Recent advances in synthetic biology have made it possible to deploy chemical reactions that implement computation inside a cell. On the theoretical side, several algorithms have been proposed that optimize for accuracy, computational speed, and resource efficiency. Most of these algorithms, however, rely on two assumptions: (i) the parameters or reaction rate constants are perfectly known,...
The implementation of abstract dynamical systems with molecular systems has gained scientific interest. Automated theoretical schemes can compile formal reaction networks into DNA oligonucleotide sequences; thereby providing a potential molecular implementation of the dynamics of the formal reaction network. In this context, we propose a novel algorithm for learning parameters of Hidden Markov...
Recent technological advances allow us to view chemical mass-action systems as analog computers. In this context, the inputs to a computation are encoded as initial values of certain chemical species while the outputs are the limiting values of other chemical species. The broad goal of this nascent field is to develop systems that can operate in the niche of a (wet) cellular environment,...
Transcriptional networks represent one of the most extensively studied types of reaction networks in synthetic biology. While transcriptional networks typically rely on cooperativity and highly non-linear behavior of transcription factors to regulate production of proteins, they are often modeled with simple linear degradation terms. In contrast, general analog computation requires both...
DNA strand displacement systems have enabled the construction of molecular circuits capable of performing complex computations, typically relying on irreversible reactions and non-equilibrium dynamics for signal amplification and restoration. An alternative paradigm is equilibrium computation, where outputs are determined by the steady-state concentrations of molecular species.
In this...
A fundamental question in the field of molecular computation is what computational tasks biochemical systems are capable of carrying out. In this talk, we will see that chemical reaction networks can do maximum likelihood estimation of log-affine models in the following sense: Given a basis for the kernel of the design matrix of a given model, we construct a detailed-balanced network such that...
A common goal in the theory of Chemical Reaction Networks (CRNs) is to design systems that reproduce or approximate a desired dynamics. This theory supports ongoing efforts in synthetic biology and molecular nanotechnology to emulate the functional molecular networks seen in nature. Here, we propose a molecular version of a recurrent artificial neural network, the RNCRN, which we prove is able...
The concept of input-independent computational time for chemistry-based analog computers was introduced in \cite{anderson2025arithmetic}, where it was shown that arithmetic operations can be computed in a fixed time independent of the input values. Here, by inputs we mean the numerical values encoded by the initial concentrations of designated input species, with the underlying reaction...
Biomolecules can be repurposed to build programmable chemical computers, either in vitro or in living cells. A particularly promising technology is DNA strand displacement, which has been shown capable of implementing arbitrary systems of chemical reactions. Since chemical reactions can perform computation, this raises fundamental mathematical questions: What types of computation can...
