A method is described that yields a series of (D+1)-element wave-vector sets giving rise to (D=2 or 3)-dimensional coherent sparse lattices of any desired Bravais symmetry and primitive cell shape, but of increasing period relative to the excitation wavelength. By applying lattice symmetry operations to any of these sets, composite lattices of N>D+1 waves are constructed, having increased spatial frequency content but unchanged crystal group symmetry and periodicity. Optical lattices of widely spaced excitation maxima of diffraction-limited confinement and controllable polarization can thereby be created, possibly useful for quan- tum optics, lithography, or multifocal microscopy.

Commentary: Develops a formalism to find a set of wavevectors that create a periodic optical lattice of any desired Bravais symmetry by the mutual interference of the corresponding plane waves. Discovers two new classes of optical lattices, sparse and composite, that together permit the creation of widely spaced, tightly confined excitation maxima in 3D potentially suitable for high speed volumetric live cell imaging. The implementation of this idea was derailed by our exclusive focus on PALM at the time, and many of its goals have since been reached with our Bessel beam plane illumination microscope. Nevertheless, sparse and composite optical lattices may prove useful in atomic physics or for the fabrication of 3D nanostructures.

Mitral/tufted cells of the olfactory bulb receive odorant information from receptor neurons and transmit this information to the cortex. Studies in awake behaving animals have found that sustained responses of mitral cells to odorants are rare, suggesting sparse combinatorial representation of the odorants. Careful alignment of mitral cell firing with the phase of the respiration cycle revealed brief transient activity in the larger population of mitral cells, which respond to odorants during a small fraction of the respiration cycle. Responses of these cells are therefore temporally sparse. Here, we propose a mathematical model for the olfactory bulb network that can reproduce both combinatorially and temporally sparse mitral cell codes. We argue that sparse codes emerge as a result of the balance between mitral cells’ excitatory inputs and inhibition provided by the granule cells. Our model suggests functional significance for the dendrodendritic synapses mediating interactions between mitral and granule cells.

We propose a version of least-mean-square (LMS) algorithm for sparse system identification. Our algorithm called online linearized Bregman iteration (OLBI) is derived from minimizing the cumulative prediction error squared along with an l 1 -l 2 norm regularizer. By systematically treating the non-differentiable regularizer we arrive at a simple two-step iteration. We demonstrate that OLBI is bias free and compare its operation with existing sparse LMS algorithms by rederiving them in the online convex optimization framework. We perform convergence analysis of OLBI for white input signals and derive theoretical expressions for the steady state mean square deviations (MSD). We demonstrate numerically that OLBI improves the performance of LMS type algorithms for signals generated from sparse tap weights.

Responses of mitral cells represent the results of the first stage of odor processing in the olfactory bulb. Most of our knowledge about mitral cell activity has been obtained from recordings in anesthetized animals. We compared odor-elicited changes in firing rate of mitral cells in awake behaving mice and in anesthetized mice. We show that odor-elicited changes in mitral cell firing rate were larger and more frequently observed in the anesthetized than in the awake condition. Only 27% of mitral cells that showed a response to odors in the anesthetized state were also odor responsive in the awake state. The amplitude of their response in the awake state was smaller, and some of the responses changed sign compared with their responses in the anesthetized state. The odor representation in the olfactory bulb is therefore sparser in awake behaving mice than in anesthetized preparations. A qualitative explanation of the mechanism responsible for this phenomenon is proposed.

Electrical microstimulation can establish causal links between the activity of groups of neurons and perceptual and cognitive functions. However, the number and identities of neurons microstimulated, as well as the number of action potentials evoked, are difficult to ascertain. To address these issues we introduced the light-gated algal channel channelrhodopsin-2 (ChR2) specifically into a small fraction of layer 2/3 neurons of the mouse primary somatosensory cortex. ChR2 photostimulation in vivo reliably generated stimulus-locked action potentials at frequencies up to 50 Hz. Here we show that naive mice readily learned to detect brief trains of action potentials (five light pulses, 1 ms, 20 Hz). After training, mice could detect a photostimulus firing a single action potential in approximately 300 neurons. Even fewer neurons (approximately 60) were required for longer stimuli (five action potentials, 250 ms). Our results show that perceptual decisions and learning can be driven by extremely brief epochs of cortical activity in a sparse subset of supragranular cortical pyramidal neurons.

