Hello!
I'm not sure about research in protein Biochemistry, but the Department of Chemistry in the School of Science at the University of Tokyo offers a master's program and PhD program completely in English. All graduate-level courses are in English and many of the students have a very good command of English. The other departments in the School of Science are also quite good if you can only speak English but to my knowledge, their courses are in Japanese. I will include the link to their graduate-level admissions page: School of Science at The University of Tokyo
The graduate-level programs in Japan work similarly to most of Europe's, where you must first get a master's degree and then you can apply for a PhD program and get a PhD.