Correction to “Monte Carlo Simulation on Complex Formation of Proteins and Polysaccharides”

Correction to “Monte Carlo Simulation on Complex Formation of Proteins and Polysaccharides

Monte Carlo Simulation on Complex Formation of Proteins and Polysaccharides

In protein–polysaccharide complex systems, how nonspecific interactions such as electrostatic and van der Waals interactions affect complex formation has not been clearly understood. On the basis of a coarse-grained model with the specificity of a target system, we have applied Monte Carlo (MC) simulation to illustrate the process of complex coacervate formation from the association of proteins and polysaccharides. The coarse-grained model is based on serum albumin and a polycation system, and the MC simulation of pH impact on complex coacervation has been carried out. We found that complex coacervates could form three ways, but the conventional association through electrostatic attraction between the protein and polysaccharide still dominated the complex coacervation in such systems. We also observed that the depletion potential always participated in protein crowding and was weakened in the presence of strong electrostatic interactions. Furthermore, we observed that the sizes of polysaccharide chains nonmonotonically increased with the number of bound proteins. Our approach provides a new way to understand the details during protein–polysaccharide complex coacervation at multiple length scales, from interaction and conformation to aggregation

Molecular Dynamics Simulation of Salt Diffusion in Polyelectrolyte Assemblies

The diffusion of salt ions and charged probe molecules in polyelectrolyte (PE) assemblies is often assumed to follow a theoretical hopping model, in which the diffusing ion hops between charged sites of chains based on electroneutrality. However, experimental verification of diffusing pathway at such microscales is difficult, and the corresponding molecular mechanisms remain elusive. In this study, we perform all-atom molecular dynamics simulations of salt diffusion in the PE assembly of poly­(sodium-4-styrenesulfonate) (PSS) and poly­(diallyldimethylammonium chloride) (PDAC). Besides the ion hopping mode, the diffusing trajectories are found to present common features of a jump process, that is, subjecting to PE relaxation, water pockets in the structure open and close; thus, the ion can move from one pocket to another. Anomalous subdiffusion of ions and water is observed because of the trapping scenarios in these water pockets. The jump events are much rarer compared with ion hopping but significantly increases salt diffusion with increasing temperature. Our result strongly indicates that salt diffusion in hydrated PDAC/PSS is a combined process of ion hopping and jump motion. This provides a new molecular explanation for the coupling of salt motion with chain motion and the nonlinear increase of salt diffusion at glass-transition temperature

Photocurrent Enhancement for Ti-Doped Fe₂O₃ Thin Film Photoanodes by an In Situ Solid-State Reaction Method

In this work, a higher concentration of Ti ions are incorporated into hydrothermally grown Ti-doped (2.2% by atomic ratio) micro-nanostructured hematite films by an in situ solid-state reaction method. The doping concentration is improved from 2.2% to 19.7% after the in situ solid-state reaction. X-ray absorption analysis indicates the substitution of Fe ions by Ti ions, without the generation of Fe²⁺ defects. Photoelectrochemical impedance spectroscopy reveals the dramatic improvement of the electrical conductivity of the hematite film after the in situ solid-state reaction. As a consequence, the photocurrent density increases 8-fold (from 0.15 mA/cm² to 1.2 mA/cm²), and it further increases up to ∼1.5 mA/cm² with the adsorption of Co ions. Our findings demonstrate that the in situ solid-state reaction is an effective method to increase the doping level of Ti ions in hematite films with the retention of the micro-nanostructure of the films and enhance the photocurrent

