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...
Neuron morphology plays an important role in defining synaptic connectivity. Clearly, only pairs of neurons with closely positioned axonal and dendritic branches can be synaptically coupled. For excitatory neurons in the cerebral cortex, such axo-dendritic oppositions, termed potential synapses, must be bridged by dendritic spines to form synaptic connections. To explore the rules by which synaptic connections are formed within the constraints imposed by neuron morphology, we compared the distributions of the numbers of actual and potential synapses between pre-and postsynaptic neurons forming different laminar projections in rat barrel cortex. Quantitative comparison explicitly ruled out the hypothesis that individual synapses between neurons are formed independently of each other. Instead, the data are consistent with a cooperative scheme of synapse formation where multiple-synaptic connections between neurons are stabilized while neurons that do not establish a critical number of synapses are not likely to remain synaptically coupled.barrel cortex ͉ connectivity ͉ morphology ͉ potential synapse ͉ pyramidal cell O ur understanding of the rules governing synaptic connectivity in the brain is hindered by the complexity of neuron morphology. To circumvent this problem, it is often necessary to explicitly account for the shapes of axonal and dendritic arbors in the analysis of synaptic connectivity (see e.g., refs. 1-4). In the cerebral cortex, the majority of synaptic connections between excitatory neurons are made on dendritic spines (5). Therefore, individual synapses between neurons occur in places where axonal branches of the presynaptic neuron are located within spine reach from the dendritic branches of the postsynaptic cell. Such axo-dendritic oppositions are termed potential synapses (6, 7). Because in the adult cerebral cortex axonal and dendritic arbors of excitatory neurons form an extremely stable scaffold (8-11), the resulting matrix of potential synapses is stable as well (see however refs. 11-13, where small, layer specific changes in terminal axonal and dendritic branches were observed). What is more, due to the stereotypic morphologies of dendritic and local axonal arbors of cortical neurons (same species, brain region, layer, etc.) (14), the matrix of potential synapses is expected to be similar among different brains (6,15). This matrix constrains possible connectivity patterns in the adult brain and provides the main avenue for the formation of new synaptic connections. A potential synapse can be converted into an actual synapse if the gap between the pre-and the postsynaptic branches is bridged by a dendritic spine.In this study, we examine the rules of excitatory connectivity within the constraints imposed by the morphologies of neurons, i.e., within the matrix of potential synapses. Different connectivity patterns can be built within this matrix by converting different sets of potential synapses into actual. However, not all such connectivity patterns are biologically plausible since even w...
IntroductionNeuron morphology plays an important role in defining synaptic connectivity. Clearly, only pairs of neurons with closely positioned axonal and dendritic branches can be synaptically coupled. For excitatory neurons in the cerebral cortex, such axo-dendritic oppositions, or potential synapses, must be bridged by dendritic spines to form synaptic connections. To explore the rules by which synaptic connections are formed within the constraints imposed by neuron morphology, we compared the distributions of the numbers of actual and potential synapses between pre-and post-synaptic neurons forming different laminar projections in rat barrel cortex. Quantitative comparison explicitly ruled out the hypothesis that individual synapses between neurons are formed independently of each other. Instead, the data are consistent with a cooperative scheme of synapse formation, where multiple-synaptic connections between neurons are stabilized, while neurons that do not establish a critical number of synapses are not likely to remain synaptically coupled.
Learning and memory formation in the brain depend on the plasticity of neural circuits. In the adult and developing cerebral cortex, this plasticity can result from the formation and elimination of dendritic spines. New synaptic contacts appear in the neuropil where the gaps between axonal and dendritic branches can be bridged by dendritic spines. Such sites are termed potential synapses. Here, we describe a theoretical framework for the analysis of spine remodeling plasticity. We provide a quantitative description of two models of spine remodeling in which the presence of a bouton is either required or not for the formation of a new synapse. We derive expressions for the density of potential synapses in the neuropil, the connectivity fraction, which is the ratio of actual to potential synapses, and the number of structurally different circuits attainable with spine remodeling. We calculate these parameters in mouse occipital cortex, rat CA1, monkey V1, and human temporal cortex. We find that, on average, a dendritic spine can choose among 4 -7 potential targets in rodents and 10 -20 potential targets in primates. The potential of neuropil for structural circuit remodeling is highest in rat CA1 (7.1-8.6 bits/m 3 ) and lowest in monkey V1 (1.3-1.5 bits/m 3 ). We also evaluate the lower bound of neuron selectivity in the choice of synaptic partners. Postsynaptic excitatory neurons in rodents make synaptic contacts with Ͼ21-30% of presynaptic axons encountered with new spine growth. Primate neurons appear to be more selective, making synaptic connections with Ͼ7-15% of encountered axons.
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