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.

Evolution perfected brain design by maximizing its functionality while minimizing costs associated with building and maintaining it. Assumption that brain functionality is specified by neuronal connectivity, implemented by costly biological wiring, leads to the following optimal design problem. For a given neuronal connectivity, find a spatial layout of neurons that minimizes the wiring cost. Unfortunately, this problem is difficult to solve because the number of possible layouts is often astronomically large. We argue that the wiring cost may scale as wire length squared, reducing the optimal layout problem to a constrained minimization of a quadratic form. For biologically plausible constraints, this problem has exact analytical solutions, which give reasonable approximations to actual layouts in the brain. These solutions make the inverse problem of inferring neuronal connectivity from neuronal layout more tractable.

During embryogenesis, limb-innervating lateral motor column (LMC) spinal motor neurons (MN) are generated in excess and subsequently nearly half of them die. Many motor neuron survival factors (MnSFs) have been shown to suppress this default programmed cell death (PCD) program through their receptors (MnSFRs), raising the possibility that they are involved in matching specific MNs with their target muscles. Published observations suggest a combinatorial model of MnSF/Rs function, which assumes that during the PCD phase, MNs are expressing combinations of MnSFRs, whereas the limb muscles innervated by these MNs express cognate combinations of MnSFs. We tested this model by expression profiling of MnSFs and their receptors in the avian lumbosacral spinal cord and limb muscles during the peak PCD period. Our findings highlight the complexity of MnSF/Rs function in the control of LMC motor neuron survival.

Two-photon probe excitation data are commonly presented as absorption cross section or molecular brightness (the detected fluorescence rate per molecule). We report two-photon molecular brightness spectra for a diverse set of organic and genetically encoded probes with an automated spectroscopic system based on fluorescence correlation spectroscopy. The two-photon action cross section can be extracted from molecular brightness measurements at low excitation intensities, while peak molecular brightness (the maximum molecular brightness with increasing excitation intensity) is measured at higher intensities at which probe photophysical effects become significant. The spectral shape of these two parameters was similar across all dye families tested. Peak molecular brightness spectra, which can be obtained rapidly and with reduced experimental complexity, can thus serve as a first-order approximation to cross-section spectra in determining optimal wavelengths for two-photon excitation, while providing additional information pertaining to probe photostability. The data shown should assist in probe choice and experimental design for multiphoton microscopy studies. Further, we show that, by the addition of a passive pulse splitter, nonlinear bleaching can be reduced-resulting in an enhancement of the fluorescence signal in fluorescence correlation spectroscopy by a factor of two. This increase in fluorescence signal, together with the observed resemblance of action cross section and peak brightness spectra, suggests higher-order photobleaching pathways for two-photon excitation.

Direction selectivity represents a fundamental visual computation. In mammalian retina, On-Off direction-selective ganglion cells (DSGCs) respond strongly to motion in a preferred direction and weakly to motion in the opposite, null direction. Electrical recordings suggested three direction-selective (DS) synaptic mechanisms: DS GABA release during null-direction motion from starburst amacrine cells (SACs) and DS acetylcholine and glutamate release during preferred direction motion from SACs and bipolar cells. However, evidence for DS acetylcholine and glutamate release has been inconsistent and at least one bipolar cell type that contacts another DSGC (On-type) lacks DS release. Here, whole-cell recordings in mouse retina showed that cholinergic input to On-Off DSGCs lacked DS, whereas the remaining (glutamatergic) input showed apparent DS. Fluorescence measurements with the glutamate biosensor intensity-based glutamate-sensing fluorescent reporter (iGluSnFR) conditionally expressed in On-Off DSGCs showed that glutamate release in both On- and Off-layer dendrites lacked DS, whereas simultaneously recorded excitatory currents showed apparent DS. With GABA-A receptors blocked, both iGluSnFR signals and excitatory currents lacked DS. Our measurements rule out DS release from bipolar cells onto On-Off DSGCs and support a theoretical model suggesting that apparent DS excitation in voltage-clamp recordings results from inadequate voltage control of DSGC dendrites during null-direction inhibition. SAC GABA release is the apparent sole source of DS input onto On-Off DSGCs.

