Phase of shear vibrations within cochlear partition leads to activation of the cochlear amplifier.

Since Georg von Bekesy laid out the place theory of the hearing, researchers have been working to understand the remarkable properties of mammalian hearing. Because access to the cochlea is restricted in live animals, and important aspects of hearing are destroyed in dead ones, models play a key role in interpreting local measurements. Wentzel-Kramers-Brillouin (WKB) models are attractive because they are analytically tractable, appropriate to the oblong geometry of the cochlea, and can predict wave behavior over a large span of the cochlea. Interest in the role the tectorial membrane (TM) plays in cochlear tuning led us to develop models that directly interface the TM with the cochlear fluid. In this work we add an angled shear between the TM and reticular lamina (RL), which serves as an input to a nonlinear active force. This feature plus a novel combination of previous work gives us a model with TM-fluid interaction, TM-RL shear, a nonlinear active force and a second wave mode. The behavior we get leads to the conclusion the phase between the shear and basilar membrane (BM) vibration is critical for amplification. We show there is a transition in this phase that occurs at a frequency below the cutoff, which is strongly influenced by TM stiffness. We describe this mechanism of sharpened BM velocity profile, which demonstrates the importance of the TM in overall cochlear tuning and offers an explanation for the response characteristics of the Tectb mutant mouse.

Stimulated acoustic emissions from coupled strings.

We consider traveling transverse waves on two identical uniform taut strings that are elastically coupled through springs that gradually decrease their stiffness over a region of finite length. The wave system can be decomposed into two modes: an in-phase mode ([Formula: see text]) that is transparent to the coupling springs, and an out-of-phase mode ([Formula: see text]) that engages the coupling springs and can resonate at a particular location depending on the excitation frequency. The system exhibits linear mode conversion whereby an incoming ([Formula: see text]) wave is reflected back from the resonance location both as a propagating ([Formula: see text]) wave and an evanescent ([Formula: see text]) wave, while both types emerge as propagating forward through the resonance location. We match a local transition layer expansion to the WKB expansion to obtain estimates of the reflection and transmission coefficients. The reflected waves may be an analog for stimulated emissions from the ear.

Dual traveling waves in an inner ear model with two degrees of freedom.

We calculate traveling waves in the mammalian cochlea, which transduces acoustic vibrations into neural signals. We use a WKB-based mechanical model with both the tectorial membrane (TM) and basilar membrane (BM) coupled to the fluid to calculate motions along the length of the cochlea. This approach generates two wave numbers that manifest as traveling waves with different modes of motion between the BM and TM. The waves add differently on each mass, producing distinct tuning curves and different characteristic frequencies (CFs) for the TM and the BM. We discuss the effect of TM stiffness and coupling on the waves and tuning curves. We also consider how the differential motions between the masses could influence the cochlear amplifier and how mode conversion could take place in the cochlea.

Illuminating solution responses of a LOV domain protein with photocoupled small-angle X-ray scattering.

The PAS-LOV domain is a signal-transducing component found in a large variety of proteins that is responsible for sensing different stimuli such as light, oxygen, and voltage. The LOV protein VVD regulates blue light responses in the filamentous fungi Neurospora crassa. Using photocoupled, time-resolved small-angle X-ray scattering, we extract the solution protein structure in both dark-adapted and light-activated states. Two distinct dark-adapted conformations are detected in the wild-type protein: a compact structure that corresponds to the crystal structure of the dark-state monomer as well as an extended structure that is well modeled by introducing conformational disorder at the N-terminus of the protein. These conformations are accentuated in carefully selected variants, in which a key residue for propagating structural transitions, Cys71, has been mutated or oxidized. Despite different dark-state conformations, all proteins form a common dimer in response to illumination. Taken together, these data support a reaction scheme that describes the mechanism for light-induced dimerization of VVD. Envelope reconstructions of the transient light-state dimer reveal structures that are best described by a parallel arrangement of subunits that have significantly changed conformation compared to the crystal structure.

