The vibrational energy flow transition in organic molecules: Theory meets experiment

Most large dynamical systems are thought to have ergodic dynamics, whereas small systems may not have free interchange of energy between degrees of freedom. This assumption is made in many areas of chemistry and physics, ranging from nuclei to reacting molecules and on to quantum dots. We examine the transition to facile vibrational energy flow in a large set of organic molecules as molecular size is increased. Both analytical and computational results based on local random matrix models describe the transition to unrestricted vibrational energy flow in these molecules. In particular, the models connect the number of states participating in intramolecular energy flow to simple molecular properties such as the molecular size and the distribution of vibrational frequencies. The transition itself is governed by a local anharmonic coupling strength and a local state density. The theoretical results for the transition characteristics compare well with those implied by experimental measurements using IR fluorescence spectroscopy of dilution factors reported by Stewart and McDonald [Stewart, G. M. & McDonald, J. D. (1983) J. Chem. Phys. 78, 3907–3915].

Advances in random matrix theory, zeta functions, and sphere packing

Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues (“the energy levels”) follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks.

Organic protomolecule assembly in igneous minerals

C—H stretching bands, νCH, in the infrared spectrum of single crystals of nominally high purity, of laboratory-grown MgO, and of natural upper mantle olivine, provide an “organic” signature that closely resembles the symmetrical and asymmetrical C—H stretching modes of aliphatic —CH2 units. The νCH bands indicate that H2O and CO2, dissolved in the matrix of these minerals, converted to form H2 and chemically reduced C, which in turn formed C—H entities, probably through segregation into defects such as dislocations. Heating causes the C—H bonds to pyrolyze and the νCH bands to disappear, but annealing at 70°C causes them to reappear within a few days or weeks. Modeling dislocations in MgO suggests that the segregation of C can lead to Cx chains, x = 4, with the terminal C atoms anchored to the MgO matrix by bonding to two O−. Allowing H2 to react with such Cx chains leads to [O2C(CH2)2CO2] or similar precipitates. It is suggested that such Cx—Hy—Oz entities represent protomolecules from which derive the short-chain carboxylic and dicarboxylic and the medium-chain fatty acids that have been solvent-extracted from crushed MgO and olivine single crystals, respectively. Thus, it appears that the hard, dense matrix of igneous minerals represents a medium in which protomolecular units can be assembled. During weathering of rocks, the protomolecular units turn into complex organic molecules. These processes may have provided stereochemically constrained organics to the early Earth that were crucial to the emergence of life.

Modulation of Cell Proliferation and Differentiation through Substrate-dependent Changes in Fibronectin Conformation

Integrin-mediated cell adhesion to extracellular matrices provides signals essential for cell cycle progression and differentiation. We demonstrate that substrate-dependent changes in the conformation of adsorbed fibronectin (Fn) modulated integrin binding and controlled switching between proliferation and differentiation. Adsorption of Fn onto bacterial polystyrene (B), tissue culture polystyrene (T), and collagen (C) resulted in differences in Fn conformation as indicated by antibody binding. Using a biochemical method to quantify bound integrins in cultured cells, we found that differences in Fn conformation altered the quantity of bound α5 and β1 integrin subunits but not αv or β3. C2C12 myoblasts grown on these Fn-coated substrates proliferated to different levels (B > T > C). Immunostaining for muscle-specific myosin revealed minimal differentiation on B, significant levels on T, and extensive differentiation on C. Differentiation required binding to the RGD cell binding site in Fn and was blocked by antibodies specific for this site. Switching between proliferation and differentiation was controlled by the levels of α5β1 integrin bound to Fn, and differentiation was inhibited by anti-α5, but not anti-αv, antibodies, suggesting distinct integrin-mediated signaling pathways. Control of cell proliferation and differentiation through conformational changes in extracellular matrix proteins represents a versatile mechanism to elicit specific cellular responses for biological and biotechnological applications.

A carbonic anhydrase from the nacreous layer in oyster pearls.

It is believed that the polymorphism observed in calcium carbonate crystals, such as aragonite and calcite in mollusk shells, is controlled by organic matrix proteins secreted from the mantle epithelia. However, the fine structures of these proteins are still unknown, and to understand the molecular mechanisms of mineralization process, detailed structural analyses of the organic matrix proteins are essential. For this, we have carried out purification, characterization, and cDNA cloning of nacrein, which is a soluble organic matrix protein in the nacreous layer of oyster pearls. Northern blot analysis showed that the nacrein transcript was specifically expressed in mantle pallial. Analysis of the deduced amino acid sequence revealed that the protein contained two functional domains: one was a carbonic anhydrase and another was a Gly-Xaa-Asn (Xaa = Asp, Asn, or Glu) repeat domain; however, the carbonic anhydrase domain was split into two subdomains with insertion of the Gly-Xaa-Asn repeat domain between them. Our findings suggest that nacrein actually functions as a matrix protein whose repeated Gly-Xaa-Asn domain possibly binds calcium and as a carbonic anhydrase that catalyzes the HCO3- formation, thus participating in calcium carbonate crystal formation of the nacreous layer.