Crowding-induced interactions of ring polymers

A mean-field theory for predicting single polymer collapse induced by neutral crowders

Macromolecular crowding can induce the collapse of a single long polymer into a globular form due to depletion forces of entropic nature. This phenomenon has been shown to play a significant role in compacting the genome within the bacterium Escherichia coli into a well-defined region of the cell known as the nucleoid. Motivated by the biological significance of this process, numerous theoretical and computational studies have searched for the primary determinants of the behavior of polymer-crowder phases. However, our understanding of this process remains incomplete and there is debate on a quantitatively unified description. In particular, different simulation studies with explicit crowders have proposed different order parameters as potential predictors for the collapse transition. In this work, we present a comprehensive analysis of published simulation data obtained from different sources. Based on the common behavior we find in this data, we develop a unified phenomenological model that we show to be predictive. Finally, to further validate the accuracy of the model, we conduct new simulations on polymers of various sizes, and investigate the role of jamming of the crowders.

Particle Deformability Enables Control of Interactions between Membrane-Anchored Nanoparticles

Nanoparticles adsorbed on a membrane can induce deformations of the membrane that give rise to effective interactions between the particles. Previous studies have focused primarily on rigid nanoparticles with fixed shapes. However, DNA origami technology has enabled the creation of deformable nanostructures with controllable shapes and mechanical properties, presenting new opportunities to modulate interactions between particles adsorbed on deformable surfaces. Here we use coarse-grained molecular dynamics simulations to investigate deformable, hinge-like nanostructures anchored to lipid membranes via cholesterol anchors. We characterize deformations of the particles and membrane as a function of the hinge stiffness. Flexible particles adopt open configurations to conform to a flat membrane, whereas stiffer particles induce deformations of the membrane. We further show that particles spontaneously aggregate and that cooperative effects lead to changes in their shape when they are close together. Using umbrella sampling methods, we quantify the effective interaction between two particles and show that stiffer hinge-like particles experience stronger and longer-ranged attraction. Our results demonstrate that interactions between deformable, membrane-anchored nanoparticles can be controlled by modifying mechanical properties of the particles, suggesting new ways to modulate the self-assembly of particles on deformable surfaces.

A Novel Fractional Brownian Dynamics Method for Simulating the Dynamics of Confined Bottle-Brush Polymers in Viscoelastic Solution

In crowded fluids, polymer segments can exhibit anomalous subdiffusion due to the viscoelasticity of the surrounding environment. Previous single-particle tracking experiments revealed that such anomalous diffusion in complex fluids (e.g., in bacterial cytoplasm) can be described by fractional Brownian motion (fBm). To investigate how the viscoelastic media affects the diffusive behaviors of polymer segments without resolving single crowders, we developed a novel fractional Brownian dynamics method to simulate the dynamics of polymers under confinement. In this work, instead of using Gaussian random numbers ("white Gaussian noise") to model the Brownian force as in the standard Brownian dynamics simulations, we introduce fractional Gaussian noise (fGn) in our homemade fractional Brownian dynamics simulation code to investigate the anomalous diffusion of polymer segments by using a simple "bottle-brush"-type polymer model. The experimental results of the velocity autocorrelation function and the exponent that characterizes the subdiffusion of the confined polymer segments can be reproduced by this simple polymer model in combination with fractional Gaussian noise (fGn), which mimics the viscoelastic media.

Transfer Learning Facilitates the Prediction of Polymer-Surface Adhesion Strength

Machine learning (ML) accelerates the exploration of material properties and their links to the structure of the underlying molecules. In previous work [Shi et al. ACS Applied Materials & Interfaces 2022, 14, 37161-37169.], ML models were applied to predict the adhesive free energy of polymer-surface interactions with high accuracy from the knowledge of the sequence data, demonstrating successes in inverse-design of polymer sequence for known surface compositions. While the method was shown to be successful in designing polymers for a known surface, extensive data sets were needed for each specific surface in order to train the surrogate models. Ideally, one should be able to infer information about similar surfaces without having to regenerate a full complement of adhesion data for each new case. In the current work, we demonstrate a transfer learning (TL) technique using a deep neural network to improve the accuracy of ML models trained on small data sets by pretraining on a larger database from a related system and fine-tuning the weights of all layers with a small amount of additional data. The shared knowledge from the pretrained model facilitates the prediction accuracy significantly on small data sets. We also explore the limits of database size on accuracy and the optimal tuning of network architecture and parameters for our learning tasks. While applied to a relatively simple coarse-grained (CG) polymer model, the general lessons of this study apply to detailed modeling studies and the broader problems of inverse materials design.