Both helix topology and counterion distribution contribute to the more effective charge screening in dsRNA compared with dsDNA.

The recent discovery of the RNA interference mechanism emphasizes the biological importance of short, isolated, double-stranded (ds) RNA helices and calls for a complete understanding of the biophysical properties of dsRNA. However, most previous studies of the electrostatics of nucleic acid duplexes have focused on DNA. Here, we present a comparative investigation of electrostatic effects in RNA and DNA. Using resonant (anomalous) and non-resonant small-angle X-ray scattering, we characterized the charge screening efficiency and counterion distribution around short (25 bp) dsDNA and RNA molecules of comparable sequence. Consistent with theoretical predictions, we find counterion mediated screening to be more efficient for dsRNA than dsDNA. Furthermore, the topology of the RNA A-form helix alters the spatial distribution of counterions relative to B-form DNA. The experimental results reported here agree well with ion-size-corrected non-linear Poisson-Boltzmann calculations. We propose that differences in electrostatic properties aid in selective recognition of different types of short nucleic acid helices by target binding partners.

Abrupt transition from a free, repulsive to a condensed, attractive DNA phase, induced by multivalent polyamine cations.

We have investigated the energetics of DNA condensation by multivalent polyamine cations. Solution small angle x-ray scattering was used to monitor interactions between short 25 base pair dsDNA strands in the free supernatant DNA phase that coexists with the condensed DNA phase. Interestingly, when tetravalent spermine is used, significant inter-DNA repulsion is observed in the free phase, in contrast with the presumed inter-DNA attraction in the coexisting condensed phase. DNA condensation thus appears to be a discrete, first-order-like, transition from a repulsive gaseous to an attractive condensed solid phase, in accord with the reported all-or-none condensation of giant DNA. We further quantify the electrostatic repulsive potentials in the free DNA phase and estimate the number of additional spermine cations that bind to DNA upon condensation.

Time-resolved dimerization of a PAS-LOV protein measured with photocoupled small angle X-ray scattering.

Time-resolved small-angle X-ray scattering (SAXS) has been used to probe photoexcitation of the blue-light signal transduction protein Vivid (VVD). Laser excitation of sample in a continuous flow cell enables time-resolved measurement of the initial response of VVD to illumination. Good signal-to-noise is achieved without relying on multiple exposures of the same sample or limiting exposure times to prevent radiation damage. The SAXS data demonstrate that VVD dimerizes within tens of milliseconds of light-state activation. Time-resolved SAXS in a flow cell format is a general method for connecting chemical changes in photoreceptors to conformationally driven output signals.

Hinge stiffness is a barrier to RNA folding.

Cation-mediated RNA folding from extended to compact, biologically active conformations relies on a temporal balance of forces. The Mg2 +-mediated folding of the Tetrahymena thermophila ribozyme is characterized by rapid nonspecific collapse followed by tertiary-contact-induced compaction. This article focuses on an autonomously folding portion of the Tetrahymena ribozyme, its P4-P6 domain, in order to probe one facet of the rapid collapse: chain flexibility. The time evolution of P4-P6 folding was followed by global and local measures as a function of Mg2 + concentration. While all concentrations of Mg2 + studied are sufficient to screen the charge on the helices, the rates of compaction and tertiary contact formation diverge as the concentration of Mg2 + increases; collapse is greatly accelerated by Mg2 +, while tertiary contact formation is not. These studies highlight the importance of chain stiffness to RNA folding; at 10 mM Mg2 +, a stiff hinge limits the rate of P4-P6 folding. At higher magnesium concentrations, the rate-limiting step shifts from hinge bending to tertiary contact formati

Mono- and trivalent ions around DNA: a small-angle scattering study of competition and interactions.

