Membranes show different permeability for different solutes that might be inside or outside the cell. The permeability of various common solutes across biological and artificial lipid bilayers is shown below. The presence of membrane proteins make biological membranes much more permeable to certain solutes than are simple artificial phosophlipid bilayers.
We have already observed that aquaporins make permeability of water higher in biological membranes than in lipid bilayers alone.
The figure below shows the various methods by which solutes can cross a biological membrane. The central role of transport proteins in the membrane is obvious here. Only certain small molecules can cross by simple diffusion (the rate of which would follow Fick's law), larger ones require a protein channel at least for movement by bulk flow (the rate of which would follow Poiseuille's equation). Others require some assistance from a carrier protein, as in facilitated diffusion (which would follow Michaelis-Menten kinetics). All three of these mechanisms are passive and do not require energy; they then also must flow downhill from an area of higher concentration to an area of lower concentration. Active transport by comparison, requires ATP or another nucleotide tri-phosphate, and can operate against a concentration gradient. Of course the rate of active transport would be dependent upon metabolic status of the cell.
The structure of the channel protein for potassium transport is shown below. As you can see, this is an integral protein with helical sections that traverse the phospholipid bilayer. The charge-sensing domains surround the channel through which the potassium ion passes. The channel itself is formed by a loop that folds to the interior between the alpha-helical regions...holding them apart enough to permit the potassium ion to pass through the channel.
The diagram below shows two ways that a solute can be brought across a membrane against its concentration gradient, but without the expenditure of energy. The membrane protein works as a kind of flip/flop. The examples shown use a gradient of protons (H+) to drive the transport of solutes A and B. In the one case, the hydrogen is coming in passively down its gradient, and brings the solute A with it (symport). In the other case, the hydrogen is coming in down its gradient, but the transport protein kicks out a solute B (antiport). Because the proton movement is energetically downhill, the energy loss can be used to drive the symport and antiport mechanisms without the use of ATP.
As you can see the H+ has accumulated outside the cell and will move toward the cytosol, down its electrochemical potential gradient as the driving force for the transport. The symport solute is more concentrated on the inside of the cell, but the cell will be able to bring another solute molecule into the cell thanks to the symport of the H+. The symport protein in the membrane accepts the hydrogen ion, creating a conformational change in the protein. The changed protein conformation now allows a solute molecule to enter the channel through the bilayer. The H+ and solute are released to the interior of the cell. Their release causes the conformation to flip-flop back into its original conformation. The process can be repeated to continue to add to the supply of the solute in the cell. It is important to note, that the solute can be accumulated against its concentration gradient without using ATP to drive it! The antiport mechanism is virtually the same, except that the solute is moving in the opposite direction from the H+. But again, the solute is moving against its concentration gradient without using any ATP. The energy comes from the energy released as the hydrogen moves down its concentration gradient.
The diagram below shows a schematic diagram of how active transport works to transport a hydrogen ion (H+) against a concentration gradient. The loss of bond energy as phosphate is cleaved from ATP. The energy causes the complex of transport proteins to spin. The energy pumps the proton from the cytosolic side to the cell wall side of the membrane. This active transport of hydrogen ions is responsible for supplying the gradient of hydrogen ions to drive all of the symport and antiport proteins of the cell.
The diagram above shows a bead model of the structure of an H+-dependent ATPase. This is an integral protein that has ten domains crossing the bilayer. Part of its structure is a proton channel, the catalytic part (facing the cytosol) binds ATP. The catalytic action causes the protons to be pumped. Proton pumps are used in a range of physiological reactions including stomatal function and cell expansion.
The diagram below gives you an overview of some of the known transport proteins in the cell membrane:
As you can see above, there are channels, sucrose facilitated diffusion carrier, calcium active transport, antiports, symports, and proton pumps to power the ports in the cell membrane. Below, you will notice that the proton-dependent ATPase can also pump protons into the vacuole.
So the pump above is accumulating acid inside the vacuole and uses ATP to pump the excess protons from the cytosol into the vacuole. Below are some example organisms that indeed accumulate acids in their vacuoles to the pH values indicated.
In a similar fashion to those in the cell membrane we can find a range of solute transport proteins in the tonoplast...the vacuole membrane.
Around this figure you can see some of the channels, symport, antiport, and proton pumps.
One thing I hope you noticed is that in both the cell membrane and the tonoplast diagrams above, there are different transporters for potassium ions (K+). Because there are multiple channels for soil minerals, there is no surprise that one might be optimized to take up the ion when it is common, and another protein is optimized to take up the ion when it is rare. Uptake of potassium then is not a monomolecular function as shown below...
As you can see, there are Michaelis-Menten kinetics for transport of K+ at two different substrate concentration ranges. This tells you two things: there are proteins involved with active sites, and there are two different such transporters. One of these transporters is optimized for lower concentrations and the other is optimized for higher concentrations of available potassium.
If you have understood this concept, then you will be able to correctly identify which transporter represents the curve on the left and which one respresents the curve on the right. Is either of them a carrier? As a hint for this latter question, here is a helpful figure: