Combinatorial Strategy for Studying Biochemical Pathways in Double Emulsion Templated Cell-Sized Compartments

Abstract Cells rely upon producing enzymes at precise rates and stoichiometry for maximizing functionalities. The reasons for this optimal control are unknown, primarily because of the interconnectivity of the enzymatic cascade effects within multi-step pathways. Here, an elegant strategy for studying such behavior, by controlling segregation/combination of enzymes/metabolites in synthetic cell-sized compartments, while preserving vital cellular elements is presented. Therefore, compartments shaped into polymer GUVs are developed, producing via high-precision double-emulsion microfluidics that enable: i) tight control over the absolute and relative enzymatic contents inside the GUVs, reaching nearly 100% encapsulation and co-encapsulation efficiencies, and ii) functional reconstitution of biopores and membrane proteins in the GUVs polymeric membrane, thus supporting in situ reactions. GUVs equipped with biopores/membrane proteins and loaded with one or more enzymes are arranged in a variety of combinations that allow the study of a three-step cascade in multiple topologies. Due to the spatiotemporal control provided, optimum conditions for decreasing the accumulation of inhibitors are unveiled, and benefited from reactive intermediates to maximize the overall cascade efficiency in compartments. The non-system-specific feature of the novel strategy makes this system an ideal candidate for the development of new synthetic routes as well as for screening natural and more complex pathways

A Coq Library of Undecidable Problems

International audienceWe propose a talk on our library of mechanised reductions to establish undecidability results in Coq. The library is a collaborative effort, growing constantly and we are seeking more outside contributors willing to work on undecidability results in Coq

A Coq Library for Mechanised First-Order Logic

International audienceWe report about an ongoing collaborative effort to consolidate several Coq developments concerning metamathematical results in first-order logic [1, 2, 11, 10, 8, 7, 6, 15, 12] into a single library. We first describe the framework regarding the representation of syntax, deduction systems, and semantics as well as its instantiation to axiom systems and tools for user-friendly interaction. Next, we summarise the included results mostly connected to completeness, undecidability, and incompleteness. Finally, we conclude by reporting on challenges experienced and anticipated during the integration. The current status of the project can be tracked in a public fork of the Coq Library of Undecidability Proofs [3]. Framework In principle, we follow ideas and suggestions present in various approaches [14, 9, 5, 4, 13] to the representation of first-order logic in CIC. Over the span of our initial projects we tried out several variants and found the final framework to be most suitable. Notably, a previous version used the Autosubst 2 tool [16] to generate the syntax, which we decided to avoid in later versions due to its use of function extensionality. The final framework, however, still follows the same design principles for binding and substitution. The syntax is represented by inductive types for terms t : T and formulas ϕ : F depending on signatures of function symbols f and relation symbols P as well as a collection of binary connectives 2 and quantifiers ∇