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Human alpha1-acid glycoprotein (AGP) or orosomucoid (ORM) is a major acute phase protein that is thought to play a crucial role in maintaining homeostasis. Human AGP is the product of a cluster of at least two adjacent genes located on HSA chromosome 9. Using a range of restriction endonucleases we have investigated DNA variation at the locus encoding the AGP genes in a panel of healthy Caucasians. Polymorphisms were identified using BamHI, EcoRI, BglII, PvuII, HindIII, TaqI and MspI. Non-random associations were found between the BamHI, EcoRI, BglII RFLPs. The RFLPs detected with PvuII, TaqI and MspI were all located in exon 6 of both AGP genes. The duplication of an AGP gene was observed in 11% of the indiviuals studied and was in linkage disequilibrium with the TaqI RFLP. The identification and characterization of these polymorphisms will prove useful for other population and forensic studies.

We have studied self-avoiding walks contained within an L Ă— L square whose end-points can lie anywhere within, or on, the boundaries of the square. We prove that such walks behave, asymptotically, as walks crossing a square (WCAS), being those walks whose end-points lie at the south-east and north-west corners of the square. We provide numerical data, enumerating all such walks, and analyse the sequence of coefficients in order to estimate the asymptotic behaviour. We also studied a subset of these walks, those that must contain at least one edge on all four boundaries of the square. We provide compelling evidence that these two classes of walks grow identically. From our analysis we conjecture that the number of such walks C L , for both problems, behaves as C L ∼ λ L 2 + b L + c â‹... L g , where (Guttmann and Jensen 2022 J. Phys. A: Math. Theor.) λ = 1.744 5498 ± 0.000 0012, b = âˆ'0.043 54 ± 0.0005, c = âˆ'1.35 ± 0.45, and g = 3.9 ± 0.1. Finally, we also studied the equivalent problem for self-avoiding polygons, also known as cycles in a square grid. The asymptotic behaviour of cycles has the same form as walks, but with different values of the parameters c, and g. Our numerical analysis shows that λ and b have the same values as for WCAS and that c = 1.776 ± 0.002 while g = âˆ'0.500 ± 0.005 and hence probably equals âˆ' 1 2 . [ABSTRACT FROM AUTHOR]

We study by computer simulation a recently introduced generalized model of self-interacting self-avoiding trails on the square lattice that distinguishes two topologically different types of self-interaction: namely, crossings where the trail passes across itself and collisions where the lattice path visits the same site without crossing. This model generalizes the canonical interacting self-avoiding trail model of polymer collapse, which has a strongly divergent specific heat at its transition point. We confirm the recent prediction that the asymmetry does not affect the universality class for a range of asymmetry. Certainly, where the weighting of collisions outweighs that of crossings this is well supported numerically. When crossings are weighted heavily relative to collisions, the collapse transition reverts to the canonical θ-point-like behavior found in interacting self-avoiding walks. [ABSTRACT FROM AUTHOR]

We find, and analyse, the exact solution of two friendly directed walks, modelling polymers, which interact with a wall via contact interactions. We specifically consider two walks that begin and end together so as to imitate a polygon. We examine a general model in which a separate interaction parameter is assigned to configurations where both polymers touch the wall simultaneously, and investigate the effect this parameter has on the integrability of the problem. We find an exact solution of the generating function of the model, and provide a full analysis of the phase diagram that admits three phases with one first-order and two second-order transition lines between these phases. We argue that one physically realizable model would see two phase transitions as the temperature is lowered. [ABSTRACT FROM AUTHOR]

Trails (bond-avoiding walks) provide an alternative lattice model of polymers to self-avoiding walks, and adding self-interaction at multiply visited sites gives a model of polymer collapse. Recently a two-dimensional model (triangular lattice) where doubly and triply visited sites are given different weights was shown to display a rich phase diagram with first- and second-order collapse separated by a multicritical point. A kinetic growth process of trails (KGTs) was conjectured to map precisely to this multicritical point. Two types of low-temperature phases, a globule phase and a maximally dense phase, were encountered. Here we investigate the collapse properties of a similar extended model of interacting lattice trails on the simple cubic lattice with separate weights for doubly and triply visited sites. Again we find first- and second-order collapse transitions dependent on the relative sizes of the doubly and triply visited energies. However, we find no evidence of a low-temperature maximally dense phase with only the globular phase in existence. Intriguingly, when the ratio of the energies is precisely that which separates the first-order from the second-order regions anomalous finite-size scaling appears. At the finite-size location of the rounded transition clear evidence exists for a first-order transition that persists in the thermodynamic limit. This location moves as the length increases, with its limit apparently at the point that maps to a KGT. However, if one fixes the temperature to sit at exactly this KGT point, then only a critical point can be deduced from the data. The resolution of this apparent contradiction lies in the breaking of crossover scaling and the difference in the shift and transition width (crossover) exponents. [ABSTRACT FROM AUTHOR]

