2,4-dimethylene-1,3-cyclobutanediyl and 2,4-dimethylenebicyclobutane. Synthesis, spectroscopy, and reactivity of a triplet biradical and its covalent isomer

The preparation and direct observation of triplet 2,4-dimethylene-1,3- cyclobutanediyl (1), the non-Kekule isomer of benzene, is described. The biradical was generated by photolysis of 5,6-dimethylene-2,3- diazabicyclo[2.1.1]hex-2-ene (2) (which was synthesized in several steps from benzvalene) under cryogenic, matrix-isolation conditions. Biradical 1 was characterized by EPR spectroscopy (‌‌‌‌‌│D/hc│ =0.0204 cm^(-1), │E/hc│ =0.0028 cm^(-1)) and found to have a triplet ground state. The Δm_s= 2 transition displays hyperfine splitting attributed to a 7.3-G coupling to the ring methine and a 5.9-G coupling to the exocyclic methylene protons. Several experiments, including application of the magnetophotoselection (mps) technique in the generation of biradical 1, have allowed a determination of the zero-field triplet sublevels as x = -0.0040, y = +0.0136, and z = -0.0096 cm^(-1), where x and y are respectively the long and short in-plane axes and z the out-of-plane axis of 1.

Triplet 1 is yellow-orange and displays highly structured absorption (λ_(max)= 506 nm) and fluorescence (λ_(max) = 510 nm) spectra, with vibronic spacings of 1520 and 620 cm^(-1) for absorption and 1570 and 620 cm^(-1) for emission. The spectra were unequivocally assigned to triplet 1 by the use of a novel technique that takes advantage of the biradical's photolability. The absorption є = 7200 M^(-1) cm^(-1) and f = 0.022, establishing that the transition is spin-allowed. Further use of the mps technique has demonstrated that the transition is x-polarized, and the excited state 1s therefore of B_(1g) symmetry, in accord with theoretical predictions.

Thermolysis or direct photolysis of diazene 2 in fluid solution produces 2,4- dimethylenebicyclo[l.l.0]butane (3), whose ^(l)H NMR spectrum (-80°C, CD_(2)Cl_(2)) consists of singlets at δ 4.22 and 3.18 in a 2:1 ratio. Compound 3 is thermally unstable and dimerizes with second-order kinetics between -80 and -25°C (∆H^(‡) = 6.8 kcal mol^(-1), (∆s^(‡) = -28 eu) by a mechanism involving direct combination of two molecules of 3 in the rate-determining step. This singlet-manifold reaction ultimately produces a mixture of two dimers, 3,8,9- trimethylenetricyclo[5.1.1.0^(2,5)]non-4-ene (75) and trans-3,10-dimethylenetricyclo[6.2.0.0^(2,5)]deca-4,8-diene (76t), with the former predominating. In contrast, triplet-sensitized photolysis of 2, which leads to triplet 1, provides, in addition to 75 and 76t, a substantial amount of trans-5,10- dimethylenetricyclo[6.2.0.0^(3,6)]deca-3,8-diene (77t) and small amounts of two unidentified dimers.

In addition, triplet biradical 1 ring-closes to 3 in rigid media both thermally (77-140 K) and photochemically. In solution 3 forms triplet 1 upon energy transfer from sensitizers having relatively low triplet energies. The implications of the thermal chemistry for the energy surfaces of the system are discussed.

A biochemical and structural characterization of Drosophila neuroglian

A number of cell-cell interactions in the nervous system are mediated by immunoglobulin gene superfamily members. For example, neuroglian, a homophilic neural cell adhesion molecule in Drosophila, has an extracellular portion comprising six C- 2 type immunoglobulin-like domains followed by five fibronectin type III (FnIII) repeats. Neuroglian shares this domain organization and significant sequence identity with Ll, a murine neural adhesion molecule that could be a functional homologue. Here I report the crystal structure of a proteolytic fragment containing the first two FnIII repeats of neuroglian (NgFn 1,2) at 2.0Å. The interpretation of photomicrographs of rotary shadowed Ng, the entire extracellular portion of neuroglian, and NgFnl-5, the five neuroglian Fn III domains, is also discussed.

