(484b) Optimal Feedback Morphology Control of Amphiphile Self-Assembly Using Markov State Models: Numerical Studies and Experimental Validation

Amphiphiles are long-chain molecules that possess a polar head and non-polar tail [1]. The unique chemistry of these molecules enables them to form a wide range of supramolecular self-assembled structures in polar solvents [2]. These structures impart unique properties to the surfactant solutions. Hence, the self-assembly process and the associated pathways have been explored extensively for colloidal systems over the past decade [3]. These studies have revealed that the process of colloidal self-assembly follows unique reaction pathways that allow them to self-assemble to reach thermodynamically stable or kinetically trapped structures [4]. Further investigation of these pathways with detailed all-atom and coarse-grained molecular simulations highlights that although self-assembly is inherently an autonomous process, external inputs like varying solution conditions or temperatures can guide the self-assembly system to a desired morphology. In this work we first develop a model to capture the dynamic evolution of the colloidal self-assembly process, and based on the model, we developed an advanced controller that can guide the system to target morphologies [6].

The self-assembly of the colloids at the molecular scales can be modeled via detailed molecular dynamics (MD) simulations. However, even with a coarse-grained model MD simulation can capture the dynamic evolution of the colloids for only a few microseconds. This certainly does not serve the purpose of capturing colloidal self-assembly because in most of the cases the formation of self-assembled nanostructures takes a few hours. Therefore, for the purpose of capturing the dynamics of the colloidal systems at longer time-scales, dissipative particle dynamics (DPD) simulations are performed in this work. Here, the parameters of the DPD simulations are obtained from shot time-scale atomistic MD simulations. However, owing to the high-dimensionality of the DPD simulations, they are computationally expensive and cannot be utilized in solving the optimal control problem online to predict the input sequence required to drive the system to target morphologies. To this end, it is essential to develop a reduced-order model that can capture the dynamics of the system in a relatively accurate fashion and at the same time is computationally inexpensive [7]. Markov state models (MSMs) that have been used in recent studies to capture the long time-scale behaviors of biological systems can be built with reduced order states of the system to capture the system dynamics in a computationally efficient fashion [8]. A Markov state model describes a process as a memoryless time series, where the state at one time step depends only on the previous state and the control action taken at the previous time-step. The transition among the discrete Markov states are captured by a transition probability matrix, which is derived using the data collected from the DPD models. Specifically, building the Markov state model for a high-dimensional system first requires the determination of reduced coordinates that can effectively capture the required features of the system. Then the transition probability of the reduced coordinates is identified from the data collected with the DPD simulations [9]. Here the reduced coordinated used are bond-angle orientation, root mean square length of monomers and structure factor. Once the Markov state model is built, it is utilized to solve the optimal control problem for the shrinking time horizon. The implementation of important constants on the free energy, which is derived as a function of the reduced coordinates alongside constraints on bond angles and bond length, allows the self-assembly system to explore the thermodynamically feasible trajectroy of the system’s energy landscape while allowing the individual monomers to retain physically relevant structures. As a case study, the self-assembly of complex nanostructures called the dynamic binary complexes (DBCs) was controlled using the MSM based control system, which was validated through experiments.

References.

[1] Lombardo, D., Kiselev, M. A., Magazù, S., & Calandra, P. (2015). Amphiphiles self-assembly: basic concepts and future perspectives of supramolecular approaches. Advances in Condensed Matter Physics, 2015.

[2] Dasgupta, A., & Das, D. (2019). Designer peptide amphiphiles: self-assembly to applications. Langmuir, 35(33), 10704-10724.

[3] Yu, T., & Schatz, G. C. (2013). Free-energy landscape for peptide amphiphile self-assembly: stepwise versus continuous assembly mechanisms. The Journal of Physical Chemistry B, 117(45), 14059-14064.

[4] Wang, L., Song, B., Li, Y., Gong, L., Jiang, X., Wang, M., ... & Li, X. (2020). Self-assembly of metallo-supramolecules under kinetic or thermodynamic control: characterization of positional isomers using scanning tunneling spectroscopy. Journal of the American Chemical Society, 142(21), 9809-9817.

[5] Weng, J., Yang, M., Wang, W., Xu, X., & Tian, Z. (2020). Revealing thermodynamics and kinetics of lipid self-assembly by Markov state model analysis. Journal of the American Chemical Society, 142(51), 21344-21352.

[6] Pahari, S., Moon, J., Akbulut, M., Hwang, S., & Kwon, J. S. I. (2021). Model predictive control for ormlike micelles (WLMs): Application to a system of CTAB and NaCl. Chemical Engineering Research and Design, 174, 30-41.

[7] Grover, M. A., Griffin, D. J., Tang, X., Kim, Y., & Rousseau, R. W. (2020). Optimal feedback control of batch self-assembly processes using dynamic programming. Journal of Process Control, 88, 32-42.

[8] Tang, X., Bevan, M. A., & Grover, M. A. (2017). The construction and application of Markov state models for colloidal self-assembly process control. Molecular Systems Design & Engineering, 2(1), 78-88.

[9] Grötsch, R. K., Wanzke, C., Speckbacher, M., Angı, A., Rieger, B., & Boekhoven, J. (2019). Pathway dependence in the fuel-driven dissipative self-assembly of nanoparticles. Journal of the American Chemical Society, 141(25), 9872-9878.