how does the transient structural conformations and different phosphorylation states of a specific membrane protein helps cells to accumulate potassium ions against a strong gradient.

Answer 1

This question requires a two part answer, so please forgive me for the longer answer in advance.

Structural conformations in structures such as ion channels are a method that certain proteins use to accomplish their function. For example, many of the various types of potassium channels sill change their shape (aka conformation) when potassium binds to them from the outside of the cell. This conformational change then pulls in the ions as it occurs, releasing them inside the cell once the change is finished. As potassium is released, the protein then changes its conformation once again, back to its 'natural' state, or the state it is in when no ions are bound to it.

Meanwhile, phosphorylation is one of the methods the cell utilizes to moderate enzyme activities. A good rule of thumb is that an enzyme is activated when it is phosphorylated, but this is not always the case. By adding one or several phosphate groups to the protein, the cells can modulate how quickly the enzyme will perform its function. Going back to our ion channel examples, many of the potassium ion channels will not be able to hydrolyze ATP while unphosphorylated. These channels are called ATP-ases, and they will require another enzyme called a protein kinase to come along and phosphorylate the channel. Then, and only then, will they be able to take energy from ATP, which is required for active transportation. Active transportation is when a membrane protein moves a molecule against its concentration gradient.