Learning in deep neural networks is known to depend critically on the knowledge embedded in the initial network weights. However, few theoretical results have precisely linked prior knowledge to learning dynamics. Here we derive exact solutions to the dynamics of learning with rich prior knowledge in deep linear networks by generalising Fukumizu's matrix Riccati solution \citep{fukumizu1998effect}. We obtain explicit expressions for the evolving network function, hidden representational similarity, and neural tangent kernel over training for a broad class of initialisations and tasks. The expressions reveal a class of task-independent initialisations that radically alter learning dynamics from slow non-linear dynamics to fast exponential trajectories while converging to a global optimum with identical representational similarity, dissociating learning trajectories from the structure of initial internal representations. We characterise how network weights dynamically align with task structure, rigorously justifying why previous solutions successfully described learning from small initial weights without incorporating their fine-scale structure. Finally, we discuss the implications of these findings for continual learning, reversal learning and learning of structured knowledge. Taken together, our results provide a mathematical toolkit for understanding the impact of prior knowledge on deep learning.

Many animals rely on vision to navigate through their environment. The pattern of changes in the visual scene induced by self-motion is the optic flow1, which is first estimated in local patches by directionally selective (DS) neurons2–4. But how should the arrays of DS neurons, each responsive to motion in a preferred direction at a specific retinal position, be organized to support robust decoding of optic flow by downstream circuits? Understanding this global organization is challenging because it requires mapping fine, local features of neurons across the animal’s field of view3. In Drosophila, the asymmetric dendrites of the T4 and T5 DS neurons establish their preferred direction, making it possible to predict DS responses from anatomy4,5. Here we report that the preferred directions of fly DS neurons vary at different retinal positions and show that this spatial variation is established by the anatomy of the compound eye. To estimate the preferred directions across the visual field, we reconstructed hundreds of T4 neurons in a full brain EM volume6 and discovered unexpectedly stereotypical dendritic arborizations that are independent of location. We then used whole-head μCT scans to map the viewing directions of all compound eye facets and found a non-uniform sampling of visual space that explains the spatial variation in preferred directions. Our findings show that the organization of preferred directions in the fly is largely determined by the compound eye, exposing an intimate and unexpected connection between the peripheral structure of the eye, functional properties of neurons deep in the brain, and the control of body movements.

Internal representations are thought to support the generation of flexible, long-timescale behavioral patterns in both animals and artificial agents. Here, we present a novel conceptual framework for how Drosophila use their internal representation of head direction to maintain preferred headings in their surroundings, and how they learn to modify these preferences in the presence of selective thermal reinforcement. To develop the framework, we analyzed flies’ behavior in a classical operant visual learning paradigm and found that they use stochastically generated fixations and directed turns to express their heading preferences. Symmetries in the visual scene used in the paradigm allowed us to expose how flies’ probabilistic behavior in this setting is tethered to their head direction representation. We describe how flies’ ability to quickly adapt their behavior to the rules of their environment may rest on a behavioral policy whose parameters are flexible but whose form is genetically encoded in the structure of their circuits. Many of the mechanisms we outline may also be relevant for rapidly adaptive behavior driven by internal representations in other animals, including mammals.

Nicotinic partial agonists provide an accepted aid for smoking cessation and thus contribute to decreasing tobacco-related disease. Improved drugs constitute a continued area of study. However, there remains no reductionist method to examine the cellular and subcellular pharmacokinetic properties of these compounds in living cells. Here, we developed new intensity-based drug sensing fluorescent reporters ('iDrugSnFRs') for the nicotinic partial agonists dianicline, cytisine, and two cytisine derivatives - 10-fluorocytisine and 9-bromo-10-ethylcytisine. We report the first atomic-scale structures of liganded periplasmic binding protein-based biosensors, accelerating development of iDrugSnFRs and also explaining the activation mechanism. The nicotinic iDrugSnFRs detect their drug partners in solution, as well as at the plasma membrane (PM) and in the endoplasmic reticulum (ER) of cell lines and mouse hippocampal neurons. At the PM, the speed of solution changes limits the growth and decay rates of the fluorescence response in almost all cases. In contrast, we found that rates of membrane crossing differ among these nicotinic drugs by > 30 fold. The new nicotinic iDrugSnFRs provide insight into the real-time pharmacokinetic properties of nicotinic agonists and provide a methodology whereby iDrugSnFRs can inform both pharmaceutical neuroscience and addiction neuroscience.

Subcellular pharmacokinetic measurements have informed the study of central nervous system (CNS)-acting drug mechanisms. Recent investigations have been enhanced by the use of genetically encoded fluorescent biosensors for drugs of interest at the plasma membrane and in organelles. We describe screening and validation protocols for identifying hit pairs comprising a drug and biosensor, with each screen including 13-18 candidate biosensors and 44-84 candidate drugs. After a favorable hit pair is identified and validated via these protocols, the biosensor is then optimized, as described in other papers, for sensitivity and selectivity to the drug. We also show sample hit pair data that may lead to future intensity-based drug-sensing fluorescent reporters (iDrugSnFRs). These protocols will assist scientists to use fluorescence responses as criteria in identifying favorable fluorescent biosensor variants for CNS-acting drugs that presently have no corresponding biosensor partner. eLife (2022), DOI: 10.7554/eLife.74648 Graphical abstract.

