Monte carlo study of the percolation in two-dimensional polymer systems

The structure of a two-dimensional film formed by adsorbed polymer chains was studied by means of Monte Carlo simulations. The polymer chains were represented by linear sequences of lattice beads and positions of these beads were restricted to vertices of a two-dimensional square lattice. Two different Monte Carlo methods were employed to determine the properties of the model system. The first was the random sequential adsorption (RSA) and the second one was based on Monte Carlo simulations with a Verdier-Stockmayer sampling algorithm. The methodology concerning the determination of the percolation thresholds for an infinite chain system was discussed. The influence of the chain length on both thresholds was presented and discussed. It was shown that the RSA method gave considerably lower thresholds for longer chains. This behavior can be explained by a different pool of chain conformations used in the calculations in both methods under consideration.

The structure of percolated polymer systems: a computer simulation study

We studied the percolation process in a system consisting of long flexible polymer chains and solvent molecules. The polymer chains were approximated by linear sequences of beads on a two-dimensional triangular lattice. The system was athermal and the excluded volume was the only potential. The properties of the model system across the entire range of polymer concentrations were determined by Monte Carlo simulations employing a cooperative motion algorithm (CMA). The scaling behavior and the structure of the percolation clusters are presented and discussed.     

Properties of star-branched and linear chains in confined space. A Monte-Carlo study

We have studied the properties of simple models of linear and star-branched polymer chains confined in a slit formed by two parallel impenetrable walls. The polymer chains consisted of identical united atoms (homopolymers) and were restricted to a simple cubic lattice. Two macromolecular architectures of the chain: linear and regular stars with three branches of equal length, were studied. The excluded volume was the only potential introduced into the model and thus the system was athermal. Monte-Carlo simulations with the sampling algorithm based on the chains local changes of conformation were carried out for chains with different lengths as well as for different distances between the confining surfaces. We found that the properties of model chains differ for both macromolecular architectures but a universal behavior for both kinds of chains was also found. Investigation of the frequency of chain-wall contacts shows that the ends of the chains are much more mobile than the rest of the chain, especially in the vicinity of the branching point in star polymers.Figure The scheme of a star-branched (left) and a linear (right) chain located between two parallel impenetrable surfaces.     

The structure of polymer chains in confinement. A Monte Carlo study

A coarse-grained model of polymer star chains confined in two parallel impenetrable surfaces, which were attractive for polymer beads was studied. The flexible homopolymer chains were built of united atoms whose positions in space were restricted to vertices of a simple cubic lattice. The chains were modeled in good solvent conditions and, thus, there were no long-range specific interactions between polymer beads—only the excluded volume was present. The influence of the polymer density and the distances between the confining surfaces on the properties of star-branched polymers was studied. It is shown that the chains adsorbed on one surface could change their position so that they swap between both surfaces with frequency depending on the size of the slit and on the density of the system only. The increase of the polymer density diminished the frequency of jumps and caused that chains became only partially adsorbed. The analysis of structural elements of chains showed that the increase of the density of the system leads to increase of the number of bridges connecting the two adsorbing surfaces, thus, the frequency of jumps between them decreases.     

Linear polyubiquitination: a new regulator of NF‐κB activation

The ubiquitin‐conjugation system regulates a vast range of biological phenomena by affecting protein function mostly through polyubiquitin conjugation. The type of polyubiquitin chain that is generated seems to determine how conjugated proteins are regulated, as they are recognized specifically by proteins that contain chain‐specific ubiquitin‐binding motifs. An enzyme complex that catalyses the formation of newly described linear polyubiquitin chains—known as linear ubiquitin chain‐assembly complex (LUBAC)—has recently been characterized, as has a particular ubiquitin‐binding domain that specifically recognizes linear chains. Both have been shown to have crucial roles in the canonical nuclear factor‐κB (NF‐κB)‐activation pathway. The ubiquitin system is intimately involved in regulating the NF‐κB pathway, and the regulatory roles of K63‐linked chains have been studied extensively. However, the role of linear chains in this process is only now emerging. This article discusses the possible mechanisms underlying linear polyubiquitin‐mediated activation of NF‐κB, and the different roles that K63‐linked and linear chains have in NF‐κB activation. Future directions for linear polyubiquitin research are also discussed.     

