Membrane transport

A cell must constantly take in nutrients and ions and get rid of wastes, yet its membrane blocks most of them (lesson 6). The solution is a set of transport mechanisms, some requiring no energy and some driven by ATP, that let the cell choose what crosses and in which direction. Membrane transport underlies nerve impulses, kidney function, nutrient absorption, plant water balance and the action of many drugs. This lesson moves from simple diffusion through osmosis and protein-mediated transport to the bulk movement of material in vesicles.

Diffusion: random motion with a direction

Molecules in a liquid jostle randomly, colliding billions of times a second. If a substance is more concentrated in one place than another, random motion alone will, on average, carry more molecules from the crowded region to the less crowded one, until the concentration is even. This net movement down a concentration gradient is diffusion. It needs no energy input beyond the heat that keeps molecules moving; the gradient itself is a form of stored energy that diffusion spends.

Diffusion is fast over short distances and hopelessly slow over long ones. The average time for a molecule to diffuse a distance \(x\) grows with the square of the distance, roughly \(t \approx x^2 / 2D\), where \(D\) is the diffusion coefficient. For a small molecule in water, \(D\) is about \(10^{-9}\) m² per second.

# Time for a small molecule (D about 1e-9 m^2/s in water) to diffuse a distance x
D = 1e-9
def fmt(seconds):
    if seconds < 1: return f"{seconds*1000:.3g} ms"
    if seconds < 3600: return f"{seconds:.3g} s"
    if seconds < 86400 * 2: return f"{seconds/3600:.3g} h"
    return f"{seconds/86400/365:.3g} years"

for label, x in [("1 um (bacterium)", 1e-6), ("10 um (animal cell)", 1e-5),
                 ("100 um (large cell)", 1e-4), ("1 mm", 1e-3), ("1 cm", 1e-2), ("1 m (nerve length)", 1.0)]:
    print(f"{label:<22} {fmt(x**2 / (2*D))}")

1 um (bacterium)       0.5 ms
10 um (animal cell)    50 ms
100 um (large cell)    5 s
1 mm                   500 s
1 cm                   13.9 h
1 m (nerve length)     15.9 years

A small molecule crosses a bacterium in half a millisecond and an animal cell in about 50 milliseconds, but would take about 15 years to diffuse a metre, the length of a nerve cell running from your spine to your toes. That is why multicellular organisms need circulatory systems, why plant leaves are thin, and why long cells transport materials actively along their cytoskeleton (lesson 11). It is also another reason cells stay small (lesson 1).

Several factors speed diffusion across a membrane: a steeper concentration gradient, higher temperature, a larger surface area, a thinner membrane, and smaller, less polar molecules. The lungs maximize area and minimize thickness: their alveoli give a surface of about 70 square metres separated from blood by barriers less than a micrometre thick.

Osmosis: the diffusion of water

Water crosses membranes too, partly through the bilayer but mostly through channel proteins called aquaporins, discovered by Peter Agre, who shared the 2003 Nobel Prize in Chemistry for the work. The net movement of water across a selectively permeable membrane, from a region of lower solute concentration to a region of higher solute concentration, is osmosis. Put another way, water moves toward where there is relatively less free water.

Biologists describe solutions relative to a cell. A hypertonic solution has a higher concentration of non-penetrating solutes than the cell, so water leaves the cell. A hypotonic solution has a lower concentration, so water enters. An isotonic solution has the same, so there is no net movement. The effects differ depending on whether a cell has a wall.

Medical solutions given intravenously must be isotonic with blood. Normal saline, 0.9 per cent sodium chloride, is about 154 mM NaCl, which gives about 308 milliosmoles per litre because each NaCl dissolves into two particles, close to the roughly 290 mOsm/L of blood plasma. Giving pure water intravenously would burst red blood cells. Freshwater protists live in a permanently hypotonic world and pump water out with contractile vacuoles; saltwater fish drink seawater and excrete salt through their gills.

Water potential

Plant biologists describe water movement with water potential (Ψ, the Greek letter psi), measured in megapascals (MPa). Water always moves from higher (less negative) to lower (more negative) water potential. Pure water at atmospheric pressure has Ψ = 0. Water potential has two main components: solute potential (Ψs), which is always zero or negative because solutes reduce free water, and pressure potential (Ψp), which is positive when a cell pushes against its wall.

In the solute potential formula, \(i\) is the number of particles each solute molecule dissolves into (1 for sucrose, about 2 for NaCl), \(C\) the molar concentration, \(R\) the gas constant (0.00831 L·MPa per mol per kelvin) and \(T\) the temperature in kelvin.

