Polymer Folding in Slitlike Nanoconfinement

Computational Approaches to Predict Protein-Protein Interactions in Crowded Cellular Environments

Investigating protein-protein interactions is crucial for understanding cellular biological processes because proteins often function within molecular complexes rather than in isolation. While experimental and computational methods have provided valuable insights into these interactions, they often overlook a critical factor: the crowded cellular environment. This environment significantly impacts protein behavior, including structural stability, diffusion, and ultimately the nature of binding. In this review, we discuss theoretical and computational approaches that allow the modeling of biological systems to guide and complement experiments and can thus significantly advance the investigation, and possibly the predictions, of protein-protein interactions in the crowded environment of cell cytoplasm. We explore topics such as statistical mechanics for lattice simulations, hydrodynamic interactions, diffusion processes in high-viscosity environments, and several methods based on molecular dynamics simulations. By synergistically leveraging methods from biophysics and computational biology, we review the state of the art of computational methods to study the impact of molecular crowding on protein-protein interactions and discuss its potential revolutionizing effects on the characterization of the human interactome.

Ethyl Vanillin Rapid Crystallization from Carboxymethyl Chitosan Ion-Switchable Hydrogels

Polymer gels are usually used for crystal growth as the recovered crystals have better properties. Fast crystallization under nanoscale confinement holds great benefits, especially in polymer microgels as its tunable microstructures. This study demonstrated that ethyl vanillin can be quickly crystallized from carboxymethyl chitosan/ethyl vanillin co-mixture gels via classical swift cooling method and supersaturation. It found that EVA appeared with bulk filament crystals accelerated by a large quantity of nanoconfinement microregions resulted from space-formatted hydrogen network between EVA and CMCS when their concentration exceeds 1:1.4 and may occasionally arise when the concentration less than 1:0.8. It was observed that EVA crystal growth has two models involving hang-wall growth at the air-liquid interface at the contact line, as well as extrude-bubble growth at any sites on the liquid surface. Further investigations found that EVA crystals can be recovered from as-prepared ion-switchable CMCS gels by 0.1 M hydrochloric acid or acetic acid without defects. Consequently, the proposed method may offer an available scheme for a large-scale preparation of API analogs.

Confinement free energy for a polymer chain: Corrections to scaling

Spatial confinement of a polymer chain results in a reduction of conformational entropy. For confinement of a flexible N-mer chain in a planar slit or cylindrical pore (confining dimension D), a blob model analysis predicts the asymptotic scaling behavior ΔF/N ∼ D^-γ with γ ≈ 1.70, where ΔF is the free energy increase due to confinement. Here, we extend this scaling analysis to include the variation of local monomer density upon confinement giving ΔF/N ∼ D^-γ(1 - h(N, D)), where the correction-to-scaling term has the form h ∼ D^y/N^Δ with exponents y = 3 - γ ≈ 1.30 and Δ = 3/γ - 1 ≈ 0.76. To test these scaling predictions, we carry out Wang-Landau simulations of confined and unconfined tangent-hard-sphere chains (bead diameter σ) in the presence of a square-well trapping potential. The fully trapped chain provides a common reference state, allowing for an absolute determination of the confinement free energy. Our simulation results for 32 ≤ N ≤ 1024 and 3 ≤ D/σ ≤ 14 are well-described by the extended scaling relation giving exponents of γ = 1.69(1), y = 1.25(2), and Δ = 0.75(6).

Melting of confined DNA: static and dynamic properties

We study dsDNA (double strand DNA) melting in detail within varying strip-like confinement in a two-dimensional lattice model. The interplay between reduced configurational entropy and attractive base-pairing energy results in a non-monotonic melting profile of DNA. Structural transitions associated with confined DNA melting reveal a stretched or extended state for very strong confinement. By using the exact enumeration method, we investigate the emergence of a local denatured zone e.g. bubbles during DNA melting. The survival time of a single bubble within varying strip width is studied from the Fokker-Planck formalism by considering the bubble size as a reaction co-ordinate. We show that a simple lattice model can capture the sequence heterogeneity effect on DNA melting and bubble dynamics within the strip. Different time scales of bubble zipping for different DNA sequences are found, which may have potential applications in denaturation mapping.

Partition-function-zero analysis of polymer adsorption for a continuum chain model

Polymer chains undergoing adsorption are expected to show universal critical behavior which may be investigated using partition function zeros. The focus of this work is the adsorption transition for a continuum chain, allowing for investigation of a continuous range of the attractive interaction and comparison with recent high-precision lattice model studies. The partition function (Fisher) zeros for a tangent-hard-sphere N-mer chain (monomer diameter σ) tethered to a flat wall with an attractive square-well potential (range λσ, depth ε) have been computed for chains up to N=1280 with 0.01≤λ≤2.0. In the complex-Boltzmann-factor plane these zeros are concentrated in an annular region, centered on the origin and open about the real axis. With increasing N, the leading zeros, w_{1}(N), approach the positive real axis as described by the asymptotic scaling law w_{1}(N)-y_{c}∼N^{-ϕ}, where y_{c}=e^{ε/k_{B}T_{c}} is the critical point and T_{c} is the critical temperature. In this work, we study the polymer adsorption transition by analyzing the trajectory of the leading zeros as they approach y_{c} in the complex plane. We use finite-size scaling (including corrections to scaling) to determine the critical point and the scaling exponent ϕ as well as the approach angle θ_{c}, between the real axis and the leading-zero trajectory. Variation of the interaction range λ moves the critical point, such that T_{c} decreases with λ, while the results for ϕ and θ_{c} are approximately independent of λ. Our values of ϕ=0.479(9) and θ_{c}=56.8(1.4)^{∘} are in agreement with the best lattice model results for polymer adsorption, further demonstrating the universality of these constants across both lattice and continuum models.

