Well, generally they are expecting that you have an overview about that what you will doing in your experiments. Understanding the techniques which you will use to get you to your target/aim. Normally, they should give you an main project which will be splitted or added into small project during your Phd Journay.
Its not easy with your description to make an clear research statment. You know that breat cancer is well studied field in oncology. So you must specify little bit more.
Field in which you will be involved are:
1. Molecular Biology - Recombinant DNA Technology, Cloning, PCR, qPCR, DNA Microarray, etc.
2. Biochemistry - Recombinant Protein Technology, SDS-PAGE, Wester-Blot, IP, Pulldown etc.
3. Cell Biology - Primary Cell, Immortalized Cell Line, Transient/Stable Transfection, siRNA and/or shRNA, MTT Test, Apoptosis Test, Proliferation Assay etc.
4. Screening - small molecules Library, Inhibitors etc.
Are the buffers bought from a company and is there SDS inside? One PhD in our Lab changed the whole Kit because she was not able to read. How stuipid, isnt? Generally, most buffer are store in RT. If there is contamination then it is quite a old solution. Try to for cell culture always aotuclaving the solution and the others in the Lab as you know wiht ddH2O and store tightly closed. Make new once if frequently used. To my knowledge like TAE or TBE or Running Buffer you can make stock solutions so there is no chance to growth for contaminants. And its not specific for TRIS its just a matter of handling your solution. If i was able to help you.
Maybe your T7 Promotor is to strong. The more is less and the less is more sometimes. And you can use a protein tag to make your ptotein soluble. Check for this pET-Manual. Use Glucose if your gene is toxic as an addition option.
Yes i know Sambrook and Maniatis. But you missed the sign behind 1000 . "Liters". But RIPA is quite a strong Lysis Buffer. However you say that there is no other technique to break the cells in high amount conc. than Lysis Buffer?