Ofer Kimchi, Ella M. King, and Michael P. Brenner. 1/19/2023. “Uncovering the mechanism for aggregation in repeat expanded RNA reveals a reentrant transition.” Nature Communications 14 (332), Pp. 1-9. Publisher's VersionAbstract
RNA molecules aggregate under certain conditions. The resulting condensates are implicated in human neurological disorders, and can potentially be designed towards specified bulk properties in vitro. However, the mechanism for aggregation—including how aggregation properties change with sequence and environmental conditions—remains poorly understood. To address this challenge, we introduce an analytical framework based on multimer enumeration. Our approach reveals the driving force for aggregation to be the increased configurational entropy associated with the multiplicity of ways to form bonds in the aggregate. Our model uncovers rich phase behavior, including a sequence-dependent reentrant phase transition, and repeat parity-dependent aggregation. We validate our results by comparison to a complete computational enumeration of the landscape, and to previously published molecular dynamics simulations. Our work unifies and extends published results, both explaining the behavior of CAG-repeat RNA aggregates implicated in Huntington’s disease, and enabling the rational design of programmable RNA condensates.
Ella M. King, Zizhao Wang, David A. Weitz, Frans Spaepen, and Michael P. Brenner. 4/2022. “Correlation Tracking: Using simulations to interpolate highly correlated particle tracks.” Phys. Rev. E, 105, 4, Pp. 044608. Publisher's VersionAbstract
Despite significant advances in particle imaging technologies over the past two decades, few advances have been made in particle tracking, i.e., linking individual particle positions across time series data. The state-of-the-art tracking algorithm is highly effective for systems in which the particles behave mostly independently. However, these algorithms become inaccurate when particle motion is highly correlated, such as in dense or strongly interacting systems. Accurate particle tracking is essential in the study of the physics of dense colloids, such as the study of dislocation formation, nucleation, and shear transformations. Here, we present a method for particle tracking that incorporates information about the correlated motion of the particles. We demonstrate significant improvement over the state-of-the-art tracking algorithm in simulated data on highly correlated systems.
Carl P. Goodrich, Ella M. King, Samuel S. Schoenholz, Ekin D. Cubuk, and Michael P. Brenner. 3/2021. “Designing self-assembling kinetics with differentiable statistical physics models.” Proceedings of the National Academy of Sciences. Publisher's VersionAbstract
The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing emergent kinetics, but this has received considerably less attention. Using recent advances in automatic differentiation, we show how kinetic pathways can be precisely designed by directly differentiating through statistical physics models, namely free energy calculations and molecular dynamics simulations. We consider two systems that are crucial to our understanding of structural self-assembly: bulk crystallization and small nanoclusters. In each case, we are able to assemble precise dynamical features. Using gradient information, we manipulate interactions among constituent particles to tune the rate at which these systems yield specific structures of interest. Moreover, we use this approach to learn nontrivial features about the high-dimensional design space, allowing us to accurately predict when multiple kinetic features can be simultaneously and independently controlled. These results provide a concrete and generalizable foundation for studying nonstructural self-assembly, including kinetic properties as well as other complex emergent properties, in a vast array of systems.
Ella M. King, Matthew A. Gebbie, and Nicholas A. Melosh. 10/2019. “Impact of Rigidity on Molecular Self-Assembly.” Langmuir. Publisher's VersionAbstract
Rigid, cage-like molecules, like diamondoids, show unique self-assembly behavior, such as templating 1-D nanomaterial assembly via pathways that are typically blocked for such bulky substituents. We investigate molecular forces between diamondoids to explore why molecules with high structural rigidity exhibit these novel assembly pathways. The rigid nature of diamondoids significantly lowers configurational entropy, and we hypothesize that this influences molecular interaction forces. To test this concept, we calculated the distance-dependent impact of entropy on assembly using molecular dynamics simulations. To isolate pairwise entropic and enthalpic contributions to assembly, we considered pairs of molecules in a thermal bath, fixed at set intermolecular separations but otherwise allowed to freely move. By comparing diamondoids to linear alkanes, we draw out the impact of rigidity on the entropy and enthalpy of pairwise interactions. We find that linear alkanes actually exhibit stronger van der Waals interactions than diamondoids at contact, because the bulky structure of diamondoids induces larger net atomic separations. Yet, we also find that diamondoids pay lower entropic penalties when assembling into contact pairs. Thus, the cage-like shape of diamondoids introduces an enthalpic penalty at contact, but the penalty is counterbalanced by entropic effects. Investigating the distance dependence of entropic forces provides a mechanism to explore how rigidity influences molecular assembly. Our results show that low entropic penalties paid by diamondoids can explain the effectiveness of diamondoids in templating nanomaterial assembly. Hence, tuning molecular rigidity can be an effective strategy for controlling the assembly of functional materials, such as biomimetic surfaces and nanoscale materials.