Every movement we make requires us to precisely coordinate muscle activity across our body in space and time. In this talk I will describe our efforts to understand how the brain generates flexible, coordinated movement. We have taken a behavior-centric approach to this problem, starting with the development of quantitative frameworks for mouse locomotion (LocoMouse; Machado et al., eLife 2015, 2020) and locomotor learning, in which mice adapt their locomotor symmetry in response to environmental perturbations (Darmohray et al., Neuron 2019). Combined with genetic circuit dissection, these studies reveal specific, cerebellum-dependent features of these complex, whole-body behaviors. This provides a key entry point for understanding how neural computations within the highly stereotyped cerebellar circuit support the precise coordination of muscle activity in space and time. Finally, I will present recent unpublished data that provide surprising insights into how cerebellar circuits flexibly coordinate whole-body movements in dynamic environments.

The emergent dynamics exhibited by collections of living organisms often shows signatures of symmetries that are broken at the single-organism level. At the same time, organism development itself encompasses a well-coordinated sequence of symmetry breaking events that successively transform a single, nearly isotropic cell into an animal with well-defined body axis and various anatomical asymmetries. Combining these key aspects of collective phenomena and embryonic development, we describe here the spontaneous formation of hydrodynamically stabilized active crystals made of hundreds of starfish embryos that gather during early development near fluid surfaces. We describe a minimal hydrodynamic theory that is fully parameterized by experimental measurements of microscopic interactions among embryos. Using this theory, we can quantitatively describe the stability, formation and rotation of crystals and rationalize the emergence of mechanical properties that carry signatures of an odd elastic material. Our work thereby quantitatively connects developmental symmetry breaking events on the single-embryo level with remarkable macroscopic material properties of a novel living chiral crystal system.

Neuronal network computation and computation by avalanche supporting networks are of interest to the fields of physics, computer science (computation theory as well as statistical or machine learning) and neuroscience. Here we show that computation of complex Boolean functions arises spontaneously in threshold networks as a function of connectivity and antagonism (inhibition), computed by logic automata (motifs) in the form of computational cascades. We explain the emergent inverse relationship between the computational complexity of the motifs and their rank-ordering by function probabilities due to motifs, and its relationship to symmetry in function space. We also show that the optimal fraction of inhibition observed here supports results in computational neuroscience, relating to optimal information processing.

While most experimental tasks aim at isolating simple cognitive processes to study their neural bases, naturalistic behaviour is often complex and multidimensional. I will present two studies revealing previously uncharacterised neural circuits for decision-making in macaques. This was possible thanks to innovative experimental tasks eliciting sophisticated behaviour, bridging the human and non-human primate research traditions. Firstly, I will describe a specialised medial frontal circuit for novel choice in macaques. Traditionally, monkeys receive extensive training before neural data can be acquired, while a hallmark of human cognition is the ability to act in novel situations. I will show how this medial frontal circuit can combine the values of multiple attributes for each available novel item on-the-fly to enable efficient novel choices. This integration process is associated with a hexagonal symmetry pattern in the BOLD response, consistent with a grid-like representation of the space of all available options. We prove the causal role played by this circuit by showing that focussed transcranial ultrasound neuromodulation impairs optimal choice based on attribute integration and forces the subjects to default to a simpler heuristic decision strategy. Secondly, I will present an ongoing project addressing the neural mechanisms driving behaviour shifts during an evidence accumulation task that requires subjects to trade speed for accuracy. While perceptual decision-making in general has been thoroughly studied, both cognitively and neurally, the reasons why speed and/or accuracy are adjusted, and the associated neural mechanisms, have received little attention. We describe two orthogonal dimensions in which behaviour can vary (traditional speed-accuracy trade-off and efficiency) and we uncover independent neural circuits concerned with changes in strategy and fluctuations in the engagement level. The former involves the frontopolar cortex, while the latter is associated with the insula and a network of subcortical structures including the habenula.