Fluorescent indicators and actuators provide a means to optically observe and perturb dynamic events in living animals. Although chemistry and protein engineering have contributed many useful tools to observe and perturb cells, an emerging strategy is to use chemigenetics: systems in which a small molecule dye interacts with a genetically encoded protein domain. Here we review chemigenetic strategies that have been successfully employed in living animals as photosensitizers for photoablation experiments, fluorescent cell cycle indicators, and fluorescent indicators for studying dynamic biological signals. Although these strategies at times suffer from challenges, e.g. delivery of the small molecule and assembly of the chemigenetic unit in living animals, the advantages of using small molecules with high brightness, low photobleaching, no chromophore maturation time and expanded color palette, combined with the ability to genetically target them to specific cell types, make chemigenetic fluorescent actuators and indicators an attractive strategy for use in living animals.

Differentiable simulations of optical systems can be combined with deep learning-based reconstruction networks to enable high performance computational imaging via end-to-end (E2E) optimization of both the optical encoder and the deep decoder. This has enabled imaging applications such as 3D localization microscopy, depth estimation, and lensless photography via the optimization of local optical encoders. More challenging computational imaging applications, such as 3D snapshot microscopy which compresses 3D volumes into single 2D images, require a highly non-local optical encoder. We show that existing deep network decoders have a locality bias which prevents the optimization of such highly non-local optical encoders. We address this with a decoder based on a shallow neural network architecture using global kernel Fourier convolutional neural networks (FourierNets). We show that FourierNets surpass existing deep network based decoders at reconstructing photographs captured by the highly non-local DiffuserCam optical encoder. Further, we show that FourierNets enable E2E optimization of highly non-local optical encoders for 3D snapshot microscopy. By combining FourierNets with a large-scale multi-GPU differentiable optical simulation, we are able to optimize non-local optical encoders 170× to 7372× larger than prior state of the art, and demonstrate the potential for ROI-type specific optical encoding with a programmable microscope.

Circadian rhythms play an essential role in many biological processes and surprisingly only three prokaryotic proteins are required to constitute a true post-translational circadian oscillator. The evolutionary history of the three Kai proteins indicates that KaiC is the oldest member and central component of the clock, with subsequent additions of KaiB and KaiA to regulate its phosphorylation state for time synchronization. The canonical KaiABC system in cyanobacteria is well understood, but little is known about more ancient systems that possess just KaiBC, except for reports that they might exhibit a basic, hourglass-like timekeeping mechanism. Here, we investigate the primordial circadian clock in Rhodobacter sphaeroides (RS) that contains only KaiBC to elucidate its inner workings despite the missing KaiA. Using a combination X-ray crystallography and cryo-EM we find a novel dodecameric fold for KaiCRS where two hexamers are held together by a coiled-coil bundle of 12 helices. This interaction is formed by the C-terminal extension of KaiCRS and serves as an ancient regulatory moiety later superseded by KaiA. A coiled-coil register shift between daytime- and nighttime-conformations is connected to the phosphorylation sites through a long-range allosteric network that spans over 160 Å. Our kinetic data identify the difference in ATP-to-ADP ratio between day and night as the environmental cue that drives the clock and further unravels mechanistic details that shed light on the evolution of self-sustained oscillators.

Homology of highly divergent genes often cannot be determined from sequence similarity alone. For example, we recently identified in the aphid Hormaphis cornu a family of rapidly evolving bicycle genes, which encode novel proteins implicated as plant gall effectors, and sequence similarity search methods yielded few putative bicycle homologs in other species. Coding sequence-independent features of genes, such as intron-exon boundaries, often evolve more slowly than coding sequences, however, and can provide complementary evidence for homology. We found that a linear logistic regression classifier using only structural features of bicycle genes identified many putative bicycle homologs in other species. Independent evidence from sequence features and intron locations supported homology assignments. To test the potential roles of bicycle genes in other aphids, we sequenced the genome of a second gall-forming aphid, Tetraneura nigriabdominalis, and found that many bicycle genes are strongly expressed in the salivary glands of the gall forming foundress. In addition, bicycle genes are strongly overexpressed in the salivary glands of a non-gall forming aphid, Acyrthosiphon pisum, and in the non-gall forming generations of Hormaphis cornu. These observations suggest that Bicycle proteins may be used by multiple aphid species to manipulate plants in diverse ways. Incorporation of gene structural features into sequence search algorithms may aid identification of deeply divergent homologs, especially of rapidly evolving genes involved in host-parasite interactions.

Learning which stimuli (classical conditioning) or which actions (operant conditioning) predict rewards or punishments can improve chances of survival. However, the circuit mechanisms that underlie distinct types of associative learning are still not fully understood. Automated, high-throughput paradigms for studying different types of associative learning, combined with manipulation of specific neurons in freely behaving animals, can help advance this field. The Drosophila melanogaster larva is a tractable model system for studying the circuit basis of behaviour, but many forms of associative learning have not yet been demonstrated in this animal. Here, we developed a high-throughput (i. e. multi-larva) training system that combines real-time behaviour detection of freely moving larvae with targeted opto- and thermogenetic stimulation of tracked animals. Both stimuli are controlled in either open- or closed-loop, and delivered with high temporal and spatial precision. Using this tracker, we show for the first time that Drosophila larvae can perform classical conditioning with no overlap between sensory stimuli (i. e. trace conditioning). We also demonstrate that larvae are capable of operant conditioning by inducing a bend direction preference through optogenetic activation of reward-encoding serotonergic neurons. Our results extend the known associative learning capacities of Drosophila larvae. Our automated training rig will facilitate the study of many different forms of associative learning and the identification of the neural circuits that underpin them.