Systematic derivation of partition functions for ligand binding to two-dimensional lattices

The Ising problem consists in finding the analytical solution of the partition function of a lattice once the interaction geometry among its elements is specified. No general analytical solution is available for this problem, except for the one-dimensional case. Using site-specific thermodynamics, it is shown that the partition function for ligand binding to a two-dimensional lattice can be obtained from those of one-dimensional lattices with known solution. The complexity of the lattice is reduced recursively by application of a contact transformation that involves a relatively small number of steps. The transformation implemented in a computer code solves the partition function of the lattice by operating on the connectivity matrix of the graph associated with it. This provides a powerful new approach to the Ising problem, and enables a systematic analysis of two-dimensional lattices that model many biologically relevant phenomena. Application of this approach to finite two-dimensional lattices with positive cooperativity indicates that the binding capacity per site diverges as Na (N = number of sites in the lattice) and experiences a phase-transition-like discontinuity in the thermodynamic limit N → ∞. The zeroes of the partition function tend to distribute on a slightly distorted unit circle in complex plane and approach the positive real axis already for a 5×5 square lattice. When the lattice has negative cooperativity, its properties mimic those of a system composed of two classes of independent sites with the apparent population of low-affinity binding sites increasing with the size of the lattice, thereby accounting for a phenomenon encountered in many ligand-receptor interactions.

Five-fold symmetry in crystalline quasicrystal lattices

To demonstrate that crystallographic methods can be applied to index and interpret diffraction patterns from well-ordered quasicrystals that display non-crystallographic 5-fold symmetry, we have characterized the properties of a series of periodic two-dimensional lattices built from pentagons, called Fibonacci pentilings, which resemble aperiodic Penrose tilings. The computed diffraction patterns from periodic pentilings with moderate size unit cells show decagonal symmetry and are virtually indistinguishable from that of the infinite aperiodic pentiling. We identify the vertices and centers of the pentagons forming the pentiling with the positions of transition metal atoms projected on the plane perpendicular to the decagonal axis of quasicrystals whose structure is related to crystalline η phase alloys. The characteristic length scale of the pentiling lattices, evident from the Patterson (autocorrelation) function, is ∼τ2 times the pentagon edge length, where τ is the golden ratio. Within this distance there are a finite number of local atomic motifs whose structure can be crystallographically refined against the experimentally measured diffraction data.

The β2-adrenergic receptor/βarrestin complex recruits the clathrin adaptor AP-2 during endocytosis

βarrestins mediate the desensitization of the β2-adrenergic receptor (β2AR) and many other G protein-coupled receptors (GPCRs). Additionally, βarrestins initiate the endocytosis of these receptors via clathrin coated-pits and interact directly with clathrin. Consequently, it has been proposed that βarrestins serve as clathrin adaptors for the GPCR family by linking these receptors to clathrin lattices. AP-2, the heterotetrameric clathrin adaptor protein, has been demonstrated to mediate the internalization of many types of plasma membrane proteins other than GPCRs. AP-2 interacts with the clathrin heavy chain and cytoplasmic domains of receptors such as those for epidermal growth factor and transferrin. In the present study we demonstrate the formation of an agonist-induced multimeric complex containing a GPCR, βarrestin 2, and the β2-adaptin subunit of AP-2. β2-Adaptin binds βarrestin 2 in a yeast two-hybrid assay and coimmunoprecipitates with βarrestins and β2AR in an agonist-dependent manner in HEK-293 cells. Moreover, β2-adaptin translocates from the cytosol to the plasma membrane in response to the β2AR agonist isoproterenol and colocalizes with β2AR in clathrin-coated pits. Finally, expression of βarrestin 2 minigene constructs containing the β2-adaptin interacting region inhibits β2AR endocytosis. These findings point to a role for AP-2 in GPCR endocytosis, and they suggest that AP-2 functions as a clathrin adaptor for the endocytosis of diverse classes of membrane receptors.

Crystal structures of the copper and nickel complexes of RNase A: Metal-induced interprotein interactions and identification of a novel copper binding motif

We report the crystal structures of the copper and nickel complexes of RNase A. The overall topology of these two complexes is similar to that of other RNase A structures. However, there are significant differences in the mode of binding of copper and nickel. There are two copper ions per molecule of the protein, but there is only one nickel ion per molecule of the protein. Significant changes occur in the interprotein interactions as a result of differences in the coordinating groups at the common binding site around His-105. Consequently, the copper- and nickel-ion-bound dimers of RNase A act as nucleation sites for generating different crystal lattices for the two complexes. A second copper ion is present at an active site residue His-119 for which all the ligands are from one molecule of the protein. At this second site, His-119 adopts an inactive conformation (B) induced by the copper. We have identified a novel copper binding motif involving the α-amino group and the N-terminal residues.

