A common rule governing differentiation kinetics of mouse cortical progenitors.

The balance between proliferation and differentiation of stem cells and progenitors determines the size of an adult brain region. While the molecular mechanisms regulating proliferation and differentiation of cortical progenitors have been intensively studied, an analysis of the kinetics of progenitor choice between self-renewal and differentiation in vivo is, due to the technical difficulties, still unknown. Here we established a descriptive mathematical model to estimate the probability of self-renewal or differentiation of cortical progenitor behaviors in vivo, a variable we have termed the expansion coefficient. We have applied the model, one which depends only on experimentally measured parameters, to the developing mouse cortex where the expansive neuroepithelial cells and neurogenic radial glial progenitors are coexisting. Surprisingly, we found that the expansion coefficients of both neuroepithelium cells and radial glial progenitors follow the same developmental trajectory during cortical development, suggesting a common rule governing self-renewal/differentiation behaviors in mouse cortical progenitor differentiation.

Scaling Principles of Distributed Circuits.

Identifying shared quantitative features of a neural circuit across species is important for 3 reasons. Often expressed in the form of power laws and called scaling relationships [1, 2], they reveal organizational principles of circuits, make insights gleaned from model systems widely applicable, and explain circuit performance and function, e.g., visual circuits [3, 4]. The visual circuit is topographic [5, 6], wherein retinal neurons target and activate predictable spatial loci in primary visual cortex. The brain, however, contains many circuits, where neuronal targets and activity are unpredictable and distributed throughout the circuit, e.g., olfactory circuits, in which glomeruli (or mitral cells) in the olfactory bulb synapse with neurons distributed throughout the piriform cortex [7-10]. It is unknown whether such circuits, which we term distributed circuits, are scalable. To determine whether distributed circuits scale, we obtained quantitative descriptions of the olfactory bulb and piriform cortex in six mammals using stereology techniques and light microscopy. Two conserved features provide evidence of scalability. First, the number of piriform neurons n and bulb glomeruli g scale as n∼g3/2. Second, the average number of synapses between a bulb glomerulus and piriform neuron is invariant at one. Using theory and modeling, we show that these two features preserve the discriminatory ability and precision of odor information across the olfactory circuit. As both abilities depend on circuit size, manipulating size provides evolution with a way to adapt a species to its niche without designing developmental programs de novo. These principles might apply to other distributed circuits like the hippocampus.

A neural data structure for novelty detection.

Novelty detection is a fundamental biological problem that organisms must solve to determine whether a given stimulus departs from those previously experienced. In computer science, this problem is solved efficiently using a data structure called a Bloom filter. We found that the fruit fly olfactory circuit evolved a variant of a Bloom filter to assess the novelty of odors. Compared with a traditional Bloom filter, the fly adjusts novelty responses based on two additional features: the similarity of an odor to previously experienced odors and the time elapsed since the odor was last experienced. We elaborate and validate a framework to predict novelty responses of fruit flies to given pairs of odors. We also translate insights from the fly circuit to develop a class of distance- and time-sensitive Bloom filters that outperform prior filters when evaluated on several biological and computational datasets. Overall, our work illuminates the algorithmic basis of an important neurobiological problem and offers strategies for novelty detection in computational systems.

Deep(er) Learning.

Animals successfully thrive in noisy environments with finite resources. The necessity to function with resource constraints has led evolution to design animal brains (and bodies) to be optimal in their use of computational power while being adaptable to their environmental niche. A key process undergirding this ability to adapt is the process of learning. Although a complete characterization of the neural basis of learning remains ongoing, scientists for nearly a century have used the brain as inspiration to design artificial neural networks capable of learning, a case in point being deep learning. In this viewpoint, we advocate that deep learning can be further enhanced by incorporating and tightly integrating five fundamental principles of neural circuit design and function: optimizing the system to environmental need and making it robust to environmental noise, customizing learning to context, modularizing the system, learning without supervision, and learning using reinforcement strategies. We illustrate how animals integrate these learning principles using the fruit fly olfactory learning circuit, one of nature's best-characterized and highly optimized schemes for learning. Incorporating these principles may not just improve deep learning but also expose common computational constraints. With judicious use, deep learning can become yet another effective tool to understand how and why brains are designed the way they are.

The distributed circuit within the piriform cortex makes odor discrimination robust.

