Compression, gain, and nonlinear distortion in an active cochlear model with subpartitions

The propagation of inhomogeneous, weakly nonlinear waves is considered in a cochlear model having two degrees of freedom that represent the transverse motions of the tectorial and basilar membranes within the organ of Corti. It is assumed that nonlinearity arises from the saturation of outer hair cell active force generation. I use multiple scale asymptotics and treat nonlinearity as a correction to a linear hydroelastic wave. The resulting theory is used to explain experimentally observed features of the response of the cochlear partition to a pure tone, including: the amplification of the response in a healthy cochlea vs a dead one; the less than linear growth rate of the response to increasing sound pressure level; and the amount of distortion to be expected at high and low frequencies at basal and apical locations, respectively. I also show that the outer hair cell nonlinearity generates retrograde waves.

A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels

Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are thought to mediate amplification in the mammalian cochlea. In vertebrates that lack these cells, and perhaps in mammals as well, active movements of hair bundles may underlie amplification. We have evaluated a mathematical model in which amplification stems from the activity of mechanoelectrical-transduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs and exerts a negative force on the hair bundle. By enhancing bundle motion, this force partially compensates for viscous damping by cochlear fluids. Linear stability analysis of a six-state kinetic model reveals Hopf bifurcations for parameter values in the physiological range. These bifurcations signal conditions under which the system’s behavior changes from a damped oscillatory response to spontaneous limit-cycle oscillation. By varying the number of stereocilia in a bundle and the rate constant for Ca2+ binding, we calculate bifurcation frequencies spanning the observed range of auditory sensitivity for a representative receptor organ, the chicken’s cochlea. Simulations using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transduction channels occur universally in hair cells, this active-channel model describes a mechanism of auditory amplification potentially applicable across species and hair-cell types.

Redesign of soluble fatty acid desaturases from plants for altered substrate specificity and double bond position

Acyl-acyl carrier protein (ACP) desaturases introduce double bonds at specific positions in fatty acids of defined chain lengths and are one of the major determinants of the monounsaturated fatty acid composition of vegetable oils. Mutagenesis studies were conducted to determine the structural basis for the substrate and double bond positional specificities displayed by acyl-ACP desaturases. By replacement of specific amino acid residues in a Δ6-palmitoyl (16:0)-ACP desaturase with their equivalents from a Δ9-stearoyl (18:0)-ACP desaturase, mutant enzymes were identified that have altered fatty acid chain-length specificities or that can insert double bonds into either the Δ6 or Δ9 positions of 16:0- and 18:0-ACP. Most notably, by replacement of five amino acids (A181T/A200F/S205N/L206T/G207A), the Δ6-16:0-ACP desaturase was converted into an enzyme that functions principally as a Δ9-18:0-ACP desaturase. Many of the determinants of fatty acid chain-length specificity in these mutants are found in residues that line the substrate binding channel as revealed by x-ray crystallography of the Δ9-18:0-ACP desaturase. The crystallographic model of the active site is also consistent with the diverged activities associated with naturally occurring variant acyl-ACP desaturases. In addition, on the basis of the active-site model, a Δ9-18:0-ACP desaturase was converted into an enzyme with substrate preference for 16:0-ACP by replacement of two residues (L118F/P179I). These results demonstrate the ability to rationally modify acyl-ACP desaturase activities through site-directed mutagenesis and represent a first step toward the design of acyl-ACP desaturases for the production of novel monounsaturated fatty acids in transgenic oilseed crops.

Rescue of stalled replication forks by RecG: Simultaneous translocation on the leading and lagging strand templates supports an active DNA unwinding model of fork reversal and Holliday junction formation

Modification of damaged replication forks is emerging as a crucial factor for efficient chromosomal duplication and the avoidance of genetic instability. The RecG helicase of Escherichia coli, which is involved in recombination and DNA repair, has been postulated to act on stalled replication forks to promote replication restart via the formation of a four-stranded (Holliday) junction. Here we show that RecG can actively unwind the leading and lagging strand arms of model replication fork structures in vitro. Unwinding is achieved in each case by simultaneous interaction with and translocation along both the leading and lagging strand templates at a fork. Disruption of either of these interactions dramatically inhibits unwinding of the opposing duplex arm. Thus, RecG translocates simultaneously along two DNA strands, one with 5′-3′ and the other with 3′-5′ polarity. The unwinding of both nascent strands at a damaged fork, and their subsequent annealing to form a Holliday junction, may explain the ability of RecG to promote replication restart. Moreover, the preferential binding of partial forks lacking a leading strand suggests that RecG may have the ability to target stalled replication intermediates in vivo in which lagging strand synthesis has continued beyond the leading strand.

