The equilibrium constants of trans and cis dimerization of membrane bound (2D) and freely moving (3D) adhesion receptors are expressed and compared using elementary statistical-thermodynamics. Both processes are mediated by the binding of extracellular subdomains whose range of motion in the 2D environment is reduced upon dimerization, defining a thin reaction shell where dimer formation and dissociation take place. We show that the ratio between the 2D and 3D equilibrium constants can be expressed as a product of individual factors describing, respectively, the spatial ranges of motions of the adhesive domains, and their rotational freedom within the reaction shell. The results predicted by the theory are compared to those obtained from a novel, to our knowledge, dynamical simulations methodology, whereby pairs of receptors perform realistic translational, internal, and rotational motions in 2D and 3D. We use cadherins as our model system. The theory and simulations explain how the strength of cis and trans interactions of adhesive receptors are affected both by their presence in the constrained intermembrane space and by the 2D environment of membrane surfaces. Our work provides fundamental insights as to the mechanism of lateral clustering of adhesion receptors after cell-cell contact and, more generally, to the formation of lateral microclusters of proteins on cell surfaces.

When two oppositely charged macroions are brought into contact, a large fraction of the mobile counterions that previously surrounded each isolated macromolecule is released into the bulk solution, thereby increasing the counterions’ translational entropy. The entropy gain associated with this counterion release mechanism is the driving force for various macroion binding processes, such as protein-membrane, protein-DNA, and DNA-membrane complexation. In this review we focus on the role of counterion release in the interaction between charged macromolecules and oppositely charged lipid membranes. The electrostatic interaction is generally coupled to other degrees of freedom of the membrane, or of the adsorbed macroion. Thus, for example, when a basic protein adsorbs onto a binary fluid membrane comprising anionic and neutral lipids then, in addition to the release of the mobile counterions to the bulk solution, the protein polarizes the membrane composition by attracting the charged lipids to its immediate vicinity. This process, which enhances the electrostatic attraction, is partly hampered by the concomitant loss of two-dimensional (2D) lipid mixing entropy, so that the resulting lipid distribution reflects the balance between these opposing tendencies. In membranes containing both monovalent and multivalent lipids, as is often the case with biological membranes, the peripheral protein preferentially interacts with (and thus immobilizes) the multivalent lipids, because a smaller number of these lipids are needed to neutralize its charge. The monovalent ‘‘counterlipids’’ are thus free to translate in the remaining area of the membrane. This entropy-driven counterlipid release mechanism in 2D is analogous to the extensively studied phenomenon of DNA condensation by polyvalent cations in 3D. Being self-assembled fluid aggregates, lipid bilayers can respond to interactions with peripheral or integral (whether charged or neutral) macromolecules in various ways. Of particular interest in this review is the interplay between electrostatic interactions, the lipid composition degrees of freedom mentioned above, and the membrane curvature elasticity, as will be discussed in some detail in the context of the thermodynamic stability and phase behavior of lipid-DNA complexes (also known as ‘‘lipoplexes’’). This article is primarily theoretical, but the systems and phenomena considered are directly related to and motivated by specific experiments. The theoretical modeling is generally based on mean-field level approaches, specifically the Poisson-Boltzmann theory for electrostatic interactions, sometimes in conjunction with coarse grained computer simulations.

Inspired by novel single-molecule and bulk solution measurements, the physics underlying the forces and pressures involved in DNA packaging into bacteriophage capsids became the focus of numerous recent theoretical models. These fall into two general categories: Continuum-elastic theories (CT), and simulation studies-mostly of the molecular dynamics (MD) genre. Both types of models account for the dependence of the force, and hence the packaging free energy (Delta F), on the loaded DNA length, but differ markedly in interpreting their origin. While DNA confinement entropy is a dominant contribution to DF in the MD simulations, in the CT theories this role is fulfilled by interstrand repulsion, and there is no explicit entropy term. The goal of this letter is to resolve this apparent contradiction, elucidate the origin of the entropic term in the MD simulations, and point out its tacit presence in the CT treatments.