Distributed circuits wherein connections between subcircuit components seem randomly distributed are common to the olfactory circuit, hippocampus, and cerebellum. In such circuits, activation patterns seem random too, showing no detectable spatial preference, and contrast with regions that have topographic connections between subcircuits and topographic activation patterns. Quantitative studies of topographic circuits in the neocortex have yielded common principles of organization. Whether distributed circuits share similar principles of organization is unknown because similar quantitative information is missing and understanding the way they encode information remains a challenge. We addressed these needs by providing a quantitative description of the mouse piriform cortex, a paleocortical distributed circuit that subserves olfaction. The quantitative information provided two insights. First, with a nearly parameter-free model of the olfactory circuit, we show that the piriform cortex robustly maintains odor information and discrimination ability present in the olfactory bulb. Second, the paleocortex is quantitatively different from the neocortex: it has a lower surface area density, which decreases from the anterior to posterior paleocortex contrasting with the uniform neuronal density of the neocortex. These insights might also apply to other distributed circuits.

Conserved features of the primate face code.

A recent paper demonstrated that the pattern of firing rates across ∼100 neurons in the anterior medial face patch is closely related to which human face (of 2,000) had been presented to a monkey [Chang L, Tsao DY (2017) Cell 169:1013-1028]. In addition, the firing rates for these neurons can be predicted for a novel human face. Although it is clear from this work that the firing rates of these face patch neurons encode faces, the properties of the face code have not yet been fully described. Based on an analysis of 98 neurons responding to 2,000 faces, I conclude that the anterior medial face patch uses a combinatorial rate code, one with an exponential distribution of neuron rates that has a mean rate conserved across faces. Thus, the face code is maximally informative (technically, maximum entropy) and is very similar to the code used by the fruit fly olfactory system.

A neural algorithm for a fundamental computing problem.

Similarity search-for example, identifying similar images in a database or similar documents on the web-is a fundamental computing problem faced by large-scale information retrieval systems. We discovered that the fruit fly olfactory circuit solves this problem with a variant of a computer science algorithm (called locality-sensitive hashing). The fly circuit assigns similar neural activity patterns to similar odors, so that behaviors learned from one odor can be applied when a similar odor is experienced. The fly algorithm, however, uses three computational strategies that depart from traditional approaches. These strategies can be translated to improve the performance of computational similarity searches. This perspective helps illuminate the logic supporting an important sensory function and provides a conceptually new algorithm for solving a fundamental computational problem.

A Statistical Description of Plant Shoot Architecture.

Plant architectures can be characterized statistically by their spatial density function, which specifies the probability of finding a branch at each location in the territory occupied by a plant. Using high-precision 3D scanning, we analyzed 557 plant shoot architectures, representing three species, grown across three to five environmental conditions, and through 20-30 developmental time points. We found two elegant properties in the spatial density functions of these architectures: all functions could be nearly modified in one direction without affecting the density in orthogonal directions (called "separability"), and all functions shared the same underlying shape, aside from stretching and compression (called "self-similarity"). Surprisingly, despite their striking visual diversity, we discovered that all architectures could be described as variations on a single underlying function: a Gaussian density function truncated at roughly two SDs. We also observed systematic variation in the spatial density functions across species, growth conditions, and time, which suggests functional specialization despite following the same general design form.

A statistical property of fly odor responses is conserved across odors.

I have reanalyzed the data presented by Hallem and Carlson [Hallem EA, Carlson JR (2006) Cell 125(1):143-160] and shown that the combinatorial odor code supplied by the fruit fly antenna is a very simple one in which nearly all odors produce, statistically, the same neuronal response; i.e., the probability distribution of sensory neuron firing rates across the population of odorant sensory neurons is an exponential for nearly all odors and odor mixtures, with the mean rate dependent on the odor concentration. Between odors, then, the response differs according to which sensory neurons are firing at what individual rates and with what mean population rate, but not in the probability distribution of firing rates. This conclusion is independent of adjustable parameters, and holds both for monomolecular odors and complex mixtures. Because the circuitry in the antennal lobe constrains the mean firing rate to be the same for all odors and concentrations, the odor code is what is known as maximum entropy.

What the fly's nose tells the fly's brain.