Analysis of brush-particle interactions using self-consistent-field theory

Non-specific protein adsorption can be reduced by attaching polymer chains by one end to a sorbent surface. End-grafted polymer modified surfaces have also found application in size-based chromatographic bioseparations. To better understand how to tailor surfaces for these applications, a numerical SCF model has been used to calculate theoretical results for the polymer density distribution of interacting polymer chains around a solute particle positioned at a fixed distance from a surface. In addition, the excess energy required to move the particle into the polymer chains (interaction energy) is calculated using a statistical mechanical treatment of the lattice model. The effect of system variables such as particle size, chain length, surface density and Flory interaction parameters on density distributions and interaction energies is also studied. Calculations for the interaction of a solute particle with a surface covered by many polymer chains (a brush) show that the polymer segments will fill in behind the particle quite rapidly as it moves toward the surface. When there is no strong energetic attraction between the polymer and solute we predict that the interaction energy will be purely repulsive upon compression due to losses in conformational entropy of the polymer chains. Above a critical chain length, which depends upon particle size, a maximum in the force required to move the particle toward the surface is observed due to an engulfment of the particle as chains attempt to access the free volume behind the particle. If an attraction exists between the polymer and solute, such that a minimum in the interaction energy is seen, the optimum conditions for solute repulsion occur at the highest surface density attainable. Long chain length can lead to increased solute concentration within the polymer layer due to the fact that an increased number of favourable polymer–solute contacts are able to occur than with short chains at a similar entropic penalty.     

Dynamics of unfolded polypeptide chains as model for the earliest steps in protein folding

The rate of formation of intramolecular interactions in unfolded proteins determines how fast conformational space can be explored during folding. Characterization of the dynamics of unfolded proteins is therefore essential for the understanding of the earliest steps in protein folding. We used triplet-triplet energy transfer to measure formation of intrachain contacts in different unfolded polypeptide chains. The time constants (1/k) for contact formation over short distances are almost independent of chain length, with a maximum value of about 5 ns for flexible glycine-rich chains and of 12 ns for stiffer chains. The rates of contact formation over longer distances decrease with increasing chain length, indicating different rate-limiting steps for motions over short and long chain segments. The effect of the amino acid sequence on local chain dynamics was probed by using a series of host-guest peptides. Formation of local contacts is only sixfold slower around the stiffest amino acid (proline) compared to the most flexible amino acid (glycine). Good solvents for polypeptide chains like EtOH, GdmCl and urea were found to slow intrachain diffusion and to decrease chain stiffness. These data allow us to determine the time constants for formation of the earliest intrachain contacts during protein folding.     

Molecular shrinkage of proteoglycans

Viscometry and gel chromatography of mixtures of proteoglycans with other linear flexible polymers suggest that proteoglycans shrink as the concentration of the linear polymer is increased. Similar behavior was observed for binary proteoglycan solutions using a differential viscometry procedure. The shrinkage does not involve specific chemical properties of the linear polymer, but rather is a consequence of purely entropic excluded volume interactions with the proteoglycans. Comparison with a hydrodynamic model supports this conclusion. The polydisperse proteoglycan preparation was subfractionated, and the individual fractions were tested for shrinkage. Fractions of lower molecular weight were found to shrink to a greater extent, suggesting that the molecules are more flexible when they contain fewer glycosaminoglycan chains.     

Ca2+, calmodulin and cyclic AMP-dependent modulation of actin-myosin interactions in aorta

Incubation of bovine aortic native actomyosin with cyclic AMP and bovine aortic cyclic AMP-dependent protein kinase produced a rightward shift in the relation between free Ca2+ and both superprecipitation and actomyosin ATPase activity. The relation between free Ca2+ and phosphorylation of myosin light chains was also shifted to the right. The concentration of free Ca2+ required for half-maximal activation of both ATPase activity and myosin light chain phosphorylation was approximately 1.0 microM for control actomyosin and 2.5 microM for actomyosin incubated with cyclic AMP-protein kinase. Neither basal nor maximal activities were significantly affected by incubation with cyclic AMP-protein kinase. Addition of e microM calmodulin to cyclic AMP-protein kinase-treated actomyosin relieved inhibition of both superprecipitation and myosin light chain phosphorylation. These findings suggest that cyclic AMP-protein kinase-mediated inhibition of actin-myosin interactions in vascular smooth muscle involve a shift in the Ca2+ sensitivity of the system. This shift probably involves Ca2+-calmodulin interactions and the control of phosphorylation of the myosin light chains.     

A Monte Carlo Simulation of Nematic and Discotic Ordering in a Polymeric Liquid Crystal

A cyclic polymeric liquid crystal system is simulated using the Metropolis Monte Carlo method in the NVT ensemble. The polymeric system consists of mesogenic moieties attached by alkyl chain spacers to siloxane ring polymers. In the model, the mesogenic moieties are represented individually by an anisotropic Lennard-Jones potential and the polymer ring is represented solely as a constraint on the relative motions of the attached mesogens. A transition from calamitic ordering to discotic ordering is observed as the ring-mesogen bond is varied from full flexible to rigid.     

Effect of polymer brush architecture on antibiofouling properties

Polymer brushes show great promise in next-generation antibiofouling surfaces. Here, we have studied the influence of polymer brush architecture on protein resistance. By carefully optimizing reaction conditions, we were able to polymerize oligoglycerol-based brushes with sterically demanding linear or dendronized side chains on gold surfaces. Protein adsorption from serum and plasma was analyzed by surface plasmon resonance. Our findings reveal a pronounced dependence of biofouling on brush architecture. Bulky yet flexible side chains as in dendronized brushes provide an ideal environment to repel protein-possibly through formation of a hydration layer, which can be further enhanced by presenting free hydroxyl groups on the polymer brushes. A deeper understanding of how brush architecture influences protein resistance will ultimately enable fabrication of surface coatings tailored to specific requirements in biomedical applications.     

Cyclic peptides from the loop region of the laminin alpha 4 chain LG4 module show enhanced biological activity over linear peptides

Laminins, heterotrimeric glycoproteins in the basement membrane, are involved in diverse biological activities. So far, five alpha, three beta, and three gamma chains have been identified, and at least 15 laminin isoforms exist composed of various combinations of the different three chains. The major cell-surface receptors for laminins are integrins and proteoglycans, such as dystroglycans and syndecans. Previously, we reported that synthetic peptide A4G82 (TLFLAHGRLVFM, mouse laminin alpha4 chain residues 1514-1525) showed strong cell attachment and syndecan binding activities. On the basis of the crystal structure of the LG module and sequence alignment, A4G82 is located in the connecting loop region between beta-strands E and F in the laminin alpha4 chain LG4 module. Here, we have focused on the structural importance of this E-F loop region for the biological activity of the alpha4 chain LG4 module. To determine the importance of the loop structure, we synthesized peptide A4G82X (cyclo-A4G82X, Cys-TLFLAHGRLVFX-Cys, X= norleucine), which was cyclized via disulfide bridges at both the N- and C-termini. The cyclic peptides derived from A4G82X inhibited the heparin binding activity of the alpha4 chain G domain and promoted HT-1080 cell attachment better than the corresponding linear peptides. We determined FLAHGRLVFX as a minimal sequence of cyclo-A4G82X important for cell adhesion and heparin binding using a series of truncated peptides. Moreover, HT-1080 cell attachment to the cyclic peptides was more efficiently blocked by heparin than cell attachment to the linear peptides. Furthermore, the cyclic peptides showed significantly enhanced syndecan-2-mediated cell attachment activity. These results indicate that the activity of A4G82 is highly conformation-dependent, suggesting that the E-F loop structure is crucial for its biological activity.     

The effect of conformation on the solution stability of linear vs. cyclic RGD peptides.

