Developmental time windows for axon growth influence neuronal network topology

Early brain connectivity development consists of multiple stages: birth of neurons, their migration and the subsequent growth of axons and dendrites. Each stage occurs within a certain period of time depending on types of neurons and cortical layers. Forming synapses between neurons either by growing axons starting at similar times for all neurons (much-overlapped time windows) or at different time points (less-overlapped) may affect the topological and spatial properties of neuronal networks. Here, we explore the extreme cases of axon formation especially concerning short-distance connectivity during early development, either starting at the same time for all neurons (parallel, i.e. maximally-overlapped time windows) or occurring for each neuron separately one neuron after another (serial, i.e. no overlaps in time windows). For both cases, the number of potential and established synapses remained comparable. Topological and spatial properties, however, differed: neurons that started axon growth early on in serial growth achieved higher out-degrees, higher local efficiency, and longer axon lengths while neurons demonstrated more homogeneous connectivity patterns for parallel growth. Second, connection probability decreased more rapidly with distance between neurons for parallel growth than for serial growth. Third, bidirectional connections were more numerous for parallel growth. Finally, we tested our predictions with C. elegans data. Together, this indicates that time windows for axon growth influence the topological and spatial properties of neuronal networks opening the possibility to a posteriori estimate developmental mechanisms based on network properties of a developed network.Comment: Biol Cybern. 2015 Jan 30. [Epub ahead of print

Population Dynamics and Long-Term Trajectory of Dendritic Spines

Structural plasticity, characterized by the formation and elimination of synapses, plays a big role in learning and long-term memory formation in the brain. The majority of the synapses in the neocortex occur between the axonal boutons and dendritic spines. Therefore, understanding the dynamics of the dendritic spine growth and elimination can provide key insights to the mechanisms of structural plasticity. In addition to learning and memory formation, the connectivity of neural networks affects cognition, perception, and behavior. Unsurprisingly, psychiatric and neurological disorders such as schizophrenia and autism are accompanied by pathological alterations in spine morphology and synapse numbers. Hence, it is vital to develop a model to understand the mechanisms governing dendritic spine dynamics throughout the lifetime. Here, we applied the density dependent Ricker population model to investigate the feasibility of ecological population concepts and mathematical foundations in spine dynamics. The model includes “immigration,” which is based on the filopodia type transient spines, and we show how this effect can potentially stabilize the spine population theoretically. For the long-term dynamics we employed a time dependent carrying capacity based on the brain's metabolic energy allocation. The results show that the mathematical model can explain the spine density fluctuations in the short-term and also account for the long term trends in the developing brain during synaptogenesis and pruning

Evolution of Excitation–Inhibition Ratio in Cortical Cultures Exposed to Hypoxia

In the core of a brain infarct, neuronal death occurs within minutes after loss of perfusion. In the penumbra, a surrounding area with some residual perfusion, neurons initially remain structurally intact, but hypoxia-induced synaptic failure impedes neuronal activity. Penumbral activity may recover or further deteriorate, reflecting cell death. Mechanisms leading to either outcome remain ill-understood, but may involve changes in the excitation to inhibition (E/I) ratio. The E/I ratio is determined by structural (relative densities of excitatory and inhibitory synapses) and functional factors (synaptic strengths). Clinical studies demonstrated excitability alterations in regions surrounding the infarct core. These may be related to structural E/I changes, but the effects of hypoxia /ischemia on structural connectivity have not yet been investigated, and the role of structural connectivity changes in excitability alterations remains unclear. We investigated the evolution of the structural E/I ratio and associated network excitability in cortical cultures exposed to severe hypoxia of varying duration. 6–12 h of hypoxia reduced the total synaptic density. In particular, the inhibitory synaptic density dropped significantly, resulting in an elevated E/I ratio. Initially, this does not lead to increased excitability due to hypoxia-induced synaptic failure. Increased excitability becomes apparent upon reoxygenation after 6 or 12 h, but not after 24 h. After 24 h of hypoxia, structural patterns of vesicular glutamate stainings change. This possibly reflects disassembly of excitatory synapses, and may account for the irreversible reduction of activity and stimulus responses seen after 24 h

A Simple Rule for Dendritic Spine and Axonal Bouton Formation Can Account for Cortical Reorganization after Focal Retinal Lesions

Lasting alterations in sensory input trigger massive structural and functional adaptations in cortical networks. The principles governing these experience-dependent changes are, however, poorly understood. Here, we examine whether a simple rule based on the neurons’ need for homeostasis in electrical activity may serve as driving force for cortical reorganization. According to this rule, a neuron creates new spines and boutons when its level of electrical activity is below a homeostaticset-point and decreases the number of spines and boutons when its activity exceeds this set-point. In addition, neurons need a minimum level of activity to form spines and boutons. Spine and bouton formation depends solely on the neuron’s own activity level, and synapses are formed by merging spines and boutons independently of activity. Using a novel computational model, we show that this simple growth rule produces neuron and network changes as observed in thevisual cortex after focal retinal lesions. In the model, as in the cortex, the turnover of dendritic spines was increased strongest in the center of the lesion projection zone, while axonal boutons displayed a marked overshoot followed by pruning. Moreover, the decrease in external input was compensated for by the formation of new horizontal connections, which caused a retinotopic remapping. Homeostatic regulation may provide a unifying framework for understanding cortical reorganization, including network repair in degenerative diseases or following focal stroke

Effects of homeostatic constraints on associative memory storage and synaptic connectivity of cortical circuits

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