Reply to the 'Comment on "Effects of topological constraints on linked ring polymers in solvents of varying quality"' by M. Tsige and H. Guo, Soft Matter, 2024, 20, DOI: 10.1039/D3SM01614E.

In the preceding Comment, Drs Tsige and Guo compare their findings about the θ-temperatures of linear chains, ring polymers and poly[n]catenanes with those of previous work by us [Z. A. Dehaghani, I. Chubak, C. N. Likos and M. R. Ejtehadi, Soft Matter, 2020, 16, 3029-3038] and point out that the ordering they obtain for these three quantities is, for large degrees of polymerisation, the reverse of the one we had found in our own investigations. We thank the authors of the Comment for their remarks and we appreciate their detailed investigations, which emphasise the importance of understanding the properties of topological polymers and their behaviour under varying solvent quality. We point out, however, that the discrepancy found by Tsige and Guo is only apparent because it pertains to the Θ-temperature of rings and poly[n]catenanes with the same overall molecular weight, whereas in our work we compared the Θ-temperature of a constituent ring of the poly[n]catenane with that of the entire mechanically linked macromulecule.

Effects of Linking Topology on the Shear Response of Connected Ring Polymers: Catenanes and Bonded Rings Flow Differently.

We perform computer simulations of mechanically linked (poly[2]catenanes, PC) and chemically bonded (bonded rings, BR) pairs of self-avoiding ring polymers in steady shear. We find that BRs develop a novel motif, termed gradient tumbling, rotating around the gradient axis. For the PCs the rings are stretched and display another new pattern, termed slip tumbling. The dynamics of BRs is continuous and oscillatory, whereas that of PCs is intermittent between slip-tumbling attempts. Our findings demonstrate the interplay between topology and hydrodynamics in dilute solutions of connected polymers.

In silico study of the impact of oxidation on pyruvate transmission across the hVDAC1 protein channel.

The overexpression of voltage dependent anion channels (VDACs), particularly VDAC1, in cancer cells compared to normal cells, plays a crucial role in cancer cell metabolism, apoptosis regulation, and energy homeostasis. In this study, we used molecular dynamics (MD) simulations to investigate the effect of a low level of VDAC1 oxidation (induced e.g., by cold atmospheric plasma (CAP)) on the pyruvate (Pyr) uptake by VDAC1. Inhibiting Pyr uptake through VDAC1 can suppress cancer cell proliferation. Our primary target was to study the translocation of Pyr across the native and oxidized forms of hVDAC1, the human VDAC1. Specifically, we employed MD simulations to analyze the hVDAC1 structure by modifying certain cysteine residues to cysteic acids and methionine residues to methionine sulfoxides, which allowed us to investigate the effect of oxidation. Our results showed that the free energy barrier for Pyr translocation through the native and oxidized channel was approximately 4.3 ± 0.7 kJ mol-1 and 10.8 ± 1.8 kJ mol-1, respectively. An increase in barrier results in a decrease in rate of Pyr permeation through the oxidized channel. Thus, our results indicate that low levels of CAP oxidation reduce Pyr translocation, resulting in decreased cancer cell proliferation. Therefore, low levels of oxidation are likely sufficient to treat cancer cells given the inhibition of Pyr uptake.

Electrochromic Sensor Augmented with Machine Learning for Enzyme-Free Analysis of Antioxidants.

Our study presents an electrochromic sensor that operates without the need for enzymes or multiple oxidant reagents. This sensor is augmented with machine learning algorithms, enabling the identification, classification, and prediction of six different antioxidants with high accuracy. We utilized polyaniline (PANI), Prussian blue (PB), and copper-Prussian blue analogues (Cu-PBA) at their respective oxidation states as electrochromic materials (ECMs). By designing three readout channels with these materials, we were able to achieve visual detection of antioxidants without relying on traditional "lock and key" specific interactions. Our sensing approach is based on the direct electrochemical reactions between oxidized electrochromic materials (ECMsox) as electron acceptors and various antioxidants, which act as electron donors. This interaction generates unique fingerprint patterns by switching the ECMsox to reduced electrochromic materials (ECMsred), causing their colors to change. Through the application of density functional theory (DFT), we demonstrated the molecular-level basis for the distinct multicolor patterns. Additionally, machine learning algorithms were employed to correlate the optical patterns with RGB data, enabling complex data analysis and the prediction of unknown samples. To demonstrate the practical applications of our design, we successfully used the EC sensor to diagnose antioxidants in serum samples, indicating its potential for the on-site monitoring of antioxidant-related diseases. This advancement holds promise for various applications, including the real-time monitoring of antioxidant levels in biological samples, the early diagnosis of antioxidant-related diseases, and personalized medicine. Furthermore, the success of our electrochromic sensor design highlights the potential for exploring similar strategies in the development of sensors for diverse analytes, showcasing the versatility and adaptability of this approach.

