Computational Neuroscience seminars

Starting with the work of Hodgkin and Huxley in the 1950s, we now have a fairly good understanding of how the spiking activity of neurons can be modelled mathematically. For cortical circuits the understanding is much more limited. Most network studies have considered stylized models with a single or a handful of neuronal populations consisting of identical neurons with statistically identical connection properties. However, real cortical networks have heterogeneous neural populations and much more structured synaptic connections. Unlike typical simplified cortical network models, real networks are also “multipurpose” in that they perform multiple functions. Historically the lack of computational resources has hampered the mathematical exploration of cortical networks. With the advent of modern supercomputers, however, simulations of networks comprising hundreds of thousands biologically detailed neurons are becoming feasible (Einevoll et al, Neuron, 2019). Further, a large-scale biologically network model of the mouse primary visual cortex comprising 230.000 neurons has recently been developed at the Allen Institute for Brain Science (Billeh et al, Neuron, 2020). Using this model as a starting point, I will discuss how we can move towards multipurpose models that incorporate the true biological complexity of cortical circuits and faithfully reproduce multiple experimental observables such as spiking activity, local field potentials or two-photon calcium imaging signals. Further, I will discuss how such validated comprehensive network models can be used to gain insights into the functioning of cortical circuits.

Both computational and experimental results in single neurons and small networks demonstrate that very similar network function can result from quite disparate sets of neuronal and network parameters. Using the crustacean stomatogastric nervous system, we study the influence of these differences in underlying structure on differential resilience of individuals to a variety of environmental perturbations, including changes in temperature, pH, potassium concentration and neuromodulation. We show that neurons with many different kinds of ion channels can smoothly move through different mechanisms in generating their activity patterns, thus extending their dynamic range.

I will review advances in understanding the cortical encoding of speech-related oral movements. These discoveries are being translated to develop algorithms to decode speech from population neural activity.

Learning is a population phenomenon. Since it is the organized activity of populations of neurons that cause movement, learning a new skill must involve reshaping those population activity patterns. Seeing how the brain does this has been elusive, but a brain-computer interface approach can yield new insight. We presented monkeys with novel BCI mappings that we knew would be difficult for them to learn how to control. Over several days, we observed the emergence of new patterns of neural activity that endowed the animals with the ability to perform better at the BCI task. We speculate that there also exists a direct relationship between new patterns of neural activity and new abilities during natural movements, but it is much harder to see in that setting.

Brain-computer interfaces (BCIs) have afforded paralysed users “mental control” of computer cursors and robots, and even of electrical stimulators that reanimate their own limbs. Most existing BCIs map the activity of hundreds of motor cortical neurons recorded with implanted electrodes into control signals to drive these devices. Despite these impressive advances, the field is facing a number of challenges that need to be overcome in order for BCIs to become widely used during daily living. In this talk, I will focus on two such challenges: 1) having BCIs that allow performing a broad range of actions; and 2) having BCIs whose performance is robust over long time periods. I will present recent studies from our group in which we apply neuroscientific findings to address both issues. This research is based on an emerging view about how the brain works. Our proposal is that brain function is not based on the independent modulation of the activity of single neurons, but rather on specific population-wide activity patters —which mathematically define a “neural manifold”. I will provide evidence in favour of such a neural manifold view of brain function, and illustrate how advances in systems neuroscience may be critical for the clinical success of BCIs.

Hydra is a fascinating model organism for neuroscience. It is transparent; new genetic lines allow one to image activity in both neurons (Dupre and Yuste, 2017) and muscle cells (Szymanski and Yuste, 2019) ; it exhibits rich behavior, and it continually rebuilds itself. Hydra’s fairly simply physical structure as a two-layered fluid-filled hydrostat and the accessibility of information about neural and muscle activity opens the possibility of a complete model of neural control of behavior. This requires understanding the transformations that occur in the muscle cell layers and a biomechanical model of the body column. We show that we can use this modeling to reverse engineer how neural activity drives behavior.

