| Learning and long-term memory rely on plasticity of neural circuits. In adult cerebral cortex plasticity can be mediated by modulation of existing synapses and structural reorganization of circuits through growth and retraction of dendritic spines.;In the first part of this thesis, we describe a theoretical framework for the analysis of spine remodeling plasticity. New synaptic contacts appear in the neuropil where gaps between axonal and dendritic branches can be bridged by dendritic spines. Such sites are termed potential synapses. We derive expressions for the densities of potential synapses in the neuropil. We calculate the ratio of actual to potential synapses, called the connectivity fraction, and use it to find the number of structurally different circuits attainable with spine remodeling. These parameters are calculated in four systems: mouse occipital cortex, rat hippocampal area CA1, monkey primary visual (V1), and human temporal cortex. The neurogeometric results indicate that a dendritic spine can choose among an average of 4-7 potential targets in rodents, while in primates it can choose from 10-20 potential targets. The potential of the neuropil to undergo circuit remodeling is found to be highest in rat CA1 (4.9-6.0 nats/mum 3) and lowest in monkey V1 (0.9-1.0 nats/mum3). We evaluate the lower bound of neuron selectivity in the choice of synaptic partners and find that post-synaptic excitatory neurons in rodents make synaptic contacts with more than 21-30% of pre-synaptic axons encountered with new spine growth. Primate neurons appear to be more selective, making synaptic connections with more than 7-15% of encountered axons.;Another plasticity mechanism is included in the second part of this work: long-term potentiation and depression of excitatory synaptic connections. Because synaptic strength is correlated with the size of the synapse, the former can be inferred from the distribution of spine head volumes. To this end we analyze and compare 166 distributions of spine head volumes and spine lengths from mouse, rat, monkey, and human brains. We develope a statistical theory in which the equilibrium distribution of dendritic spine shapes is governed by the principle of synaptic entropy maximization under a "generalized cost" constraint. We find the generalized cost of dendritic spines and show that it universally depends on the spine shape, i.e. the dependence is the same in all the considered systems. We show that the modulatory and structural plasticity mechanisms in adults are in a statistical equilibrium with each other, the numbers of dendritic spines in different cortical areas are nearly optimally chosen for memory storage, and the distribution of spine shapes is governed by a single parameter -- the effective temperature. Our results suggest that the effective temperature of a cortical area may be viewed as a measure of longevity of stored memories. Finally, we test the hypothesis that the number of spines in the neuropil is chosen to optimize its storage information capacity. |
