(56g) A Computational Topology Framework for Molecular Dynamics Data: A Case Study in Soft Gels

In this work we describe a computational framework that combines topological data analysis (TDA) and molecular simulations to characterize complex multi-scale structures of soft gels [1]. Soft gels, formed via the self-assembly of particulate organic materials, exhibit intricate multi-scale structures that provides them with flexibility and resilience when subjected to external stresses. Particulate gel technology is a versatile and innovative solution with widespread applications across diverse industries, including pharmaceuticals, foods, and construction. In the pharmaceutical and medical device industries, these gels play a pivotal role, serving as effective drug delivery vehicles, encapsulation systems, and scaffolds [2].

Our TDA analysis focuses on the use of the Euler characteristic (EC) [3], which is an interpretable and computationally-scalable topological descriptor that is combined with filtration operations to obtain information on the geometric (local) and topological (global) structure of soft gels. Specifically, we represent the raw molecular dynamics data (3D atomistic positions of gel particles) as a point cloud. We then conduct filtration by defining a ball region of fixed radius and connecting all points within such region, thus creating a simplicial complex (a generalization of a graph to high dimensions) [4]. We then calculate the basic topological features of the simplicial complex (e.g., connected components and void spaces) to compute the Euler characteristic. This procedure is repeated by defining ball regions of different radius lengths, effectively obtaining a range of EC values that characterizes topology at different length scales. The EC values are used to compute a topological summary that is known as the EC curve. We reduce the EC curve using principal component analysis (PCA) and show that this provides an informative low-dimensional representation of the complex gel structure.

We use the proposed computational framework to investigate the influence of gel preparation (e.g., quench rate, volume fraction) on soft gel structure and to explore dynamic deformations that emerge under oscillatory shear in various response regimes (linear, nonlinear, and flow). Our analysis identifies specific scales and extents at which hierarchical structures in soft gels are affected; moreover, correlations between structural deformations and mechanical phenomena (such as shear stiffening) are explored.

In summary, we show that TDA facilitates the mathematical representation, quantification, and analysis of soft gel structures, extending traditional network analysis methods to capture both local and global organization. Moreover, we show that TDA provides a computationally scalable approach to quantify the shape of molecular simulation data; for instance, we show that we can compute topological descriptors for molecular environments containing 16,000 particles in seconds. The proposed framework can be used to analyze general and high-dimensional molecular dynamics data [5].

[1] Smith, A., Donley, G. J., Del Gado, E., & Zavala, V. M. (2024). Topological Data Analysis for Particulate Gels. arXiv preprint arXiv:2404.02991.

[2] Paulomi Burey, BR Bhandari, Tony Howes, and MJ Gidley. Hydrocolloid gel particles: formation, characterization, and application. Critical reviews in food science and nutrition, 48(5):361–377, 2008.

[3] Smith, A., & Zavala, V. M. (2021). The Euler characteristic: A general topological descriptor for complex data. Computers & Chemical Engineering, 154, 107463.

[4] Smith, A. D., DÅ‚otko, P., & Zavala, V. M. (2021). Topological data analysis: concepts, computation, and applications in chemical engineering. Computers & Chemical Engineering, 146, 107202.

[5] Smith, A., Runde, S., Chew, A. K., Kelkar, A. S., Maheshwari, U., Van Lehn, R. C., & Zavala, V. M. (2023). Topological analysis of molecular dynamics simulations using the euler characteristic. Journal of Chemical Theory and Computation, 19(5), 1553-1567.