Intermembrane space of mitochondrion

This article describes a component of the organelle mitochondrion in cells.
Unless otherwise specified, information about this component is about its in situ occurrence in vivo, i.e., its occurrence in its usual location in living cells.

Definition

The intermembrane space of mitochondrion (IMS) is a space between the two membranes of a mitochondrion: the outer mitochondrial membrane (bounding it on the outside, and separating it from the cytosol or adjacent mitochondria in the mitochondrial network) and inner mitochondrial membrane (bounding it on the inside, and separating it from the mitochondrial matrix).

Summary

Item	Value
Type of organisms whose cells contain the intermembrane space	Same as the organisms whose cells contain mitochondria: eukaryotic cells only, including plant cells, animal cells, and the cells of protists and fungi
Type of cells within the organisms that contain the intermembrane space	Same as the cells that contain mitochondria: all cells except red blood cells in mammals (other vertebrates do have mitochondria in their red blood cells).
Number of intermembrane spaces per cell	Same as the number of mitochondria: 1 to 1000s, depending on the energy needs of the cell
Size	$~200$ angstrom or $~20nm$ thickness (very approximate), accounting for less than 5% of the length (less than 10% even if you consider that it's on both sides).
Location within the mitochondrion	It is right inside of the boundary of the mitochondrion (the boundary is the outer mitochondrial membrane).
What's on both sides of it	Inside: inner mitochondrial membrane (separating it from the mitochondrial matrix), outside: outer mitochondrial membrane (separating it from the cytosol or adjacent mitochondria in the mitochondrial network)
Structural components	The intracristal space is the part of the intermembrane space between the folds (cristae) of the inner mitochondrial membrane. The peripheral space is the part of the intermembrane space farther out of the inner mitochondrial membrane.
pH	About 7.0 to 7.4. Although still a little alkaline, it is less so than the mitochondrial matrix and less so than the rest of the cell, due to the pumping out of protons from the mitochondrial matrix as part of the electron transport chain.

Size and shape

Limitations of study

Unlike the mitochondrion as a whole, the intermembrane space of mitochondrion is too small to be seen with a light microscope. The electron microscope that is necessary to see it can be destructive to the living cell and may change the shape of the mitochondrion.

Shape

The entire mitochondrion (bounded by the outer mitochondrial membrane) can be approximated as a rounded cylinder (cylinder with rounded edges) and the mitochondrial matrix (bounded by the inner mitochondrial membrane) can be approximated as a rounded cylinder that is fully inside it. The intermembrane space is the region that's in the bigger rounded cylinder and outside the smaller rounded cylinder, and its thickness (up to 20 nm) represents the margin around the smaller cylinder.

This crude description captures the concept of the peripheral intermembrane space. The intracristal space is a bunch of little crevices in the inner cylinder.

Size and volume calculation

We use this size range for the mitochondrion:

The length is generally at least 1 $\mu m$ and at most 4 $\mu m$ .
The tubular radius is generally at least 0.5 $\mu m$ and at most 1 $\mu m$ .

We also use that the thickness of the intermembrane space is about 20 $nm$ .

Illustratively, and using the biggest size estimates, let's say the mitochondrion has a length of 4 $\mu m$ , a tubular radius of 1 $\mu m$ , and an intermembrane space that is uniformly 20 $nm$ thickness. Let's model the mitochondrion and mitochondrial matrix as cylinders.

Volume of the mitochondrion is $\pi r^{2}h$ where $r=1\mu m,h=4\mu m$ , giving $12.57\mu m^{3}$
Volume of the mitochondrial matrix (the inner cylinder) is $\pi r^{2}h$ where $r=0.98\mu m,h=3.96\mu m$ (these values are obtained by subtracting the thickness of the IMS from the radius and twice the thickness of the IMS from the height), giving $11.95\mu m^{3}$ . The difference is $0.62\mu m^{3}$ .

A cubic micrometer ( $\mu m^{3}$ ) is the same as a femtoliter, or $10^{-15}$ liters. So the volume of the intermembrane space works out to be $0.62fL$ . But this is the upper end. The lower end would be roughly about 1/16 of this, or about $0.04fL$ .

Note that this calculation is most faithful for the peripheral IMS. The intercristal IMS is not covered here, but likely does not cover much volume (its significance is more in terms of the high surface area that it covers, not the volume).

Mass

Since most cellular matter is approximately as dense as water, we can approximate the density of the intermembrane space using the density of water, which is about 1 gram per milliliter. Based on the volume estimate above, we get that the mass of a mitochondrion is approximately between 0.04 and 0.62 picograms, where a picogram is $10^{-12}$ grams.

Comparison with the sizes of protein and phospholipids (the constituents of the membranes surrounding it) (within one order of magnitude apart)

The intermembrane space is the space between two biological membranes: the inner mitochondrial membrane and the outer mitochondrial membrane. Each of these is a lipid bilayer with membrane proteins, including membrane proteins that are partly or wholly on the intermembrane space side. (Any membrane transport protein -- any protein that transports stuff across the membranes -- must be a transmembrane protein and hence be on both sides).

