ViDa: Visualizing DNA hybridization trajectories with
  biophysics-informed deep graph embeddings
Chenwei Zhang Jordan Lovrod Boyan Beronov Khanh Dao Duc Anne Condon
Visualization tools can help synthetic biologists and molecular programmers
understand the complex reactive pathways of nucleic acid reactions, which can
be designed for many potential applications and can be modelled using a
continuous-time Markov chain (CTMC). Here we present ViDa, a new visualization
approach for DNA reaction trajectories that uses a 2D embedding of the
secondary structure state space underlying the CTMC model. To this end, we
integrate a scattering transform of the secondary structure adjacency, a
variational autoencoder, and a nonlinear dimensionality reduction method. We
augment the training loss with domain-specific supervised terms that capture
both thermodynamic and kinetic features. We assess ViDa on two well-studied DNA
hybridization reactions. Our results demonstrate that the domain-specific
features lead to significant quality improvements over the state-of-the-art in
DNA state space visualization, successfully separating different folding
pathways and thus providing useful insights into dominant reaction mechanisms.