Dynamics of fluid bilayer vesicles: Soft meshes and robust curvature energy discretization.

Continuum models like the Helfrich Hamiltonian are widely used to describe fluid bilayer vesicles. Here we study the molecular dynamics compatible dynamics of the vertices of two-dimensional meshes representing the bilayer, whose in-plane motion is only weakly constrained. We show (i) that Jülicher's discretization of the curvature energy offers vastly superior robustness for soft meshes compared to the commonly employed expression by Gommper and Kroll and (ii) that for sufficiently soft meshes, the typical behavior of fluid bilayer vesicles can emerge even if the mesh connectivity remains fixed throughout the simulations. In particular, soft meshes can accommodate large shape transformations, and the model can generate the typical ℓ^{-4} signal for the amplitude of surface undulation modes of nearly spherical vesicles all the way up to the longest wavelength modes. Furthermore, we compare results for Newtonian, Langevin, and Brownian dynamics simulations of the mesh vertices to demonstrate that the internal friction of the membrane model is negligible, making it suitable for studying the internal dynamics of vesicles via coupling to hydrodynamic solvers or particle-based solvent models.

Programmable Transport of C60 by Straining Graphene Substrate.

Controlling the maneuverability of nanocars and molecular machines on the surface is essential for the targeted transportation of materials and energy at the nanoscale. Here, we evaluate the motion of fullerene, as the most popular candidate for use as a nanocar wheel, on the graphene nanoribbons with strain gradients based on molecular dynamics (MD), and theoretical approaches. The strain of the examined substrates linearly decreases by 20%, 16%, 12%, 8%, 4%, and 2%. MD calculations were performed with the open source LAMMPS solver. The essential physics of the interactions is captured by Lennard-Jones and Tersoff potentials. The motion of C60 on the graphene nanoribbon is simulated in canonical ensemble, which is implanted by using a Nose-Hoover thermostat. Since the potential energy of C60 is lower on the unstrained end of nanoribbons, this region is energetically more favorable for the molecule. As the strain gradient of the surface increases, the trajectories of the motion and the C60 velocity indicate more directed movements along the gradient of strain on the substrate. Based on the theoretical relations, it was shown that the driving force and diffusion coefficient of the C60 motion respectively find linear and quadratic growth with the increase of strain gradient, which is confirmed by MD simulations. To understand the effect of temperature, at each strain gradient of substrate, the simulations are repeated at the temperatures of 100, 200, 300, and 400 K. The large ratio of longitudinal speed to the transverse speed of fullerene at 100 and 200 K refers to the rectilinear motion of molecule at low temperatures. Using successive strain gradients on the graphene in perpendicular directions, we steered the motion of C60 to the desired target locations. The programmable transportation of nanomaterials on the surface has a significant role in different processes at the nanoscale, such as bottom-up assembly.

Counterintuitive properties of evolutionary measures: A stochastic process study in cyclic population structures with periodic environments.

Local environmental interactions are a major factor in determining the success of a new mutant in structured populations. Spatial variations in the concentration of genotype-specific resources change the fitness of competing strategies locally and thus can drastically change the outcome of evolutionary processes in unintuitive ways. The question is how such local environmental variations in network population structures change the condition for selection and fixation probability of an advantageous (or deleterious) mutant. We consider linear graph structures and focus on the case where resources have a spatial periodic pattern. This is the simplest model with two parameters, length scale and fitness scales, representing heterogeneity. We calculate fixation probability and fixation times for a constant population birth-death process as fitness heterogeneity and period vary. Fixation probability is affected by not only the level of fitness heterogeneity but also spatial scale of resources variations set by period of distribution T. We identify conditions for which a previously a deleterious mutant (in a uniform environment) becomes beneficial as fitness heterogeneity is increased. We observe cases where the fixation probability of both mutant and resident types are more than their neutral value, 1/N, simultaneously. This coincides with exponential increase in time to fixation which points to potential coexistence of resident and mutant types. Finally, we discuss the effect of the 'fitness shift' where the fitness function of two types has a phase difference. We observe significant increases (or decreases) in the fixation probability of the mutant as a result of such phase shift.

Nanocar swarm movement on graphene surfaces.

Investigation of nanomachine swarm motion is useful in the design of molecular transportation systems as well as in understanding the assembly process on the surface. Here, we evaluate the motion of the clusters of nanocars on graphene surfaces, using molecular dynamics (MD) simulations. The mechanism of motion of single nanocars is evaluated by considering the rotation of the wheels, direction of the nanocars' speed and comparing the characteristics of the surface motion of nanocars and similar absorbed molecules. The mentioned analyses reveal that, in the thermally activated surface motion of the nanocars, sliding movements are the dominant mode of motion. A coarse grained (CG) model is proposed for some preliminary studies such as finding the stable orientation of two nanocars. The established model indicates three stable orientations for a pair of nanocars, which are verified by MD simulations and the analysis of potential energy. The radius of gyration and the root mean square deviation (RMSD) are employed to evaluate the configuration of larger nanocar clusters. Nanocar clusters change their configuration at 300 K and higher temperatures; however, there is a threshold temperature (600 K) at which different clusters are broken because at this temperature the thermal fluctuation energy dominates the vdW attraction between a nanocar in the perimeter and the other nanocars of the cluster. The surface motions of the nanocar clusters are investigated at temperatures at which the clusters are thermally stable by computing different motion parameters such as mean square displacements (MSDs), diffusion coefficients and anomaly parameters. As the population of clusters increases from 1 to 10 nanocars, the motion regime changes from long-range to small-range displacements which is attributed to the energy wasted by intermolecular vdW interactions. The anomaly parameters of the motions reveal that the clusters experience almost normal diffusion at low temperatures, while they find a super-diffusive regime at higher temperatures. Ultimately, the preferred arrangement of nanocar assembly can be utilized to fabricate special nanostructures on the surface including molecular rings and chains.

Electronic polarization effects on membrane translocation of anti-cancer drugs.

Free-energy calculations are crucial for investigating biomolecular interactions. However, in theoretical studies, the neglect of electronic polarization can reduce predictive capabilities, specifically for free-energy calculations. To effectively mimick polarization, we explore a Charge Switching (CS) model, aiming to narrow the gap between computational and experimental results. The model requires quantum-level partial charge calculations of the molecule in different environments, combined with atomistic MD simulations. Studying three different anti-cancer drug molecules with three different phospholipid membranes, we show that the method significantly improves agreement with available experimental data. In contrast, using conventional fixed charge atomistic methods, qualitative discrepancies with experiments are observed, and we show that neglecting polarization may lead to an unphysical free energy sign inversion. While the CS method is here applied to anti-cancer drug-membrane translocation, it could be used more generally to study processes considering solvent effects.

Collective movement and thermal stability of fullerene clusters on the graphene layer.