The objective of this study was to evaluate the relationship between conformational flexibility and solution stability of a linear RGD peptide (Arg-Gly-Asp-Phe-OH; 1) and a cyclic RGD peptide (cyclo-(1, 6)-Ac-Cys-Arg-Gly-Asp-Phe-Pen-NH2; 2); as a function of pH. Previously, it was found that cyclic peptide 2 was 30-fold more stable than linear peptide 1. Therefore, this study was performed to explain the increase in chemical stability based on the preferred conformation of the peptides. Molecular dynamics simulations and energy minimizations were conducted to evaluate the backbone flexibility of both peptides under simulated pH conditions of 3, 7 and 10 in the presence of water. The reactive sites for degradation for both molecules were also followed during the simulations. The backbone of linear peptide 1 exhibited more flexibility than that of cyclic peptide 2, which was reflected in the rotation about the phi and psi dihedral angles. This was further supported by the low r.m.s. deviations of the backbone atoms for peptide 2 compared with those of peptide 1 that were observed among structures sampled during the molecular dynamics simulations. The presence of a salt bridge between the side chain groups of the Arg and Asp residues was also indicated for the cyclic peptide under simulated conditions of neutral pH. The increase in stability of the cyclic peptide 2 compared with the linear peptide 1, especially at neutral pH, is due to decreased structural flexibility imposed by the ring, as well as salt bridge formation between the side chains of the Arg and Asp residues in cyclic peptide 2. This rigidity would prevent the Asp side chain carboxylic acid from orienting itself in the appropriate position for attack on the peptide backbone.     

Molecular Dynamics Simulation of Linear Polymers in a Solvent

This paper reports a series of simulations of a single linear polymer chain in solution. Both the monomer units and the solvent particles are represented by “beads” which interact via a purely repulsive shifted Lennard-Jones potential; the chains themselves are constructed by linking beads with relatively stiff elastic bonds. The chain lenghts range from 8 to 48 beads, and the total system size is between 1000 and 14000 beads. The static and dynamic properties of the polymer chains obtained from long simulations of these systems (over 10⁶ timesteps) are discussed, and the size and density dependence of the chain behavior examined.     

New insights into the structure of (1→3,1→6)-β-D-glucan side chains in the Candida glabrata cell wall

β-Glucan is a (1→3)-β-linked glucose polymer with (1→6)-β-linked side chains and a major component of fungal cell walls. β-Glucans provide structural integrity to the fungal cell wall. The nature of the (1-6)-β-linked side chain structure of fungal (1→3,1→6)-β-D-glucans has been very difficult to elucidate. Herein, we report the first detailed structural characterization of the (1→6)-β-linked side chains of Candida glabrata using high-field NMR. The (1→6)-β-linked side chains have an average length of 4 to 5 repeat units spaced every 21 repeat units along the (1→3)-linked polymer backbone. Computer modeling suggests that the side chains have a bent curve structure that allows for a flexible interconnection with parallel (1→3)-β-D-glucan polymers, and/or as a point of attachment for proteins. Based on these observations we propose new approaches to how (1→6)-β-linked side chains interconnect with neighboring glucan polymers in a manner that maximizes fungal cell wall strength, while also allowing for flexibility, or plasticity.     

Chemical modification of wheat protein-based natural polymers: grafting and cross-linking reactions with poly(ethylene oxide) diglycidyl ether and ethyl diamine

Mobile poly(ethylene oxide) diglycidyl ether (PEODGE) segments were chemically grafted onto a soluble wheat protein (WP), and different network structures were formed via coupling reactions with ethyl diamine (EDA) in different PEODGE/EDA (PE) ratios. When the PE ratio was 1:1, linear PEs were the predominant segments grafted onto WP chains and the whole WP-PEODGE-EDA (WPE) system was still soluble with an increased molecular weight. Reducing the amount of EDA in the systems produced insoluble cross-linked WPE networks. The broad distribution of network structures and chain mobility resulted in a broad glass transition for the WPE materials. However, the glass transition started at lower temperatures, and the materials became flexible at room temperature. The PE segments were present in all rigid, intermediate, and mobile phases in WPE networks, while the proportion of mobile WP chains was increased as a result of the plasticization effect from the mobile PE segments. The mobility of the most mobile component lipid was also restricted to some extent when forming the cross-linked WPE networks. The study demonstrated that the formation of different network structures with PE segments could significantly improve the flexibility of WP materials, vary the solubility, and modify the mechanical performance of WP-based natural polymer materials.     