Spike Timing Dependent Plasticity (STDP) is argued to modulate synaptic strength depending on the timing of pre- and postsynaptic spikes. Physiological experiments identified a variety of temporal kernels: Hebbian, anti-Hebbian and symmetrical LTP/LTD. In this work we present a novel plasticity model, the Voltage-Dependent Pathway Model (VDP), which is able to replicate those distinct kernel types and intermediate versions with varying LTP/LTD ratios and symmetry features. In addition, unlike previous models it retains these characteristics for different neuron models, which allows for comparison of plasticity in different neuron types. The plastic updates depend on the relative strength and activation of separately modeled LTP and LTD pathways, which are modulated by glutamate release and postsynaptic voltage. We used the 15 neuron type parametrizations in the GLIF5 model presented by Teeter et al. (2018) in combination with the VDP to simulate a range of standard plasticity protocols including standard STDP experiments, frequency dependency experiments and low frequency stimulation protocols. Slight variation in kernel stability and frequency effects can be identified between the neuron types, suggesting that the neuron type may have an effect on the effective learning rule. This plasticity model builds a middle ground between biophysical and phenomenological models allowing not just for the combination with more complex and biophysical neuron models, but is also computationally efficient so can be used in network simulations. Therefore it offers the possibility to explore the functional role of the different kernel types and electrophysiological differences in heterogeneous networks in future work.

Neuroscientists have many questions about connectomes that revolve around the ability to compare networks. For example, comparing connectomes could help explain how neural wiring is related to individual differences, genetics, disease, development, or learning. One such question is that of bilateral symmetry: are the left and right sides of a connectome the same? Here, we investigate the bilateral symmetry of a recently presented connectome of an insect brain, the Drosophila larva. We approach this question from the perspective of two-sample testing for networks. First, we show how this question of “sameness” can be framed as a variety of different statistical hypotheses, each with different assumptions. Then, we describe test procedures for each of these hypotheses. We show how these different test procedures perform on both the observed connectome as well as a suite of synthetic perturbations to the connectome. We also point out that these tests require careful attention to parameter alignment and differences in network density in order to provide biologically meaningful results. Taken together, these results provide the first statistical characterization of bilateral symmetry for an entire brain at the single-neuron level, while also giving practical recommendations for future comparisons of connectome networks.

In a famous philosophical paradox, Buridan's ass perishes because he is equally hungry and thirsty, and cannot make up his mind whether to first drink or eat. We are faced daily with the need to pick between alternatives that are equally attractive (or not) to us. What are the processes that allow us to avoid paralysis and to rapidly select between such equal options when there are no preferences or rational reasons to rely on? One solution that was offered is that although on a higher cognitive level there is symmetry between the alternatives, on a neuronal level the symmetry does not maintain. What is the nature of this asymmetry of the neuronal level? In this talk I will present experiments addressing this important phenomenon using measures of human behavior, EEG, EMG and large scale neural network modeling, and discuss mechanisms involved in the process of intention formation and execution, in the face of alternatives to choose from. Specifically, I will show results revealing the temporal dynamics of rapid intention formation and, moreover, ‘change of intention’ in a free choice picking scenario, in which the alternatives are on a par for the participant. The results suggest that even in arbitrary choices, endogenous or exogenous biases that are present in the neural system for selecting one or another option may be implicitly overruled; thus creating an implicit and non-conscious ‘change of mind’. Finally, the question is raised: in what way do such rapid implicit ‘changes of mind’ help retain one’s self-control and free-will behavior?

It is generally agreed upon that qualities of conscious experience instantiate structural properties, usually called relations. They furnish a representation of qualities (or qualia, in fact) in terms of a mathematical space Q (rather than a set), which is crucial to both modelling and measuring of conscious experience." "What is usually disregarded is that “only such structural properties generalize across individuals” (Austen Clark), but that qualities themselves as differentiated by stimulus specifications, behavior or reports do not. We show that this implies that only the part of Q which is invariant with respect to the automorphism group has a well-defined referent, while individual elements do not. This poses a prima facie limitation of any theory or experiment that aims to address individual qualities. We show how mathematical theories of consciousness can overcome this limitation via symmetry groups and group actions, making accessible to science what is properly called private language.

