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.

“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

Host factor I, Hfq, binds to Escherichia coli ompA mRNA in a growth rate-dependent fashion and regulates its stability

The stability of the ompA mRNA depends on the bacterial growth rate. The 5′ untranslated region is the stability determinant of this transcript and the target of the endoribonuclease, RNase E, the key player of mRNA degradation. An RNA-binding protein with affinity for the 5′ untranslated region ompA was purified and identified as Hfq, a host factor initially recognized for its function in phage Qβ replication. The ompA RNA-binding activity parallels the amount of Hfq, which is elevated in bacteria cultured at slow growth rate, a condition leading to facilitated degradation of the ompA mRNA. In hfq mutant cells with a deficient Hfq gene product, the RNA-binding activity is missing, and analysis of the ompA mRNA showed that the growth-rate dependence of degradation is lost. Furthermore, the half-life of the ompA mRNA is prolonged in the mutant cells, irrespective of growth rate. Hfq has no affinity for the lpp transcript whose degradation, like that of bulk mRNA, is not affected by bacterial growth rate. Compatible with our results, we found that the intracellular concentration of RNase E and its associated degradosome components is independent of bacterial growth rate. Thus our results suggest a regulatory role for Hfq that specifically facilitates the ompA mRNA degradation in a growth rate-dependent manner.

Rhizobium gone native: Unexpected plasmid stability of indigenous Rhizobium leguminosarum

Lateral transfer of bacterial plasmids is thought to play an important role in microbial evolution and population dynamics. However, this assumption is based primarily on investigations of medically or agriculturally important bacterial species. To explore the role of lateral transfer in the evolution of bacterial systems not under intensive, human-mediated selection, we examined the association of genotypes at plasmid-encoded and chromosomal loci of native Rhizobium, the nitrogen-fixing symbiont of legumes. To this end, Rhizobium leguminosarum strains nodulating sympatric species of native Trifolium were characterized genetically at plasmid-encoded symbiotic (sym) regions (nodulation AB and nodulation CIJT loci) and a repeated chromosomal locus not involved in the symbiosis with legumes. Restriction fragment length polymorphism analysis was used to distinguish genetic groups at plasmid and chromosomal loci. The correlation between major sym and chromosomal genotypes and the distribution of genotypes across host plant species and sampling location were determined using χ2 analysis. In contrast to findings of previous studies, a strict association existed between major sym plasmid and chromosomal genetic groups, suggesting a lack of successful sym plasmid transfer between major Rhizobium chromosomal types. These data indicate that previous observations of sym plasmid transfer in agricultural settings may seriously overestimate the rates of successful conjugation in systems not impacted by human activities. In addition, a nonrandom distribution of Rhizobium genotypes across host plant species and sampling site demonstrates the importance of both factors in shaping Rhizobium population dynamics.

Transition-state structure as a unifying basis in protein-folding mechanisms: Contact order, chain topology, stability, and the extended nucleus mechanism

I attempt to reconcile apparently conflicting factors and mechanisms that have been proposed to determine the rate constant for two-state folding of small proteins, on the basis of general features of the structures of transition states. Φ-Value analysis implies a transition state for folding that resembles an expanded and distorted native structure, which is built around an extended nucleus. The nucleus is composed predominantly of elements of partly or well-formed native secondary structure that are stabilized by local and long-range tertiary interactions. These long-range interactions give rise to connecting loops, frequently containing the native loops that are poorly structured. I derive an equation that relates differences in the contact order of a protein to changes in the length of linking loops, which, in turn, is directly related to the unfavorable free energy of the loops in the transition state. Kinetic data on loop extension mutants of CI2 and α-spectrin SH3 domain fit the equation qualitatively. The rate of folding depends primarily on the interactions that directly stabilize the nucleus, especially those in native-like secondary structure and those resulting from the entropy loss from the connecting loops, which vary with contact order. This partitioning of energy accounts for the success of some algorithms that predict folding rates, because they use these principles either explicitly or implicitly. The extended nucleus model thus unifies the observations of rate depending on both stability and topology.

