I am reading about a paper about inferencing pathway information in cancer cells. Authors refer to ERBB2 as a gene and a pathway. I don't have solid biology background. What exactly means when we refer to ERBB2 as a pathway? Does it refer to activity of a protein encoded by ERBB2?
ErbB2 is a receptor tyrosine kinase. This is a class of receptors, which are located in the membrane ob the cell and which pass signals from the outside of the cell into it, so it can for example react to changing conditions.
ErbB2 (which is also called HER2, which translates into "human epidermal growth factor receptor 2") normally reacts when it binds it ligand epidermal growth factor (EGF). Upon binding, ErbB2 changes its conformation, phosphorylates itself (meaning it adds phosphogroups to specific amino acids of the protein) which leads phosphorylation (and therefore activation) of other proteins, which finally results in changed expression of genes, which are involved in cellular proliferation, differentiation, and survival (see this reference: "Review of epidermal growth factor receptor biology.").
This leads to the second part of your question what pathway means in this context: The sequence of different molecules which start at the receptor and finally induces changes of gene expression in the cells nucleus are called pathway. For members of the Erb-family of receptors there are different possibilites, but the picture below shows how this works in principle:
The image is from the Wikipeadiapage on EGFR. You can see, that the ligand binds extracellular to the receptor, which is then phosphorylated, and then passes the signal downstream for example to Ras-Raf-Mek-Erk and then into the nucleur (in fact, activated Erk enters the nucleus).
This cascade also shows, why these receptors are often mutated in cancers: They are involved in the regulation of genes important for survival, proliferation and differentiation, which is very important for cancer cells. ErbB2 for example is mutated in about 30% of breast cancers. These mutations often lead to a constitutive active receptor which is permanently phosphorylated independent of ligand binding. This leads to a permanent activation of the downstream pathways which is obviously not a good thing, since these genes are normally under a very tight regulation.
ERBB2 appears to be a (tyrosine kinase) receptor; that is, it lives in the cell membrane; with a part that sticks outside of the cell, and part that sits inside. When the right molecule attaches to the outside part, the inside part changes shape, which alters its function, causing it to start phosphorylating other proteins, which alters their functions.
So the ERBB2 pathway is the set of genes/proteins whose behavior is affected by ERBB2.
Google "ERBB2 pathway" and "tyrosine kinase receptor" for more info.