Cells and microorganisms produce and consume all sorts of chemicals, from nutrients to signalling molecules. The same happens at the nanoscale inside cells themselves, where enzymes catalyse the production and consumption of the chemicals needed for life. In this work, we have found a generic mechanism by which such chemically-active particles, be it cells or enzymes or engineered synthetic colloids, can "sense" each other and ultimately self- organize in a multitude of ways. A peculiarity of these chemical-mediated interactions is that they break action-reaction symmetry : for example, one particle may be repelled from a second particle, which is in turn attracted to the first one, so that it ends up "chasing" it. Such chasing interactions allow for the formation of large clusters of particles that "swim" autonomously. Regarding enzymes, we find that they can spontaneously aggregate into clusters with precisely the right composition, so that the product of one enzyme is passed on, without lack or excess, to the next enzyme in the metabolic cascade.

'Shape' of microorganisms are diverse. However, we sometimes approximate them as a sphere or a spheroid when we mathematically model the hydrodynamics of motile and non-motile cells. Such a geometrical simplification can be theoretically validated for motions in a linear background flow, since the dynamics, known as the Jeffery orbit, only contain a single geometric parameter, called the Bretherton constant. In this talk, we generalise the Jeffery equations for a chiral axisymmetric object using the low-Reynolds-number hydrokinetic symmetry and then demonstrate that the dynamics of a certain type of chiral object in a fluid flow are characterised by a new chiral parameter in addition to the Bretherton constant. We also discuss how the generalised Jeffery orbits are applied to biased locomotion of bacteria in a bulk shear flow and we will share the idea of hydrodynamic `shape' of microorganisms to simplify the description of their dynamics.

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.

Figure-ground organisation and perceptual grouping are classic topics in Gestalt and perceptual psychology. They often appear alongside one another in introductory textbook chapters on perception and have a long history of investigation. However, they are typically discussed as separate processes of perceptual organisation with their own distinct phenomena and mechanisms. Here, I will propose that perceptual grouping and figure-ground organisation are strongly linked. In particular, perceptual grouping can provide a basis for, and may share mechanisms with, a wide range of figure-ground principles. To support this claim, I will describe a new class of figure-ground principles based on perceptual grouping between edges and demonstrate that this inter-edge grouping (IEG) is a powerful influence on figure-ground organisation. I will also draw support from our other results showing that grouping between edges and regions (i.e., edge-region grouping) can affect figure-ground organisation (Palmer & Brooks, 2008) and that contextual influences in figure-ground organisation can be gated by perceptual grouping between edges (Brooks & Driver, 2010). In addition to these modern observations, I will also argue that we can describe some classic figure-ground principles (e.g., symmetry, convexity, etc.) using perceptual grouping mechanisms. These results suggest that figure-ground organisation and perceptual grouping have more than a mere association under the umbrella topics of Gestalt psychology and perceptual organisation. Instead, perceptual grouping may provide a mechanism underlying a broad class of new and extant figure-ground principles.

Diversity in the natural world emerges from the collective behavior of large numbers of interacting objects. Statistical physics provides the framework relating microscopic to macroscopic properties. A fundamental assumption underlying this approach is that we have complete knowledge of the interactions between the microscopic entities. But what if that, even though possible in principle becomes impossible in practice ? Can we still construct a framework for describing their collective behavior ? Dense suspensions and granular materials are two often quoted examples where we face this challenge. These are systems where because of the complicated surface properties of particles there is extreme sensitivity of the interactions to particle positions. In this talk, I will present a perspective based on notions of constraint satisfaction that provides a way forward. I will focus on our recent work on the emergence of elasticity in the absence of any broken symmetry, and sketch out other problems that can be addressed using this perspective.