Crowding-Induced Spatial Organization of Gene Expression in Cell-Sized Vesicles

Cell-free protein synthesis is an important tool for studying gene expression and harnessing it for applications. In cells, gene expression is regulated in part by the spatial organization of transcription and translation. Unfortunately, current cell-free approaches are unable to control the organization of molecular components needed for gene expression, which limits the ability to probe and utilize its effects. Here, we show, using complementary computational and experimental approaches, that macromolecular crowding can be used to control the spatial organization and translational efficiency of gene expression in cell-sized vesicles. Computer simulations and imaging experiments reveal that, as crowding is increased, DNA plasmids become localized at the inner surface of vesicles. Ribosomes, in contrast, remain uniformly distributed, demonstrating that crowding can be used to differentially organize components of gene expression. We further carried out cell-free protein synthesis reactions in cell-sized vesicles and quantified mRNA and protein abundance. At sufficiently high levels of crowding, we observed localization of mRNA near vesicle surfaces, a decrease in translational efficiency and protein abundance, and anomalous scaling of protein abundance as a function of vesicle size. These results are consistent with high levels of crowding causing altered spatial organization and slower diffusion. Our work demonstrates a straightforward way to control the organization of gene expression in cell-sized vesicles and provides insight into the spatial regulation of gene expression in cells.

Predicting Adhesive Free Energies of Polymer-Surface Interactions with Machine Learning

Polymer-surface interactions are crucial to many biological processes and industrial applications. Here we propose a machine learning method to connect a model polymer's sequence with its adhesion to decorated surfaces. We simulate the adhesive free energies of 20000 unique coarse-grained one-dimensional polymer sequences interacting with functionalized surfaces and build support vector regression models that demonstrate inexpensive and reliable prediction of the adhesive free energy as a function of sequence. Our work highlights the promising integration of coarse-grained simulation with data-driven machine learning methods for the design of functional polymers and represents an important step toward linking polymer compositions with polymer-surface interactions.

Membrane-mediated interactions between hinge-like particles

Adsorption of nanoparticles on a membrane can give rise to interactions between particles, mediated by membrane deformations, that play an important role in self-assembly and membrane remodeling. Previous theoretical and experimental research has focused on nanoparticles with fixed shapes, such as spherical, rod-like, and curved nanoparticles. Recently, hinge-like DNA origami nanostructures have been designed with tunable mechanical properties. Inspired by this, we investigate the equilibrium properties of hinge-like particles adsorbed on an elastic membrane using Monte Carlo and umbrella sampling simulations. The configurations of an isolated particle are influenced by competition between bending energies of the membrane and the particle, which can be controlled by changing adsorption strength and hinge stiffness. When two adsorbed particles interact, they effectively repel one another when the strength of adhesion to the membrane is weak. However, a strong adhesive interaction induces an effective attraction between the particles, which drives their aggregation. The configurations of the aggregate can be tuned by adjusting the hinge stiffness: tip-to-tip aggregation occurs for flexible hinges, whereas tip-to-middle aggregation also occurs for stiffer hinges. Our results highlight the potential for using the mechanical features of deformable nanoparticles to influence their self-assembly when the particles and membrane mutually influence one another.

Adsorption of semiflexible polymers in crowded environments

Macromolecular crowding is a feature of cellular and cell-free systems that, through depletion effects, can impact the interactions of semiflexible biopolymers with surfaces. In this work, we use computer simulations to study crowding-induced adsorption of semiflexible polymers on otherwise repulsive surfaces. Crowding particles are modeled explicitly, and we investigate the interplay between the bending stiffness of the polymer and the volume fraction and size of crowding particles. Adsorption to flat surfaces is promoted by stiffer polymers, smaller crowding particles, and larger volume fractions of crowders. We characterize transitions from non-adsorbed to partially and strongly adsorbed states as a function of bending stiffness. The crowding-induced transitions occur at smaller values of the bending stiffness as the volume fraction of crowders increases. Concomitant effects on the size and shape of the polymer are reflected by crowding- and stiffness-dependent changes to the radius of gyration. For various polymer lengths, we identify a critical crowding fraction for adsorption and analyze its scaling behavior in terms of polymer stiffness. We also consider crowding-induced adsorption in spherical confinement and identify a regime in which increasing the bending stiffness induces desorption. The results of our simulations shed light on the interplay of crowding and bending stiffness on the spatial organization of biopolymers in encapsulated cellular and cell-free systems.