The way you asked your question has very limited choices. Usually, changes in the tertiary structure of a protein are due to some changes in secondary structures. But in your question you excluded that. So, I would think that we have a case, most likely theoretical, how to determine the changes in the size of protein without solving the structure, and without using Circular Dichroism (CD) spectroscopy.
Still there is a method, and that would be, in my opinion, Dynamic Light Scattering (DLS). This method will allow you to measure changes in the size of a protein due to, for example, changes in pH, or ligand concentration, probably even due to temperature changes.
Tryptophan fluorescence and near-UV circular dichroism are methods can detect changes in tertiary structure of a protein. Microscale thermophoresis is another method. Still another is limited proteolysis, in which you look for changes in protease sensitivity by SDS-PAGE.
Yes, I already tried CD. It does not show any changes in near and far UV region (but as I learned, no change in near UV does not definitely mean that there isn't a change in tertiary structure.) Do you have any suggestions to have the detection of this region more sensitive (because signals are much smaller in near UV region)?
No changes in Fluorescence =(
For the DLS: Which instrument would you use? Our Malvern Zetasizer Nano ZS measures at its limit with this protein of about 10 nm size. (But indeed I see a small difference between the conformations).
To explain a little bit more: I need to characterize a protein which appears in either linear or circular form (circular form with both ends interacting at a small region). That's why it's possible that there are no change in secondary structure (or too small to detect in CD) but a large change in tertiary structure.
The equipment you have should be fine. Just few more questions. How big is your protein? Based on what you are getting ~10nm (100 Angstrom), it is equivalent to the size of 360KDa, is your protein that big? And I checked specifications of your equipment 10nm is the upper limit (which means not reliable).
1. If ends of the molecule may interact and form a circular form, what prevents your protein using that feature to form linear oligomers? Maybe you have to adjust the concentration (or other conditions) and make sure that the weigh and the size of your protein are correlated with calculations based on the sequence of your protein.
2. You have to make sure that you have only one form (a linear or circular) in the solution, and not a mixture of both forms. You have to find conditions which stabilize one or another form and perform measurements at those conditions.
These rules apply to any method you are going to use, not only DSL. You have to make sure that you have a stable form (linear), which under external conditions will change to another stable form (circular). You have to know and control conditions at which transition is happening, and avoid measuring at that point
If you can label your protein with fluorescent markers, you could also use FRET to measure the differences in the distance between the two ends of your protein in the two different forms. This should give you even more information about the two conformations than the suggest other methods.
If you can reach a high concentration of your protein (e.g. 1+ mg/ml) and have some Trp in the protein, you might also consider CD spectroscopy in near-UV region. This doesn't tell you what exactly happens, but may show significant changes. If your protein is big, than also techniques like AUC or, DLS can be used. I assume, you don't have access to Cryo-EM, which might be interesting for really big proteins or complexes.