Modular verification of chemical reaction network encodings via serializability analysis

Abstract

Chemical reaction networks are a powerful means of specifying the intended behaviour of synthetic biochemical systems. A high-level formal specification, expressed as a chemical reaction network, may be compiled into a lower-level encoding, which can be directly implemented in wet chemistry and may itself be expressed as a chemical reaction network. Here we present conditions under which a lower-level encoding correctly emulates the sequential dynamics of a high-level chemical reaction network. We require that encodings are transactional, such that their execution is divided by a “commit reaction” that irreversibly separates the reactant-consuming phase of the encoding from the product-generating phase. We also impose restrictions on the sharing of species between reaction encodings, based on a notion of “extra tolerance”, which defines species that may be shared between encodings without enabling unwanted reactions. Our notion of correctness is serializability of interleaved reaction encodings, and if all reaction encodings satisfy our correctness properties then we can infer that the global dynamics of the system are correct. This allows us to infer correctness of any system constructed using verified encodings. As an example, we show how this approach may be used to verify two- and four-domain DNA strand displacement encodings of chemical reaction networks, and we generalize our result to the limit where the populations of helper species are unlimited.

Comparing chemical reaction networks: A categorical and algorithmic perspective

“…CRN comparisons have been recently proposed in several works [16,17,22], but none of them takes reaction rates into account. A notion of CRN comparison that considers kinetics is presented in [23], but this is specialized for a specific implementation of a CRN using DNA; furthermore, technically the result of correspondence therein established is based on an asymptotic fast-slow decomposition of the dynamics whereby fast species are assumed to be found in the stationary regime, while emulation requires equivalent traces at all time points.…”

A Reaction Network Scheme Which Implements Inference and Learning for Hidden Markov Models

“…The technology of implementing abstract reaction networks with molecules is a subfield of molecular systems engineering that has witnessed rapid advances in recent times. Several researchers [1][2][3][4][5][6][7][8] have proposed theoretical schemes for implementing arbitrary reaction networks with DNA oligonucleotides. There is a growing body of experimental demonstrations of such schemes [2,7,[9][10][11].…”

Automated sequence-level analysis of kinetics and thermodynamics for domain-level DNA strand-displacement systems

“…The design and verification of DNA systems is often initially performed without regard to specific DNA sequences by describing systems using domains , functionally distinct contiguous sections composing each DNA strand. Under certain idealized assumptions about interactions between domains, it is possible to verify the system by enumerating all possible reactions between domain-level DNA complexes [36–38] and establishing a correspondence with a formal description of the intended circuit function [39–42].…”