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1. A multiscale approach to study molecular and interfacial characteristics of vesicles

   https://doi.org/10.1039/c8me00029h  

   Yu, Xiang; Dutt, Meenakshi (December 2018, Molecular Systems Design & Engineering)

   null (Ed.)

   The functions of colloids, such as membranes and vesicles, are dictated by interfacial properties which are determined by an interplay of physical interactions and processes spanning multiple spatiotemporal scales. The multiscale characteristics of membranes and vesicles can be resolved by the hybrid molecular dynamics-lattice Boltzmann technique. This technique enables the resolution of particle dynamics along with long range electrostatic and hydrodynamic interactions. We have examined the feasibility of an implementation of the hybrid technique in conjunction with a Martini-based implicit solvent coarse-grained force field to capture the molecular and interfacial characteristics of membranes and vesicles. For simplicity, we have examined two types of vesicles whose molecular components have different sustained interactions with the solvent. One of the vesicles encompassed phospholipids and the other vesicle was composed of phospholipids and poly ethylene glycol (PEG)-grafted lipids. The molecular and interfacial characteristics of the phospholipid vesicle and PEGylated, or hairy, vesicles are found to be in good agreement with earlier experimental, computational and theoretical findings. These results demonstrate that the multiscale hybrid technique used with a Martini-based implicit solvent coarse-grained model is suitable for capturing the molecular and interfacial characteristics of membranes and vesicles. Furthermore, other implicit solvent coarse-grained models can be used in conjunction with the hybrid molecular dynamics-lattice Boltzmann technique to examine the molecular and interfacial characteristics of membranes and vesicles. Our study demonstrates the potential of the hybrid technique in capturing multiscale interfacial characteristics of intra- and inter-colloid interactions in suspensions under different flow conditions, and their relation to molecular properties. In addition, this technique can be applied to design colloids with multiscale characteristics which yield desired interactions with other colloids and responses to external stimuli. 

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2. Multiscale Model Reduction of the Unsaturated Flow Problem in Heterogeneous Porous Media with Rough Surface Topography

   https://doi.org/10.3390/math8060904  

   Spiridonov, Denis; Vasilyeva, Maria; Chung, Eric T.; Efendiev, Yalchin; Jana, Raghavendra (June 2020, Mathematics)

   In this paper, we consider unsaturated filtration in heterogeneous porous media with rough surface topography. The surface topography plays an important role in determining the flow process and includes multiscale features. The mathematical model is based on the Richards’ equation with three different types of boundary conditions on the surface: Dirichlet, Neumann, and Robin boundary conditions. For coarse-grid discretization, the Generalized Multiscale Finite Element Method (GMsFEM) is used. Multiscale basis functions that incorporate small scale heterogeneities into the basis functions are constructed. To treat rough boundaries, we construct additional basis functions to take into account the influence of boundary conditions on rough surfaces. We present numerical results for two-dimensional and three-dimensional model problems. To verify the obtained results, we calculate relative errors between the multiscale and reference (fine-grid) solutions for different numbers of multiscale basis functions. We obtain a good agreement between fine-grid and coarse-grid solutions. 

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3. Molecular Dynamics Study of the Effect of Grafting Density on Ion Diffusivity in a MARTINI Coarse-Grained Strong Polyelectrolyte Brush

   https://doi.org/10.1021/acs.macromol.4c01018  

   Boyle, Michael J; Radhakrishnan, Ravi; Composto, Russell J (July 2024, Macromolecules)

   Because surface-grafted polyelectrolyte brushes (PEBs) are responsive to external stimuli, such as electric fields and ionic strength, PEBs are attractive for applications ranging from drug delivery to separations technologies. Essential to PEB utilization is understanding how critical parameters like grafting density (σ) impact PEB structure and the dynamics of the PEB and counterions. To study the effect of σ on PEB and counterion structure and dynamics, we fine-tune a coarse-grained model that retains the chemical specificity of a strong polyelectrolyte, poly[(2-(methacryloyloxy)ethyl) trimethylammonium chloride] (PMETAC), using the MARTINI forcefield. Using “salt-free” conditions where the counterion concentration balances the charge on the brush, we build coarse-grained (CG) molecular dynamics simulations for MARTINI PMETAC brushes (N=150 monomers; MW = 31.2 kg/mol) at experimentally relevant values of σ = 0.05, 0.10, 0.20, and 0.40 chains/nm2. Using 5 µs simulations, we investigate the effects of grafting density on PEB structure, ion dissociation dynamics, polymer mobility, and counterion diffusivity. Results show that competition between electrostatic interactions, steric hindrance, and polymer mobility controls counterion diffusivity. The interplay of these factors leads to diffusivity that depends non-monotonically on σ, with counterion diffusivity peaking at an intermediate σ = 0.10 chains/nm2. 

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4. Multi-resolution simulation of DNA transport through large synthetic nanostructures

   https://doi.org/10.1039/d1cp04589j  

   Choudhary, Adnan; Maffeo, Christopher; Aksimentiev, Aleksei (February 2022, Physical Chemistry Chemical Physics)

   Modeling and simulation has become an invaluable partner in development of nanopore sensing systems. The key advantage of the nanopore sensing method – the ability to rapidly detect individual biomolecules as a transient reduction of the ionic current flowing through the nanopore – is also its key deficiency, as the current signal itself rarely provides direct information about the chemical structure of the biomolecule. Complementing experimental calibration of the nanopore sensor readout, coarse-grained and all-atom molecular dynamics simulations have been used extensively to characterize the nanopore translocation process and to connect the microscopic events taking place inside the nanopore to the experimentally measured ionic current blockades. Traditional coarse-grained simulations, however, lack the precision needed to predict ionic current blockades with atomic resolution whereas traditional all-atom simulations are limited by the length and time scales amenable to the method. Here, we describe a multi-resolution framework for modeling electric field-driven passage of DNA molecules and nanostructures through to-scale models of synthetic nanopore systems. We illustrate the method by simulating translocation of double-stranded DNA through a solid-state nanopore and a micron-scale slit, capture and translocation of single-stranded DNA in a double nanopore system, and modeling ionic current readout from a DNA origami nanostructure passage through a nanocapillary. We expect our multi-resolution simulation framework to aid development of the nanopore field by providing accurate, to-scale modeling capability to research laboratories that do not have access to leadership supercomputer facilities. 

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5. Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations

   https://doi.org/10.3390/math8050720  

   Zhang, Zecheng; Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat (May 2020, Mathematics)

   In this paper, we investigate and design multiscale simulations for stochastic multiscale PDEs. As for the space, we consider a coarse grid and a known multiscale method, the generalized multiscale finite element method (GMsFEM). In order to obtain a small dimensional representation of the solution in each coarse block, the uncertainty space needs to be partitioned (coarsened). This coarsenining collects realizations that provide similar multiscale features as outlined in GMsFEM (or other method of choice). This step is known to be computationally demanding as it requires many local solves and clustering based on them. In this work, we take a different approach and learn coarsening the uncertainty space. Our methods use deep learning techniques in identifying clusters (coarsening) in the uncertainty space. We use convolutional neural networks combined with some techniques in adversary neural networks. We define appropriate loss functions in the proposed neural networks, where the loss function is composed of several parts that includes terms related to clusters and reconstruction of basis functions. We present numerical results for channelized permeability fields in the examples of flows in porous media. 

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