Bernstein SmartSteps

Vision begins in the eye, and what the “retina tells the brain” is a major interest in visual neuroscience. To deduce what the retina encodes (“tells”), computational models are essential. The most important models in the retina currently aim to understand the responses of the retinal output neurons – the ganglion cells. Typically, these models make simplifying assumptions about the neurons in the retinal network upstream of ganglion cells. One important assumption is linear spatial integration. In this talk, I first define what it means for a neuron to be spatially linear or nonlinear and how we can experimentally measure these phenomena. Next, I introduce the neurons upstream to retinal ganglion cells, with focus on bipolar cells, which are the connecting elements between the photoreceptors (input to the retinal network) and the ganglion cells (output). This pivotal position makes bipolar cells an interesting target to study the assumption of linear spatial integration, yet due to their location buried in the middle of the retina it is challenging to measure their neural activity. Here, I present bipolar cell data where I ask whether the spatial linearity holds under artificial and natural visual stimuli. Through diverse analyses and computational models, I show that bipolar cells are more complex than previously thought and that they can already act as nonlinear processing elements at the level of their somatic membrane potential. Furthermore, through pharmacology and current measurements, I illustrate that the observed spatial nonlinearity arises at the excitatory inputs to bipolar cells. In the final part of my talk, I address the functional relevance of the nonlinearities in bipolar cells through combined recordings of bipolar and ganglion cells and I show that the nonlinearities in bipolar cells provide high spatial sensitivity to downstream ganglion cells. Overall, I demonstrate that simple linear assumptions do not always apply and more complex models are needed to describe what the retina “tells” the brain.

Activity dependent synaptic plasticity is considered to be a primary mechanism underlying learning and memory. Yet it is unclear whether plasticity rules such as STDP measured in vitro apply in vivo. Network models with STDP predict that activity patterns (e.g., place-cell spatial selectivity) should change much faster than observed experimentally. We address this gap by investigating a nonlinear calcium-based plasticity rule fit to experiments done in physiological conditions. In this model, LTP and LTD result from intracellular calcium transients arising almost exclusively from synchronous coactivation of pre- and postsynaptic neurons. We analytically approximate the full distribution of nonlinear calcium transients as a function of pre- and postsynaptic firing rates, and temporal correlations. This analysis directly relates activity statistics that can be measured in vivo to the changes in synaptic efficacy they cause. Our results highlight that both high-firing rates and temporal correlations can lead to significant changes to synaptic efficacy. Using a mean-field theory, we show that the nonlinear plasticity rule, without any fine-tuning, gives a stable, unimodal synaptic weight distribution characterized by many strong synapses which remain stable over long periods of time, consistent with electrophysiological and behavioral studies. Moreover, our theory explains how memories encoded by strong synapses can be preferentially stabilized by the plasticity rule. We confirmed our analytical results in a spiking recurrent network. Interestingly, although most synapses are weak and undergo rapid turnover, the fraction of strong synapses are sufficient for supporting realistic spiking dynamics and serve to maintain the network’s cluster structure. Our results provide a mechanistic understanding of how stable memories may emerge on the behavioral level from an STDP rule measured in physiological conditions. Furthermore, the plasticity rule we investigate is mathematically equivalent to other learning rules which rely on the statistics of coincidences, so we expect that our formalism will be useful to study other learning processes beyond the calcium-based plasticity rule.

The interaction between spontaneously and externally evoked neuronal activity is fundamental for a functional brain. Increasing evidence suggests that bursts of high-power oscillations in the 15-30 Hz beta-band represent activation of resting state networks and can mask perception of external cues. Yet demonstration of the effect of beta power modulation on perception in real-time is missing, and little is known about the underlying mechanism. In this talk I will present the methods we developed to fill this gap together with our recent results. We used a closed-loop stimulus-intensity adjustment system based on online burst-occupancy analyses in rats involved in a forepaw vibrotactile detection task. We found that the masking influence of burst-occupancy on perception can be counterbalanced in real-time by adjusting the vibration amplitude. Offline analysis of firing-rates and local field potentials across cortical layers and frequency bands confirmed that beta-power in the somatosensory cortex anticorrelated with sensory evoked responses. Mechanistically, bursts in all bands were accompanied by transient synchronization of cell assemblies, but only beta-bursts were followed by a reduction of firing-rate. Our closed loop approach reveals that spontaneous beta-bursts reflect a dynamic state that competes with external stimuli.

