The elasticity and failure of fluid-filled cellular solids: Theory and experiment

We extend and apply theories of filled foam elasticity and failure to recently available data on foods. The predictions of elastic modulus and failure mode dependence on internal pressure and on wall integrity are borne out by photographic evidence of distortion and failure under compressive loading and under the localized stress applied by a knife blade, and by mechanical data on vegetables differing only in their turgor pressure. We calculate the dry modulus of plate-like cellular solids and the cross over between dry-like and fully fluid-filled elastic response. The bulk elastic properties of limp and aging cellular solids are calculated for model systems and compared with our mechanical data, which also show two regimes of response. The mechanics of an aged, limp beam is calculated, thus offering a practical procedure for comparing experiment and theory. This investigation also thereby offers explanations of the connection between turgor pressure and crispness and limpness of cellular materials.

Comparing in vitro, in situ, and in vivo experimental data in a three-dimensional model of mammalian cochlear mechanics

Normal mammalian hearing is refined by amplification of the motion of the cochlear partition. This partition, comprising the organ of Corti sandwiched between the basilar and tectorial membranes, contains the outer hair cells that are thought to drive this amplification process. Force generation by outer hair cells has been studied extensively in vitro and in situ, but, to understand cochlear amplification fully, it is necessary to characterize the role played by each of the components of the cochlear partition in vivo. Observations of cochlear partition motion in vivo are severely restricted by its inaccessibility and sensitivity to surgical trauma, so, for the present study, a computer model has been used to simulate the operation of the cochlea under different experimental conditions. In this model, which uniquely retains much of the three-dimensional complexity of the real cochlea, the motions of the basilar and tectorial membranes are fundamentally different during in situ- and in vivo-like conditions. Furthermore, enhanced outer hair cell force generation in vitro leads paradoxically to a decrease in the gain of the cochlear amplifier during sound stimulation to the model in vivo. These results suggest that it is not possible to extrapolate directly from experimental observations made in vitro and in situ to the normal operation of the intact organ in vivo.

From ab initio quantum mechanics to molecular neurobiology: A cation–π binding site in the nicotinic receptor

The nicotinic acetylcholine receptor is the prototype ligand-gated ion channel. A number of aromatic amino acids have been identified as contributing to the agonist binding site, suggesting that cation–π interactions may be involved in binding the quaternary ammonium group of the agonist, acetylcholine. Here we show a compelling correlation between: (i) ab initio quantum mechanical predictions of cation–π binding abilities and (ii) EC50 values for acetylcholine at the receptor for a series of tryptophan derivatives that were incorporated into the receptor by using the in vivo nonsense-suppression method for unnatural amino acid incorporation. Such a correlation is seen at one, and only one, of the aromatic residues—tryptophan-149 of the α subunit. This finding indicates that, on binding, the cationic, quaternary ammonium group of acetylcholine makes van der Waals contact with the indole side chain of α tryptophan-149, providing the most precise structural information to date on this receptor. Consistent with this model, a tethered quaternary ammonium group emanating from position α149 produces a constitutively active receptor.

The degree of nonlinearity and anisotropy of blood vessel elasticity

Blood vessel elasticity is important to physiology and clinical problems involving surgery, angioplasty, tissue remodeling, and tissue engineering. Nonlinearity in blood vessel elasticity in vivo is important to the formation of solitons in arterial pulse waves. It is well known that the stress–strain relationship of the blood vessel is nonlinear in general, but a controversy exists on how nonlinear it is in the physiological range. Another controversy is whether the vessel wall is biaxially isotropic. New data on canine aorta were obtained from a biaxial testing machine over a large range of finite strains referred to the zero-stress state. A new pseudo strain energy function is used to examine these questions critically. The stress–strain relationship derived from this function represents the sum of a linear stress–strain relationship and a definitely nonlinear relationship. This relationship fits the experimental data very well. With this strain energy function, we can define a parameter called the degree of nonlinearity, which represents the fraction of the nonlinear strain energy in the total strain energy per unit volume. We found that for the canine aorta, the degree of nonlinearity varies from 5% to 30%, depending on the magnitude of the strains in the physiological range. In the case of canine pulmonary artery in the arch region, Debes and Fung [Debes, J. C. & Fung, Y. C.(1995) Am. J. Physiol. 269, H433–H442] have shown that the linear regime of the stress–strain relationship extends from the zero-stress state to the homeostatic state and beyond. Both vessels, however, are anisotropic in both the linear and nonlinear regimes.

