Biochemical Combinatorics Through Coarse Grain Neural Network Potentials, DNA Nanocages, & Virtual Reality

In this work, we utilize various approaches based strongly in combinatorics and mathematics to explore different questions in biochemistry. We begin with a broad biochemical space in order to define the challenges of developing a coarse grain neural network potential. Following this we build a toy model to test our new ideas with a novel modification of atom-centered symmetry function based neural network potentials. By doing so we demonstrate enough confidence in our approach to build a novel network which successfully learns the potential mean force of highly coarse grain protein systems. Upon which we investigate weaknesses in our method and suggest improvements, focusing on updating our data set, incorporating different target physical properties, and considering different network approaches. Ultimately, utilizing our initial combinatorics theory to demonstrate why caution must be taken with simulating highly coarse grain systems, generally. Subsequently, we apply our combinatorics approaches on DNA Nanocages by analyzing different topologies and their interactions with different ionic concentrations through molecular dynamics simulations. We do this by a novel volume metric which pulls from Delauny Hull Triangulation and uses a network approach to determine the internal volume. From this methodology we determine that smaller rectangular prisms are more driven by enthalpic effects compared to the larger cubic prism which is driven more by entropy. An analogous effect we observe in similar size but topologically distinct triangular, rectangular, and pentagonal prisms. Where the rectangular and pentagonal prisms are unlikely to optimally collapse due to the greater sampling possible from their increased amount of DNA. Finally, we explore virtual reality (VR) to reduce the complexity of chemical molecules to students. In which we show that students who experienced molecules in VR have better understanding than those whom have not.