Neuroscience is witnessing extraordinary progress in experimental techniques, especially at the neural circuit level. These advances are largely aimed at enabling us to understand precisely how neural circuit computations mechanistically cause behavior. Establishing this type of causal understanding will require multiple perturbational (e.g optogenetic) experiments. It has been unclear exactly how many such experiments are needed and how this number scales with the size of the nervous system in question. Here, using techniques from Theoretical Computer Science, we prove that establishing the most extensive notions of understanding need exponentially-many experiments in the number of neurons, in many cases, unless a widely-posited hypothesis about computation is false (i.e. unless P = NP). Furthermore, using data and estimates, we demonstrate that the feasible experimental regime is typically one where the number of experiments performable scales sub-linearly in the number of neurons in the nervous system. This remarkable gulf between the worst-case and the feasible suggests an algorithmic barrier to such an understanding. Determining which notions of understanding are algorithmically tractable to establish in what contexts, thus, becomes an important new direction for investigation. TL; DR: Non-existence of tractable algorithms for neural circuit interrogation could pose a barrier to comprehensively understanding how neural circuits cause behavior. Preprint: https://biorxiv.org/content/10.1101/639724v1/…

Animals are able to perceive self-motion and navigate in their environment using optic flow information. They often perform visually guided stabilization behaviors like the optokinetic (OKR) or optomotor response (OMR) in order to maintain their eye and body position relative to the moving surround. But how does the animal manage to perform appropriate behavioral response and how are processing tasks divided between the various non-cortical visual brain areas? Experiments have shown that the zebrafish pretectum, which is homologous to the mammalian accessory optic system, is involved in the OKR and OMR. The optic tectum (superior colliculus in mammals) is involved in processing of small stimuli, e.g. during prey capture. We have previously shown that many pretectal neurons respond selectively to rotational or translational motion. These neurons are likely detectors for specific optic flow patterns and mediate behavioral choices of the animal based on optic flow information. We investigate the motion feature extraction of brain structures that receive input from retinal ganglion cells to identify the visual computations that underlie behavioral decisions during prey capture, OKR, OMR and other visually mediate behaviors. Our study of receptive fields shows that receptive field sizes in pretectum (large) and tectum (small) are very different and that pretectal responses are diverse and anatomically organized. Since calcium indicators are slow and receptive fields for motion stimuli are difficult to measure, we also develop novel stimuli and statistical methods to infer the neuronal computations of visual brain areas.

Both computational and experimental results in single neurons and small networks demonstrate that very similar network function can result from quite disparate sets of neuronal and network parameters. Using the crustacean stomatogastric nervous system, we study the influence of these differences in underlying structure on differential resilience of individuals to a variety of environmental perturbations, including changes in temperature, pH, potassium concentration and neuromodulation. We show that neurons with many different kinds of ion channels can smoothly move through different mechanisms in generating their activity patterns, thus extending their dynamic range. The talk will be simultaneously translated to spanish by the interpreter Liliana Viera, MSc. Los resultados tanto computacionales como experimentales en neuronas individuales y redes pequeñas demuestran que funcionamientos de redes muy similares pueden pueden resultar de conjuntos bastante dispares de parámetros neuronales y de las redes. Utilizando el sistema nervioso estomatogástrico de los crustáceos, estudiamos la influencia de estas diferencias en la estructura subyacente en la resistencia diferencial de los individuos a una variedad de perturbaciones ambientales, incluidos los cambios de temperatura, pH, concentración de potasio y neuromodulación. Mostramos que neuronas con muchos tipos diferentes de canales iónicos pueden moverse suavemente a través de diferentes mecanismos para generar sus patrones de actividad, extendiendo así su rango dinámico. La conferencia será traducida simultáneamente al español por la intérprete Liliana Viera MSc.

Inhibitory interneurons come in different classes and form intricate circuits. While our knowledge of these circuits has advanced substantially over the last decades, it is not fully understood how the structure of these circuits relates to their function. I will present some of our recent attempts to “understand” the structure of interneuron circuits by means of computational modeling. Surprisingly (at least for us), we found that prominent features of inhibitory circuitry can be accounted for by an optimisation for excitation-inhibition (E/I) balance. In particular, we find that such an optimisation generates networks that resemble mouse V1 in terms of the structure of synaptic efficacies between principal cells and parvalbumin-positive interneurons. Moreover, an optimisation for E/I balance across neuronal compartments promotes a functional diversification of interneurons into two classes that resemble parvalbumin and somatostatin-positive interneurons. Time permitting, I may briefly touch on recent work in which we link E/I balance to prediction error coding in V1.