Functional Hierarchy of Simultaneously Expressed Adhesion Receptors: Integrin α2β1 but Not CD44 Mediates MV3 Melanoma Cell Migration and Matrix Reorganization within Three-dimensional Hyaluronan-containing Collagen MatricesV⃞

Haptokinetic cell migration across surfaces is mediated by adhesion receptors including β1 integrins and CD44 providing adhesion to extracellular matrix (ECM) ligands such as collagen and hyaluronan (HA), respectively. Little is known, however, about how such different receptor systems synergize for cell migration through three-dimensionally (3-D) interconnected ECM ligands. In highly motile human MV3 melanoma cells, both β1 integrins and CD44 are abundantly expressed, support migration across collagen and HA, respectively, and are deposited upon migration, whereas only β1 integrins but not CD44 redistribute to focal adhesions. In 3-D collagen lattices in the presence or absence of HA and cross-linking chondroitin sulfate, MV3 cell migration and associated functions such as polarization and matrix reorganization were blocked by anti-β1 and anti-α2 integrin mAbs, whereas mAbs blocking CD44, α3, α5, α6, or αv integrins showed no effect. With use of highly sensitive time-lapse videomicroscopy and computer-assisted cell tracking techniques, promigratory functions of CD44 were excluded. 1) Addition of HA did not increase the migratory cell population or its migration velocity, 2) blocking of the HA-binding Hermes-1 epitope did not affect migration, and 3) impaired migration after blocking or activation of β1 integrins was not restored via CD44. Because α2β1-mediated migration was neither synergized nor replaced by CD44–HA interactions, we conclude that the biophysical properties of 3-D multicomponent ECM impose more restricted molecular functions of adhesion receptors, thereby differing from haptokinetic migration across surfaces.

Crystal structures of the trimeric human immunodeficiency virus type 1 matrix protein: implications for membrane association and assembly.

The human immunodeficiency virus type 1 (HIV-1) matrix protein forms a structural shell associated with the inner viral membrane and performs other essential functions throughout the viral life cycle. The crystal structure of the HIV-1 matrix protein, determined at 2.3 angstrom resolution, reveals that individual matrix molecules are composed of five major helices capped by a three-stranded mixed beta-sheet. Unexpectedly, the protein assembles into a trimer in three different crystal lattices, burying 1880 angstrom2 of accessible surface area at the trimer interfaces. Trimerization appears to create a large, bipartite membrane binding surface in which exposed basic residues could cooperate with the N-terminal myristoyl groups to anchor the protein on the acidic inner membrane of the virus.

Projection structure of frog rhodopsin in two crystal forms.

Rhodopsin is the G protein-coupled receptor that upon light activation triggers the visual transduction cascade. Rod cell outer segment disc membranes were isolated from dark-adapted frog retinas and were extracted with Tween detergents to obtain two-dimensional rhodopsin crystals for electron crystallography. When Tween 80 was used, tubular structures with a p2 lattice (a = 32 A, b = 83 A, gamma = 91 degrees) were formed. The use of a Tween 80/Tween 20 mixture favored the formation of larger p22(1)2(1) lattices (a = 40 A, b = 146 A, gamma = 90 degrees). Micrographs from frozen hydrated frog rhodopsin crystals were processed, and projection structures to 7-A resolution for the p22(1)2(1) form and to 6-A resolution for the p2 form were calculated. The maps of frog rhodopsin in both crystal forms are very similar to the 9-A map obtained previously for bovine rhodopsin and show that the arrangement of the helices is the same. In a tentative topographic model, helices 4, 6, and 7 are nearly perpendicular to the plane of the membrane. In the higher-resolution projection maps of frog rhodopsin, helix 5 looks more tilted than it appeared previously. The quality of the two frog rhodopsin crystals suggests that they would be suitable to obtain a three-dimensional structure in which all helices would be resolved.

Sustained delivery of erythropoietin in mice by genetically modified skin fibroblasts.

We have examined whether the secretion of erythropoietin (Epo) from genetically modified cells could represent an alternative to repeated injections of the recombinant hormone for treating chronic anemias responsive to Epo. Primary mouse skin fibroblasts were transduced with a retroviral vector in which the murine Epo cDNA is expressed under the control of the murine phosphoglycerate kinase promoter. "Neo-organs" containing the genetically modified fibroblasts embedded into collagen lattices were implanted into the peritoneal cavity of mice. Increased hematocrit (> 80%) and elevated serum Epo concentration (ranging from 60 to 408 milliunits/ml) were observed in recipient animals over a 10-month observation period. Hematocrit values measured in recipient mice varied according to the number of implanted Epo-secreting fibroblasts (ranging from 2.5 to 20 x 10(6)). The implantation of neo-organs containing Epo-secreting fibroblasts appeared, therefore, as a convenient method to achieve permanent in vivo delivery of the hormone. We estimated that the biological efficacy of the approach may be relevant for the treatment of human hemoglobinopathies.