A reaction network scheme for hidden Markov model parameter learning.

With a view towards artificial cells, molecular communication systems, molecular multiagent systems and federated learning, we propose a novel reaction network scheme (termed the Baum-Welch (BW) reaction network) that learns parameters for hidden Markov models (HMMs). All variables including inputs and outputs are encoded by separate species. Each reaction in the scheme changes only one molecule of one species to one molecule of another.

A Compressed Sensing Approach to Pooled RT-PCR Testing for COVID-19 Detection.

We propose 'Tapestry', a single-round pooled testing method with application to COVID-19 testing using quantitative Reverse Transcription Polymerase Chain Reaction (RT-PCR) that can result in shorter testing time and conservation of reagents and testing kits, at clinically acceptable false positive or false negative rates. Tapestry combines ideas from compressed sensing and combinatorial group testing to create a new kind of algorithm that is very effective in deconvoluting pooled tests. Unlike Boolean group testing algorithms, the input is a quantitative readout from each test and the output is a list of viral loads for each sample relative to the pool with the highest viral load.

Pooling Samples to Increase SARS-CoV-2 Testing.

As SARS-CoV-2 continues to propagate around the world, it is becoming increasingly important to scale up testing. This is necessary both at the individual level, to inform diagnosis, treatment and contract tracing, as well as at the population level to inform policies to control spread of the infection. The gold-standard RT-qPCR test for the virus is relatively expensive and takes time, so combining multiple samples into "pools" that are tested together has emerged as a useful way to test many individuals with less than one test per person.

Designing the optimal bit: balancing energetic cost, speed and reliability.

We consider the challenge of operating a reliable bit that can be rapidly erased. We find that both erasing and reliability times are non-monotonic in the underlying friction, leading to a trade-off between erasing speed and bit reliability. Fast erasure is possible at the expense of low reliability at moderate friction, and high reliability comes at the expense of slow erasure in the underdamped and overdamped limits.

Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks.

We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well-known Lyapunov function of reaction network theory as a scaling limit of the non-equilibrium potential of the stationary distribution of stochastically modeled complex balanced systems. We extend this result to general birth-death models and demonstrate via example that similar scaling limits can yield Lyapunov functions even for models that are not complex or detailed balanced, and may even have multiple equilibria.

Autocatalysis in reaction networks.

The persistence conjecture is a long-standing open problem in chemical reaction network theory. It concerns the behavior of solutions to coupled ODE systems that arise from applying mass-action kinetics to a network of chemical reactions. The idea is that if all reactions are reversible in a weak sense, then no species can go extinct.

Catalysis in reaction networks.

We define catalytic networks as chemical reaction networks with an essentially catalytic reaction pathway: one which is "on" in the presence of certain catalysts and "off" in their absence. We show that examples of catalytic networks include synthetic DNA molecular circuits that have been shown to perform signal amplification and molecular logic. Recall that a critical siphon is a subset of the species in a chemical reaction network whose absence is forward invariant and stoichiometrically compatible with a positive point.

DNA triangles and self-assembled hexagonal tilings.

We have designed and constructed DNA complexes in the form of triangles. We have created hexagonal planar tilings from these triangles via self-assembly. Unlike previously reported structures self-assembled from DNA, our structures appear to involve bending of double helices.