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 relevant work focuses on modeling the emergence and dynamics of autocatalytic sets in so-called protocells (membrane-bounded vesicles) , or on using more realistic models to generate chemical reaction networks, such as graph grammars .
In terms of experiments, protocell dynamics and evolvability are being investigated using sophisticated microfluidics techniques . This can provide experimental validation for the theoretical and computational models, and provide useful feedback to improve and fine-tune these models.
Future work will consist of combining several of these theoretical and experimental techniques to further study the emergence and evolution of autocatalytic sets in protocells. Given the highly interdisciplinary nature of such work, our team consists of a diverse group of scientists spanning the entire range of required expertise.
 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.
 R. Serra and M. Villani. Modelling Protocells. Springer, 2017.
 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.
 S. Matsumara, A. Kun, M. Ryckelynck, F. Coldren, A. Szilágyi, F. Jossinet, C. Rick, P. Nghe, E. Szathmáry and A. D. Griffiths. Transient compartmentalization of RNA replicators prevents extinction due to parasites. Science 354: 1293-1296, 2016.