Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

We review the main results from extensive Monte Carlo (MC) simulations on athermal polymer packings in the bulk and under confinement. By employing the simplest possible model of excluded volume, macromolecules are represented as freely-jointed chains of hard spheres of uniform size. Simulations are carried out in a wide concentration range: from very dilute up to very high volume fractions, reaching the maximally random jammed (MRJ) state. We study how factors like chain length, volume fraction and flexibility of bond lengths affect the structure, shape and size of polymers, their packing efficiency and their phase behaviour (disorder–order transition). In addition, we observe how these properties are affected by confinement realized by flat, impenetrable walls in one dimension. Finally, by mapping the parent polymer chains to primitive paths through direct geometrical algorithms, we analyse the characteristics of the entanglement network as a function of packing density.

Spin-lattice relaxation of laser-polarized xenon in human blood

The nuclear spin polarization of 129Xe can be enhanced by several orders of magnitude by using optical pumping techniques. The increased sensitivity of xenon NMR has allowed imaging of lungs as well as other in vivo applications. The most critical parameter for efficient delivery of laser-polarized xenon to blood and tissues is the spin-lattice relaxation time (T1) of xenon in blood. In this work, the relaxation of laser-polarized xenon in human blood is measured in vitro as a function of blood oxygenation. Interactions with dissolved oxygen and with deoxyhemoglobin are found to contribute to the spin-lattice relaxation time of 129Xe in blood, the latter interaction having greater effect. Consequently, relaxation times of 129Xe in deoxygenated blood are shorter than in oxygenated blood. In samples with oxygenation equivalent to arterial and venous blood, the 129Xe T1s at 37°C and a magnetic field of 1.5 T were 6.4 s ± 0.5 s and 4.0 s ± 0.4 s, respectively. The 129Xe spin-lattice relaxation time in blood decreases at lower temperatures, but the ratio of T1 in oxygenated blood to that in deoxygenated blood is the same at 37°C and 25°C. A competing ligand has been used to show that xenon binding to albumin contributes to the 129Xe spin-lattice relaxation in blood plasma. This technique is promising for the study of xenon interactions with macromolecules.

Adsorption from a one-dimensional lattice gas and the Brunauer–Emmett–Teller equation

An exact treatment of adsorption from a one-dimensional lattice gas is used to eliminate and correct a well-known inconsistency in the Brunauer–Emmett–Teller (B.E.T.) equation—namely, Gibbs excess adsorption is not taken into account and the Gibbs integral diverges at the transition point. However, neither model should be considered realistic for experimental adsorption systems.

Amphipols: Polymers that keep membrane proteins soluble in aqueous solutions

Amphipols are a new class of surfactants that make it possible to handle membrane proteins in detergent-free aqueous solution as though they were soluble proteins. The strongly hydrophilic backbone of these polymers is grafted with hydrophobic chains, making them amphiphilic. Amphipols are able to stabilize in aqueous solution under their native state four well-characterized integral membrane proteins: (i) bacteriorhodopsin, (ii) a bacterial photosynthetic reaction center, (iii) cytochrome b6f, and (iv) matrix porin.

Energy-based de novo protein folding by conformational space annealing and an off-lattice united-residue force field: Application to the 10-55 fragment of staphylococcal protein A and to apo calbindin D9K

The conformational space annealing (CSA) method for global optimization has been applied to the 10-55 fragment of the B-domain of staphylococcal protein A (protein A) and to a 75-residue protein, apo calbindin D9K (PDB ID code 1CLB), by using the UNRES off-lattice united-residue force field. Although the potential was not calibrated with these two proteins, the native-like structures were found among the low-energy conformations, without the use of threading or secondary-structure predictions. This is because the CSA method can find many distinct families of low-energy conformations. Starting from random conformations, the CSA method found that there are two families of low-energy conformations for each of the two proteins, the native-like fold and its mirror image. The CSA method converged to the same low-energy folds in all cases studied, as opposed to other optimization methods. It appears that the CSA method with the UNRES force field, which is based on the thermodynamic hypothesis, can be used in prediction of protein structures in real time.

