594
14 Neural Networks and Brains
millimolar. Use the Nernst–Planck equation to estimate the electric potential (in
millivolts) that would be created by this concentration difference acting alone.
14.5 Now consider the cell membrane for the neuron in the previous problem
as also permeable to potassium, chloride, and calcium ions, with equilibrium
concentrations of C(K, out) = 2.2 mM, C(K, in) = 125 mM, C(Cl, out) =
78 mM, C(Cl, in) = 1.6 mM, C(Ca, out) = 10 mM, C(Ca, in) = 10 −4 mM,
with effective permeabilities of the membrane to each ion found to be: p(Na) =
5 × 10 −10 m/s; p(K) = 5 × 10 −9 m/s, p(Cl) = 1 × 10 −10 m/s, and p(Ca) =
1 × 10 −12 m/s. Use the Goldman–Hodgkin–Katz voltage equation to predict the
resulting electric potential which the neuron must maintain. Because the permeability of the calcium ions is small compared to the other ions, you do not need to
include their effect to get a reasonable prediction.
14.6 Argue either for or against the proposition that awake dogs are normally
conscious.
14.7 Show that if a brain has more than four neurons, they cannot all be simply
connected to each other in less than a three-dimensional space. However, with
a more complicated design for connection crossings, complex networks can be
formed.
14 Neural Networks and Brains
millimolar. Use the Nernst–Planck equation to estimate the electric potential (in
millivolts) that would be created by this concentration difference acting alone.
14.5 Now consider the cell membrane for the neuron in the previous problem
as also permeable to potassium, chloride, and calcium ions, with equilibrium
concentrations of C(K, out) = 2.2 mM, C(K, in) = 125 mM, C(Cl, out) =
78 mM, C(Cl, in) = 1.6 mM, C(Ca, out) = 10 mM, C(Ca, in) = 10 −4 mM,
with effective permeabilities of the membrane to each ion found to be: p(Na) =
5 × 10 −10 m/s; p(K) = 5 × 10 −9 m/s, p(Cl) = 1 × 10 −10 m/s, and p(Ca) =
1 × 10 −12 m/s. Use the Goldman–Hodgkin–Katz voltage equation to predict the
resulting electric potential which the neuron must maintain. Because the permeability of the calcium ions is small compared to the other ions, you do not need to
include their effect to get a reasonable prediction.
14.6 Argue either for or against the proposition that awake dogs are normally
conscious.
14.7 Show that if a brain has more than four neurons, they cannot all be simply
connected to each other in less than a three-dimensional space. However, with
a more complicated design for connection crossings, complex networks can be
formed.