For the initial thought experiment, suppose that we start values?" The biophysical properties of axons and denwith a small sample of cortical neuropil that is arranged drites dictate that wire should occupy 3/5 of the voljust like some actual cortical region (same shape, size, ume in an optimally wired gray matter. We have meaand relative positions of all axons, dendrites, and synsured the fraction of the volume occupied by each apses). We shall investigate the effect of changing the cellular component and find that the volume of wire volume of "wire": "wire" is made up of axons and denis close to the predicted optimal value. drites, and "non-wire" consists of boutons (or, more precisely, the portion of the bouton that is larger than Introduction the axon segment with the same length), spine heads, glial processes, and extracellular space. We consider The problem of wiring a brain can be appreciated by here samples of cortex without cell bodies and capillarconsidering the number of components that must be ies. Initially, we give our general argument in a simplified packed into every cortical region: a microliter of cortex form by supposing that wire consists only of axons and contains approximately 10 5 neurons, 10 9 synapses, and ignore the contribution of dendrites. Later we shall indi-4 km of axons (Braitenberg and Schü z, 1998). Furthercate why including dendrites in "wire" does not alter more, each cortical neighborhood must not only pack the conclusions we reach through this initial thought the cellular components at high density, but must also experiment. Our first goal is to examine the effect of have just the right balance of components. If too many changing axon diameter (while holding biophysical dendrites were present in a particular mm cube of corproperties of the membrane constant) on conduction tex, for example, insufficient space would remain for the delays from one point in the circuit to another. axons and synapses needed to make the required circuit Start with a limiting case in which axon diameters in connections. the cortical sample have been reduced to zero (so that In considering how neural circuits are constructed, axons take up no space) and the other components we made the surprising discovery that cortical function have been moved closer together to fill up the vacant is optimal-in ways described below-when the volume space but are otherwise unchanged in size and physioof axons and dendrites combine to occupy 3/5 of the logical properties; additionally, axons have been shortneuropil volume; this combined quantity is designated ened to run as directly as possible between locations the wire fraction. We derived an equation (see below) where they make synapses in the actual circuit. Furtherthat describes how the wire fraction depends on four more, we require that the biophysical properties of axfactors: the conduction delay along axons, the cable ons are kept constant so that the proportionality conattenuation of signals in dendrites, the number of synstant between conduction velocity and the square root apses, and a "layout" parameter that specifies the length of axon diameter (Rushton, 1951) is unchanged. Beof wire used for a particular arrangement of compocause the conduction velocity of unmyelinated axons is nents. The derivation of this equation makes use of the proportional to the square root of their diameter, such geometrical properties of axons and dendrites, and of a hypothetical cortex would not, of course, function: the fact-derived from the cable equation-that denconduction delays would be infinite. We ask: "What axon diameter minimizes conduction delays?" To answer this question, now imagine that the axon diameters are all
In particular, the idea of minimizing conduction delay has been used to explain why axons and dendrites take a certain fraction of the neuropil REF .
Wiring Optimization in Cortical Circuits
Neuron
Neuron
Medicine Biology