Torsional directed walks, entropic elasticity, and DNA twist stiffness

DNA and other biopolymers differ from classical polymers because of their torsional stiffness. This property changes the statistical character of their conformations under tension from a classical random walk to a problem we call the “torsional directed walk.” Motivated by a recent experiment on single lambda-DNA molecules [Strick, T. R., Allemand, J.-F., Bensimon, D., Bensimon, A. & Croquette, V. (1996) Science 271, 1835–1837], we formulate the torsional directed walk problem and solve it analytically in the appropriate force regime. Our technique affords a direct physical determination of the microscopic twist stiffness C and twist-stretch coupling D relevant for DNA functionality. The theory quantitatively fits existing experimental data for relative extension as a function of overtwist over a wide range of applied force; fitting to the experimental data yields the numerical values C = 120 nm and D = 50 nm. Future experiments will refine these values. We also predict that the phenomenon of reduction of effective twist stiffness by bend fluctuations should be testable in future single-molecule experiments, and we give its analytic form.

Dynamics and elasticity of the fibronectin matrix in living cell culture visualized by fibronectin–green fluorescent protein

Fibronectin (FN) forms the primitive fibrillar matrix in both embryos and healing wounds. To study the matrix in living cell cultures, we have constructed a cell line that secretes FN molecules chimeric with green fluorescent protein. These FN–green fluorescent protein molecules were assembled into a typical matrix that was easily visualized by fluorescence over periods of several hours. FN fibrils remained mostly straight, and they were seen to extend and contract to accommodate movements of the cells, indicating that they are elastic. When fibrils were broken or detached from cells, they contracted to less than one-fourth of their extended length, demonstrating that they are highly stretched in the living culture. Previous work from other laboratories has suggested that cryptic sites for FN assembly may be exposed by tension on FN. Our results show directly that FN matrix fibrils are not only under tension but are also highly stretched. This stretched state of FN is an obvious candidate for exposing the cryptic assembly sites.

The importance of reactant positioning in enzyme catalysis: A hybrid quantum mechanics/molecular mechanics study of a haloalkane dehalogenase

Hybrid quantum mechanics/molecular mechanics calculations using Austin Model 1 system-specific parameters were performed to study the SN2 displacement reaction of chloride from 1,2-dichloroethane (DCE) by nucleophilic attack of the carboxylate of acetate in the gas phase and by Asp-124 in the active site of haloalkane dehalogenase from Xanthobacter autotrophicus GJ10. The activation barrier for nucleophilic attack of acetate on DCE depends greatly on the reactants having a geometry resembling that in the enzyme or an optimized gas-phase structure. It was found in the gas-phase calculations that the activation barrier is 9 kcal/mol lower when dihedral constraints are used to restrict the carboxylate nucleophile geometry to that in the enzyme relative to the geometries for the reactants without dihedral constraints. The calculated quantum mechanics/molecular mechanics activation barriers for the enzymatic reaction are 16.2 and 19.4 kcal/mol when the geometry of the reactants is in a near attack conformer from molecular dynamics and in a conformer similar to the crystal structure (DCE is gauche), respectively. This haloalkane dehalogenase lowers the activation barrier for dehalogenation of DCE by 2–4 kcal/mol relative to the single point energies of the enzyme's quantum mechanics atoms in the gas phase. SN2 displacements of this sort in water are infinitely slower than in the gas phase. The modest lowering of the activation barrier by the enzyme relative to the reaction in the gas phase is consistent with mutation experiments.

How can statistical mechanics contribute to social science?

A model of interdependent decision making has been developed to understand group differences in socioeconomic behavior such as nonmarital fertility, school attendance, and drug use. The statistical mechanical structure of the model illustrates how the physical sciences contain useful tools for the study of socioeconomic phenomena.

Molecular mechanics calculations of the riboacetal internucleotide linkage in double and triple helices.

Structures of Watson-Crick base paired 15-nucleobase oligomer strands in A-type or B-type conformation in which one strand [a strand of alternating nucleotide and riboacetal thymidine nucleoside (RT) units, RP] is DNA and the other is composed of alternating nucleotides and riboacetal nucleosides have been studied by molecular mechanics. Analogously, oligomer strands of RNA in place of DNA have been modeled. The calculations indicate that the RP strand is more stable when complexed in an A-type duplex relative to a B-type form and that this conformational preference is presumably due to the more uniform nature of the former. Nearly planar ribose rings were more commonly observed in the minimized structures of the B-type DNA.RP duplexes as compared with A-type duplexes, despite the fact that planar ribofuranose rings are known to be energetically unfavorable in oligonucleotides. Computed relative stabilities of all duplexes containing the RP strand suggest that such heteroduplexes are less stable than the corresponding double-stranded DNA and double-stranded RNA species. These findings are in agreement with experimental results which show, when equivalent sequences were compared, that a DNA.RNA control forms a more stable duplex than RP hound to a complementary single-stranded RNA strand. In contrast, molecular mechanics studies of complementary triple-helical (DNA)2.RP, (DNA)2.DNA, and (DNA)2.RNA structures indicate that the binding of RP as a Hoogsteen strand stabilizes the underlying duplex to a greater extent compared with native oligonucleotides. These calculations suggest that puckering of the ribose ring in the riboacetal linkage leads to a more favorable interaction with a complementary nucleic acid target than the proposed planar geometry and that this puckering may account for the enhanced binding of RP to a double-stranded target.