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Finney AR, Salvalaglio M. A variational approach to assess reaction coordinates for two-step crystallization. J Chem Phys 2023; 158:094503. [PMID: 36889939 DOI: 10.1063/5.0139842] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/16/2023] Open
Abstract
Molecule- and particle-based simulations provide the tools to test, in microscopic detail, the validity of classical nucleation theory. In this endeavor, determining nucleation mechanisms and rates for phase separation requires an appropriately defined reaction coordinate to describe the transformation of an out-of-equilibrium parent phase for which myriad options are available to the simulator. In this article, we describe the application of the variational approach to Markov processes to quantify the suitability of reaction coordinates to study crystallization from supersaturated colloid suspensions. Our analysis indicates that collective variables (CVs) that correlate with the number of particles in the condensed phase, the system potential energy, and approximate configurational entropy often feature as the most appropriate order parameters to quantitatively describe the crystallization process. We apply time-lagged independent component analysis to reduce high-dimensional reaction coordinates constructed from these CVs to build Markov State Models (MSMs), which indicate that two barriers separate a supersaturated fluid phase from crystals in the simulated environment. The MSMs provide consistent estimates for crystal nucleation rates, regardless of the dimensionality of the order parameter space adopted; however, the two-step mechanism is only consistently evident from spectral clustering of the MSMs in higher dimensions. As the method is general and easily transferable, the variational approach we adopt could provide a useful framework to study controls for crystal nucleation.
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Affiliation(s)
- A R Finney
- Thomas Young Centre and Department of Chemical Engineering, University College London, London WC1E 7JE, United Kingdom
| | - M Salvalaglio
- Thomas Young Centre and Department of Chemical Engineering, University College London, London WC1E 7JE, United Kingdom
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Affiliation(s)
- C. Perego
- Department of Chemistry and Applied Biosciences, ETH Zurich, Zurich, Switzerland
- Institute of Computational Science, Università della Svizzera Italiana, Lugano, Switzerland
| | - M. Salvalaglio
- Institute of Computational Science, Università della Svizzera Italiana, Lugano, Switzerland
- Institute of Process Engineering, ETH Zurich, Zurich, Switzerland
| | - M. Parrinello
- Department of Chemistry and Applied Biosciences, ETH Zurich, Zurich, Switzerland
- Institute of Computational Science, Università della Svizzera Italiana, Lugano, Switzerland
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Moiani D, Salvalaglio M, Cavallotti C, Bujacz A, Redzynia I, Bujacz G, Dinon F, Pengo P, Fassina G. Structural Characterization of a Protein A Mimetic Peptide Dendrimer Bound to Human IgG. J Phys Chem B 2009; 113:16268-75. [DOI: 10.1021/jp909405b] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- D. Moiani
- Department of Chimica, Materiali e Ingegneria Chimica, Politecnico di Milano, 20131 Milano, Italy, Institute of Technical Biochemistry, Technical University of Lodz, Stefanowskiego 4/10, Lodz, Poland, and Xeptagen S.p.A., VEGA Science Park-Building Auriga Via delle Industrie 9, I-30175 Marghera (VE), Italy
| | - M. Salvalaglio
- Department of Chimica, Materiali e Ingegneria Chimica, Politecnico di Milano, 20131 Milano, Italy, Institute of Technical Biochemistry, Technical University of Lodz, Stefanowskiego 4/10, Lodz, Poland, and Xeptagen S.p.A., VEGA Science Park-Building Auriga Via delle Industrie 9, I-30175 Marghera (VE), Italy
| | - C. Cavallotti
- Department of Chimica, Materiali e Ingegneria Chimica, Politecnico di Milano, 20131 Milano, Italy, Institute of Technical Biochemistry, Technical University of Lodz, Stefanowskiego 4/10, Lodz, Poland, and Xeptagen S.p.A., VEGA Science Park-Building Auriga Via delle Industrie 9, I-30175 Marghera (VE), Italy
| | - A. Bujacz
- Department of Chimica, Materiali e Ingegneria Chimica, Politecnico di Milano, 20131 Milano, Italy, Institute of Technical Biochemistry, Technical University of Lodz, Stefanowskiego 4/10, Lodz, Poland, and Xeptagen S.p.A., VEGA Science Park-Building Auriga Via delle Industrie 9, I-30175 Marghera (VE), Italy
| | - I. Redzynia
- Department of Chimica, Materiali e Ingegneria Chimica, Politecnico di Milano, 20131 Milano, Italy, Institute of Technical Biochemistry, Technical University of Lodz, Stefanowskiego 4/10, Lodz, Poland, and Xeptagen S.p.A., VEGA Science Park-Building Auriga Via delle Industrie 9, I-30175 Marghera (VE), Italy
| | - G. Bujacz
- Department of Chimica, Materiali e Ingegneria Chimica, Politecnico di Milano, 20131 Milano, Italy, Institute of Technical Biochemistry, Technical University of Lodz, Stefanowskiego 4/10, Lodz, Poland, and Xeptagen S.p.A., VEGA Science Park-Building Auriga Via delle Industrie 9, I-30175 Marghera (VE), Italy
| | - F. Dinon
- Department of Chimica, Materiali e Ingegneria Chimica, Politecnico di Milano, 20131 Milano, Italy, Institute of Technical Biochemistry, Technical University of Lodz, Stefanowskiego 4/10, Lodz, Poland, and Xeptagen S.p.A., VEGA Science Park-Building Auriga Via delle Industrie 9, I-30175 Marghera (VE), Italy
| | - P. Pengo
- Department of Chimica, Materiali e Ingegneria Chimica, Politecnico di Milano, 20131 Milano, Italy, Institute of Technical Biochemistry, Technical University of Lodz, Stefanowskiego 4/10, Lodz, Poland, and Xeptagen S.p.A., VEGA Science Park-Building Auriga Via delle Industrie 9, I-30175 Marghera (VE), Italy
| | - G. Fassina
- Department of Chimica, Materiali e Ingegneria Chimica, Politecnico di Milano, 20131 Milano, Italy, Institute of Technical Biochemistry, Technical University of Lodz, Stefanowskiego 4/10, Lodz, Poland, and Xeptagen S.p.A., VEGA Science Park-Building Auriga Via delle Industrie 9, I-30175 Marghera (VE), Italy
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