Researchers take the average density of proteins to be 1.38×10^3kg/m^3.

On protein folding, residues are transferred from solution to the close-packed interior of the molecule. This change produces different effects on different groups: aliphatic groups occupy smaller volumes in proteins than they do in solution; polar groups occupy larger volumes. Examination of the surfaces buried in a wide range of proteins shows that the proportions of these groups that become buried is essentially constant and are such that the positive and negative volume changes cancel each other out. So the net volume changes on folding/unfolding are very small. Therefore there isn't a significant density difference between folded & unfolded states of a protein. You can check the link:

https://doi.org/10.1016/S1359-0278(98)00016-9

I am not an specialist on that, but, from experimental measurements of the partial thermal expansion coefficient of a protein as a function of the temperature using Pressure Perturbation Calorimetry (a technique similar to DSC for determining thermal and volumetric properties of macromolecules), there would be a non-zero change in the partial molar volume of the protein upon unfolding. Then, that non-zero change in the partial molar volume would be associated to a non-zero change in density for the protein.

Dear Meranda,

Wish you well in your studies. The question is absolutely fascinating. It is fascinating from several points of view.

1) Despite tons of literature on the nature of proteins there is no comprehensive view what they are.

2) From the point of view of organic chemist these are just simply polypeptides, i.e. the linear heterogenous polymers built of many components. By the way speaking about amino acids is irrelevant in this context as multiple level of chemical modification causes it almost never be a pure polymer as synthesized.

3) From the point of view of physics these are monomers or oligomers of randomly packed atoms of different and sometimes varied ionic or atomic radii.

4) From the point of thermodynamicist it is a very badly defined object that changes properties depending on the surroundings.

5) This all must be so because form the point of view of a biologist this must be a completely fascinating object a little bit dead and a little bit alive. As a representative of four dominant biochemical substances contributing to building live organisms it must share with these substances (nucleic acids, proteins, lipids and sugars) this mixed signature life/dead.

So what it has to do with the density. Everything.

What I described above must mean that neither of the pure methodologies of pure sciences can address what proteins are.

We define density as an average or a derivative as we would define in pure math. We know that for existence of a derivative the infinitesimals must exist. Obviously, in reference to proteins, existence of atoms preclude such math definition. So maybe we can define an average number of atoms of each kind and then count density. This is even more futile approach. Proteins are excellent buffering molecules therefore they exchange atoms and ions with the exterior. By the way internal water molecules behave as covalently bound entities for all practical purposes. So maybe w can at least use an approximation (like we do in experimental physics: define the conditions (fixed temperature, pH, solutes etc). Unfortunately, this also does not work as proteins are in constant motion. Actually their properties are derived form dynamical coupling with the solvent. So a protein is never packed tightly and it always changes its rate of vibration in response to the environment. I even neglected the Quantum Mechanics type of effects like softness of electron cloud defining the atomic distances. Moreover from the point of advanced physics this is a "self organized criticality" that exists only by coupling with the environment. So maybe we can use additional simplification like taking a representative structure from the data base. This also does not work as almost all the proteins have multiple representatives in PDB and very rarely they are identical/similar even taking into account (neglecting) the experimental errors. Unfortunately, it gets even worse. When one wants to define a folding class or a type of the protein and makes all these assumptions, an apparent density changes from protein to protein. But it gets even more complex than that. If one becomes curious and tries to select only one type of a protein and disregards the different conformers present in the literature one finds that upon fragmentation into small volumes containing representative numbers of atoms, and uses this small volume to move around a single structure/model this number (read density) changes and changes sometimes significantly. Depending a class of folding or even functionality, the definition of an average density becomes almost meaningless.

Proteins are designed for function not for structure. Every atom comes with its own "caging effect" (the name is borrowed from the theory of glasses to which proteins semi-formally belong). So the rate of rattling in these semi-stable cages determines not only the structure but also the function of the individual protein.

So in essence listen to the advice given by two responders above how and what to do, but filter it through what I said. Try to discuss this with your supervising scientist to design a reasonable inquiry instead of mindless number crunching that unfortunately dominates protein science. Experimental approaches would be even more difficult as you see from what I said, but some approximations can be made and reasonable data extracted. But it takes an effort.

Good Luck.

Bog

Answer to your Question is that the change in volume of the protein is very very small for the process Unfolded state Folded state at low pressure.

Read a very interesting paper by Chotia and associates:

Volume changes on protein folding

Yehouda Harpaz , Mark Gerstein and Cyrus Chothia

Background: Protein volumes change very little on folding at low pressure, but at high pressure the unfolded state is more compact. So far, the molecular origins of this behaviour have not been explained: it is the opposite of that expected from the model of the hydrophobic effect based on the transfer of non-polar solutes from water to organic solvent.

Results: We redetermined the mean volumes occupied by residues in the interior of proteins. The new residue volumes are smaller than those given by previous calculations which were based on much more limited data. They show that the packing density in protein interiors is exceptionally high. Comparison of the volumes that residues occupy in proteins with those they occupy in solution shows that aliphatic groups have smaller volumes in protein interiors than in solution, while peptide and charged groups have larger volumes. The cancellation of these volume changes is the reason that the net change on folding is very small.

Conclusions: The exceptionally high density of the protein interior shown here implies that packing forces play a more important role in protein stability than has been believed hitherto.

Structure (1994) 2:641-649

Yes, the volume change upon unfolding may be quite small, but it is not zero.

For example, -0.31% and -0.30% for RNaseA and Lysozyme unfolding