Active control of waves in a cochlear model with subpartitions.

Multiscale asymptotic methods developed previously to study macromechanical wave propagation in cochlear models are generalized here to include active control of a cochlear partition having three subpartitions, the basilar membrane, the reticular lamina, and the tectorial membrane. Activation of outer hair cells by stereocilia displacement and/or by lateral wall stretching result in a frequency-dependent force acting between the reticular lamina and basilar membrane. Wavelength-dependent fluid loads are estimated by using the unsteady Stokes' equations, except in the narrow gap between the tectorial membrane and reticular lamina, where lubrication theory is appropriate. The local wavenumber and subpartition amplitude ratios are determined from the zeroth order equations of motion. A solvability relation for the first order equations of motion determines the subpartition amplitudes. The main findings are as follows: The reticular lamina and tectorial membrane move in unison with essentially no squeezing of the gap; an active force level consistent with measurements on isolated outer hair cells can provide a 35-dB amplification and sharpening of subpartition waveforms by delaying dissipation and allowing a greater structural resonance to occur before the wave is cut off; however, previously postulated activity mechanisms for single partition models cannot achieve sharp enough tuning in subpartitioned models.

Activities and response to DNA damage of latent and active sequence-specific DNA binding forms of mouse p53

The mouse p53 protein generated by alternative splicing (p53as) has amino acid substitutions at its C terminus that result in constitutively active sequence-specific DNA binding (active form), whereas p53 protein itself binds inefficiently (latent form) unless activated by C-terminal modification. Exogenous p53as expression activated transcription of reporter plasmids containing p53 binding sequences and inhibited growth of mouse and human cells lacking functional endogenous p53. Inducible p53as in stably transfected p53 null fibroblasts increased p21WAF1/Cip-1/Sdi and decreased bcl-2 protein steady-state levels. Endogenous p53as and p53 proteins differed in response to cellular DNA damage. p53 protein was induced transiently in normal keratinocytes and fibroblasts whereas p53as protein accumulation was sustained in parallel with induction of p21WAF1/Cip-1/Sdi protein and mRNA, in support of p53as transcriptional activity. Endogenous p53 and p53as proteins in epidermal tumor cells responded to DNA damage with different kinetics of nuclear accumulation and efficiencies of binding to a p53 consensus DNA sequence. A model is proposed in which C-terminally distinct p53 protein forms specialize in functions, with latent p53 forms primarily for rapid non-sequence-specific binding to sites of DNA damage and active p53 forms for sustained regulation of transcription and growth.

Intrastriatal injection of an adenoviral vector expressing glial-cell-line-derived neurotrophic factor prevents dopaminergic neuron degeneration and behavioral impairment in a rat model of Parkinson disease

Glial-cell-line-derived neurotrophic factor (GDNF) is a potent neurotrophic factor for adult nigral dopamine neurons in vivo. GDNF has both protective and restorative effects on the nigro-striatal dopaminergic (DA) system in animal models of Parkinson disease. Appropriate administration of this factor is essential for the success of its clinical application. Since it cannot cross the blood–brain barrier, a gene transfer method may be appropriate for delivery of the trophic factor to DA cells. We have constructed a recombinant adenovirus (Ad) encoding GDNF and injected it into rat striatum to make use of its ability to infect neurons and to be retrogradely transported by DA neurons. Ad-GDNF was found to drive production of large amounts of GDNF, as quantified by ELISA. The GDNF produced after gene transfer was biologically active: it increased the survival and differentiation of DA neurons in vitro. To test the efficacy of the Ad-mediated GDNF gene transfer in vivo, we used a progressive lesion model of Parkinson disease. Rats received injections unilaterally into their striatum first of Ad and then 6 days later of 6-hydroxydopamine. We found that mesencephalic nigral dopamine neurons of animals treated with the Ad-GDNF were protected, whereas those of animals treated with the Ad-β-galactosidase were not. This protection was associated with a difference in motor function: amphetamine-induced turning was much lower in animals that received the Ad-GDNF than in the animals that received Ad-β-galactosidase. This finding may have implications for the development of a treatment for Parkinson disease based on the use of neurotrophic factors.

