How do proteins and genes participate in learning?
The storage of memories in cells is rarely thought of on the protein level of the cell.  Cells are usually given a developmental state, but no memory.  A cell may become a liver cell, cancerous, or diabetic, but this is not memory, but a physiological change in the cell which is usually not reversible to a previous state.  

For example cancer treatments are entirely focused on identifying the cancerous cells and killing them.   Internally the genomes of cancer cells often have deletions and duplications.  They are cancerous, they have not learned to be cancerous. Though not as dramatic, it is now thought that cellular differentiation which creates different types of cells is heavily influenced by epigenetic modification of the genome; the DNA is marked by methyl groups which dictates the state of the cell by modifying the gene.  This is mediated by proteins for sure, but is quite complex and not well understood at this time. Epigenetic markers can even change gene behavior between generations of offspring as well, though that is not usually called memory. 

How is information stored in the brain?  This is thought to be reflected in the organization of the neurons in the brain.  There are many kinds of neurons.  They can be distinguished by the sorts of axons and dendrites that emanate from the cell body.  They can also be distinguished by the chemical variety of neurotransmitter they use (there are a score of different molecules).  So to a great extent the type of cell and the specific proteins it chooses to use to mediate information is very important.  

That being said, information is currently thought to highly related to the placement of the axons and dendrites connecting the neuron to sometimes scores of other cells, sometimes touching the cell body, other times other dendrites or neurons.  As neural activity ensues, the cells will reconfigure their connections by physically moving them.  

More recently, investigators have tried to understand the genes which internally modulate the neural signals within the cells.  This nobel prize lecture discusses how the CREB/MAPK pathway can modulate Long Term Potentiation - the shape of the neuron response to a signal over time (days or hours). 

Taken as a whole, you can see that memory is likely to be stored on several levels at once - the kinds of cells (dictated by differentiation) involved, structural arrangement of the neurons (axons and dendrites connecting to various cells and places on cells), as well as internal signaling circuitry that generates and modulate the electrical and chemical activity within the cell. 

"Marker protein" only refers to a protein that you can follow to see some sort of activity in the cell. A typical example is Green Fluorescent Protein, which is colored, fused with a protein of interest.  It has no specific meaning regarding learning I think.