[excerpt starts]

The Nernst equation is commonly used in medical textbooks to describe the electrochemical gradients and cellular transport of molecules. Equation 1.6a states that the electrochemical gradient of an uncharged molecule like glucose is solely determined by its concentration gradient across the cell membrane. Therefore, the concentration gradient would be expected to drive glucose into the cell. On the other hand, Equation 1.6b shows that for a charged ion like K+, the electrochemical gradient is determined by both the concentration gradient and the membrane voltage (Vm). The Nernst equilibrium potential for K+ (EK+) is calculated using equation 1.5a and is equal to -90.8 mV at equilibrium. The concentration gradient and the membrane voltage together create an electrochemical gradient that drives K+ out of the cell. The net driving force is equivalent to 2.97 kJ/mol (equivalent to 30.8 mV), causing K+ to move out of the cell.

The Nernst equation demonstrates that for univalent ions (e.g., Na+, K+, Cl−), a 10-fold concentration gradient across the membrane is equal to an electrical potential difference of 61.5 mV (at 37° C), while a 100-fold gradient is equivalent to 123 mV. For divalent ions like Ca++, a 10-fold concentration gradient is equal to a 30.7-mV electrical potential difference because z in equations 1.6a and 1.6b is equal to 2.

When a molecule moves across a membrane in the direction predicted by the electrochemical gradient, it is referred to as passive transport. In Fig. 1.6, the movement of glucose into the cell and the movement of K+ out of the cell are examples of passive transport. Passive transport is also known as "downhill transport" or "transport with the electrochemical gradient." In contrast, if the net movement of a molecule across the membrane goes against the electrochemical gradient, it is called active transport. This process requires the input of energy, such as ATP. Active transport is sometimes referred to as "uphill transport" or "transport against the electrochemical gradient."

Different classes of plasma membrane transport proteins exhibit different types of transport. The movement of water through water channels, ions through ion channels, and molecules via uniporters (e.g., glucose transport via GLUT-1) are passive processes. On the other hand, ATPase-dependent transporters, such as Na+,K+-ATPase, H+-ATPase, or ABC transporters, utilize the energy from ATP to drive active transport. This type of transport is known as primary active transport since it is directly coupled to ATP hydrolysis. Solute carriers that transport two or more molecules (e.g., 3Na+,Ca++ antiporter) can move one or more molecules against their electrochemical gradient by utilizing the energy from the electrochemical gradient of another molecule or molecules. This mechanism is called secondary active transport.

The movement of water across cell membranes occurs through osmosis, a passive process driven by the osmotic pressure difference across the cell membrane.

[excerpt ends]
Equation 1.6a 61 5. mV [X]i
Equation 1.6b 615. mV [X]E = log o x zx [X]i •Fig. 1.6 Electrochemicalgradientsandcellulartransportofmolecules.A, Becauseglucoseisuncharged,theelectrochemicalgradientisdeterminedsolelybytheconcentrationgradientforglucoseacrossthecellmembrane.Asshown,theglucoseconcentrationgradientwouldbeexpectedtodriveglucoseintothecell.B, BecauseK+ ischarged,theelectrochemicalgradientisdeterminedbyboththeconcentrationgradientandthemembranevoltage(Vm).TheNernstequilibriumpotentialforK+ (EK+ ),calculatedwith eq.1.5a ,is−90.8mV(EK+= Vm atequilibrium).Theenergyintheconcentrationgradient,whichdrivesK+ outofthecell,isthusproportionalto+90.8mV.Themembranevoltageof−60mVdrivesK+ intothecell.Thustheelectrochemicalgradient,ornetdrivingforce,is2.97kJ/mol(equivalentto30.8mV),whichdrivesK+ outofthecell.
These are the most common forms of the Nernst equation in use. In these equations, it is apparent that for a univalent ion (e.g., Na+ , K+ , Cl−), a 10-fold concentration gradient across the membrane is equivalent in energy to an electrical potential difference of 61.5 mV (at 37° C), and a 100-fold gradient is equivalent to an electrical potential difference of 123 mV. Similarly, for a divalent ion (e.g., Ca++), a 10-fold concentration gradient is equivalent to a 30.7-mV electrical potential difference, because z in eqs. 1.6a and 1.6b is equal to 2.
When the net movement of a molecule across a membrane occurs in the direction predicted by the electrochemical gradient, that movement is termed passive transport. Thus for the examples given in
Fig. 1.6 , the movement of glucose into the cell and the movement of K+ out of the cell would be considered passive transport. Transport that is passive is sometimes referred to as either “downhill transport” or “transport with the electrochemical gradient.” In contrast, if the net movement of a molecule across the membrane is opposite to that predicted by the electrochemical gradient, that movement is termed active transport, a process that requires the input of energy (e.g., ATP). Active transport is sometimes referred to as either “uphill transport” or “transport against the electrochemical gradient.”
In the various classes of plasma membrane transport proteins, the movement of H2O through water channels is a passive process (see later discussion), as is the movement of ions through ion channels and the transport of molecules via uniporters (e.g., transport of glucose via GLUT-1). The ATPase-dependent transporters can use the energy in ATP to drive active transport of molecules (e.g., Na+,K+-ATPase, H+-ATPase, or ABC transporters). Because the transport is directly coupled to the hydrolysis of ATP, it is referred to as primary active transport. Solute carriers that couple movement of two or more molecules (e.g., 3Na+,Ca++ antiporter) often transport one or more molecules (one Ca++ molecule in this example) against their respective electrochemical gradient through the use of the energy in the electrochemical gradient of the other molecule or molecules (three Na+ in this example). When this occurs, the molecule or molecules transported against their electrochemical gradient are said to be transported by secondary active transport mechanisms (
Fig. 1.7
The movement of water across cell membranes occurs by the process of osmosis. The movement of water is passive, with the driving force for this movement being the osmotic pressure difference across the cell membrane.