Coarse-grained molecular dynamics simulations of nanoplastics interacting with a hydrophobic environment in aqueous solution

Nanoplastics (NPs) are emerging threats for marine and terrestrial ecosystems, but little is known about their fate in the environment at the molecular scale. In this work, coarse-grained molecular dynamics simulations were performed to investigate nature and strength of the interaction between NPs and hydrophobic environments. Specifically, NPs were simulated with different hydrophobic and hydrophilic polymers while carbon nanotubes (CNTs) were used to mimic surface and confinement effects of hydrophobic building blocks occurring in a soil environment. The hydrophobicity of CNTs was modified by introducing different hydrophobic and hydrophilic functional groups at their inner surfaces. The results show that hydrophobic polymers have a strong affinity to adsorb at the outer surface and to be captured inside the CNT. The accumulation within the CNT is even increased in presence of hydrophobic functional groups. This contribution is a first step towards a mechanistic understanding of a variety of processes connected to interaction of nanoscale material with environmental systems. Regarding the fate of NPs in soil, the results point to the critical role of the hydrophobicity of NPs and soil organic matter (SOM) as well as of the chemical nature of functionalized SOM cavities/voids in controlling the accumulation of NPs in soil. Moreover, the results can be related to water treatment technologies as it is shown that the hydrophobicity of CNTs and functionalization of their surfaces may play a crucial role in enhancing the adsorption capacity of CNTs with respect to organic compounds and thus their removal efficiency from wastewater.

The binding mechanisms of nanoplastics (NPs) to carbon nanotubes as hydrophobic environmental systems have been explored by coarse-grained MD simulations. The results could be closely connected to fate of NPs in soil and water treatment technologies.

Effects of macromolecular crowding on the folding of a polymer chain: A Wang-Landau simulation study

A flexible polymer chain in the presence of inert macromolecular crowders will experience a loss of configurational entropy due to the crowder excluded volume. This entropy reduction will be most pronounced in good solvent conditions where the chain assumes an expanded coil conformation. For polymers that undergo a folding transition from a coil to a compact ordered state, as is the case for many globular proteins, macromolecular crowding is expected to stabilize the folded state and thereby shift the transition location. Here, we study such entropic stabilization effects for a tangent square-well sphere chain (monomer diameter σ) in the presence of hard-sphere (HS) crowders (diameter D ≥ σ). We use the Wang-Landau simulation algorithm to construct the density of states for this chain in a crowded environment and are thus able to directly compute the reduction in configurational entropy due to crowding. We study both a chain that undergoes all-or-none folding directly from the coil state and a chain that folds via a collapsed-globule intermediate state. In each case, we find an increase in entropic stabilization for the compact states with an increase in crowder density and, for fixed crowder density, with a decrease in crowder size (concentrated, small crowders have the largest effect). The crowder significantly reduces the average size for the unfolded states while having a minimal effect on the size of the folded states. In the athermal limit, our results directly provide the confinement free energy due to crowding for a HS chain in a HS solvent.

All-or-none folding of a flexible polymer chain in cylindrical nanoconfinement

Geometric confinement of a polymer chain results in a loss of conformational entropy. For a chain that can fold into a compact native state via a first-order-like transition, as is the case for many small proteins, confinement typically provides an entropic stabilization of the folded state, thereby shifting the location of the transition. This allows for the possibility of confinement (entropy) driven folding. Here, we investigate such confinement effects for a flexible square-well-sphere N-mer chain (monomer diameter σ) confined within a long cylindrical pore (diameter D) or a closed cylindrical box (height H = D). We carry out Wang-Landau simulations to construct the density of states, which provides access to the complete thermodynamics of the system. For a wide pore, an entropic stabilization of the folded state is observed. However, as the pore diameter approaches the size of the folded chain (D ∼ N^1/3σ), we find a destabilization effect. For pore diameters smaller than the native ground-state, the chain folds into a different, higher energy, ground state ensemble and the T vs D phase diagram displays non-monotonic behavior as the system is forced into different ground states for different ranges of D. In this regime, isothermal reduction of the confinement dimension can induce folding, unfolding, or crystallite restructuring. For the cylindrical box, we find a monotonic stabilization effect with decreasing D. Scaling laws for the confinement free energy in the athermal limit are also investigated.

Entropy deepens loading chemical potentials of small alcohols by narrow carbon nanotubes

Small alcohol confinement within narrow carbon nanotubes has been extensively and systematically studied via rigorous free-energy calculations.