We show on general theoretical grounds that the two ends of single-stranded (ss) RNA molecules (consisting of roughly equal proportions of A, C, G and U) are necessarily close together, largely independent of their length and sequence. This is demonstrated to be a direct consequence of two generic properties of the equilibrium secondary structures, namely that the average proportion of bases in pairs is similar to 60% and that the average duplex length is similar to 4. Based on mfold and Vienna computations on large numbers of ssRNAs of various lengths (1000-10 000 nt) and sequences (both random and biological), we find that the 5’-3’ distance-defined as the sum of H-bond and covalent (ss) links separating the ends of the RNA chain-is small, averaging 15-20 for each set of viral sequences tested. For random sequences this distance is similar to 12, consistent with the theory. We discuss the relevance of these results to evolved sequence complementarity and specific protein binding effects that are known to be important for keeping the two ends of viral and messenger RNAs in close proximity. Finally we speculate on how our conclusions imply indistinguishability in size and shape of equilibrated forms of linear and covalently circularized ssRNA molecules.

We introduce a simple model for folding random-sequence RNA molecules, arguing that it provides a direct route to predicting and rationalizing several average properties of RNA secondary structures. The first folding step involves identifying the longest possible duplex, thereby dividing the molecule into a pair of daughter loops. Successive steps involve identifying similarly the longest duplex in each new pair of daughter loops, with this process proceeding sequentially until the loops are too small for a viable duplex to form. Approximate analytical solutions are found for the average fraction of paired bases, the average duplex length, and the average loop size, all of which are shown to be independent of sequence length for long enough molecules. Numerical solutions to the model provide estimates for these average secondary structure properties that agree well with those obtained from more sophisticated folding algorithms. We also use the model to derive the asymptotic power law for the dependence of the maximum ladder distance on chain length.

Because of the branching arising from partial self-complementarity, long single-stranded (ss) RNA molecules are significantly more compact than linear arrangements (e. g., denatured states) of the same sequence of monomers. To elucidate the dependence of compactness on the nature and extent of branching, we represent ssRNA secondary structures as tree graphs which we treat as ideal branched polymers, and use a theorem of Kramers for evaluating their root-mean-square radius of gyration, (R) over cap (g) = root < R(g)(2)>. We consider two sets of sequences-random and viral-with nucleotide sequence lengths (N) ranging from 100 to 10 000. The RNAs of icosahedral viruses are shown to be more compact (i.e., to have smaller (R) over cap (g) ) than the random RNAs. For the random sequences we find that (R) over cap (g) varies as N(1/3). These results are contrasted with the scaling of (R) over cap (g) for ideal randomly branched polymers (N(1/4)), and with that from recent modeling of (relatively short, N <= 161) RNA tertiary structures (N(2/5)). (C) 2011 American Institute of Physics. [doi: 10.1063/1.3652763]

Membrane-bound receptors often form large assemblies resulting from binding to soluble ligands, cell-surface molecules on other cells and extracellular matrix proteins(1). For example, the association of membrane proteins with proteins on different cells (trans-interactions) can drive the oligomerization of proteins on the same cell(2) (cis-interactions). A central problem in understanding the molecular basis of such phenomena is that equilibrium constants are generally measured in three-dimensional solution and are thus difficult to relate to the two-dimensional environment of a membrane surface. Here we present a theoretical treatment that converts three-dimensional affinities to two dimensions, accounting directly for the structure and dynamics of the membrane-bound molecules. Using a multiscale simulation approach, we apply the theory to explain the formation of ordered, junction-like clusters by classical cadherin adhesion proteins. The approach features atomic-scale molecular dynamics simulations to determine interdomain flexibility, Monte Carlo simulations of multidomain motion and lattice simulations of junction formation(3). A finding of general relevance is that changes in interdomain motion on trans-binding have a crucial role in driving the lateral, cis-, clustering of adhesion receptors.