Analysis of microsatellite mutations in the mitochondrial DNA of Saccharomyces cerevisiae

In the nuclear genome of Saccharomyces cerevisiae, simple, repetitive DNA sequences (microsatellites) mutate at rates much higher than nonrepetitive sequences. Most of these mutations are deletions or additions of repeat units. The yeast mitochondrial genome also contains many microsatellites. To examine the stability of these sequences, we constructed a reporter gene (arg8m) containing out-of-frame insertions of either poly(AT) or poly(GT) tracts within the coding sequence. Yeast strains with this reporter gene inserted within the mitochondrial genome were constructed. Using these strains, we showed that poly(GT) tracts were considerably less stable than poly(AT) tracts and that alterations usually involved deletions rather than additions of repeat units. In contrast, in the nuclear genome, poly(GT) and poly(AT) tracts had similar stabilities, and alterations usually involved additions rather than deletions. Poly(GT) tracts were more stable in the mitochondria of diploid cells than in haploids. In addition, an msh1 mutation destabilized poly(GT) tracts in the mitochondrial genome.

Simultaneous two-photon excitation of distinct labels for dual-color fluorescence crosscorrelation analysis

Confocal fluorescence correlation spectroscopy as a time-averaging fluctuation analysis combining maximum sensitivity with high statistical confidence has proved to be a very versatile and powerful tool for detection and temporal investigation of biomolecules at ultralow concentrations on surfaces, in solutions, and in living cells. To probe the interaction of different molecular species for a detailed understanding of biologically relevant mechanisms, crosscorrelation studies on dual or multiple fluorophore assays with spectrally distinct excitation and emission are particularly promising. Despite the considerable improvement of detection specificity provided by fluorescence crosscorrelation analysis, few applications have so far been reported, presumably because of the practical challenges of properly aligning and controlling the stability of the experimental setup. In this work, we demonstrate that two-photon excitation combined with dual-color fluorescence correlation spectroscopy can be the key to simplifying simultaneous investigations of multiple fluorescent species significantly on a single-molecule scale. Two-photon excitation allows accession of common fluorophores of largely distinct emission by the same excitation wavelength, because differences in selection rules and vibronic coupling can induce considerable shifts between the one-photon and two-photon excitation spectra. The concept of dual-color two-photon fluorescence crosscorrelation analysis is introduced and experimentally demonstrated with an established assay probing the selective cleavage of dual-labeled DNA substrates by restriction endonuclease EcoRI.

The 3′ untranslated region of a rice α-amylase gene functions as a sugar-dependent mRNA stability determinant

In plants, sugar feedback regulation provides a mechanism for control of carbohydrate allocation and utilization among tissues and organs. The sugar repression of α-amylase gene expression in rice provides an ideal model for studying the mechanism of sugar feedback regulation. We have shown previously that sugar repression of α-amylase gene expression in rice suspension cells involves control of both transcription rate and mRNA stability. The α-amylase mRNA is significantly more stable in sucrose-starved cells than in sucrose-provided cells. To elucidate the mechanism of sugar-dependent mRNA turnover, we have examined the effect of αAmy3 3′ untranslated region (UTR) on mRNA stability by functional analyses in transformed rice suspension cells. We found that the entire αAmy3 3′ UTR and two of its subdomains can independently mediate sugar-dependent repression of reporter mRNA accumulation. Analysis of reporter mRNA half-lives demonstrated that the entire αAmy3 3′ UTR and the two subdomains each functioned as a sugar-dependent destabilizing determinant in the turnover of mRNA. Nuclear run-on transcription analysis further confirmed that the αAmy3 3′ UTR and the two subdomains did not affect the transcription rate of promoter. The identification of sequence elements in the α-amylase mRNA that dictate the differential stability has very important implications for the study of sugar-dependent mRNA decay mechanisms.

