Many features of synaptic connectivity are ubiquitous among cortical systems. Cortical networks are dominated by excitatory neurons and synapses, are sparsely connected, and function with stereotypically distributed connection weights. We show that these basic structural and functional features of synaptic connectivity arise readily from the requirement of efficient associative memory storage. Our theory makes two fundamental predictions. First, we predict that, despite a large number of neuron classes, functional connections between potentially connected cells must be realized with <50% probability if the presynaptic cell is excitatory and >50% probability if the presynaptic cell is inhibitory. Second, we establish a unique relation between probability of connection and coefficient of variation in connection weights. These predictions are consistent with a dataset of 74 published experiments reporting connection probabilities and distributions of postsynaptic potential amplitudes in various cortical systems. What is more, our theory explains the shapes of the distributions obtained in these experiments.learning and memory | cortical connectivity | synaptic weight | perceptron | critical capacity F undamental functions of the brain, such as learning and memory storage, are mediated by many mechanisms of excitatory (1-4) and inhibitory (5-9) synaptic plasticity. Working together with the genetically encoded developmental mechanisms of circuit formation, synaptic plasticity shapes neural circuits by creating, modifying, and eliminating individual synaptic connections in an experience-dependent manner. It is, therefore, reasonable to hypothesize that many stereotypic features of adult synaptic connectivity, whether established through evolution or the developmental learning process, have arisen to facilitate memory storage.In this study, we focus on three such features of cortical connectivity. Cortical connectivity is predominantly excitatory; it is mediated by two major classes of neurons-excitatory glutamatergic and inhibitory GABAergic cells. Chemical synapses made by the axons of inhibitory cells in the adult brain are believed to be all inhibitory, whereas those synapses made by the axons of excitatory neurons are believed to be all excitatory (10). The resulting connectivity is largely excitatory, with only about 15-20% of inhibitory neurons and inhibitory synapses (11). The second stereotypic feature of cortical connectivity is sparseness. Networks in the cortex are thought to be organized into relatively small units ranging from hundreds to tens of thousands of neurons in size. Such units may include mini columns (12, 13), structural columns (14, 15), and a variety of functional columns (16,17). Analysis of neuron morphology (14,(18)(19)(20)(21) has shown that cells within such units have the potential of being connected by structural synaptic plasticity (22-24). However, despite this potential, synaptic connectivity within the units is sparse. For example, nearby excitatory neurons in the neocortex are sy...

Chapeton et al. show that alpha oscillations in the human cortex satisfy several constraints that are necessary for using oscillatory coherence as a means of modulating large-scale cortical communication. The results are specific to the alpha band and supported by single-unit spiking activity.

Automating the process of neurite tracing from light microscopy stacks of images is essential for large-scale or high-throughput quantitative studies of neural circuits. While the general layout of labeled neurites can be captured by many automated tracing algorithms, it is often not possible to differentiate reliably between the processes belonging to different cells. The reason is that some neurites in the stack may appear broken due to imperfect labeling, while others may appear fused due to the limited resolution of optical microscopy. Trained neuroanatomists routinely resolve such topological ambiguities during manual tracing tasks by combining information about distances between branches, branch orientations, intensities, calibers, tortuosities, colors, as well as the presence of spines or boutons. Likewise, to evaluate different topological scenarios automatically, we developed a machine learning approach that combines many of the above mentioned features. A specifically designed confidence measure was used to actively train the algorithm during user-assisted tracing procedure. Active learning significantly reduces the training time and makes it possible to obtain less than 1% generalization error rates by providing few training examples. To evaluate the overall performance of the algorithm a number of image stacks were reconstructed automatically, as well as manually by several trained users, making it possible to compare the automated traces to the baseline inter-user variability. Several geometrical and topological features of the traces were selected for the comparisons. These features include the total trace length, the total numbers of branch and terminal points, the affinity of corresponding traces, and the distances between corresponding branch and terminal points. Our results show that when the density of labeled neurites is sufficiently low, automated traces are not significantly different from manual reconstructions obtained by trained users.

The impact of learning and long-term memory storage on synaptic connectivity is not completely understood. In this study, we examine the effects of associative learning on synaptic connectivity in adult cortical circuits by hypothesizing that these circuits function in a steady-state, in which the memory capacity of a circuit is maximal and learning must be accompanied by forgetting. Steady-state circuits should be characterized by unique connectivity features. To uncover such features we developed a biologically constrained, exactly solvable model of associative memory storage. The model is applicable to networks of multiple excitatory and inhibitory neuron classes and can account for homeostatic constraints on the number and the overall weight of functional connections received by each neuron. The results show that in spite of a large number of neuron classes, functional connections between potentially connected cells are realized with less than 50% probability if the presynaptic cell is excitatory and generally a much greater probability if it is inhibitory. We also find that constraining the overall weight of presynaptic connections leads to Gaussian connection weight distributions that are truncated at zero. In contrast, constraining the total number of functional presynaptic connections leads to non-Gaussian distributions, in which weak connections are absent. These theoretical predictions are compared with a large dataset of published experimental studies reporting amplitudes of unitary postsynaptic potentials and probabilities of connections between various classes of excitatory and inhibitory neurons in the cerebellum, neocortex, and hippocampus.