Mitotic and cytokinetic processes harness cell machinery to drive chromosomal segregation and the physical separation of dividing cells. Here, we investigate the functional requirements for exocyst complex function during cell division in vivo, and demonstrate a common mechanism that directs anaphase cell elongation and cleavage furrow progression during cell division. We show that onion rings (onr) and funnel cakes (fun) encode the Drosophila homologs of the Exo84 and Sec8 exocyst subunits, respectively. In onr and fun mutant cells, contractile ring proteins are recruited to the equatorial region of dividing spermatocytes. However, cytokinesis is disrupted early in furrow ingression, leading to cytokinesis failure. We use high temporal and spatial resolution confocal imaging with automated computational analysis to quantitatively compare wild-type versus onr and fun mutant cells. These results demonstrate that anaphase cell elongation is grossly disrupted in cells that are compromised in exocyst complex function. Additionally, we observe that the increase in cell surface area in wild type peaks a few minutes into cytokinesis, and that onr and fun mutant cells have a greatly reduced rate of surface area growth specifically during cell division. Analysis by transmission electron microscopy reveals a massive build-up of cytoplasmic astral membrane and loss of normal Golgi architecture in onr and fun spermatocytes, suggesting that exocyst complex is required for proper vesicular trafficking through these compartments. Moreover, recruitment of the small GTPase Rab11 and the PITP Giotto to the cleavage site depends on wild-type function of the exocyst subunits Exo84 and Sec8. Finally, we show that the exocyst subunit Sec5 coimmunoprecipitates with Rab11. Our results are consistent with the exocyst complex mediating an essential, coordinated increase in cell surface area that potentiates anaphase cell elongation and cleavage furrow ingression.

Targeted manipulation of activity in specific populations of neurons is important for investigating the neural circuit basis of behavior. Optogenetic approaches using light-sensitive microbial rhodopsins have permitted manipulations to reach a level of temporal precision that is enabling functional circuit dissection. As demand for more precise perturbations to serve specific experimental goals increases, a palette of opsins with diverse selectivity, kinetics, and spectral properties will be needed. Here, we introduce a novel approach of "topological engineering"-inversion of opsins in the plasma membrane-and demonstrate that it can produce variants with unique functional properties of interest for circuit neuroscience. In one striking example, inversion of a Channelrhodopsin variant converted it from a potent activator into a fast-acting inhibitor that operates as a cation pump. Our findings argue that membrane topology provides a useful orthogonal dimension of protein engineering that immediately permits as much as a doubling of the available toolkit.

In optical microscopy, fine structural details are resolved by using refraction to magnify images of a specimen. We discovered that by synthesizing a swellable polymer network within a specimen, it can be physically expanded, resulting in physical magnification. By covalently anchoring specific labels located within the specimen directly to the polymer network, labels spaced closer than the optical diffraction limit can be isotropically separated and optically resolved, a process we call expansion microscopy (ExM). Thus, this process can be used to perform scalable superresolution microscopy with diffraction-limited microscopes. We demonstrate ExM with apparent ~70-nanometer lateral resolution in both cultured cells and brain tissue, performing three-color superresolution imaging of ~107 cubic micrometers of the mouse hippocampus with a conventional confocal microscope.

Expansion microscopy (ExM) is a recently developed technique that enables nanoscale-resolution imaging of preserved cells and tissues on conventional diffraction-limited microscopes via isotropic physical expansion of the specimens before imaging. In ExM, biomolecules and/or fluorescent labels in the specimen are linked to a dense, expandable polymer matrix synthesized evenly throughout the specimen, which undergoes 3-dimensional expansion by ∼4.5 fold linearly when immersed in water. Since our first report, versions of ExM optimized for visualization of proteins, RNA, and other biomolecules have emerged. Here we describe best-practice, step-by-step ExM protocols for performing analysis of proteins (protein retention ExM, or proExM) as well as RNAs (expansion fluorescence in situ hybridization, or ExFISH), using chemicals and hardware found in a typical biology lab. Furthermore, a detailed protocol for handling and mounting expanded samples and for imaging them with confocal and light-sheet microscopes is provided. © 2018 by John Wiley & Sons, Inc.

Expansion microscopy (ExM) is a physical form of magnification that increases the effective resolving power of any microscope. Here, we describe the fundamental principles of ExM, as well as how recently developed ExM variants build upon and apply those principles. We examine applications of ExM in cell and developmental biology for the study of nanoscale structures as well as ExM's potential for scalable mapping of nanoscale structures across large sample volumes. Finally, we explore how the unique anchoring and hydrogel embedding properties enable postexpansion molecular interrogation in a purified chemical environment. ExM promises to play an important role complementary to emerging live-cell imaging techniques, because of its relative ease of adoption and modification and its compatibility with tissue specimens up to at least 200 μm thick. Expected final online publication date for the , Volume 35 is October 7, 2019. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.