The origins of stability of spontaneous vesicles

Equilibrium unilamellar vesicles are stabilized by one of two distinct mechanisms depending on the value of the bending constant. Helfrich undulations ensure that the interbilayer potential is always repulsive when the bending constant, K, is of order kBT. When K ≫ kBT, unilamellar vesicles are stabilized by the spontaneous curvature that picks out a particular vesicle radius; other radii are disfavored energetically. We present measurements of the bilayer elastic constant and the spontaneous curvature, Ro, for three different systems of equilibrium vesicles by an analysis of the vesicle size distribution determined by cryo-transmission electron microscopy and small-angle neutron scattering. For cetyltrimethylammonium bromide (CTAB)/sodium octyl sulfonate catanionic vesicles, K = .7 kBT, suggesting that the unilamellar vesicles are stabilized by Helfrich-undulation repulsions. However, for CTAB and sodium perfluorooctanoate (FC7) vesicles, K = 6 kBT, suggesting stabilization by the energetic costs of deviations from the spontaneous curvature. Adding electrolyte to the sodium perfluorooctanoate/CTAB vesicles leads to vesicles with two bilayers; the attractive interactions between the bilayers can overcome the cost of small deviations from the spontaneous curvature to form two-layer vesicles, but larger deviations to form three and more layer vesicles are prohibited. Vesicles with a discrete numbers of bilayers at equilibrium are possible only for bilayers with a large bending modulus coupled with a spontaneous curvature.

High-resolution minisatellite-based typing as a portable approach to global analysis of Mycobacterium tuberculosis molecular epidemiology

The worldwide threat of tuberculosis to human health emphasizes the need to develop novel approaches to a global epidemiological surveillance. The current standard for Mycobacterium tuberculosis typing based on IS6110 restriction fragment length polymorphism (RFLP) suffers from the difficulty of comparing data between independent laboratories. Here, we propose a high-resolution typing method based on variable number tandem repeats (VNTRs) of genetic elements named mycobacterial interspersed repetitive units (MIRUs) in 12 human minisatellite-like regions of the M. tuberculosis genome. MIRU-VNTR profiles of 72 different M. tuberculosis isolates were established by PCR analysis of all 12 loci. From 2 to 8 MIRU-VNTR alleles were identified in the 12 regions in these strains, which corresponds to a potential of over 16 million different combinations, yielding a resolution power close to that of IS6110-RFLP. All epidemiologically related isolates tested were perfectly clustered by MIRU-VNTR typing, indicating that the stability of these MIRU-VNTRs is adequate to track outbreak episodes. The correlation between genetic relationships inferred from MIRU-VNTR and IS6110-RFLP typing was highly significant. Compared with IS6110-RFLP, high-resolution MIRU-VNTR typing has the considerable advantages of being fast, appropriate for all M. tuberculosis isolates, including strains that have a few IS6110 copies, and permitting easy and rapid comparison of results from independent laboratories. This typing method opens the way to the construction of digital global databases for molecular epidemiology studies of M. tuberculosis.

RNA analysis by ion-pair reversed-phase high performance liquid chromatography

Ion-pair reversed-phase high performance liquid chromatography (IP RP HPLC) is presented as a new, superior method for the analysis of RNA. IP RP HPLC provides a fast and reliable alternative to classical methods of RNA analysis, including separation of different RNA species, quantification and purification. RNA is stable under the analysis conditions used; degradation of RNA during the analyses was not observed. The versatility of IP RP HPLC for RNA analysis is demonstrated. Components of an RNA ladder, ranging in size from 155 to 1770 nt, were resolved. RNA transcripts of up to 5219 nt were analyzed, their integrity determined and they were quantified and purified. Purification of mRNA from total RNA is described, separating mouse rRNA from poly(A)+ mRNA. IP RP HPLC is also suitable for the separation and purification of DIG-labeled from unlabeled RNA. RNA purified by IP RP HPLC exhibits improved stability.

Proteomic analysis of the bacterial cell cycle

A global approach was used to analyze protein synthesis and stability during the cell cycle of the bacterium Caulobacter crescentus. Approximately one-fourth (979) of the estimated C. crescentus gene products were detected by two-dimensional gel electrophoresis, 144 of which showed differential cell cycle expression patterns. Eighty-one of these proteins were identified by mass spectrometry and were assigned to a wide variety of functional groups. Pattern analysis revealed that coexpression groups were functionally clustered. A total of 48 proteins were rapidly degraded in the course of one cell cycle. More than half of these unstable proteins were also found to be synthesized in a cell cycle-dependent manner, establishing a strong correlation between rapid protein turnover and the periodicity of the bacterial cell cycle. This is, to our knowledge, the first evidence for a global role of proteolysis in bacterial cell cycle control.

