Power-law for axon diameters at branch point

BACKGROUND: Axon calibers vary widely among different animals, neuron classes, and even within the same neuron. What determines the diameter of axon branches? RESULTS: We pursue the hypothesis that the axon caliber has evolved to minimize signal propagation delays, while keeping arbor volume to a minimum. For a general cost function, we show that the optimal diameters of mother and daughter branches at a bifurcation satisfy a power law. The derivation relies on the fact that the axon conduction speed scales as a power of axon diameter. Although available data are consistent with the law, there is a large spread in the data. Future experimental tests will determine whether this spread is due to biological variability or measurement error. CONCLUSIONS: Minimization of arbor volume and signal propagation delay may have been an important factor in the evolution of the brain

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

26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 - Meeting Abstracts - Antwerp, Belgium. 15–20 July 2017

This work was produced as part of the activities of FAPESP Research,\ud Disseminations and Innovation Center for Neuromathematics (grant\ud 2013/07699-0, S. Paulo Research Foundation). NLK is supported by a\ud FAPESP postdoctoral fellowship (grant 2016/03855-5). ACR is partially\ud supported by a CNPq fellowship (grant 306251/2014-0)