Intercellullar junctions formed by cadherins, including desmosomes and adherens junctions, comprise two dimensional arrays of ‘‘trans’’ dimers formed between monomers emanating from opposing cell surfaces. Lateral ‘‘cis’’ interfaces between cadherins from the same cell surface have been proposed to play a role in cadherin clustering. Although the molecular details of cis interactions remain uncertain, they must define an anisotropic arrangement where binding is favorable only in certain orientations. Here we report Monte Carlo simulations performed on a 2D lattice constructed to account for the anisotropy in cadherin cis interactions. A crucial finding is that the ‘‘phase transition’’ between freely diffusing cadherin monomers and dimers and a condensed ordered 2D junction formed by dimers alone is a cooperative process involving both trans and cis interactions. Moreover, cis interactions, despite being too weak to be measured in solution, are critical to the formation of an ordered junction structure. We discuss these results in light of available experimental information on cadherin binding free energies that are transformed from their bulk solution values to interaction energies on a 2D lattice.

In order to recognize the problems associated with the transport mechanism of containment during the ventilation process of a laboratory fume hood, a transparent, full scale chemical fume hood is constructed for experimental studies. Distributions of mean velocity and velocity fluctuation in the sash plane are measured using a thermal anemometer. Flow patterns and tracer-gas concentration leakages are respectively diagnosed via the laser-assisted flow visualization method and the EN 14175-3 test protocol. The magnitudes of measured velocity fluctuations exhibit a sharp peak along the perimeter of the sash opening. The results of flow visualization verify that the elevated turbulence fluctuations are induced by the boundary-layer separation when the flow passes over the edges of sash perimeter. The tracer gas experiment shows that the regions where high degree containment leakages detected are located along the perimeter of hood aperture. Eleven commercial hoods which are claimed with fine aerodynamic design are further tested for confirmation of these observations. The results show similar correlations. Conclusions thus are made that large-scale vortex structures occurring around the perimeters of hood aperture due to the boundary-layer separation could induce strong turbulence, and therefore enhance dispersion of the hood containment.

BACKGROUND: Rahnella is a widely distributed genus belonging to the Enterobacteriaceae and frequently present on vegetables. Although Rahnella has interesting agro-economical and industrial properties and several strains possess antibiotic resistances and toxin genes which might spread within microbial communities, little is known about plasmids of this genus. Thus, we isolated a number of Rahnella strains and investigated their complements of small plasmids. RESULTS: In total 53 strains were investigated and 11 plasmids observed. Seven belonged to the ColE1 family; one was ColE2-like and three shared homology to rolling circle plasmids. One of them belonged to the pC194/pUB110 family and two showed similarity to poorly characterised plasmid groups. The G+C content of two rolling circle plasmids deviated considerably from that of Rahnella, indicating that their usual hosts might belong to other genera. Most ColE1-like plasmids formed a subgroup within the ColE1 family that seems to be fairly specific for Rahnella. Intriguingly, the multimer resolution sites of all ColE1-like plasmids had the same orientation with respect to the origin of replication. This arrangement might be necessary to prevent inappropriate synthesis of a small regulatory RNA that regulates cell division. Although the ColE1-like plasmids did not possess any mobilisation system, they shared large parts with high sequence identity in coding and non-coding regions. In addition, highly homologous regions of plasmids isolated from Rahnella and the chromosomes of Erwinia tasmaniensis and Photorhabdus luminescens could be identified. CONCLUSIONS: For the genus Rahnella we observed plasmid-containing isolates at a frequency of 19%, which is in the average range for Enterobacteriaceae. These plasmids belonged to different groups with members of the ColE1-family most frequently found. Regions of striking sequence homology of plasmids and bacterial chromosomes highlight the importance of plasmids for lateral gene transfer (including chromosomal sequences) to distinct genera.