Using diffusion to describe the transport of molecules across cell membranes has its limitations, but it is crucial for understanding gas exchange in the lungs, the movement of molecules through the cytoplasm of the cell, and the movement of molecules between cells in the extracellular fluid. When skeletal muscles respond to exercise, they recruit or open capillaries that are not perfused at rest. This opening of capillaries increases capillary density, reducing the diffusion distance between the capillary and the muscle fiber. As a result, oxygen and cellular fuels such as fatty acids and glucose can be delivered more quickly to the contracting muscle fiber. The average distance of a muscle fiber from a capillary decreases from 40 µm at rest to 20 µm or less during exercise.

The electrochemical gradient, also known as the electrochemical potential difference, quantifies the driving force that causes molecules to move across a membrane. The electrochemical gradient (Δµx) for any molecule is calculated using Equation 1.4: ˜µx = RTln([X]i/[X]o) + zFVm, where R is the gas constant, T is the temperature in degrees Kelvin, Ln is the natural logarithm, [X]i is the concentration of X inside the cell, [X]o is the concentration of X outside the cell, z is the valence of charged molecules, F is the Faraday constant, and Vm is the membrane potential (Vm = Vi − Vo).

The electrochemical gradient measures the free energy available for transporting molecules across the membrane and consists of two components. The first component represents the energy in the concentration gradient for X across the membrane (chemical potential difference). The second component represents the energy associated with moving charged molecules, such as ions, across the membrane when a membrane potential exists (Vm ≠ 0 mV). When considering the movement of glucose across a membrane, only the concentrations of glucose inside and outside the cell need to be considered. However, the movement of K+ across the membrane depends on both the K+ concentrations inside and outside the cell and the membrane voltage.

Equation 1.4 can be used to derive the Nernst equation for the equilibrium condition across the membrane (Δµ = 0), represented by Equation 1.5a and Equation 1.5b. The Nernst equilibrium potential (Ex) is the calculated Vm at which there is no net transport of the molecule across the membrane. The Nernst equilibrium potential quantifies the energy in a concentration gradient and expresses that energy in millivolts. For example, in a cell where the membrane potential is Vm = -60 mV and the Nernst equilibrium potential for K+ (EK+) is 90.8 mV, the energy in the K+ gradient causes K+ to move out of the cell. This energy is opposite to, and of greater magnitude than, the energy in the membrane voltage. Consequently, the electrochemical gradient results in the net movement of K+ out of the cell, driven by a net driving force of 30.8 mV (Vm − EK+).

The Nernst equation, at 37° C, can be written as follows by replacing the natural logarithm function with the base 10 logarithm function: [Nernst equation].
Despite the limitations of using diffusion to describe and understand the transport of molecules across cell membranes, it is also important for understanding gas exchange in the lungs (see ), the movement of molecules through the cytoplasm of the cell, and the movement of molecules between cells in the extracellular fluid. For example, one of the physiological responses of skeletal muscle to exercise is the recruitment or opening of capillaries that are not perfused at rest. This opening of previously closed capillaries increases capillary density and thereby reduces the diffusion distance between the capillary and the muscle fiber so that oxygen and cellular fuels (e.g., fatty acids and glucose) can be delivered more quickly to the contracting muscle fiber. In resting muscle, the average distance of a muscle fiber from a capillary is estimated to be 40 µm. However, with exercise, this distance decreases to 20 µm or less.
The electrochemical gradient (also called the electrochemical potential difference) is used to quantitate the driving force acting on a molecule to cause it to move across a membrane. The electrochemical gradient for any molecule (Δµx) is calculated as follows:
Equation 1.4 ˜µx = RTln + zFV ,[X]o xm where R = the gas constant T = temperature in degrees Kelvin Ln = natural logarithm [X]i = the concentration of X inside the cell [X]o = the concentration of X outside the cell zx = the valence of charged molecules F = the Faraday constant Vm = the membrane potential (Vm = Vi − Vo)
The electrochemical gradient is a measure of the free energy available to carry out the useful work of transporting the molecule across the membrane. It has two components: One component represents the energy in the concentration gradient for X across the membrane (chemical potential bBy convention, membrane voltages are determined and reported with regard to the exterior of the cell. In a typical cell, the resting membrane potential (Vm) is negative. Positive Vm values can be observed in some excitable cells at the peak of an action potential.
CHAPTER 1 Principles of Cell and Membrane Function difference). The second component (electrical potential difference) represents the energy associated with moving charged molecules (e.g., ions) across the membrane when a membrane potential exits (i.e., Vm ≠ 0 mV). Thus for the movement of glucose across a membrane, only the concentrations of glucose inside and outside of the cell need to be considered (Fig. 1.6A ). However, the movement of K+ across the membrane, for example, would be determined both from the K+ concentrations inside and outside of the cell and from the membrane voltage (see
Fig. 1.6B
Eq. 1.4 can be used to derive the Nernst equation for the situation in which a molecule is at equilibrium across the membrane (i.e., Δµ = 0):
Equation 1.5a
Equation 1.5b
The value of Vm calculated with the Nernst equation represents the equilibrium condition and is referred to as the Nernst equilibrium potential (Ex, the Vm at which there is no net transport of the molecule across the membrane). It should be apparent that the Nernst equilibrium potential quantitates the energy in a concentration gradient and expresses that energy in millivolts. For example, for the cell depicted in
Fig. 1.6B , the energy in the K+ gradient (derived from the Nernst equilibrium potential for K+ [EK+]) is proportional to 90.8 mV (causing K+ to move out of the cell). This is opposite to, and of greater magnitude than, the energy in the membrane voltage (Vm =−60 mV), which causes K+ to enter the cell. As a result, the electrochemical gradient is such that the net movement of K+ across the membrane will be out of the cell. Another way to state this is that the net driving force for K+ (Vm − EK+) is 30.8 mV (driving K+ out of the cell). This is described in more detail in
The Nernst equation, at 37° C, can be written as follows by replacing the natural logarithm function with the base 10 logarithm function: