Swollen-Collapsed Transition in Random Hetero-Polymers

A lattice model of a hetero-polymer with random hydrophilic-hydrophobic charges interacting with the solvent is introduced, whose continnuum counterpart has been proposed by T. Garel, L. Leibler and H. Orland {J. Phys. II France 4, 2139 (1994)]. The transfer matrix technique is used to study various constrained annealed systems which approximate at various degrees of accuracy the original quenched model. For highly hydrophobic chains an ordinary $\theta$-point transition is found from a high temperature swollen phase to a low temperature compact phase. Depending on the type of constrained averages, at very low temperatures a swollen phase or a coexistence between compact and swollen phases are found. The results are carefully compared with the corresponding ones obtained in the continuum limit, and various improvements in the original calculations are discussed.Comment: 13 pages, 8 figures; revised version with minor changes, accepted for publication in European Physical Journal

Cluster Derivation of the Parisi Scheme for Disordered Systems

We propose a general quantitative scheme in which systems are given the freedom to sacrifice energy equi-partitioning on the relevant time-scales of observation, and have phase transitions by separating autonomously into ergodic sub-systems (clusters) with different characteristic time-scales and temperatures. The details of the break-up follow uniquely from the requirement of zero entropy for the slower cluster. Complex systems, such as the Sherrington-Kirkpatrick model, are found to minimise their free energy by spontaneously decomposing into a hierarchy of ergodically equilibrating degrees of freedom at different (effective) temperatures. This leads exactly and uniquely to Parisi's replica symmetry breaking scheme. Our approach, which is somewhat akin to an earlier one by Sompolinsky, gives new insight into the physical interpretation of the Parisi scheme and its relations with other approaches, numerical experiments, and short range models. Furthermore, our approach shows that the Parisi scheme can be derived quantitatively and uniquely from plausible physical principles.Comment: 6 pages, 3 figures, proceedings of international conference on "Disordered And Complex Systems", 10-14 July 2000 King's College Londo

Solvable Lattice Gas Models of Random Heteropolymers at Finite Density: II. Dynamics and Transitions to Compact States

In this paper we analyse both the dynamics and the high density physics of the infinite dimensional lattice gas model for random heteropolymers recently introduced in \cite{jort}. Restricting ourselves to site-disordered heteropolymers, we derive exact closed deterministic evolution equations for a suitable set of dynamic order parameters (in the thermodynamic limit), and use these to study the dynamics of the system for different choices of the monomer polarity parameters. We also study the equilibrium properties of the system in the high density limit, which leads to a phase diagram exhibiting transitions between swollen states, compact states, and regions with partial compactification. Our results find excellent verification in numerical simulations, and have a natural and appealing interpretation in terms of real heteropolymers.Comment: 12 pages, 8 eps figures, revised version (to be published in EPJ

Magnetization enumerator of real-valued symmetric channels in Gallager error-correcting codes

Using the magnetization enumerator method, we evaluate the practical and theoretical limitations of symmetric channels with real outputs. Results are presented for several regular Gallager code constructions.Comment: 5 pages, 1 figure, to appear as Brief Report in Physical Review

Dependence of endothelial cell growth on substrate-bound fibronectin

A better understanding of the mechanism of adhesion, spreading and proliferation of human endothelial cells (HEC) on polymeric surfaces may lead to the development of vascular prostheses which allow the formation of an endothelial lining on the luminal surface. In the present investigation the interaction of HEC with polyethylene precoated with monoclonal antibodies directed against HEC membrane antigens and against extracellular matrix compounds was studied. F(ab¿)2 fragments of a monoclonal antibody, directed against an endothelial cell membrane antigen, and F(ab')2 fragments of a monoclonal antibody, directed against cellular fibronectin, were also included in this study. Preadsorption of these antibodies and F(ab')2 fragments, including mixtures of antibodies and mixtures of F(ab')2 fragments, resulted in cell adhesion and spreading as well as moderate cell proliferation (or no proliferation) for several days. However, a good proliferation of HEC was only observed on polyethylene precoated with fibronectin or CLB-HEC-FN-140 (directed against fibronectin). These results strongly suggest that fibronectin, bound to a solid substrate, provides a biochemical signal necessary for the proliferation of HEC. The initial proliferation of HEC on other preadsorbed antibodies or F(ab')2 fragments may be explained by the fact that suspended HEC, used for cell seeding, still possess cell membrane-bound fibronectin