Monte Carlo Study of Polyelectrolyte Adsorption on Mixed Lipid Membrane

Monte Carlo simulations are employed to investigate the adsorption of a flexible linear cationic polyelectrolyte onto a fluid mixed membrane containing neutral (phosphatidyl-choline, PC), multivalent (phosphatidylinositol, PIP₂), and monovalent (phosphatidylserine, PS) anionic lipids. We systematically study the effect of chain length and charge density of the polyelectrolyte, the solution ionic strength, as well as the membrane compositions on the conformational and interfacial properties of the model system. In particular, we explore (i) the adsorption/desorption limit, (ii) the interfacial structure variations of the adsorbing polyelectrolyte and the lipid membrane, and (iii) the overcharging of the membrane. Polyelectrolyte adsorbs on the membrane when anionic lipid demixing entropy loss and polyelectrolyte flexibility loss due to adsorption are dominated by electrostatic attraction between polyelectrolyte and anionic lipids on the membrane. Polyelectrolytes with longer chain length and higher charge density can adsorb on the membrane with increased anionic lipid density under a higher critical ionic concentration. Below the critical ionic concentration, the adsorption extent increases with the charge density and chain length of the polyelectrolyte and decreases with the ionic strength of the solution. The diffusing anionic lipids prohibit the polyelectrolyte chain from forming too long tails. The adsorbing polyelectrolyte with long chain length and high charge density can overcharge a membrane with low charge density, and conversely, the membrane charge inversion forces the polyelectrolyte chain to form extended loops and tails in the solution

Effects of Chain Rigidity on the Adsorption of a Polyelectrolyte Chain on Mixed Lipid Monolayer: A Monte Carlo Study

We apply Monte Carlo simulation to explore the adsorption of a positively charged polyelectrolyte on a lipid monolayer membrane, composed of electronically neutral, monovalent anionic and mulvitalent anionic phospholipids. We systematically assess the influence of various factors, including the intrinsic rigidity of the polyelectrolyte chain, the bead charge density of the polyelectrolyte, and the ionic strength of the saline solution, on the interfacial structural properties of the polyelectrolyte/monolayer complex. The enhancement of the polyelectrolyte chain intrinsic rigidity reduces the polyelectrolyte conformational entropy loss and the energy gains in electrostatic interaction, but elevates the segregated anionic lipid demixing entropy loss. This energy-entropy competition results in a nonmonotonic dependence of the polyelectrolyte/monolayer association strength on the degree of chain rigidity. The semiflexible polyelectrolyte, i.e., the one with an intermediate degree of chain rigidity, is shown to associate onto the ternary membane below a higher critical ionic concentration. In this ionic concentration regime, the semiflexible polyelectrolyte binds onto the monolayer more firmly than the pancake-like flexible one and exhibits a stretched conformation. When the chain is very rigid, the polyelectrolyte with bead charge density <i>Z</i>_b = +1 exhibits a larger tail and tends to dissociate from the membrane, whereas the one with <i>Z</i>_b= +2 can still bind onto the membrane in a bridge-like conformation. Our results imply that chain intrinsic rigidity serves as an efficient molecular factor for tailoring the adsorption/desorption transition and interfacial structure of the polyelectrolyte/monolayer complex

Strain Hardening Behavior of Poly(vinyl alcohol)/Borate Hydrogels

The large-amplitude oscillatory shear (LAOS) behavior of poly­(vinyl alcohol) (PVA)/borate hydrogels was investigated with the change of scanning frequency (ω) as well as concentrations of borate and PVA. The different types (Types I–IV) of LAOS behavior are successfully classified by the mean number of elastically active subchains per PVA chain (<i>f</i>_eas) and Deborah number (<i>D</i>_e = ωτ, τ is the relaxation time of sample). For the samples with Type I behavior (both storage modulus <i>G</i>′ and loss modulus <i>G</i>″ increase with strain amplitude γ, i.e., intercycle strain hardening), the critical value of strain amplitude (γ_crit) at the onset of intercycle strain hardening is almost the same when <i>D</i>_e > ∼2 (Region 3), while the value of Weissenberg number (<i>Wi</i> = γ<i>D</i>_e) at γ_crit is similar when <i>D</i>_e < ∼0.2 (Region 1). For intracycle behavior in the Lissajous curve, intracycle strain hardening is only observed in viscous Lissajous curve of Region 1 or in the elastic Lissajous curve of Region 3. In Region 1, both intercycle and intracycle strain hardening are mainly caused by the strain rate-induced increase in the number of elastically active chains, while non-Gaussian stretching of polymer chains starts to contribute as <i>Wi</i> > 1. In Region 3, strain-induced non-Gaussian stretching of polymer chains results in both intercycle and intracycle strain hardening. In Region 2 (∼0.2 < <i>D</i>_e < ∼2), two involved mechanisms both contribute to intercycle strain hardening. Furthermore, by analyzing the influence of characteristic value of <i>D</i>_e as 1 on the rheological behavior of PVA/borate hydrogels, it is concluded that intercycle strain hardening is dominated by strain-rate-induced increase in the number of elastically active chains when <i>D</i>_e < 1, while strain-induced non-Gaussian stretching dominates when <i>D</i>_e > 1