Many networks in the brain are sparsely connected, and the brain eliminates synapses during development and learning. How could the brain decide which synapses to prune? In a recurrent network, determining the importance of a synapse between two neurons is a difficult computational problem, depending on the role that both neurons play and on all possible pathways of information flow between them. Noise is ubiquitous in neural systems, and often considered an irritant to be overcome. In the first part of this talk, I will suggest that noise could play a functional role in synaptic pruning, allowing the brain to probe network structure and determine which synapses are redundant. I will introduce a simple, local, unsupervised plasticity rule that either strengthens or prunes synapses using only synaptic weight and the noise-driven covariance of the neighboring neurons. For a subset of linear and rectified-linear networks, this rule provably preserves the spectrum of the original matrix and hence preserves network dynamics even when the fraction of pruned synapses asymptotically approaches 1. The plasticity rule is biologically-plausible and may suggest a new role for noise in neural computation. Time permitting, I will then turn to the problem of extracting structure from neural population data sets using dimensionality reduction methods. I will argue that nonlinear structures naturally arise in neural data and show how these nonlinearities cause linear methods of dimensionality reduction, such as Principal Components Analysis, to fail dramatically in identifying low-dimensional structure.

Paramecium is a unicellular organism that swims in fresh water using cilia. When it is stimulated (mechanically, chemically, optically, thermally, etc), it often swims backward then turns and swims forward again: this is called the avoiding reaction. This reaction is triggered by a calcium-based action potential. For this reason, it enjoyed a period of glory in the 1970s as a model organism for neuroscience. I will describe the behavior and electrophysiology of this “swimming neuron”, then I will present our ongoing attempts at developing an integrative quantitative model of Paramecium.

Synaptic inputs on cortical dendrites are organized with remarkable subcellular precision at the micron level. This organization emerges during early postnatal development through patterned spontaneous activity and manifests both locally where synapses with similar functional properties are clustered, and globally along the axis from dendrite to soma. Recent experiments reveal species-specific differences in the local and global synaptic organization in mouse, ferret and macaque visual cortex. I will present a computational framework that implements functional and structural plasticity from spontaneous activity patterns to generate these different types of organization across species and scales. Within this framework, a single anatomical factor - the size of the visual cortex and the resulting magnification of visual space - can explain the observed differences. This allows us to make predictions about the organization of synapses also in other species and indicates that the proximal-distal axis of a dendrite might be central in endowing a neuron with powerful computational capabilities.

Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) for processing sequential data, and also in neuroscience, to understand the emergent properties of networks of real neurons. Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions. However, real neurons can have gating i.e. multiplicative interactions, and gating is also a central feature of the best performing RNNs in machine learning. Here, we develop a dynamical mean-field theory (DMFT) to study the consequences of gating in RNNs. We use random matrix theory to show how gating robustly produces marginal stability and line attractors – important mechanisms for biologically-relevant computations requiring long memory. The long-time behavior of the gated network is studied using its Lyapunov spectrum, and the DMFT is used to provide a novel analytical expression for the maximum Lyapunov exponent demonstrating its close relation to relaxation-time of the dynamics. Gating is also shown to give rise to a novel, discontinuous transition to chaos, where the proliferation of critical points (topological complexity) is decoupled from the appearance of chaotic dynamics (dynamical complexity), contrary to a seminal result for additive RNNs. Critical surfaces and regions of marginal stability in the parameter space are indicated in phase diagrams, thus providing a map for principled parameter choices for ML practitioners. Finally, we develop a field-theory for gradients that arise in training, by incorporating the adjoint sensitivity framework from control theory in the DMFT. This paves the way for the use of powerful field-theoretic techniques to study training/gradients in large RNNs.

Deep learning is a prime example of how brain-inspired computing can benefit development of artificial intelligence. But what else can we learn from the brain for bringing AI and robotics to the next level? Energy efficiency and data efficiency are the major features of the brain and human cognition that today’s deep learning has yet to deliver. The brain can be seen as a multi-agent system of heterogeneous learners using different representations and algorithms. The flexible use of reactive, model-free control and model-based “mental simulation” appears to be the basis for computational and data efficiency of the brain. How the brain efficiently acquires and flexibly combines prediction and control modules is a major open problem in neuroscience and its solution should help developments of more flexible and autonomous AI and robotics.