Ants, bees and other insects have the ability to return to their nest or hive using a navigation strategy known as path integration. Similarly, fruit flies employ path integration to return to a previously visited food source. An important component of path integration is the ability of the insect to keep track of its heading relative to salient visual cues. A highly conserved brain region known as the central complex has been identified as being of key importance for the computations required for an insect to keep track of its heading. However, the similarities or differences of the underlying heading tracking circuit between species are not well understood. We sought to address this shortcoming by using reverse engineering techniques to derive the effective underlying neural circuits of two evolutionary distant species, the fruit fly and the locust. Our analysis revealed that regardless of the anatomical differences between the two species the essential circuit structure has not changed. Both effective neural circuits have the structural topology of a ring attractor with an eight-fold radial symmetry (Fig. 1). However, despite the strong similarities between the two ring attractors, there remain differences. Using computational modelling we found that two apparently small anatomical differences have significant functional effect on the ability of the two circuits to track fast rotational movements and to maintain a stable heading signal. In particular, the fruit fly circuit responds faster to abrupt heading changes of the animal while the locust circuit maintains a heading signal that is more robust to inhomogeneities in cell membrane properties and synaptic weights. We suggest that the effects of these differences are consistent with the behavioural ecology of the two species. On the one hand, the faster response of the ring attractor circuit in the fruit fly accommodates the fast body saccades that fruit flies are known to perform. On the other hand, the locust is a migratory species, so its behaviour demands maintenance of a defined heading for a long period of time. Our results highlight that even seemingly small differences in the distribution of dendritic fibres can have a significant effect on the dynamics of the effective ring attractor circuit with consequences for the behavioural capabilities of each species. These differences, emerging from morphologically distinct single neurons highlight the importance of a comparative approach to neuroscience.

Many innate behaviours are the result of multiple sensorimotor programs that are dynamically coordinated to produce higher-order behaviours such as courtship or architecture construction. Extendend phenotypes such as architecture are especially useful for ethological study because the structure itself is a physical record of behavioural intent. A particularly elegant and easily quantifiable structure is the spider orb-web. The geometric symmetry and regularity of these webs have long generated interest in their behavioural origin. However, quantitative analyses of this behaviour have been sparse due to the difficulty of recording web-making in real-time. To address this, we have developed a novel assay enabling real-time, high-resolution tracking of limb movements and web structure produced by the hackled orb-weaver Uloborus diversus. With its small brain size of approximately 100,000 neurons, the spider U. diversus offers a tractable model organism for the study of complex behaviours. Using deep learning frameworks for limb tracking, and unsupervised behavioural clustering methods, we have developed an atlas of stereotyped movement motifs and are investigating the behavioural state transitions of which the geometry of the web is an emergent property. In addition to tracking limb movements, we have developed algorithms to track the web’s dynamic graph structure. We aim to model the relationship between the spider’s sensory experience on the web and its motor decisions, thereby identifying the sensory and internal states contributing to this sensorimotor transformation. Parallel efforts in our group are establishing 2-photon in vivo calcium imaging protocols in this spider, eventually facilitating a search for neural correlates underlying the internal and sensory state variables identified by our behavioural models. In addition, we have assembled a genome, and are developing genetic perturbation methods to investigate the genetic underpinnings of orb-weaving behaviour. Together, we aim to understand how complex innate behaviours are coordinated by underlying neuronal and genetic mechanisms.

Understanding how neural circuits in the brain compute information not only requires determining how individual inhibitory and excitatory elements of circuits are wired together, but also a detailed knowledge of their functional interactions. Recent advances in optogenetic techniques and mouse genetics now offer ways to specifically probe the functional properties of neural circuits with unprecedented specificity. Perhaps one of the most heavily interrogated circuits in the mouse brain is one in the retina that is involved in coding direction (reviewed by Mauss et al., 2017; Vaney et al., 2012). In this circuit, direction is encoded by specialized direction-selective (DS) ganglion cells (DSGCs), which respond robustly to objects moving in a ‘preferred’ direction but not in the opposite or ‘null’ direction (Barlow and Levick, 1965). We now know this computation relies on the coordination of three transmitter systems: glutamate, GABA and acetylcholine (ACh). In this talk, I will discuss the synaptic mechanisms that produce the spatiotemporal patterns of inhibition and excitation that are crucial for shaping directional selectivity. Special emphasis will be placed on the role of ACh, as it is unclear whether it is mediated by synaptic or non-synaptic mechanisms, which is in fact a central issue in the CNS. Barlow, H.B., and Levick, W.R. (1965). The mechanism of directionally selective units in rabbit's retina. J Physiol 178, 477-504. Mauss, A.S., Vlasits, A., Borst, A., and Feller, M. (2017). Visual Circuits for Direction Selectivity. Annu Rev Neurosci 40, 211-230. Vaney, D.I., Sivyer, B., and Taylor, W.R. (2012). Direction selectivity in the retina: symmetry and asymmetry in structure and function. Nat Rev Neurosci 13, 194-208