Efficient associative memory storage in cortical circuits of inhibitory and excitatory neurons.

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.

Cooperative synapse formation in the neocortex.

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.

Structural plasticity of circuits in cortical neuropil.

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/mum(3)) and lowest in monkey V1 (1.3-1.5 bits/mum(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 >21-30% of presynaptic axons encountered with new spine growth. Primate neurons appear to be more selective, making synaptic connections with >7-15% of encountered axons.