Spontaneous firing, observed in many neurons, is often attributed to ion channel or network level noise. Cortical cells during slow wave sleep exhibit transitions between so called Up and Down states. In this sleep state, with limited sensory stimuli, neurons fire in the Up state. Spontaneous firing is also observed in slices of cholinergic interneurons, cerebellar Purkinje cells and even brainstem inspiratory neurons. In such in vitro preparations, where the functional relevance is long lost, neurons continue to display a rich repertoire of firing properties. It is perplexing that these neurons, instead of saving their energy during information downtime and functional irrelevance, are eager to fire. We propose that spontaneous firing is not a chance event but instead, a vital activity for the well-being of a neuron. We postulate that neurons, in anticipation of synaptic inputs, keep their ATP levels at maximum. As recovery from inputs requires most of the energy resources, neurons are ATP surplus and ADP scarce during synaptic quiescence. With ADP as the rate-limiting step, ATP production stalls in the mitochondria when ADP is low. This leads to toxic Reactive Oxygen Species (ROS) formation, which are known to disrupt many cellular processes. We hypothesize that spontaneous firing occurs at these conditions - as a release valve to spend energy and to restore ATP production, shielding the neuron against ROS. By linking a mitochondrial metabolism model to a conductance-based neuron model, we show that spontaneous firing depends on baseline ATP usage and on ATP-cost-per-spike. From our model, emerges a mitochondrial mediated homeostatic mechanism that provides a recipe for different firing patterns. Our findings, though mostly affecting intracellular dynamics, may have large knock-on effects on the nature of neural coding. Hitherto it has been thought that the neural code is optimised for energy minimisation, but this may be true only when neurons do not experience synaptic quiescence.

Engineered pattern-recognition systems strive for short time-to-solution and low energy-to-solution characteristics. This represents one of the main driving forces behind the development of neuromorphic devices. For both them and their biological archetypes, this corresponds to using as few spikes as early as possible. The concept of few and early spikes is used as the founding principle in the time-to-first-spike coding scheme. Within this framework, we have developed a spike-timing-based learning algorithm, which we used to train neuronal networks on the mixed-signal neuromorphic platform BrainScaleS-2. We derive, from first principles, error-backpropagation-based learning in networks of leaky integrate-and-fire (LIF) neurons relying only on spike times, for specific configurations of neuronal and synaptic time constants. We explicitly examine applicability to neuromorphic substrates by studying the effects of reduced weight precision and range, as well as of parameter noise. We demonstrate the feasibility of our approach on continuous and discrete data spaces, both in software simulations and on BrainScaleS-2. This narrows the gap between previous models of first-spike-time learning and biological neuronal dynamics and paves the way for fast and energy-efficient neuromorphic applications.

Synaptic plasticity is believed to be a key physiological mechanism for learning. It is well-established that it depends on pre and postsynaptic activity. However, models that rely solely on pre and postsynaptic activity for synaptic changes have, to date, not been able to account for learning complex tasks that demand hierarchical networks. Here, we show that if synaptic plasticity is regulated by high-frequency bursts of spikes, then neurons higher in the hierarchy can coordinate the plasticity of lower-level connections. Using simulations and mathematical analyses, we demonstrate that, when paired with short-term synaptic dynamics, regenerative activity in the apical dendrites, and synaptic plasticity in feedback pathways, a burst-dependent learning rule can solve challenging tasks that require deep network architectures. Our results demonstrate that well-known properties of dendrites, synapses, and synaptic plasticity are sufficient to enable sophisticated learning in hierarchical circuits.

Back-propagation is a powerful supervised learning algorithm in artificial neural networks, because it solves the credit assignment problem (essentially: what should the hidden layers do?). This algorithm has led to the deep learning revolution. But unfortunately, back-propagation cannot be used directly in spiking neural networks (SNN). Indeed, it requires differentiable activation functions, whereas spikes are all-or-none events which cause discontinuities. Here we present two strategies to overcome this problem. The first one is to use a so-called 'surrogate gradient', that is to approximate the derivative of the threshold function with the derivative of a sigmoid. We will present some applications of this method for time series processing (audio, internet traffic, EEG). The second one concerns a specific class of SNNs, which process static inputs using latency coding with at most one spike per neuron. Using approximations, we derived a latency-based back-propagation rule for this sort of networks, called S4NN, and applied it to image classification.