Facilitated diffusion is a passive process in which membrane channels mediate the transport of polar, or big molecules that are not solvable in the cell membrane. Co-transport, on the other hand, is active transport, as it depends on the electrochemical gradient of ions across the cell's membrane, particularly Na+. Because ATP or other energetic compounds are not directly involved in co-transport, it is referred to as secondary active transport. The electrochemical ion gradient is mainly established by the Na+,K+-ATPase.
As commented upon by others, your question is not entirely clear and the best way to approach this question is by defining the various terminologies and physiological mechanisms used in your question:
- Active transport needs an energy source such as ATP. For example, the Na+,K+-ATPase is an enzyme that pumps Na+ and K+ ions against their concentration gradients into the cytosol (K+) or out of the cell (Na+). Note that both Na+ and K+ are transported against their chemical gradients (and Na+ also against its electrical gradient as the cell is negative). Therefore your statement that
[...] in the active process, substance x is transported against the gradient, and substance y down its electrochemical gradient is untrue, and likely the cause of your confusion.
- Passive transport is mediated by diffusion, which typically occurs through a concentration gradient. Only small, relatively hydrophobic molecules are able to diffuse across a phospholipid bilayer at significant rates. Examples are gases (such as O2 and CO2) in the lungs, and small polar but uncharged molecules (such as H2O and ethanol) (Cooper, 2000).
- Facilitated diffusion is an example of passive diffusion, but aided by membrane-spanning channel proteins that span the lipid bilayer. Therefore the particles (molecules or ions) do not have to dissolve in the cell membrane's hydrophobic lipid bilayer, allowing hydrophylic and larger molecules (carbohydrates, ions) to be transported into the cell. No external source of energy is needed and travel across the membrane in the direction determined by their concentration gradients and, in the case of charged molecules, by the electric potential across the membrane (Cooper, 2000).
- Co-transport is active transport, where the energetically unfavorable transport of a particle against its electrochemical gradient is facilitated by the co-transport of a favorable one down its gradient. In other words, multiple particles are transported so as to neutralize the sum of the transport. For example, sodium-dependent glucose tranporters transport glucose into the cell against the concentration gradient (unfavorable) and Na+ is transported along with it into the cell which is a favorable transport (Haraki & Inagaki, 2012). This is an example of a symporter. An example of an antiporter is the Na+/Ca2+ antiporter found in the heart to transport Ca2+ out of the cell against a steep concentration gradient and electrical gradient, while 3 Na+ is imported into the cell to balance the unfavorable Ca2+ transport. Note that all these mentioned co-transporters and many others are dependent on the Na,K-ATPase that ultimately generates the Na+ and K+ gradients by pumping Na+ out of the cell and K+ into the cell using ATP (Freeman, 2000). This generated membrane potential works like a battery being charged, and co-transporters discharge it by using the energy stored by importing Na+. Hence, it is referred to as secondary active transport, as no direct energy input from ATP is needed, but instead it utilizes the electrochemical gradient created by the Na+,K+-ATPase.
These considerations should clarify your issues and answer your question on what co-transport exactly is. Specifically, the glucose transporter mentioned, GLUT1 as you refer to, is a symporter that mediates secondary active transport.
- Cooper, The Cell, 2000
- Haraki & Inagaki, J Diabetes Invest 2012; 3: 352-3
- Molecular Cell Biology, 2000