Understanding the motion characteristics of fullerene clusters on the graphene surface is critical for designing surface manipulation systems. Toward this purpose, using the molecular dynamics method, we evaluated six clusters of fullerenes including 1, 2, 3, 5, 10, and 25 molecules on the graphene surface, in the temperature range of 25 to 500 K. First, the surface motion of clusters is studied at 200 K and lower temperatures, in which fullerenes remain as a single group. The trajectories of the motion as well as the diffusion coefficients indicate the reduction of surface mobility as a response to the increase of the fullerene number. The clusters show normal diffusion at the temperature of 25 K, while they follow the super-diffusion regime at higher temperatures. The separation of fullerenes occurs at 300 K and higher temperatures. Due to the increase of vdW attraction with the increase of the fullerene number, the separation of fullerenes in larger clusters occurs at higher temperatures. The thermal energy at 500 K is sufficient to divide the large C60 clusters into smaller clusters. This energy level is related to the saturation of the interaction energy experienced by individual fullerenes, which can be estimated from the potential energy analysis. The results of simulations reveal that the separation occurs at the edge of clusters. Moreover, we studied the thermal stability of multilayer fullerene clusters on graphene. The simulation results indicate the tendency of multilayer clusters to locate on the surface, which implies the wetting property of C60s on the graphene layer.

A modified Jarzynski free-energy estimator to eliminate non-conservative forces and its application in nanoparticle-membrane interactions.

Computational methods to understand interactions in bio-complex systems are however limited to time-scales typically much shorter than in Nature. For example, on the nanoscale level, interactions between nanoparticles (NPs)/molecules/peptides and membranes are central in complex biomolecular processes such as membrane-coated NPs or cellular uptake. This can be remedied by the application of e.g. Jarzynski's equality where thermodynamic properties are extracted from non-equilibrium simulations. Although, the out of equilibrium work leads to non-conservative forces. We here propose a correction Pair Forces method, that removes these forces. Our proposed method is based on the calculation of pulling forces in backward and forward directions for the Jarzynski free-energy estimator using steered molecular dynamics simulation. Our results show that this leads to much improvement for NP-membrane translocation free energies. Although here we have demonstrated the application of the method in molecular dynamics simulation, it could be applied for experimental approaches.

Effect of Cysteine Oxidation in SARS-CoV-2 Receptor-Binding Domain on Its Interaction with Two Cell Receptors: Insights from Atomistic Simulations.

Binding of the SARS-CoV-2 S-glycoprotein to cell receptors is vital for the entry of the virus into cells and subsequent infection. ACE2 is the main cell receptor for SARS-CoV-2, which can attach to the C-terminal receptor-binding domain (RBD) of the SARS-CoV-2 S-glycoprotein. The GRP78 receptor plays an anchoring role, which attaches to the RBD and increases the chance of other RBDs binding to ACE2. Although high levels of reactive oxygen and nitrogen species (RONS) are produced during viral infections, it is not clear how they affect the RBD structure and its binding to ACE2 and GRP78. In this research, we apply molecular dynamics simulations to study the effect of oxidation of the highly reactive cysteine (Cys) amino acids of the RBD on its binding to ACE2 and GRP78. The interaction energy of both ACE2 and GRP78 with the whole RBD, as well as with the RBD main regions, is compared in both the native and oxidized RBDs. Our results show that the interaction energy between the oxidized RBD and ACE2 is strengthened by 155 kJ/mol, increasing the binding of the RBD to ACE2 after oxidation. In addition, the interaction energy between the RBD and GRP78 is slightly increased by 8 kJ/mol after oxidation, but this difference is not significant. Overall, these findings highlight the role of RONS in the binding of the SARS-CoV-2 S-glycoprotein to host cell receptors and suggest an alternative mechanism by which RONS could modulate the entrance of viral particles into the cells.

Glycan-mediated functional assembly of IL-1RI: structural insights into completion of the current description for immune response.

Interleukin 1 Receptor type I (IL-1RI) is a multi-domain transmembrane receptor that triggers the inflammatory response. Understanding its detailed mechanism of action is crucial for treating immune disorders. IL-1RI is activated upon formation of its functional assembly that occurs by binding of the IL-1 cytokine and the accessory protein (Il-1RAcP) to it. X-ray crystallography, small-Angle X-ray Scattering and molecular dynamics simulation studies showed that IL-1RI adopts two types of 'compact' and 'extended' conformational states in its dynamical pattern. Furthermore, glycosylation has shown to play a critical role in its activation process. Here, classical and accelerated atomistic molecular dynamics were carried out to examine the role of full glycosylation of IL-1RI and IL-1RAcP in arrangement of the functional assembly. Simulations showed that the 'compact' and 'extended' IL-1RI form two types of 'cytokine-inaccessible-non-signaling' and 'cytokine-accessible-signaling' assemblies with the IL-1RacP, respectively that are both abiding in the presence of glycans. Suggesting that the cytokine binding to IL-1RI is not required for the formation of IL-1RI-IL-1RAcP complex and the 'compact' complex could act as a down-regulatory mechanism. The 'extended' complex is maintained by formation of several persistent hydrogen bonds between the IL-1RI-IL-1RAcP inter-connected glycans. Taken together, it was shown that full glycosylation regulates formation of the IL-1RI functional assembly and play critical role in cytokine biding and triggering the IL-1RI involved downstream pathways in the cell.Communicated by Ramaswamy H. Sarma.