A model system to study genomic imprinting of human genes

Somatic-cell hybrids have been shown to maintain the correct epigenetic chromatin states to study developmental globin gene expression as well as gene expression on the active and inactive X chromosomes. This suggests the potential use of somatic-cell hybrids containing either a maternal or a paternal human chromosome as a model system to study known imprinted genes and to identify as-yet-unknown imprinted genes. Testing gene expression by using reverse transcription followed by PCR, we show that functional imprints are maintained at four previously characterized 15q11–q13 loci in hybrids containing a single human chromosome 15 and at two chromosome 11p15 loci in hybrids containing a single chromosome 11. In contrast, three γ-aminobutyric acid type A receptor subunit genes in 15q12–q13 are nonimprinted. Furthermore, we have found that differential DNA methylation imprints at the SNRPN promoter and at a CpG island in 11p15 are also maintained in somatic-cell hybrids. Somatic-cell hybrids therefore are a valid and powerful system for studying known imprinted genes as well as for rapidly identifying new imprinted genes.

Antigen-driven CD4+ T cell and HIV-1 dynamics: Residual viral replication under highly active antiretroviral therapy

Antigen-induced stimulation of the immune system can generate heterogeneity in CD4+ T cell division rates capable of explaining the temporal patterns seen in the decay of HIV-1 plasma RNA levels during highly active antiretroviral therapy. Posttreatment increases in peripheral CD4+ T cell counts are consistent with a mathematical model in which host cell redistribution between lymph nodes and peripheral blood is a function of viral burden. Model fits to patient data suggest that, although therapy reduces HIV replication below replacement levels, substantial residual replication continues. This residual replication has important consequences for long-term therapy and the evolution of drug resistance and represents a challenge for future treatment strategies.

Folding thermodynamics of a model three-helix-bundle protein

The calculated folding thermodynamics of a simple off-lattice three-helix-bundle protein model under equilibrium conditions shows the experimentally observed protein transitions: a collapse transition, a disordered-to-ordered globule transition, a globule to native-state transition, and the transition from the active native state to a frozen inactive state. The cooperativity and physical origin of the various transitions are explored with a single “optimization” parameter and characterized with the Lindemann criterion for liquid versus solid-state dynamics. Below the folding temperature, the model has a simple free energy surface with a single basin near the native state; the surface is similar to that calculated from a simulation of the same three-helix-bundle protein with an all-atom representation [Boczko, E. M. & Brooks III, C. L. (1995) Science 269, 393–396].

The prion model for [URE3] of yeast: Spontaneous generation and requirements for propagation

The genetic properties of the non-Mendelian element, [URE3], suggest that it is a prion (infectious protein) form of Ure2p, a mediator of nitrogen regulation in Saccharomyces cerevisiae. Into a ure2Δ strain (necessarily lacking [URE3]), we introduced a plasmid overproducing Ure2p. This induced the frequent “spontaneous generation” of [URE3], with properties identical to the original [URE3]. Altering the translational frame only in the prion-inducing domain of URE2 shows that it is Ure2 protein (and not URE2 RNA) that induces appearance of [URE3]. The proteinase K-resistance of Ure2p is unique to [URE3] strains and is not seen in nitrogen regulation of normal strains. The prion-inducing domain of Ure2p (residues 1–65) can propagate [URE3] in the absence of the C-terminal part of the molecule. In contrast, the C-terminal part of Ure2p cannot be converted to the prion (inactive) form without the prion-inducing domain covalently attached. These experiments support the prion model for [URE3] and extend our understanding of its propagation.

Contribution of S opponent cells to color appearance

We measured the regions in isoluminant color space over which observers perceive red, yellow, green, and blue and examined the extent to which the colors vary in perceived amount within these regions. We compared color scaling of various isoluminant stimuli by using large spots, which activate all cone types, to that with tiny spots in the central foveola, where S cones, and thus S opponent (So) cell activity, are largely or entirely absent. The addition of So input to that from the L and M opponent cells changes the chromatic appearance of all colors, affecting each primary color in different chromatic regions in the directions and by the amount predicted by our color model. Shifts from white to the various chromatic stimuli we used produced sinusoidal variations in cone activation as a function of color angle for each cone type and in the responses of lateral geniculate cells. However, psychophysical color-scaling functions for 2° spots were nonsinusoidal, being much more peaked. The color-scaling functions are well fit by sine waves raised to exponents between 1 and 3. The same is true for the color responses of a large subpopulation of striate cortex cells. The narrow color tuning, the discrepancies between the spectral loci of the peaks of the color-scaling curves and those of lateral geniculate cells, and the changes in color appearance produced by eliminating So input provide evidence for a cortical processing stage at which the color axes are rotated by a combination of the outputs of So cells with those of L and M opponent cells in the manner that we postulated earlier. There seems to be an expansive response nonlinearity at this stage.