Stretching lattice models of protein folding

A new class of experiments that probe folding of individual protein domains uses mechanical stretching to cause the transition. We show how stretching forces can be incorporated in lattice models of folding. For fast folding proteins, the analysis suggests a complex relation between the force dependence and the reaction coordinate for folding.

Branched co-polymers of histidine and lysine are efficient carriers of plasmids

We previously determined that a linear co-polymer of histidine and lysine (HK) in combination with liposomes enhanced the transfection efficiency of cationic liposomes. In the current study, we designed a series of HK polymers with increased branching and/or histidine/lysine ratio to determine if either variable affects transfection efficiency. In the presence of liposomes, the branched polymer with the highest number of histidines, HHK4b, was the most effective at enhancing gene expression. Furthermore, when serum was added to the medium during transfection, the combination of HHK4b and liposomes as a gene-delivery vehicle increased luciferase expression 400-fold compared to liposomes alone. In contrast to linear HK polymers, the higher branched HHK polymers were effective carriers of plasmids in the absence of liposomes. Without liposomes, the HHK4b carrier enhanced luciferase expression 15-fold in comparison with the lesser branched HHK2b carrier and increased expression by 5-logs in comparison with the HHK or HK carrier. The interplay of several parameters including increased condensation of DNA, buffering of acidic endosomes and differential binding affinities of polymer with DNA have a role in the enhancement of transfection by the HK polymers. In addition to suggesting that branched HK polymers are promising gene-delivery vehicles, this study provides a framework for the development of more efficient peptide-bond-based polymers of histidine and lysine.

Cooperative enhancement of specificity in a lattice of T cell receptors

Two of the most important models to account for the specificity and sensitivity of the T cell receptor (TCR) are the kinetic proofreading and serial ligation models. However, although kinetic proofreading provides a means for individual TCRs to measure accurately the length of time they are engaged and signal appropriately, the stochastic nature of ligand dissociation means the kinetic proofreading model implies that at high concentrations the response of the cell will be relatively nonspecific. Recent ligand experiments have revealed the phenomenon of both negative and positive crosstalk among neighboring TCRs. By using a Monte Carlo simulation of a lattice of TCRs, we integrate receptor crosstalk with the kinetic proofreading and serial ligation models and discover that receptor cooperativity can enhance T cell specificity significantly at a very modest cost to the sensitivity of the response.

Novel polymers: Molecular to nanoscale order in three dimensions

The assembly of polymer chains in solution is a powerful method that is leading to the preparation of interesting and unique macromolecular-based synthetic nanostructures. Specific control over the intramolecular and intermolecular physical interactions dictates either the folding of single chains or the aggregation and ordering of multiple chains. This control is provided through the selective placement of functional groups along the polymer backbone and the relative strengths of their attractive and repulsive interactions.

Folding funnels and frustration in off-lattice minimalist protein landscapes

A full quantitative understanding of the protein folding problem is now becoming possible with the help of the energy landscape theory and the protein folding funnel concept. Good folding sequences have a landscape that resembles a rough funnel where the energy bias towards the native state is larger than its ruggedness. Such a landscape leads not only to fast folding and stable native conformations but, more importantly, to sequences that are robust to variations in the protein environment and to sequence mutations. In this paper, an off-lattice model of sequences that fold into a β-barrel native structure is used to describe a framework that can quantitatively distinguish good and bad folders. The two sequences analyzed have the same native structure, but one of them is minimally frustrated whereas the other one exhibits a high degree of frustration.

