reduction, compartmental models

There is little consensus on the level of spatial complexity at which dendrites operate. On the one hand, emergent evidence indicates that synapses cluster at micrometer spatial scales. On the other hand, most modelling and network studies ignore dendrites altogether. This dichotomy raises an urgent question: what is the smallest relevant spatial scale for understanding dendritic computation?
We have developed a method to construct compartmental models at any level of spatial complexity. Through carefully chosen parameter fits, solvable in the least-squares sense, we obtain accurate reduced compartmental models. Thus, we are able to systematically construct passive as well as active dendrite models at varying degrees of spatial complexity. We evaluate which elements of the dendritic computational repertoire are captured by these models.
We show that many canonical elements of the dendritic computational repertoire can be reproduced with few compartments. For instance, for a model to behave as a two-layer network, it is sufficient to fit a reduced model at the soma and at locations at the dendritic tips. In the basal dendrites of an L2/3 pyramidal model, we reproduce the backpropagation of somatic action potentials (APs) with a single dendritic compartment at the tip. Further, we obtain the well-known Ca-spike coincidence detection mechanism in L5 Pyramidal cells with as few as eleven compartments, the requirement being that their spacing along the apical trunk supports AP backpropagation.
We also investigate whether afferent spatial connectivity motifs admit simplification by ablating targeted branches and grouping affected synapses onto the next proximal dendrite. We find that voltage in the remaining branches is reproduced if temporal conductance fluctuations stay below a limit that depends on the average difference in input resistance between the ablated branches and the next proximal dendrite. Consequently, when the average conductance load on distal synapses is constant, the dendritic tree can be simplified while appropriately decreasing synaptic weights. When the conductance level fluctuates strongly, for instance through a-priori unpredictable fluctuations in NMDA activation, a constant weight rescale factor cannot be found, and the dendrite cannot be simplified.
We have created an open source Python toolbox (NEAT – that automatises the simplification process. A NEST implementation of the reduced models, currently under construction, will enable the simulation of few-compartment models in large-scale networks, thus bridging the gap between cellular and network level neuroscience.