Year: 2012
Type: preprint
Abstract: Chemical reaction networks (CRNs) formally model chemistry in a well-mixed solution. CRNs are widely used to describe information processing occurring in natural cellular regulatory networks, and with upcoming advances in synthetic biology, CRNs are a promising language for the design of artificial molecular control circuitry. Nonetheless, despite the widespread use of CRNs in the natural sciences, the range of computational behaviors exhibited by CRNs is not well understood. CRNs have been shown to be efficiently Turing-universal when allowing for a small probability of error. CRNs that are guaranteed to converge on a correct answer, on the other hand, have been shown to decide only the semilinear predicates. We introduce the notion of function, rather than predicate, computation by representing the output of a function f:N^k --> N^l by a count of some molecular species, i.e., if the CRN starts with n_1,...,n_k molecules of some "input" species X1,...,Xk, the CRN is guaranteed to converge to having f(n_1,...,n_k) molecules of the "output" species Y1,...,Yl. We show that a function f:N^k --> N^l is deterministically computed by a CRN if and only if its graph {(x,y) | f(x) = y} is a semilinear set. Furthermore, each semilinear function f can be computed on input x in expected time O(polylog(|x|)).
Source: arXiv (Cornell University)
Authors: Chen, Ho-Lin, Doty, David, Soloveichik, David
Language: English
Topic: DNA and Biological Computing
Subfield: Molecular Biology
Domain: Life Sciences
Open Access status: green
Awards: Exploring Design Principles of Cellular Control Circuits, The Second CI Fellows Project, Collaborative Research: The Molecular Programming Project, SHF:Medium:Collaborative Research:Scaling Up Programmable and Algorithmic DNA Self-Assembly, G6276702551, AF: Small: Theory of Molecular Programming: Computability and Complexity
OpenAlex ID: W2952273698