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 the Hidden Markov Model (HMM), a flexible statistical framework widely used in Bioinformatics, Machine Learning, and Data Science to model an underlying hidden structure.
Our algorithm is specified by a network of chemical reactions and mimics the Baum-Welch algorithm which is the standard learning algorithm for HMMs. The Baum-Welch algorithm is an iterative Expectation-Maximization (EM) algorithm where one step is performed at a time in a prescribed sequence. The reaction network scheme is divided into four subnetworks that correspond to the forward, backward, expectation, and maximization steps of the Baum-Welch algorithm. Each subnetwork describes a system of ordinary differential equations that might be run separately, exactly mimicking the steps of the Baum-Welch algorithm, or simultaneously, thereby obtaining a variant on the Baum-Welch algorithm. Promising areas of application of this work come from cellular biology. In the future, a moleculebased HMM device might learn a molecular environment within an organism by sensing and interacting with the environment at the molecular level. It might take action according to the learning outcome, for example, choosing among different drug options, or a molecule-based HMM might be used as a building block in an artificial cell or population of cells, enabling cooperative behavior among cells or facilitating various tasks.
Joint work with Abhinav Singh, Abhishek Behera, and Manoj Gopalkrishnan.