Diffusion of macromolecules in agarose gels: comparison of linear and globular configurations.

The diffusion coefficients (D) of different types of macromolecules (proteins, dextrans, polymer beads, and DNA) were measured by fluorescence recovery after photobleaching (FRAP) both in solution and in 2% agarose gels to compare transport properties of these macromolecules. Diffusion measurements were conducted with concentrations low enough to avoid macromolecular interactions. For gel measurements, diffusion data were fitted according to different theories: polymer chains and spherical macromolecules were analyzed separately. As chain length increases, diffusion coefficients of DNA show a clear shift from a Rouse-like behavior (DG congruent with N0-0.5) to a reptational behavior (DG congruent with N0-2.0). The pore size, a, of a 2% agarose gel cast in a 0.1 M PBS solution was estimated. Diffusion coefficients of the proteins and the polymer beads were analyzed with the Ogston model and the effective medium model permitting the estimation of an agarose gel fiber radius and hydraulic permeability of the gels. Not only did flexible macromolecules exhibit greater mobility in the gel than did comparable-size rigid spherical particles, they also proved to be a more useful probe of available space between fibers.     

Mesoscopic gel at low agarose concentration in water: a dynamic light scattering study.

Previous work in our laboratory has shown that at very low agarose concentration in water gelation still occurs within mutually disconnected, high concentration regions generated by spinodal demixing. The freely diffusing particles obtained in these conditions are studied in the present work by depolarized dynamic light scattering and probe diffusion experiments. These particles are found to behave as large (in fact, mesoscopic) polymer fibers entangled in a continuously rearranged mesh with scaling parameters typical of partially flexible, neutral chains. The present results allow specifying the notion of mesoscopic gelation. They also reveal that the same symmetry-breaking mechanism that allows macroscopic gelation at polymer concentrations well below the threshold for random cross-link percolation generates additional and unexpected phenomena.     

A novel cyclic octapeptide as an analogue of cyclic peptide in triostin A

This paper reported an ongoing study of cyclic peptides as carriers of potential anti-tumor agents. In an effort to carry out anti-cancer drug design, we synthesized another novel cyclic peptide as the analogue of the cyclic peptide in Triostin A. The linear peptide chains were synthesized by coupling protected amino acid residues according to Pfp/DCC methods (Pfp: Pentafluorophenol, DCC: N,N'-Dicyclohexyl-carbodiimide) in solution. After deblocking the Boc- group of the linear octapeptide chain, the cyclic product was achieved by employing diphenylphosphoryl azide (DPPA) as cyclic agent at low temperature in DMF. Further study on cyclic octapeptide-drug conjugates is in progress.     

Computational entropy estimation of linear polyether-modified surfaces and correlation with protein resistant properties of such surfaces

The non-specific adsorption of proteins on surfaces is a well-known and mostly undesirable phenomena, which is reduced by a surface coating with the linear polyether poly(ethylene glycol) (PEG) as the current benchmark material. However, the molecular mechanism of protein-resistant surfaces is still not fully understood. Two main hypotheses are generally applied. The first one is steric repulsion of the highly flexible tethered polymer chains, leading to an entropic penalty by adsorption of proteins due to the reduction in polymer chain mobility. The second one argues with well-hydrated polymer chains generating a repulsive interfacial water layer. In this article, we compare the three different protein-resistant polyether structures PEG, linear polyglycerol (LPG(OH)) and linear poly(methyl glycerol) (LPG(OMe)) to get new insights into the molecular mechanism behind protein resistance. In a theoretical approach, we apply an entropy estimator that assesses the conformational states of the tethered polyethers from MD simulations. It reveals the entropy differences between these polyethers to be in the order PEG>LPG(OH) > LPG(OMe). Moreover, experiments on fibrinogen adsorption of these surfaces via surface plasmon resonance spectroscopy are performed and correlated with the theoretical studies. We find that protein resistant properties of surfaces are likely to arise from an interplay of different factors.