Strain Hardening Behavior of Poly(vinyl alcohol)/Borate Hydrogels

The large-amplitude oscillatory shear (LAOS) behavior of poly­(vinyl alcohol) (PVA)/borate hydrogels was investigated with the change of scanning frequency (ω) as well as concentrations of borate and PVA. The different types (Types I–IV) of LAOS behavior are successfully classified by the mean number of elastically active subchains per PVA chain (<i>f</i>_eas) and Deborah number (<i>D</i>_e = ωτ, τ is the relaxation time of sample). For the samples with Type I behavior (both storage modulus <i>G</i>′ and loss modulus <i>G</i>″ increase with strain amplitude γ, i.e., intercycle strain hardening), the critical value of strain amplitude (γ_crit) at the onset of intercycle strain hardening is almost the same when <i>D</i>_e > ∼2 (Region 3), while the value of Weissenberg number (<i>Wi</i> = γ<i>D</i>_e) at γ_crit is similar when <i>D</i>_e < ∼0.2 (Region 1). For intracycle behavior in the Lissajous curve, intracycle strain hardening is only observed in viscous Lissajous curve of Region 1 or in the elastic Lissajous curve of Region 3. In Region 1, both intercycle and intracycle strain hardening are mainly caused by the strain rate-induced increase in the number of elastically active chains, while non-Gaussian stretching of polymer chains starts to contribute as <i>Wi</i> > 1. In Region 3, strain-induced non-Gaussian stretching of polymer chains results in both intercycle and intracycle strain hardening. In Region 2 (∼0.2 < <i>D</i>_e < ∼2), two involved mechanisms both contribute to intercycle strain hardening. Furthermore, by analyzing the influence of characteristic value of <i>D</i>_e as 1 on the rheological behavior of PVA/borate hydrogels, it is concluded that intercycle strain hardening is dominated by strain-rate-induced increase in the number of elastically active chains when <i>D</i>_e < 1, while strain-induced non-Gaussian stretching dominates when <i>D</i>_e > 1

Effects of Concentration and Ionization Degree of Anchoring Cationic Polymers on the Lateral Heterogeneity of Anionic Lipid Monolayers

We employed coarse-grained Monte Carlo simulations to investigate a system composed of cationic polymers and a phosphatidyl-choline membrane monolayer, doped with univalent anionic phosphatidylserine (PS) and tetravalent anionic phosphatidylinositol 4,5-bisphosphate (PIP₂) lipid molecules. For this system, we consider the conditions under which multiple cationic polymers can anchor onto the monolayer and explore how the concentration and ionization degree of the polymers affect the lateral rearrangement and fluidity of the negatively charged lipids. Our work shows that the anchoring cationic polymers predominantly bind the tetravalent anionic PIP₂ lipids and drag the PIP₂ clusters to migrate on the monolayer. The polymer/PIP₂ binding is found to be drastically enhanced by increasing the polymer ionization fraction, which causes the PIP₂ lipids to form into larger clusters and reduces the mobility of the polymer/PIP₂ complexes. As expected, stronger competition effects between anchoring polymers occur at higher polymer concentrations, for which each anchoring polymer partially dissociates from the monolayer and hence sequesters a smaller PIP₂ cluster. The desorbed segments of the anchored polymers exhibit a faster mobility on the membrane, whereas the PIP₂ clusters are closely restrained by the limited adhering cationic segments of anchoring polymers. We further demonstrate that the PIP₂ molecules display a hierarchical mobility in the PIP₂ clusters, which is regulated by the synergistic effect between the cationic segments of the polymers. The PS lipids sequester in the vicinity of the polymer/PIP₂ complexes if the tetravalent PIP₂ lipids cannot sufficiently neutralize the cationic polymers. Finally, we illustrate that the increase in the ionic concentration of the solution weakens the lateral clustering and the mobility heterogeneity of the charged lipids. Our work thus provides a better understanding of the fundamental biophysical mechanism of the concentration gradients and the hierarchical mobility of the anionic lipids in the membrane caused by the cationic polymer anchoring on length and time scales that are generally inaccessible by atomistic models. It also offers insight into the development and design of novel biological applications on the basis of the modulation of signaling lipids