Conformation- and phosphorylation-dependent electron tunnelling across self-assembled monolayers of tau peptides.

We report on charge transport across self-assembled monolayers (SAMs) of short tau peptides by probing the electron tunneling rates and quantum mechanical simulation. We measured the electron tunneling rates across SAMs of carboxyl-terminated linker molecules (C6H12O2S) and short cis-tau (CT) and trans-tau (TT) peptides, supported on template-stripped gold (AuTS) bottom electrode, with Eutectic Gallium-Indium (EGaIn)(EGaIn) top electrode. Measurements of the current density across thousands of AuTS/linker/tau//Ga2O3/EGaIn single-molecule junctions show that the tunneling current across CT peptide is one order of magnitude lower than that of TT peptide. Quantum mechanical simulation demonstrated a wider energy bandgap of the CT peptide, as compared to the TT peptide, which causes a reduction in its electron tunneling current. Our findings also revealed the critical role of phosphorylation in altering the charge transport characteristics of short peptides; more specifically, we found that the presence of phosphate groups can reduce the energy band gap in tau peptides and alter their electrical properties. Our results suggest that conformational and phosphorylation of short peptides (e.g., tau) can significantly change their charge transport characteristics and energy levels.

Monte Carlo simulation of a lattice model for the dynamics of randomly branching double-folded ring polymers.

Supercoiled DNA, crumpled interphase chromosomes, and topologically constrained ring polymers often adopt treelike, double-folded, randomly branching configurations. Here we study an elastic lattice model for tightly double-folded ring polymers, which allows for the spontaneous creation and deletion of side branches coupled to a diffusive mass transport, which is local both in space and on the connectivity graph of the tree. We use Monte Carlo simulations to study systems falling into three different universality classes: ideal double-folded rings without excluded volume interactions, self-avoiding double-folded rings, and double-folded rings in the melt state. The observed static properties are in good agreement with exact results, simulations, and predictions of Flory theory for randomly branching polymers. For example, in the melt state rings adopt compact configurations and exhibit territorial behavior. In particular, we show that the emergent dynamics is in excellent agreement with a recent scaling theory and illustrate the qualitative differences with the familiar reptation dynamics of linear chains.

Impact of temporal correlations on high risk outbreaks of independent and cooperative SIR dynamics.

We first propose a quantitative approach to detect high risk outbreaks of independent and coinfective SIR dynamics on three empirical networks: a school, a conference and a hospital contact network. This measurement is based on the k-means clustering method and identifies proper samples for calculating the mean outbreak size and the outbreak probability. Then we systematically study the impact of different temporal correlations on high risk outbreaks over the original and differently shuffled counterparts of each network. We observe that, on the one hand, in the coinfection process, randomization of the sequence of the events increases the mean outbreak size of high-risk cases. On the other hand, these correlations do not have a consistent effect on the independent infection dynamics, and can either decrease or increase this mean. Randomization of the daily pattern correlations has no strong impact on the size of the outbreak in either the coinfection or the independent spreading cases. We also observe that an increase in the mean outbreak size does not always coincide with an increase in the outbreak probability; therefore, we argue that merely considering the mean outbreak size of all realizations may lead us into falsely estimating the outbreak risks. Our results suggest that some sort of contact randomization in the organizational level in schools, events or hospitals might help to suppress the spreading dynamics while the risk of an outbreak is high.

