MicroRNA (or miRNA or even miR-) are endogenous small molecule post-transcriptional regulators that were discovered by Ambros et al in 1993. The second miRNA were characterized in 2000 but since then the field has erupted into action. A wide variety of studies have found miRNA to be involved in all types of cells and are more in number in neurons - being involved in a wide variety of functions ranging from neurogenesis, proliferation, differentiation... even pro-apoptosis and anti-apoptosis.
miRNA play a role similar to RNA interference but are more specific in their action as they act upon the 3' end of the untranslated regions of mRNA and may be involved in both switching off or modulation of gene expression. Since this is the central pathway to protein formation, miRNA play a powerful role. Interestingly, miRNA are present in both exons and introns within non-protein coding genes and due to the earlier notion that introns were not useful, miRNA have earned the epithet "jewels from the junk".
Specific miRNA have been implicated in a wide range of neurological disorders - Parkinson's disease, Alzheimers, Motor neuron disease, Schizophrenia, Bipolar disorder etc. miRNAiTechnology (miRNA interference) is being developed for therapeutic purposes.
While miRNA play a significant role in gene expression, they are themselves regulated by genes and so are definitely not beyond the gene (addressing the question posed by title of the seminar). Viji then briefly explored Prions (proteinaceous infectious substances) that were discovered by Stanley Prusiner if they could meet the criteria "beyond the gene". Prions are misfolded proteins. They don't have any nucleic acid (RNA, DNA etc) that can carry forward the information for causing information. Instead, they serve as templates for future proteins to get misfolded and are extremely stable (don't get denatured easily), hard to remove and cause damage and cell death.
The biogenesis of prions is unknown but they do impact protein formation and so the question is... could they be said to be beyond the gene?