Crystal structure of the HIV-1 integrase catalytic core and C-terminal domains: A model for viral DNA binding

Insolubility of full-length HIV-1 integrase (IN) limited previous structure analyses to individual domains. By introducing five point mutations, we engineered a more soluble IN that allowed us to generate multidomain HIV-1 IN crystals. The first multidomain HIV-1 IN structure is reported. It incorporates the catalytic core and C-terminal domains (residues 52–288). The structure resolved to 2.8 Å is a Y-shaped dimer. Within the dimer, the catalytic core domains form the only dimer interface, and the C-terminal domains are located 55 Å apart. A 26-aa α-helix, α6, links the C-terminal domain to the catalytic core. A kink in one of the two α6 helices occurs near a known proteolytic site, suggesting that it may act as a flexible elbow to reorient the domains during the integration process. Two proteins that bind DNA in a sequence-independent manner are structurally homologous to the HIV-1 IN C-terminal domain, suggesting a similar protein–DNA interaction in which the IN C-terminal domain may serve to bind, bend, and orient viral DNA during integration. A strip of positively charged amino acids contributed by both monomers emerges from each active site of the dimer, suggesting a minimally dimeric platform for binding each viral DNA end. The crystal structure of the isolated catalytic core domain (residues 52–210), independently determined at 1.6-Å resolution, is identical to the core domain within the two-domain 52–288 structure.

A model for individual and collective cell movement in Dictyostelium discoideum

The cellular slime mold Dictyostelium discoideum is a widely used model system for studying a variety of basic processes in development, including cell–cell signaling, signal transduction, pattern formation, cell motility, and the movement of tissue-like aggregates of cells. Many aspects of cell motion are poorly understood, including how individual cell behavior produces the collective motion of cells observed within the mound and slug. Herein, we describe a biologically realistic model for motile D. discoideum cells that can generate active forces, that interact via surface molecules, and that can detect and respond to chemotactic signals. We model the cells as deformable viscoelastic ellipsoids and incorporate signal transduction and cell–cell signaling by using a previously developed model. The shape constraint restricts the admissible deformations but makes the simulation of a large number of interacting cells feasible. Because the model is based on known processes, the parameters can be estimated or measured experimentally. We show that this model can reproduce the observations on the chemotactic behavior of single cells, streaming during aggregation, and the collective motion of an aggregate of cells driven by a small group of pacemakers. The model predicts that the motion of two-dimensional slugs [Bonner, J. T. (1998) Proc. Natl. Acad. Sci. USA 95, 9355–9359] results from the same behaviors that are exhibited by individual cells; it is not necessary to invoke different mechanisms or behaviors. Our computational experiments also suggest previously uncharacterized phenomena that may be experimentally observable.

Identification of the vitamin K-dependent carboxylase active site: Cys-99 and Cys-450 are required for both epoxidation and carboxylation

The vitamin K-dependent carboxylase modifies and renders active vitamin K-dependent proteins involved in hemostasis, cell growth control, and calcium homeostasis. Using a novel mechanism, the carboxylase transduces the free energy of vitamin K hydroquinone (KH2) oxygenation to convert glutamate into a carbanion intermediate, which subsequently attacks CO2, generating the γ-carboxylated glutamate product. How the carboxylase effects this conversion is poorly understood because the active site has not been identified. Dowd and colleagues [Dowd, P., Hershline, R., Ham, S. W. & Naganathan, S. (1995) Science 269, 1684–1691] have proposed that a weak base (cysteine) produces a strong base (oxygenated KH2) capable of generating the carbanion. To define the active site and test this model, we identified the amino acids that participate in these reactions. N-ethyl maleimide inhibited epoxidation and carboxylation, and both activities were equally protected by KH2 preincubation. Amino acid analysis of 14C- N-ethyl maleimide-modified human carboxylase revealed 1.8–2.3 reactive residues and a specific activity of 7 × 108 cpm/hr per mg. Tryptic digestion and liquid chromatography electrospray mass spectrometry identified Cys-99 and Cys-450 as active site residues. Mutation to serine reduced both epoxidation and carboxylation, to 0.2% (Cys-99) or 1% (Cys-450), and increased the Kms for a glutamyl substrate 6- to 8-fold. Retention of some activity indicates a mechanism for enhancing cysteine/serine nucleophilicity, a property shared by many active site thiol enzymes. These studies, which represent a breakthrough in defining the carboxylase active site, suggest a revised model in which the glutamyl substrate indirectly coordinates at least one thiol, forming a catalytic complex that ionizes a thiol to initiate KH2 oxygenation.