## Computer Science ETDs

## Publication Date

Fall 12-16-2023

## Abstract

The specificity and predictability of DNA make it an excellent programmable material and have allowed bio-programmers to build sophisticated molecular circuits. These molecular devices should be precise, correct, and function as intended. In order to implement these circuits, the challenge is to build a robust, reliable, and scalable logic circuit with ideally minimum unwanted signal release. Performing experiments are expensive and time-consuming, so modeling and analyzing these bio-molecular systems become crucial in designing molecular circuits. This dissertation aimed to develop algorithms and build computational tools for automated analysis of molecular circuits that incorporate the molecular geometry of nanostructures. Molecular circuits can be implemented by attaching components to a surface, for example, a DNA origami tile. These tethered circuits have potential speed advantages as only localized diffusion is involved between interacting species. Accurately measuring these tethered systems’ reaction rates is difficult due to the high speed of the interactions. Therefore, as part of this work, we attempted to estimate the reaction rate of localized circuits. When modeling such systems, a question arises whether two tethered species can physically reach each other to interact. Hence, molecular geometry becomes essential in determining whether the two species interact. We developed an automated method for estimating reaction rates in tethered molecular circuits that considers the geometry of the tethered species. We probabilistically generate samples of structure distributions based on simple biophysical models and use these to estimate essential parameters for kinetic models. Another way to implement molecular circuits is through diffusion. The dynamics of these molecular circuits can be studied by examining the reactions that can occur. In previous work, graph theory was used to compute a complete reaction network that implemented strand displacement for diffusible circuits. It covered many complex structures that required enumeration rules with complicated side conditions. This dissertation presents an alternative approach to tackle the problem of enumerating reactions by using molecular geometry of structures to decide whether reactions can happen or not. We simplify the rulesets from previous work by replacing complicated side conditions with a general check on the geometric plausibility of structures generated by the enumeration algorithm. We solve the geometric constraints using a structure sampling approach in which we randomly generate sets of physical coordinates and check whether they satisfy all the constraints simultaneously. We apply our system to several examples from the literature where molecular geometry plays an important role, including DNA hairpin binding reactions and remote toehold reactions. We further extend the geometric framework to enumerate reactions for localized circuits. We used our system to model the hairpin chain reaction that has been experimentally realized. Then we enumerated reactions for cargo sorting molecular robots and studied the robot’s random walk and cargo pickup and drop-off behavior. These systems must be studied to design a better tack layout that will improve the robot’s performance. We found that the geometric constraints such as the distance between the tracks and domain lengths affect the robot’s random walk as well as the picking-up and dropping-off of any cargo. Here, we also demonstrate that our system can automatically determine the possible paths a robot can take. The proposed system is a step towards more realistic automated modeling and analysis of DNA strand displacement based systems, and analysis of molecular geometry could be integrated with other domain-level based software in a similar manner.

## Language

English

## Keywords

DNA strand displacement, Computational modeling, Reaction enumeration, Molecular geometry

## Document Type

Thesis

## Degree Name

Computer Science

## Level of Degree

Doctoral

## Department Name

Department of Computer Science

## First Committee Member (Chair)

Dr. Matthew Lakin

## Second Committee Member

Prof. Lydia Tapia

## Third Committee Member

Dr. Shuang Luan

## Fourth Committee Member

Dr. William Bricker

## Project Sponsors

NSF

## Recommended Citation

Kumar, Sarika. "Computational Study of the Effect of Geometry on Molecular Interactions." (2023). https://digitalrepository.unm.edu/cs_etds/120