We provide the exact solution of several variants of simple models of the zipping transition of two bound polymers, such as occurs in DNA/RNA, in two and three dimensions using pairs of directed lattice paths. In three dimensions the solutions are written in terms of complete Elliptic integrals. In one case the transition occurs at infinite temperature so is less interesting but in other cases occur at finite temperatures. We analyse the phase transition associated in each model giving the scaling of the partition function. We also extend the models to include a pulling force between one end of the pair of paths. • Several variants of models of the zipping transition for two polymers are solved. • These are simple models of DNA/RNA. • Phase diagrams are fully characterised. • First study of a solvable interacting polymer model in three dimensions [ABSTRACT FROM AUTHOR]

Using extensive Monte Carlo simulations, we investigate the surface adsorption of self-avoiding trails on the triangular lattice with two- and three-body on-site monomer-monomer interactions. In the parameter space of two-body, three-body, and surface interaction strengths, the phase diagram displays four phases: swollen (coil), globule, crystal, and adsorbed. For small values of the surface interaction, we confirm the presence of swollen, globule, and crystal bulk phases. For sufficiently large values of the surface interaction, the system is in an adsorbed state, and the adsorption transition can be continuous or discontinuous, depending on the bulk phase. As such, the phase diagram contains a rich phase structure with transition surfaces that meet in multicritical lines joining in a single special multicritical point. The adsorbed phase displays two distinct regions with different characteristics, dominated by either single- or double-layer adsorbed ground states. Interestingly, we find that there is no finite-temperature phase transition between these two regions though rather a smooth crossover. [ABSTRACT FROM AUTHOR]

We have investigated a polymer growth process on the triangular lattice where the configurations produced are self-avoiding trails. We show that the scaling behavior of this process is similar to the analogous process on the square lattice. However, while the square lattice process maps to the collapse transition of the canonical interacting self-avoiding trail (ISAT) model on that lattice, the process on the triangular lattice model does not map to the canonical equilibrium model. On the other hand, we show that the collapse transition of the canonical ISAT model on the triangular lattice behaves in a way reminiscent of the θ point of the interacting self-avoiding walk (ISAW) model, which is the standard model of polymer collapse. This implies an unusual lattice dependency of the ISAT collapse transition in two dimensions. By studying an extended ISAT model, we demonstrate that the growth process maps to a multicritical point in a larger parameter space. In this extended parameter space the collapse phase transition may be either θ-point-like (second order) or first order, and these two are separated by a multicritical point. It is this multicritical point to which the growth process maps. Furthermore, we provide evidence that in addition to the high-temperature gaslike swollen polymer phase (coil) and the low-temperature liquid-drop-like collapse phase (globule) there is also a maximally dense crystal-like phase (crystal) at low temperatures dependent on the parameter values. The multicritical point is the meeting point of these three phases. Our hypothesized phase diagram resolves the mystery of the seemingly differing behaviors of the ISAW and ISAT models in two dimensions as well as the behavior of the trail growth process.

Human alpha(1)-acid glycoprotein (AGP) or orosomucoid (ORM) is a major acute phase protein that is thought to play a crucial role in maintaining homeostasis. Human AGP is the product of a cluster of at least two adjacent genes located on HSA chromosome 9. Using a range of restriction endonucleases we have investigated DNA variation at the locus encoding the AGP genes in a group of healthy Caucasians. Polymorphisms were identified using BamHI, EcoRI, BglII, PvuII, HindIII, TaqI and MspI. Nonrandom associations were found between the BamHI, EcoRI and BglII RFLPs. The RFLPs detected with PvuII, TaqI and MspI were all located in exon 6 of both AGP genes. The duplication of an AGP gene was observed in 11% of the individuals studied and was in linkage disequilibrium with the TaqI RFLP. The identification and characterization of these polymorphisms should prove useful for other population and forensic studies.