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.