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

Abstract

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...

Robust associative learning is sufficient to explain structural and dynamical properties of local cortical circuits

“…According to this measure, neurons exhibit greater irregular activity when memory load and rescaled robustness are high, with CV of ISI values saturating at around 0.9. This is consistent with the range of CV of ISI values reported for different cortical systems, 0.7-1.1 [5][6][7][8][9] . To examine the extent of synchrony in neuron activity we calculated spike train cross-correlation coefficients for pairs of neurons ( Figure 4C).…”

“…These predictions are consistent with a large number of experimental studies of connectivity in local cortical circuits. Other models, including only some of the constraints considered in this study, have been previously described [4][5][6][7][8][9] .…”

“…This model is based on a number of assumptions and approximations, some of which have been previously discussed 7,8 :  We consider a recurrent network of N all-to-all potentially connected 10,11 McCulloch and Pitts neurons 12 . Each neuron may belong to one of several classes defined by the values of the firing threshold, h, firing probability, f, average absolute weight of input connections, w, and robustness parameter, κ.…”

“…We solve the above two models concurrently by following the steps of the replica theory solution outlined in 7,8 . We begin by calculating the volume of the connection weight space,  …”

“…For example, individual neurons exhibit highly irregular spiking activity, resembling Poisson processes with close to one CV in inter-spike-intervals [5][6][7][8][9] . Spike trains of nearby neurons are only 4 connections of each neuron are homeostatically constrained to have a fixed average absolute weight, w [28][29][30] .…”