The question I provided asks for a detailed explanation of the mechanisms and pathways within the gut-brain axis that are affected by psychobiotics. It also seeks to understand how these interactions between psychobiotics and the gut-brain axis ultimately impact aspects of mental health and cognitive function. This question delves into the scientific and technical aspects of the field of psychobiotics, which explores the connection between gut microbiota and mental well-being. Researchers in this field investigate how certain microorganisms, often referred to as psychobiotics, can influence brain function and mental health through the gut-brain axis. A comprehensive answer would require a detailed understanding of microbiology, neurobiology, and their complex interactions.