Sparse coding may be a general strategy of neural systems for augmenting memory capacity. In Drosophila melanogaster, sparse odor coding by the Kenyon cells of the mushroom body is thought to generate a large number of precisely addressable locations for the storage of odor-specific memories. However, it remains untested how sparse coding relates to behavioral performance. Here we demonstrate that sparseness is controlled by a negative feedback circuit between Kenyon cells and the GABAergic anterior paired lateral (APL) neuron. Systematic activation and blockade of each leg of this feedback circuit showed that Kenyon cells activated APL and APL inhibited Kenyon cells. Disrupting the Kenyon cell-APL feedback loop decreased the sparseness of Kenyon cell odor responses, increased inter-odor correlations and prevented flies from learning to discriminate similar, but not dissimilar, odors. These results suggest that feedback inhibition suppresses Kenyon cell activity to maintain sparse, decorrelated odor coding and thus the odor specificity of memories.

Lipid droplets (LDs) are neutral lipid storage organelles that transfer lipids to various organelles including peroxisomes. Here, we show that the hereditary spastic paraplegia protein M1 Spastin, a membrane-bound AAA ATPase found on LDs, coordinates fatty acid (FA) trafficking from LDs to peroxisomes through two inter-related mechanisms. First, M1 Spastin forms a tethering complex with peroxisomal ABCD1 to promote LD-peroxisome contact formation. Second, M1 Spastin recruits the membrane-shaping ESCRT-III proteins IST1 and CHMP1B to LDs via its MIT domain to facilitate LD-to-peroxisome FA trafficking, possibly through IST1 and CHMP1B modifying LD membrane morphology. Furthermore, M1 Spastin, IST1 and CHMP1B are all required to relieve LDs of lipid peroxidation. The roles of M1 Spastin in tethering LDs to peroxisomes and in recruiting ESCRT-III components to LD-peroxisome contact sites for FA trafficking may help explain the pathogenesis of diseases associated with defective FA metabolism in LDs and peroxisomes.

How RNA-binding proteins recognize specific sets of target mRNAs remains poorly understood because current approaches depend primarily on sequence information. In this study, we demonstrate that specific recognition of messenger RNAs (mRNAs) by RNA-binding proteins requires the correct spatial positioning of these sequences. We characterized both the cis-acting sequence elements and the spatial restraints that define the mode of RNA binding of the zipcode-binding protein 1 (ZBP1/IMP1/IGF2BP1) to the β-actin zipcode. The third and fourth KH (hnRNP K homology) domains of ZBP1 specifically recognize a bipartite RNA element comprised of a 5' element (CGGAC) followed by a variable 3' element (C/A-CA-C/U) that must be appropriately spaced. Remarkably, the orientation of these elements is interchangeable within target transcripts bound by ZBP1. The spatial relationship of this consensus binding site identified conserved transcripts that were verified to associate with ZBP1 in vivo. The dendritic localization of one of these transcripts, spinophilin, was found to be dependent on both ZBP1 and the RNA elements recognized by ZBP1 KH34.

Tissue and organ function has been conventionally understood in terms of the interactions among discrete and homogeneous cell types. This approach has proven difficult in neuroscience due to the marked diversity across different neuron classes, but it may be further hampered by prominent within-class variability. Here, we considered a well-defined canonical neuronal population-hippocampal CA1 pyramidal cells (CA1 PCs)-and systematically examined the extent and spatial rules of transcriptional heterogeneity. Using next-generation RNA sequencing, we identified striking variability in CA1 PCs, such that the differences within CA1 along the dorsal-ventral axis rivaled differences across distinct pyramidal neuron classes. This variability emerged from a spectrum of continuous gene-expression gradients, producing a transcriptional profile consistent with a multifarious continuum of cells. This work reveals an unexpected amount of variability within a canonical and narrowly defined neuronal population and suggests that continuous, within-class heterogeneity may be an important feature of neural circuits.

The hepatocytes within the liver present an immense capacity to adapt to changes in nutrient availability. Here, by using high resolution volume electron microscopy, we map how hepatic subcellular spatial organization is regulated during nutritional fluctuations and as a function of liver zonation. We identify that fasting leads to remodeling of endoplasmic reticulum (ER) architecture in hepatocytes, characterized by the induction of single rough ER sheet around the mitochondria, which becomes larger and flatter. These alterations are enriched in periportal and mid-lobular hepatocytes but not in pericentral hepatocytes. Gain- and loss-of-function in vivo models demonstrate that the Ribosome receptor binding protein1 (RRBP1) is required to enable fasting-induced ER sheet-mitochondria interactions and to regulate hepatic fatty acid oxidation. Endogenous RRBP1 is enriched around periportal and mid-lobular regions of the liver. In obesity, ER-mitochondria interactions are distinct and fasting fails to induce rough ER sheet-mitochondrion interactions. These findings illustrate the importance of a regulated molecular architecture for hepatocyte metabolic flexibility.