Unfortunately there still seems to be somewhat of a gap between theoretical and experimental work on autocatalytic sets. However, several initials steps towards closing this gap have already been made.
For example, the experimental system from the Lehman lab has been studied formally using RAF theory . Not only did this lead to an accurate reproduction of many of the experimental results, but also to new insights and predictions that would have been very difficult to obtain from experiments alone.
Furthermore, the metabolic network of E. coli has been investigated with the formal RAF framework . This study found that 98% of the reactions in this metabolic network together form an autocatalytic set. These results also recover certain properties of the metabolic network that were known from a biological perspective, and which are now verified and supported in a mathematical way.
Other important work focuses on modeling the emergence and dynamics of autocatalytic sets in so-called protocells (membrane-bounded vesicles) , or on using more realistic models of chemistry such as graph grammars .
These important initial steps show the applicability and validity of the formal autocatalytic sets framework to real chemical and biological systems, supporting the original idea of life as functionally closed and self-sustaining systems. Further work on bringing experiments and theory closer together is part of the current collaboration.
 W. Hordijk and M. Steel. A formal model of autocatalytic sets emerging in an RNA replicator system. Journal of Systems Chemistry 4: 3, 2013.
 F. L. Sousa, W. Hordijk, M. Steel and W. F. Martin. Autocatalytic sets in E. coli metabolism. Journal of Systems Chemistry 6:4, 2015.
 M. Villani, A. Filisetti, A. Graudenzi, C. Damiani, T. Carletti and R. Serra. Growth and division in a dynamic protocell model. Life 4: 837–864, 2014.
 J. L. Andersen, C. Flamm, D. Merkle and P. F. Stadler. Inferring chemical reaction patterns using rule composition in graph grammars. Journal of Systems Chemistry 4: 4, 2013.