The presence of small numbers of multivalent ions in DNA-containing solutions results in strong attractive forces between DNA strands. Despite the biological importance of this interaction, e.g., DNA condensation, its physical origin remains elusive. We carried out a series of experiments to probe interactions between short DNA strands as small numbers of trivalent ions are included in a solution containing DNA and monovalent ions. Using resonant (anomalous) and nonresonant small angle x-ray scattering, we coordinated measurements of the number and distribution of each ion species around the DNA with the onset of attractive forces between DNA strands. DNA-DNA interactions occur as the number of trivalent ions increases. Surprisingly good agreement is found between data and size-corrected numerical Poisson-Boltzmann predictions of ion competition for non- and weakly interacting DNAs. We also obtained an estimate for the minimum number of trivalent ions needed to initiate DNA-DNA attraction.

Closing the lid on DNA end-to-end stacking interactions.

Recent experiments suggest that short DNA strands associate by end-to-end stacking. Here, we report interactions between DNAs with modified ends. DNA duplexes, 20 bp long, were capped with short T(4) loops at 2, 1 or 0 ends, and were placed in solutions containing 20 mM Mg(2+). Association was observed only in constructs with one or more uncapped ends. DNA-DNA interactions were characterized by measuring variations in small angle x-ray scattering (SAXS) curves at the lowest scattering angles. Second virial coefficients were computed from the SAXS data. Our results confirm that end-to-end stacking plays an important role in short strand DNA-DNA interactions.

Inter-DNA attraction mediated by divalent counterions.

Can nonspecifically bound divalent counterions induce attraction between DNA strands? Here, we present experimental evidence demonstrating attraction between short DNA strands mediated by Mg2+ ions. Solution small angle x-ray scattering data collected as a function of DNA concentration enable model independent extraction of the second virial coefficient. As the [Mg2+] increases, this coefficient turns from positive to negative reflecting the transition from repulsive to attractive inter-DNA interaction. This surprising observation is corroborated by independent light scattering experiments. The dependence of the observed attraction on experimental parameters including DNA length provides valuable clues to its origin.

Measuring inter-DNA potentials in solution.

Interactions between short strands of DNA can be tuned from repulsive to attractive by varying solution conditions and have been quantified using small angle x-ray scattering techniques. The effective DNA interaction charge was extracted by fitting the scattering profiles with the generalized one-component method and inter-DNA Yukawa pair potentials. A significant charge is measured at low to moderate monovalent counterion concentrations, resulting in strong inter-DNA repulsion. The charge and repulsion diminish rapidly upon the addition of divalent counterions. An intriguing short range attraction is observed at surprisingly low divalent cation concentrations, approximately 16 mM Mg2+. Quantitative measurements of inter-DNA potentials are essential for improving models of fundamental interactions in biological systems.

Concordant exploration of the kinetics of RNA folding from global and local perspectives.

Time-resolved small-angle X-ray scattering (SAXS) with millisecond time-resolution reveals two discrete phases of global compaction upon Mg2+-mediated folding of the Tetrahymena thermophila ribozyme. Electrostatic relaxation of the RNA occurs rapidly and dominates the first phase of compaction during which the observed radius of gyration (R(g)) decreases from 75 angstroms to 55 angstroms. A further decrease in R(g) to 45 angstroms occurs in a well-defined second phase. An analysis of mutant ribozymes shows that the latter phase depends upon the formation of long-range tertiary contacts within the P4-P6 domain of the ribozyme; disruption of the three remaining long-range contacts linking the peripheral helices has no effect on the 55-45 angstroms compaction transition. A better understanding of the role of specific tertiary contacts in compaction was obtained by concordant time-resolved hydroxyl radical (OH) analyses that report local changes in the solvent accessibility of the RNA backbone. Comparison of the global and local measures of folding shows that formation of a subset of native tertiary contacts (i.e. those defining the ribozyme core) can occur within a highly compact ensemble whose R(g) is close to that of the fully folded ribozyme. Analyses of additional ribozyme mutants and reaction conditions establish the generality of the rapid formation of a partially collapsed state with little to no detectable tertiary structure. These studies directly link global RNA compaction with formation of tertiary structure as the molecule acquires its biologically active structure, and underscore the strong dependence on salt of both local and global measures of folding kinetics.