To get a better sense of the thickness of the intermembrane space, therefore, it makes sense to compare this with the size of phospholipids (the stuff the lipid bilayer is made of) and proteins (in general, and the particular ones found in the IMS).

Lipid bilayers are in the 3-7 nm range.
Protein diameters can vary between 2 nm and 12 nm, with most proteins in the 2-6 nm range. Not all of this protein diameter would be on the IMS side though; for the transmembrane proteins, some of the protein would be on the other side.

Overall, the thickness of the IMS is about 3 to 10 times the range of thicknesses for the membranes and membrane proteins. A visual analogy here might be to think (locally) of the IMS as a corridor and the lipid bilayers of the inner and outer mitochondrial membranes as the walls on the two sides of the corridor, with the proteins being the doors. This analogy helps give a rough sense of the relative scales.

Chemical composition

Number of hydrogen ions

NOTE: In practice, hydrogen ions are rarely floating freely -- they are usually bound to at least one water molecule, forming a hydronium ion. For ease of discourse, we say "hydrogen ion"; the term "proton" may also be used, but it's important to keep in mind that this is referring to single-proton atomic nuclei, not to protons that exist in larger atomic nuclei.

The pH of the IMS ranges between 7.0 and 7.4. In other words, it's a little more alkaline than neutral pH (at human body temperature, neutral pH is about 6.8). Combining this with the size calculation, we can estimate the number of protons (hydrogen ions) in the IMS.

At the upper end would be the case of a pH of 7.0. That means that there are $10^{-7}$ moles of hydrogen per liter. Our upper estimate for IMS volume is $0.62fL=0.62*10^{-15}L$ , which gives a total of $0.62*10^{-22}$ moles of hydrogen ions in the IMS. 1 mole of something is $6.023*10^{23}$ many of that, so plugging that in, we get:

$0.62*10^{-22}*6.023*10^{23}=37.34$

So we get a grand total of 37.34 hydrogen ions in the IMS! That's not a lot of hydrogen ions. Obviously, the numbers here are all approximations -- the actual number of ions at any given time should be an integer. But note that this is using the high-end estimates, so at the lower end of the range, we have even fewer hydrogen ions. Overall, we expect a single-digit or double-digit number of hydrogen ions in the IMS.

The IMS has the ability to freely exchange hydrogen ions across the outer mitochondrial membrane with both its neighbor mitochondria (the adjacent nodes to it in the mitochondrial network) and the cytosol. Thus, even though the number of hydrogen ions in a single IMS may seem too small to be stable, the ability to exchange hydrogen ions means there is a bit more stability in numbers. Relatedly, it's worth noting that the cytosolic pH is at the high end (about 7.4). Therefore, protons would be expected to diffuse out from the IMS into the much bigger cytosol, eventually causing the IMS to get to a pH of 4. The reason this doesn't usually happen, and the IMS is able to maintain a slightly lower pH (higher concentration of hydrogen ions) than the surrounding cytosol is the pumping of protons from the mitochondrial matrix across the inner mitochondrial membrane.

Other small molecules

As the outer mitochondrial membrane is freely permeable to small molecules, the intermembrane space can be thought of as being contiguous with the cytosol as far as small molecules are concerned. In particular, the concentration of each molecule in the IMS is expected to roughly match the concentration in the cytosol. Hydrogen ions, as discussed in the preceding section, are a partial exception, insofar as the IMS has somewhat higher concentration of hydrogen ions due to receiving these ions regularly from the mitochondrial matrix.

The IMS can differ quite a bit from the mitochondrial matrix, since the inner mitochondrial membrane, that separates the two, is extremely selective.

Example calculation: in human cells, cellular potassium concentration is about 150 mmol/L. With a volume of $0.62*10^{-15}L$ , that works out to:

$0.62*10^{-15}*150*10^{-3}*6.023*10^{23}=56013900$

That's about 56 million potassium ions. It's a lot more than hydrogen ions, which is as expected from the fact that there's a million-fold concentration difference.

Proteins

Large molecules, such as proteins, cannot freely move through the outer mitochondrial membrane. So, the protein composition of the IMS can (and does) differ from that of the cytosol. It also differs from the protein composition of the mitochondrial matrix, as proteins are not freely transported across the inner mitochondrial membrane.

The intermembrane space cannot make its own protein, so the protein it does get it must get from the cytosol, and it can get only those proteins from the cytosol that the outer mitochondrial membrane allows.

The determination of what proteins are allowed is itself done by complexes of membrane transport proteins (these are transmembrane proteins that help transport stuff across the membrane):

The translocase of the outer membrane (TOM) complex is a complex of membrane transport proteins on the outer mitochondrial membrane that control what proteins are allowed to move across the outer mitochondrial membrane (between the cytosol and the intermembrane space).
The translocase of the inner membrane (TIM) complex is a complex of membrane transport proteins on the inner mitochondrial membrane that control what proteins are allowed to move across the inner mitochondrial membrane (between the intermembrane space and mitochondrial matrix).

Together, these complexes control the protein composition of the intermembrane space. The TOM complex determines what gets in from the cytosol outside, and the TIM complex determines what of it goes into the mitochondrial matrix.