I’m not sure we can compute this for “cells,” as that term is to imprecise to be useful.
What @Art did very helpfully is point out a key paradox that traces to one of the great mysteries of science: hydrophobicity. It is a very reliable macroscopic observation, but just as the term implies (hydro=water) it seems idiosyncratic to water in many ways. At the atomic scale, we see it operating too too. This is a key “force” driving a great deal of “ordering” within cells, but we did not even know what it was for a long time.
It is because of hydrophobicity that:
- Most protein-protein interactions take place.
- Cell membranes made of lipid bilayers are such good insulators.
- Lipid bilayers form spontaneously in solution with water from constituent parts.
It turns out that our mental image of proteins floating around in space is all wrong. Instead, everything is actually in tight association with water molecules. Note that I said molecules. Turns out that to understand hydrophobic “force” we have to understand how discrete water molecules interact with one another. The hydrophobic “force” emerges from these interactions as an entropic penalty incurred by limiting degrees of freedom in solute-associated water molecules.
At room temperature, water is a liquid but it is an ordered liquid, because of a spontaneous hydrogen bond forming networks (enthalpic bonus), but in liquid form is also an unstable network (entropic bonus). This is, as I understand it, an important for explaining another paradox of water: remember, water expands when it freezes, unlike just about everything else. That is a discussion for another day.
Regarding hydrophobic force, we find out that
water molecules can form an extended three-dimensional network. Introduction of a non-hydrogen-bonding surface disrupts this network. The water molecules rearrange themselves around the surface, so as to minimize the number of disrupted hydrogen bonds. This is in contrast to hydrogen fluoride (which can accept 3 but donate only 1) or ammonia (which can donate 3 but accept only 1), which mainly form linear chains.
That special arrangement increases the enthalpy relative to another configuration, but in decreases the entropy substantially. Now the waters are stuck in a cage around the solute.
The water molecules that form the “cage” (or clathrate) have restricted mobility. In the solvation shell of small nonpolar particles, the restriction amounts to some 10%. For example, in the case of dissolved xenon at room temperature a mobility restriction of 30% has been found. In the case of larger nonpolar molecules, the reorientational and translational motion of the water molecules in the solvation shell may be restricted by a factor of two to four; thus, at 25 °C the reorientational correlation time of water increases from 2 to 4-8 picoseconds. Generally, this leads to significant losses in translational and rotational entropy of water molecules and makes the process unfavorable in terms of the free energy in the system. By aggregating together, nonpolar molecules reduce the surface area exposed to water and minimize their disruptive effect.
The hydrophobic effect was found to be entropy-driven at room temperature because of the reduced mobility of water molecules in the solvation shell of the non-polar solute; however, the enthalpic component of transfer energy was found to be favorable, meaning it strengthened water-water hydrogen bonds in the solvation shell due to the reduced mobility of water molecules.
This fact alone is enough to explain why it is easy to form a folded protein. Essentially, all you need is alternating blocks of hydrophobic and hydrophilic residues. Because the size of the blocks is no that important, this arises by random chance very easily.
Any how, I am very appreciative to @art for reminding me of this.
How does this impact the discussion? Well, the issue is that our natural intutions here are not helping us. It seems right that the cell is more ordered. However, that does not mean it has lower entropy. That claim requires