On 28th June 2022, I passed my PhD Viva with minor corrections. One of the main things I did during my PhD was to author a software package called hydrogels which I used to design and execute molecular dynamics simulations of reaction diffusion systems. In this post I will explain why the act of simulating reaction-diffusion systems is important, through an extraction from one of my thesis chapters.

The intelligent design of hydrogels for controlled release has been an area of interest to drug development for over 30 years. At the same time, rapid advances in computing have allowed computational strategies for designing therapeutics. Hardware development has followed Moore’s law reliably, resulting in an exponential increase in simulation capabilities doubling every two years, and in the area of software development, advances in parallelisation, utilising advance architectures such as GPU programming have allowed the simulation of unprecedented timescales.

While the development of powerful computers and efficient software is at the forefront of computational advancements, another important area of research has been the development of easy-to-use program that can be accessed by a wider range of user in particular those who are not experts in computational techniques. For example, the molecular dynamics software package LAMMPS is a highly computational efficient and complex program. It combines a very high level of customisation for experienced users with the ability to perform standard molecular dynamics simulations with relative ease, enabling increased accessibility for novice users. The wide range of users has resulted in LAMMPS being used by those simulating metal systems for aeronautics, biomolecular systems, or simulating clays to learn more about the surface of the moon.

The typical approach in modelling hydrogel degradation has been to translate the problem into a reaction-diffusion equation. This quasi-analytical approach builds on the works of Debye on modelling the dissolution of crystals. However, this continuum approach requires strongly simplifying assumptions to obtain an analytical solution. For example, the system is treated as continuum, disregarding the molecular essence of a hydrogel, and for this reason, structural effects such as the dependence of the degradation rate as a function of the cross-linking density in the hydrogel cannot be predicted but instead have to be somehow provided as a pseudo-parameter to the underlying reaction-diffusion equation, for example has a difference effective diffusion coefficient for the degradation enzyme inside the gel.

A more direct approach that can remove some of these simplifying assumptions is to use particle based simulations to take in to account the discrete, rather than continuum, nature of such a system. Conducting such a simulation has only become possible through recent algorithmic advances, which have been implemented during the past decade in a simulation software known as ReaDDy which has been developed by the lab of Frank Noé. ReaDDy has undergone significant evolution and now runs from a traditional C++ backend, whilst being accessed via a Python wrapper, providing significant ease-of-use. This act of creating Python wrapper libraries is common, having also been done for LAMMPS and another software package that is used in this work oxDNA.

In practice, ReaDDy combines Brownian Dynamics with a Gillespie algorithm to simulate reactions, a general term referring to the conversion of particles from a given species to another. ReaDDy’s implementation cannot by default simulate the degradation of a polymer system via bond breaking mechanisms such as hydrolysis because it relies on separating topological changes and spatial reaction events. Additionally, studying the degradation of a gel requires having a realistic starting model for its structure, and beyond this an ensemble of probable starting architectures to account for the heterogeneity of the system, since on a molecular level each individual microgel particle is slightly different from its neighbour.