How to calculate the tilt angle of a protein

Question

[sizeineb]

Hi,

I have a coarse-grained trajectory of a transmembrane protein with 5 TM helices and I would like to calculate the tilt angle of the protein over time and compare it with some published data. In the publication, the tilt angle was calculated between the membrane normal (Z axis) and protein axis. The protein axis was calculated as the sum of TM secondary structure segment vectors.

Any ideas about a tool that does this or how I can calculate it, please?

Thank you in advance for your help.

[natasha.sernova]

I found a definition in their methods (long link in the bottom)!

Revisiting Hydrophobic Mismatch with Free Energy Simulation Studies

of Transmembrane Helix Tilt and Rotation

"Methods Defining the tilt and rotation angles

The orientation of a TM helix is defined by its tilt (τ) and rotation (ρ) angles.

With the Z axis parallel to the membrane normal, τ is defined as the angle

between the helical principal axis and the unit vector along the Z axis (22)".

Their ref 22 is this short link below:

https://www.sciencedirect.com/science/article/abs/pii/S0009261407005763

https://pdf.sciencedirectassets.com/277708/1-s2.0-S0006349510X00145/1-s2.0-S0006349510004789/main.pdf?x-amz-security-token=AgoJb3JpZ2luX2VjENb%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaCXVzLWVhc3QtMSJIMEYCIQCoObGya6RmhWDhTtaRFgzIQZKnxOeOCn3kcePGpaZ4KAIhAO8lc85lPGgljpMCIynR3oBaZCxISzvPbRPFYn1v6EsqKtoDCH8QAhoMMDU5MDAzNTQ2ODY1IgzHYZacWFuKN08gon0qtwOR%2FlkXMcTFKUPThhnSUy%2BIi2EV4ucKvztTBUllbo3TcJgZKrpjDNzt%2BBc%2BVDcbt2ulhGD9FPZoCVcw%2FXNtP20pdbNx%2Fr5VMPY%2BsYgd329R00PByyErmxzvKexdsGJEJwAtOJaT71qKug88Wl9VQ7XE7DvK%2BUg8ftXU8q6p2wQl5zaR6%2BR80wMiDilNniSo1eX%2BGEqGKLFTzM58W5VvzCpTLYDzqfoRdYHZwSkWCXqTURUdPvr7xcma%2FfpZifHcipD%2FP%2FODRqmQrxp5f2o5o2M4VSXZLrBzCWNoQfCThIyiv4IVt5G%2FWn7J%2FQIQ2UKUw8%2BUqaoRpyt70UPsQB11R%2BHoV8UKhgFux2gSOaEXwEdQaTtBziGLwKkGLVywH5KDrNYGU8VNNTR2VRJqhiLmw%2Bh01Q1kHqKUJks11Ae5dP3k7SqkpinAUmO2k5OrOK7e2yUy3QO3dCZ1ckX09wWYJ52aHl8BAelQYvkl5OQGzXxQ5Hz8qLeoOGYDxdX26ixnWsQkrM4lrH8YAisfsP7%2BRK06mNwESWbpXaUuPKbKI8ESaRapfBfhcO15gj1Akv4HgjwPQYChP%2BgWMPWA0OQFOrMBKpzxiRiwK3HyXsGP3Af74TQPekVws6VhxtuYSD1ObG8GhwXHH0OLaw7VEKE7uCHrkcgnVSdzHnPWekE4yJ1r7R9UaUjWJbhoF9ivvORgPOptoalRrGwTQ9SLqoialeR9Qq4pr61jwUkKkNmvfsrmNjoMpKHlWrwNQoPBJo%2BSTMzW1JJMPNc2fXIzSu57goIkIp%2F9Ui5FfK3vsPyRCs9ZE3YDY%2BX%2BMbjIsOpOGSTMYQ67ziY%3D&AWSAccessKeyId=ASIAQ3PHCVTY2DLZLM4T&Expires=1553206715&Signature=QM5ffTYMtGDFzAjFRueA3hS5LK8%3D&hash=c07268b8722822963b76a2432075591522028c24358bf34fab158c90ae01a606&host=68042c943591013ac2b2430a89b270f6af2c76d8dfd086a07176afe7c76c2c61&pii=S0006349510004789&tid=spdf-2681f800-a478-46b8-9e1e-7fd61fd1bbc0&sid=dd9b8ab8331fa54a3638d032d7971db8d259gxrqb&type=client

[sizeineb]

Thanks a lot Natasha!