The role of cellular fibronectin in the interaction of human endothelial cells with polymers

During in-vitro adhesion, spreading and proliferation of human endothelial cells (HEC) on tissue culture polystyrene (TCPS), cellular fibronectin is deposited onto the surface of TCPS in spite of the fact that relatively large amounts of proteins have been adsorbed from the serum-containing culture medium to this surface. Evidence is presented that serum proteins, adsorbed to the TCPS surface, are displaced by cellular fibronectin. In addition, the interaction of HEC with polyethylene, precoated with monoclonal antibodies directed against HEC membrane antigens and against extracellular matrix compounds, was studied. F(ab')2 fragments of two monoclonal antibodies were also included in this study. Preadsorption of these antibodies and F(ab')2 fragments resulted in cell adhesion and spreading as well as moderate cell proliferation (or no proliferation) for several days. A good cell proliferation of HEC was only observed on polyethylene precoated with fibronectin or an antibody directed against fibronectin. The results indicate that the direct or indirect deposition of fibronectin is a prerequisite for the proliferation of HEC. It is suggested that fibronectin, bound to a solid substrate, provides a biochemical signal necessary for the proliferation of HEC

A Solvable Model of Secondary Structure Formation in Random Hetero-Polymers

We propose and solve a simple model describing secondary structure formation in random hetero-polymers. It describes monomers with a combination of one-dimensional short-range interactions (representing steric forces and hydrogen bonds) and infinite range interactions (representing polarity forces). We solve our model using a combination of mean field and random field techniques, leading to phase diagrams exhibiting second-order transitions between folded, partially folded and unfolded states, including regions where folding depends on initial conditions. Our theoretical results, which are in excellent agreement with numerical simulations, lead to an appealing physical picture of the folding process: the polarity forces drive the transition to a collapsed state, the steric forces introduce monomer specificity, and the hydrogen bonds stabilise the conformation by damping the frustration-induced multiplicity of states.Comment: 24 pages, 14 figure

Survey propagation for the cascading Sourlas code

We investigate how insights from statistical physics, namely survey propagation, can improve decoding of a particular class of sparse error correcting codes. We show that a recently proposed algorithm, time averaged belief propagation, is in fact intimately linked to a specific survey propagation for which Parisi's replica symmetry breaking parameter is set to zero, and that the latter is always superior to belief propagation in the high connectivity limit. We briefly look at further improvements available by going to the second level of replica symmetry breaking.Comment: 14 pages, 5 figure

Cluster derivation of Parisi's RSB solution for disordered systems

We propose a general scheme in which disordered systems are allowed to sacrifice energy equi-partitioning and separate into a hierarchy of ergodic sub-systems (clusters) with different characteristic time-scales and temperatures. The details of the break-up follow from the requirement of stationarity of the entropy of the slower cluster, at every level in the hierarchy. We apply our ideas to the Sherrington-Kirkpatrick model, and show how the Parisi solution can be {\it derived} quantitatively from plausible physical principles. Our approach gives new insight into the physics behind Parisi's solution and its relations with other theories, numerical experiments, and short range models.Comment: 7 pages 5 figure

Palaeoecological study of a Weichselian wetland site in the Netherlands suggests a link with Dansgaard-Oeschger climate oscillation

Botanical microfossils, macroremains and oribatid mites of a Weichselian interstadial deposit in the central Netherlands point to a temporary, sub-arctic wetland in a treeless landscape. Radiocarbon dates and OSL dates show an age between ca. 54.6 and 46.6 ka cal BP. The vegetation succession, starting as a peat-forming wetland that developed into a lake, might well be linked with a Dansgaard-Oeschger climatic cycle. We suggest that during the rapid warming at the start of a D-O cycle, relatively low areas in the landscape became wetlands where peat was formed. During the more gradual temperature decline that followed, evaporation diminished; the wetlands became inundated and lake sediments were formed. During subsequent sub-arctic conditions the interstadial deposits were covered with wind-blown sand. Apart from changes in effective precipitation also the climate-related presence and absence of permafrost conditions may have played a role in the formation of the observed sedimentological sequence from sand to peat, through lacustrine sediment, with coversand on top. The Wageningen sequence may correspond with D-O event 12, 13 or 14. Some hitherto not recorded microfossils were described and illustrated