Ever since Bliss and Lømo discovered the phenomenon of long-term potentiation (LTP) in rabbit dentate gyrus in the 1960s, Hebb’s rule—neurons that fire together wire together—gained popularity to explain learning and memory. Accumulating evidence, however, suggests that neural activity is homeostatically regulated. Homeostatic mechanisms are mostly interpreted to stabilize network dynamics. However, recent theoretical work has shown that linking the activity of a neuron to its connectivity within the network provides a robust alternative implementation of Hebb’s rule, although entirely based on negative feedback. In this setting, both natural and artificial stimulation of neurons can robustly trigger network rewiring. We used computational models of plastic networks to simulate the complex temporal dynamics of network rewiring in response to external stimuli. In parallel, we performed optogenetic stimulation experiments in the mouse anterior cingulate cortex (ACC) and subsequently analyzed the temporal profile of morphological changes in the stimulated tissue. Our results suggest that the new theoretical framework combining neural activity homeostasis and structural plasticity provides a consistent explanation of our experimental observations.

To prevail in a dynamic and noisy environment, the brain must create reliable and meaningful representations from sensory inputs that are often ambiguous or corrupt. Since only information that permeates the cortical hierarchy can influence sensory perception and decision-making, it is critical that noisy external stimuli are encoded and propagated through different processing stages with minimal signal degradation. Here we hypothesize that stimulus-specific pathways akin to cortical topographic maps may provide the structural scaffold for such signal routing. We investigate whether the feature-specific pathways within such maps, characterized by the preservation of the relative organization of cells between distinct populations, can guide and route stimulus information throughout the system while retaining representational fidelity. We demonstrate that, in a large modular circuit of spiking neurons comprising multiple sub-networks, topographic projections are not only necessary for accurate propagation of stimulus representations, but can also help the system reduce sensory and intrinsic noise. Moreover, by regulating the effective connectivity and local E/I balance, modular topographic precision enables the system to gradually improve its internal representations and increase signal-to-noise ratio as the input signal passes through the network. Such a denoising function arises beyond a critical transition point in the sharpness of the feed-forward projections, and is characterized by the emergence of inhibition-dominated regimes where population responses along stimulated maps are amplified and others are weakened. Our results indicate that this is a generalizable and robust structural effect, largely independent of the underlying model specificities. Using mean-field approximations, we gain deeper insight into the mechanisms responsible for the qualitative changes in the system’s behavior and show that these depend only on the modular topographic connectivity and stimulus intensity. The general dynamical principle revealed by the theoretical predictions suggest that such a denoising property may be a universal, system-agnostic feature of topographic maps, and may lead to a wide range of behaviorally relevant regimes observed under various experimental conditions: maintaining stable representations of multiple stimuli across cortical circuits; amplifying certain features while suppressing others (winner-take-all circuits); and endow circuits with metastable dynamics (winnerless competition), assumed to be fundamental in a variety of tasks.

Neuronal computations are matched to optimally encode the sensory information that is available and relevant for the animal. However, the physical distribution of sensory information is often shaped by the animal’s own behavior. One prominent example is the encoding of optic flow fields that are generated during self-motion of the animal and will therefore depend on the type of locomotion. How evolution has matched computational resources to the behavioral constraints of an animal is not known. Here we use in vivo two photon imaging to record from a population of >3.500 local-direction selective cells. Our data show that the local direction-selective T4/T5 neurons in Drosophila form a population code that is matched to represent optic flow fields generated during translational and rotational self-motion of the fly. This coding principle for optic flow is reminiscent to the population code of local direction-selective ganglion cells in the mouse retina, where four direction-selective ganglion cells encode four different axes of self-motion encountered during walking (Sabbah et al., 2017). However, in flies we find six different subtypes of T4 and T5 cells that, at the population level, represent six axes of self-motion of the fly. The four uniformly tuned T4/T5 subtypes described previously represent a local snapshot (Maisak et al. 2013). The encoding of six types of optic flow in the fly as compared to four types of optic flow in mice might be matched to the high degrees of freedom encountered during flight. Thus, a population code for optic flow appears to be a general coding principle of visual systems, resulting from convergent evolution, but matching the individual ethological constraints of the animal.

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 - https://neatdend.readthedocs.io/en/latest/) 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.

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.

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.

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.

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 2x2 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.

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.