# Water potential: psi = psi_s + psi_p, psi_s = -i C R T
R = 0.00831     # L MPa / (mol K)
def solute_potential(i, molar, temp_c):
    return -i * molar * R * (temp_c + 273.15)

cell = -0.70 + 0.30
for name, i, c in [("pure water", 1, 0.0), ("0.10 M sucrose", 1, 0.10),
                   ("0.20 M sucrose", 1, 0.20), ("0.15 M NaCl", 2, 0.15)]:
    psi = solute_potential(i, c, 20)
    direction = "into cell" if psi > cell else ("out of cell" if psi < cell else "none")
    print(f"{name:<15} psi = {psi:6.2f} MPa   water moves {direction}")

pure water      psi =  -0.00 MPa   water moves into cell
0.10 M sucrose  psi =  -0.24 MPa   water moves into cell
0.20 M sucrose  psi =  -0.49 MPa   water moves out of cell
0.15 M NaCl     psi =  -0.73 MPa   water moves out of cell

Passive transport with proteins: channels and carriers

Ions and polar molecules cross membranes with the help of transport proteins. When they move down their gradient, no energy is needed, and the process is called facilitated diffusion. There are two kinds of proteins involved.

Channel proteins form water-filled pores through the membrane. They are highly selective: a potassium channel lets potassium ions through about 10,000 times more readily than the slightly smaller sodium ions, because its narrow filter is shaped to fit a potassium ion stripped of its water. Channels are fast, passing up to tens of millions of ions per second. Many are gated, opening only in response to a voltage change, a binding molecule or mechanical stretch. Gated sodium and potassium channels produce nerve impulses, a subject for neurobiology (BIOL-420).

Carrier proteins bind a specific molecule on one side, change shape, and release it on the other. They are slower than channels, typically hundreds to thousands of molecules per second, and they saturate: once all carriers are busy, adding more substrate does not speed transport, just as an enzyme reaches a maximum rate (lesson 8). The GLUT family of glucose transporters are carriers; GLUT4 in muscle and fat cells is moved to the cell surface when insulin signals, which is how insulin lowers blood sugar.

Active transport: pumping uphill

To move a substance against its gradient, from low to high concentration, a cell must spend energy. In primary active transport, the energy comes directly from ATP. The most important example is the sodium–potassium pump (Na+/K+-ATPase), discovered by Jens Christian Skou, who shared the 1997 Nobel Prize in Chemistry. In each cycle it uses one ATP to pump three sodium ions out of the cell and two potassium ions in.

The pump keeps sodium about ten times more concentrated outside the cell than inside, and potassium about thirty times more concentrated inside. Because it moves more positive charge out than in, it also helps make the inside of the cell negative, typically about −70 millivolts. In neurons the pump can use a large share of the cell's ATP, and the brain as a whole uses about 20 per cent of the body's resting energy, much of it to restore ion gradients.

# Energy budget of the sodium-potassium pump (illustrative numbers)
pumps_per_cell = 1_000_000       # a typical order of magnitude
cycles_per_second = 100          # each pump at moderate activity
atp_per_second = pumps_per_cell * cycles_per_second
print(f"ATP used per second by pumps: {atp_per_second:.1e}")
print(f"Na+ exported per second:      {3 * atp_per_second:.1e}")
print(f"K+ imported per second:       {2 * atp_per_second:.1e}")
print("Net positive charges moved out per cycle:", 3 - 2)

ATP used per second by pumps: 1.0e+08
Na+ exported per second:      3.0e+08
K+ imported per second:       2.0e+08
Net positive charges moved out per cycle: 1

The gradients the pump builds are themselves a store of energy, which cells spend in secondary active transport. Here a transporter couples the downhill movement of one substance, usually sodium flowing back into the cell, to the uphill movement of another. In symport (cotransport), both move the same way: the sodium–glucose cotransporter (SGLT1) in the intestine uses sodium flowing in to drag glucose into cells even when glucose is more concentrated inside. In antiport (exchange), they move in opposite directions: the sodium–calcium exchanger in heart cells uses sodium entry to push calcium out.

That coupling has saved millions of lives. Oral rehydration solution, a simple mixture of salts and glucose in water, treats the severe dehydration caused by cholera and other diseases that cause severe diarrhea. It works because the sodium–glucose cotransporter keeps working during cholera, so glucose and sodium are absorbed together and water follows by osmosis. It has been estimated to have saved tens of millions of lives since the 1970s.

Bulk transport: vesicles in and out

Large molecules such as proteins and polysaccharides, and even whole bacteria, are too big for transporters. Cells move them in membrane-bound vesicles. In exocytosis, a vesicle from the Golgi fuses with the plasma membrane and releases its contents outside; neurons release neurotransmitters this way, and the pancreas releases insulin. In endocytosis, the plasma membrane folds inward and pinches off a vesicle containing material from outside.

There are three forms of endocytosis. In phagocytosis (cell eating), cells such as macrophages and amoebas extend their membrane around a large particle, such as a bacterium, and engulf it; the vesicle then fuses with a lysosome. In pinocytosis (cell drinking), cells take in droplets of extracellular fluid with whatever is dissolved in it. In receptor-mediated endocytosis, specific receptors on the cell surface bind particular molecules, cluster into pits coated with the protein clathrin, and pull in their cargo efficiently. Cells take up cholesterol this way, carried in blood as low-density lipoprotein (LDL). People with familial hypercholesterolemia have faulty LDL receptors, so cholesterol stays in their blood and they develop heart disease early, a discovery that won Michael Brown and Joseph Goldstein the 1985 Nobel Prize in Physiology or Medicine.