The fly olfactory system has a three-layer architecture: The fly's olfactory receptor neurons send odor information to the first layer (the encoder) where this information is formatted as combinatorial odor code, one which is maximally informative, with the most informative neurons firing fastest. This first layer then sends the encoded odor information to the second layer (decoder), which consists of about 2,000 neurons that receive the odor information and "break" the code. For each odor, the amplitude of the synaptic odor input to the 2,000 second-layer neurons is approximately normally distributed across the population, which means that only a very small fraction of neurons receive a large input. Each odor, however, activates its own population of large-input neurons and so a small subset of the 2,000 neurons serves as a unique tag for the odor. Strong inhibition prevents most of the second-stage neurons from firing spikes, and therefore spikes from only the small population of large-input neurons is relayed to the third stage. This selected population provides the third stage (the user) with an odor label that can be used to direct behavior based on what odor is present.

Predicting visual acuity from the structure of visual cortex.

Three decades ago, Rockel et al. proposed that neuronal surface densities (number of neurons under a square millimeter of surface) of primary visual cortices (V1s) in primates is 2.5 times higher than the neuronal density of V1s in nonprimates or many other cortical regions in primates and nonprimates. This claim has remained controversial and much debated. We replicated the study of Rockel et al. with attention to modern stereological precepts and show that indeed primate V1 is 2.5 times denser (number of neurons per square millimeter) than many other cortical regions and nonprimate V1s; we also show that V2 is 1.7 times as dense. As primate V1s are denser, they have more neurons and thus more pinwheels than similar-sized nonprimate V1s, which explains why primates have better visual acuity.

Control of organ size: development, regeneration, and the role of theory in biology.

How organs grow to be the right size for the animal is one of the central mysteries of biology. In a paper in BMC Biology, Khammash et al. propose a mechanism for escaping from the deficiencies of feedback control of growth as a mechanism.

Novel neural circuit mechanism for visual edge detection.

The primary visual cortex is organized in a way that assigns a specific collection of neurons the job of providing the rest of the brain with all of the information it needs about each small part of the image present on the retina: Neighboring patches of the visual cortex provide the information about neighboring patches of the visual world. Each one of these cortical patches--often identified as a "pinwheel"--contains thousands of neurons, and its corresponding image patch is centered on a particular location in the retina. For stimuli within their image patch, neurons respond selectively to lines or edges with a particular slope (orientation tuning) and to regions of the patch of different sizes (known as spatial frequency tuning). The same number of neurons is devoted to reporting each possible slope (orientation). For the cells that cover different-sized regions of their image patch, however, the number of neurons assigned depends strongly on their preferred region size. Only a few neurons report on large and small parts of the image patch, but many neurons report visual information from medium-sized areas. I show here that having different numbers of neurons responsible for image regions of different sizes actually carries out a computation: Edges in the image patch are extracted. I also explain how this edge-detection computation is done.

NSF workshop report: discovering general principles of nervous system organization by comparing brain maps across species.

Efforts to understand nervous system structure and function have received new impetus from the federal Brain Research through Advancing Innovative Neurotechnologies (BRAIN) Initiative. Comparative analyses can contribute to this effort by leading to the discovery of general principles of neural circuit design, information processing, and gene-structure-function relationships that are not apparent from studies on single species. We here propose to extend the comparative approach to nervous system 'maps' comprising molecular, anatomical, and physiological data. This research will identify which neural features are likely to generalize across species, and which are unlikely to be broadly conserved. It will also suggest causal relationships between genes, development, adult anatomy, physiology, and, ultimately, behavior. These causal hypotheses can then be tested experimentally. Finally, insights from comparative research can inspire and guide technological development. To promote this research agenda, we recommend that teams of investigators coalesce around specific research questions and select a set of 'reference species' to anchor their comparative analyses. These reference species should be chosen not just for practical advantages, but also with regard for their phylogenetic position, behavioral repertoire, well-annotated genome, or other strategic reasons. We envision that the nervous systems of these reference species will be mapped in more detail than those of other species. The collected data may range from the molecular to the behavioral, depending on the research question. To integrate across levels of analysis and across species, standards for data collection, annotation, archiving, and distribution must be developed and respected. To that end, it will help to form networks or consortia of researchers and centers for science, technology, and education that focus on organized data collection, distribution, and training. These activities could be supported, at least in part, through existing mechanisms at NSF, NIH, and other agencies. It will also be important to develop new integrated software and database systems for cross-species data analyses. Multidisciplinary efforts to develop such analytical tools should be supported financially. Finally, training opportunities should be created to stimulate multidisciplinary, integrative research into brain structure, function, and evolution.

NSF workshop report: discovering general principles of nervous system organization by comparing brain maps across species.

Efforts to understand nervous system structure and function have received new impetus from the federal Brain Research through Advancing Innovative Neurotechnologies (BRAIN) Initiative. Comparative analyses can contribute to this effort by leading to the discovery of general principles of neural circuit design, information processing, and gene-structure-function relationships that are not apparent from studies on single species. We here propose to extend the comparative approach to nervous system 'maps' comprising molecular, anatomical, and physiological data. This research will identify which neural features are likely to generalize across species, and which are unlikely to be broadly conserved. It will also suggest causal relationships between genes, development, adult anatomy, physiology, and, ultimately, behavior. These causal hypotheses can then be tested experimentally. Finally, insights from comparative research can inspire and guide technological development. To promote this research agenda, we recommend that teams of investigators coalesce around specific research questions and select a set of 'reference species' to anchor their comparative analyses. These reference species should be chosen not just for practical advantages, but also with regard for their phylogenetic position, behavioral repertoire, well-annotated genome, or other strategic reasons. We envision that the nervous systems of these reference species will be mapped in more detail than those of other species. The collected data may range from the molecular to the behavioral, depending on the research question. To integrate across levels of analysis and across species, standards for data collection, annotation, archiving, and distribution must be developed and respected. To that end, it will help to form networks or consortia of researchers and centers for science, technology, and education that focus on organized data collection, distribution, and training. These activities could be supported, at least in part, through existing mechanisms at NSF, NIH, and other agencies. It will also be important to develop new integrated software and database systems for cross-species data analyses. Multidisciplinary efforts to develop such analytical tools should be supported financially. Finally, training opportunities should be created to stimulate multidisciplinary, integrative research into brain structure, function, and evolution.

Structural uniformity of neocortex, revisited.

The number of neurons under a square millimeter of cortical surface has been reported to be the same across five cortical areas and five species [Rockel et al. (1980) Brain 103(2):221-244] despite differences in cortical thickness between the areas. Although the accuracy of this result has been the subject of sharp debate since its publication approximately 30 y ago, the experiments of Rockel et al. have never been directly replicated with modern stereological methods. We have replicated these experiments and confirm the accuracy of the original report. In addition, we have observed that the number of glial cells under a square millimeter of cortical surface depends on cortical thickness, but not on cortical area or species.

Short-term plasticity constrains spatial organization of a hippocampal presynaptic terminal.

Although the CA3-CA1 synapse is critically important for learning and memory, experimental limitations have to date prevented direct determination of the structural features that determine the response plasticity. Specifically, the local calcium influx responsible for vesicular release and short-term synaptic facilitation strongly depends on the distance between the voltage-dependent calcium channels (VDCCs) and the presynaptic active zone. Estimates for this distance range over two orders of magnitude. Here, we use a biophysically detailed computational model of the presynaptic bouton and demonstrate that available experimental data provide sufficient constraints to uniquely reconstruct the presynaptic architecture. We predict that for a typical CA3-CA1 synapse, there are ~70 VDCCs located 300 nm from the active zone. This result is surprising, because structural studies on other synapses in the hippocampus report much tighter spatial coupling. We demonstrate that the unusual structure of this synapse reflects its functional role in short-term plasticity (STP).

The fraction of cortical GABAergic neurons is constant from near the start of cortical neurogenesis to adulthood.

Approximately one in five neurons is GABAergic in many neocortical areas and species, forming a critical balance between inhibition and excitation in adult circuits. During development, cortical GABAergic neurons are generated in ventral telencephalon and migrate up to developing cortex where the excitatory glutamatergic neurons are born. We ask here: when during development is the adult GABAergic/glutamatergic neuron ratio first established? To answer this question, we have determined the fraction of all neocortical GABAergic neurons that will become inhibitory (GAD67(+)) in mice from embryonic day 10.5 (E10.5) to postnatal day 28 (P28). We find that this fraction is close to 1/5, the adult value, starting from early in corticogenesis (E14.5, when GAD67(+) neurons are still migrating tangentially to the cortex) and continuing at the same 1/5 value throughout the remainder of brain development. Thus our data indicate the one-in-five fraction of GABAergic neurons is already established during their neuronal migration and well before significant synapse formation.