Polygalacturonase-Mediated Solubilization and Depolymerization of Pectic Polymers in Tomato Fruit Cell Walls1 : Regulation by pH and Ionic Conditions

The hydrolysis of cell wall pectins by tomato (Lycopersicon esculentum) polygalacturonase (PG) in vitro is more extensive than the degradation affecting these polymers during ripening. We examined the hydrolysis of polygalacturonic acid and cell walls by PG isozyme 2 (PG2) under conditions widely adopted in the literature (pH 4.5 and containing Na+) and under conditions approximating the apoplastic environment of tomato fruit (pH 6.0 and K+ as the predominate cation). The pH optima for PG2 in the presence of K+ were 1.5 and 0.5 units higher for the hydrolysis of polygalacturonic acid and cell walls, respectively, compared with activity in the presence of Na+. Increasing K+ concentration stimulated pectin solubilization at pH 4.5 but had little influence at pH 6.0. Pectin depolymerization by PG2 was extensive at pH values from 4.0 to 5.0 and was further enhanced at high K+ levels. Oligomers were abundant products in in vitro reactions at pH 4.0 to 5.0, decreased sharply at pH 5.5, and were negligible at pH 6.0. EDTA stimulated PG-mediated pectin solubilization at pH 6.0 but did not promote oligomer production. Ca2+ suppressed PG-mediated pectin release at pH 4.5 yet had minimal influence on the proportional recovery of oligomers. Extensive pectin breakdown in processed tomato might be explained in part by cation- and low-pH-induced stimulation of PG and other wall-associated enzymes.

Lattice model for rapidly folding protein-like heteropolymers.

Protein folding is a relatively fast process considering the astronomical number of conformations in which a protein could find itself. Within the framework of a lattice model, we show that one can design rapidly folding sequences by assigning the strongest attractive couplings to the contacts present in a target native state. Our protein design can be extended to situations with both attractive and repulsive contacts. Frustration is minimized by ensuring that all the native contacts are again strongly attractive. Strikingly, this ensures the inevitability of folding and accelerates the folding process by an order of magnitude. The evolutionary implications of our findings are discussed.

Pseudoscalar susceptibilities and quark condensates: chiral restoration and lattice screening masses

We derive the formal Ward identities relating pseudoscalar susceptibilities and quark condensates in three-flavor QCD, including consistently the 77-n' sector and the U-A(1) anomaly. These identities are verified in the low-energy realization provided by ChPT, both in the standard SU(3) framework for the octet case and combining the use of the SU(3) framework and the large-Nc expansion of QCD to account properly for the nonet sector and anomalous contributions. The analysis is performed including finite temperature corrections as well as the calculation of U(3) quark condensates and all pseudoscalar susceptibilities, which together with the full set of Ward identities, are new results of this work. Finally, the Ward identities are used to derive scaling relations for pseudoscalar masses which explain the behavior with temperature of lattice screening masses near chiral symmetry restoration.

Quantum simulation of a topological Mott insulator with Rydberg atoms in a Lieb lattice

We propose a realistic scheme to quantum simulate the so-far experimentally unobserved topological Mott insulator phase-an interaction-driven topological insulator-using cold atoms in an optical Lieb lattice. To this end, we study a system of spinless fermions in a Lieb lattice, exhibiting repulsive nearest-and next-to-nearest-neighbor interactions and derive the associated zero-temperature phase diagram within mean-field approximation. In particular, we analyze how the interactions can dynamically generate a charge density wave ordered, a nematic, and a topologically nontrivial quantum anomalous Hall phase. We characterize the topology of the different phases by the Chern number and discuss the possibility of phase coexistence. Based on the identified phases, we propose a realistic implementation of this model using cold Rydberg-dressed atoms in an optical lattice. The scheme, which allows one to access, in particular, the topological Mott insulator phase, robustly and independently of its exact position in parameter space, merely requires global, always-on off-resonant laser coupling to Rydberg states and is feasible with state-of-the-art experimental techniques that have already been demonstrated in the laboratory.

Some examples of modeling in chemical engineering: thermal treatment of polymers, phase equilibrium calculations and process design

Presentation submitted to PSE Seminar, Chemical Engineering Department, Center for Advanced Process Design-making (CAPD), Carnegie Mellon University, Pittsburgh (USA), October 2012.