Optimizing the stability of single-chain proteins by linker length and composition mutagenesis

Linker length and composition were varied in libraries of single-chain Arc repressor, resulting in proteins with effective concentrations ranging over six orders of magnitude (10 μM–10 M). Linkers of 11 residues or more were required for biological activity. Equilibrium stability varied substantially with linker length, reaching a maximum for glycine-rich linkers containing 19 residues. The effects of linker length on equilibrium stability arise from significant and sometimes opposing changes in folding and unfolding kinetics. By fixing the linker length at 19 residues and varying the ratio of Ala/Gly or Ser/Gly in a 16-residue-randomized region, the effects of linker flexibility were examined. In these libraries, composition rather than sequence appears to determine stability. Maximum stability in the Ala/Gly library was observed for a protein containing 11 alanines and five glycines in the randomized region of the linker. In the Ser/Gly library, the most stable protein had seven serines and nine glycines in this region. Analysis of folding and unfolding rates suggests that alanine acts largely by accelerating folding, whereas serine acts predominantly to slow unfolding. These results demonstrate an important role for linker design in determining the stability and folding kinetics of single-chain proteins and suggest strategies for optimizing these parameters.

Prediction of the stability of DNA triplexes.

We present rules that allow one to predict the stability of DNA pyrimidine.purine.pyrimidine (Y.R.Y) triple helices on the basis of the sequence. The rules were derived from van't Hoff analysis of 23 oligonucleotide triplexes tested at a variety of pH values. To predict the enthalpy of triplex formation (delta H degrees), a simple nearest-neighbor model was found to be sufficient. However, to accurately predict the free energy of the triplex (delta G degrees), a combination model consisting of five parameters was needed. These parameters were (i) the delta G degrees for helix initiation, (ii) the delta G degrees for adding a T-A.T triple, (iii) the delta G degrees for adding a C(+)-G.C triple, (iv) the penalty for adjacent C bases, and (v) the pH dependence of the C(+)-G.C triple's stability. The fitted parameters are highly consistent with thermodynamic data from the basis set, generally predicting both delta H degrees and delta G degrees to within the experimental error. Examination of the parameters points out several interesting features. The combination model predicts that C(+) -G.C. triples are much more stabilizing than T-A.T triples below pH 7.0 and that the stability of the former increases approximately equal to 1 kcal/mol per pH unit as the pH is decreased. Surprisingly though, the most stable sequence is predicted to be a CT repeat, as adjacent C bases partially cancel the stability of one another. The parameters successfully predict tm values from other laboratories, with some interesting exceptions.

Mutagenesis of the putative alpha-helical domain of the Vpr protein of human immunodeficiency virus type 1: effect on stability and virion incorporation.

vpr is one of the auxiliary genes of human immunodeficiency virus type 1 (HIV-1) and is conserved in the related HIV-2/simian immunodeficiency virus lentiviruses. The unique feature of Vpr is that it is the only nonstructural protein incorporated into the virus particle. Secondary structural analysis predicted an amphipathic alpha-helical domain in the amino terminus of Vpr (residues 17-34) which contains five acidic and four leucine residues. To evaluate the role of specific residues of the helical domain for virion incorporation, mutagenesis of this domain was carried out. Substitution of proline for any of the individual acidic residues (Asp-17 and Glu-21, -24, -25, and -29) eliminated the virion incorporation of Vpr and also altered the stability of Vpr in cells. Conservative replacement of glutamic residues of the helical domain with aspartic residues resulted in Vpr characteristic of wild type both in stability and virion incorporation, as did substitution of glutamine for the acidic residues. In contrast, replacement of leucine residues of the helical domain (residues 20, 22, 23, and 26) by alanine eliminated virion incorporation function of Vpr. These data indicate that acidic and hydrophobic residues and the helical structure in this region are critical for the stability of Vpr and its efficient incorporation into virus-like particles.