S494 O-glycosylation site on the SARS-CoV-2 RBD affects the virus affinity to ACE2 and its infectivity; a molecular dynamics study.

SARS-CoV-2 is a strain of Coronavirus family that caused the ongoing pandemic of COVID-19. Several studies showed that the glycosylation of virus spike (S) protein and the Angiotensin-Converting Enzyme 2 (ACE2) receptor on the host cell is critical for the virus infectivity. Molecular Dynamics (MD) simulations were used to explore the role of a novel mutated O-glycosylation site (D494S) on the Receptor Binding Domain (RBD) of S protein. This site was suggested as a key mediator of virus-host interaction. By exploring the dynamics of three O-glycosylated models and the control systems of unglcosylated S4944 and S494D complexes, it was shown that the decoration of S494 with elongated O-glycans results in stabilized interactions on the direct RBD-ACE2. Calculation of the distances between RBD and two major H1, H2 helices of ACE2 and the interacting pairs of amino acids in the interface showed that the elongated O-glycan maintains these interactions by forming several polar contacts with the neighbouring residues while it would not interfere in the direct binding interface. Relative binding free energy of RBD-ACE2 is also more favorable in the O-glycosylated models with longer glycans. The increase of RBD binding affinity to ACE2 depends on the size of attached O-glycan. By increasing the size of O-glycan, the RBD-ACE2 binding affinity will increase. Hence, this crucial factor must be taken into account for any further inhibitory approaches towards RBD-ACE2 interaction.

Nanoscale characterization of the biomolecular corona by cryo-electron microscopy, cryo-electron tomography, and image simulation.

The biological identity of nanoparticles (NPs) is established by their interactions with a wide range of biomolecules around their surfaces after exposure to biological media. Understanding the true nature of the biomolecular corona (BC) in its native state is, therefore, essential for its safe and efficient application in clinical settings. The fundamental challenge is to visualize the biomolecules within the corona and their relationship/association to the surface of the NPs. Using a synergistic application of cryo-electron microscopy, cryo-electron tomography, and three-dimensional reconstruction, we revealed the unique morphological details of the biomolecules and their distribution/association with the surface of polystyrene NPs at a nanoscale resolution. The analysis of the BC at a single NP level and its variability among NPs in the same sample, and the discovery of the presence of nonspecific biomolecules in plasma residues, enable more precise characterization of NPs, improving predictions of their safety and efficacies.

Locomotion of the C60-based nanomachines on graphene surfaces.

We provide a comprehensive computational characterization of surface motion of two types of nanomachines with four C60 "wheels": a flexible chassis Nanocar and a rigid chassis Nanotruck. We study the nanocars' lateral and rotational diffusion as well as the wheels' rolling motion on two kinds of graphene substrates-flexible single-layer graphene which may form surface ripples and an ideally flat graphene monolayer. We find that the graphene surface ripples facilitate the translational diffusion of Nanocar and Nanotruck, but have little effect on their surface rotation or the rolling of their wheels. The latter two types of motion are strongly affected by the structure of the nanomachines instead. Surface diffusion of both nanomachines occurs preferentially via a sliding mechanism whereas the rolling of the "wheels" contributes little. The axial rotation of all "wheels" is uncorrelated.

Thermal conductivity of the cell membrane in the presence of cholesterol and amyloid precursor protein.

The cell membrane is responsible for the transportation of heat between inside and outside the cell. Whether the thermal properties of the cell membrane are affected by the cholesterol concentration or the membrane proteins has not been investigated so far. Although the experimental measurement of the membrane thermal conductivity was not available until very recently, computational methods have been widely used for this purpose. In this study, we carry out molecular dynamics simulations to investigate the relation between the concentration of cholesterol and the thermal conductivity of a model membrane. Our results suggest an increase in the membrane thermal conductivity upon increasing the concentration of cholesterol in the membrane. Moreover, we find that the asymmetric distribution of cholesterol in the two membrane leaflets decreases thermal conductivity. We also find a rectification effect when heat flows in opposite directions through a model membrane decorated with the amyloid precursor protein. The results of this study apply to the advancement of selective treatment methods, as well as the development of new materials such as biological rectifiers.