The structure of NgFn 1,2 consists of two roughly cylindrical β-barrel structural motifs arranged in a head-to-tail fashion with the domains meeting at an angle of ~120, as defined by the cylinder axes. The folding topology of each domain is identical to that previously observed for single FnIII domains from tenascin and fibronectin. The domains of NgFn1,2 are related by an approximate two fold screw axis that is nearly parallel to the longest dimension of the fragment. Assuming this relative orientation is a general property of tandem FnIII repeats, the multiple tandem FnIII domains in neuroglian and other proteins are modeled as thin straight rods with two domain zig-zag repeats. When combined with the dimensions of pairs of tandem immunoglobulin-like domains from CD4 and CD2, this model suggests that neuroglian is a long narrow molecule (20 - 30 Å in diameter) that extends up to 370Å from the cell surface.

In photomicrographs, rotary shadowed Ng and NgFn1-5 appear to be highly flexible rod-like molecules. NgFn 1-5 is observed to bend in at least two positions and has a mean total length consistent with models generated from the NgFn1,2 structure. Ng molecules have up to four bends and a mean total length of 392 Å, consistent with a head-to-tail packing of neuroglian's C2-type domains.

Travel time tomographic studies of seismic structures around subducted lithospheric slabs

The nature of the subducted lithospheric slab is investigated seismologically by tomographic inversions of ISC residual travel times. The slab, in which nearly all deep earthquakes occur, is fast in the seismic images because it is much cooler than the ambient mantle. High resolution three-dimensional P and S wave models in the NW Pacific are obtained using regional data, while inversion for the SW Pacific slabs includes teleseismic arrivals. Resolution and noise estimations show the models are generally well-resolved.

The slab anomalies in these models, as inferred from the seismicity, are generally coherent in the upper mantle and become contorted and decrease in amplitude with depth. Fast slabs are surrounded by slow regions shallower than 350 km depth. Slab fingering, including segmentation and spreading, is indicated near the bottom of the upper mantle. The fast anomalies associated with the Japan, Izu-Bonin, Mariana and Kermadec subduction zones tend to flatten to sub-horizontal at depth, while downward spreading may occur under parts of the Mariana and Kuril arcs. The Tonga slab appears to end around 550 km depth, but is underlain by a fast band at 750-1000 km depths.

The NW Pacific model combined with the Clayton-Comer mantle model predicts many observed residual sphere patterns. The predictions indicate that the near-source anomalies affect the residual spheres less than the teleseismic contributions. The teleseismic contributions may be removed either by using a mantle model, or using teleseismic station averages of residuals from only regional events. The slab-like fast bands in the corrected residual spheres are are consistent with seismicity trends under the Mariana Tzu-Bonin and Japan trenches, but are inconsistent for the Kuril events.

The comparison of the tomographic models with earthquake focal mechanisms shows that deep compression axes and fast velocity slab anomalies are in consistent alignment, even when the slab is contorted or flattened. Abnormal stress patterns are seen at major junctions of the arcs. The depth boundary between tension and compression in the central parts of these arcs appears to depend on the dip and topology of the slab.

A genetic and biochemical analysis of pre-mRNA splicing in Saccharomyces cerevisiae

Pre-mRNA splicing requires interaction of cis- acting intron sequences with trans -acting factors: proteins and small nuclear ribonucleoproteins (snRNPs). The assembly of these factors into a large complex, the spliceosome, is essential for the subsequent two step splicing reaction. First, the 5' splice site is cleaved and free exon 1 and a lariat intermediate (intron- exon2) form. In the second reaction the 3' splice site is cleaved the exons ligated and lariat intron released. A combination of genetic and biochemical techniques have been used here to study pre-mRNA splicing in yeast.

Yeast introns have three highly conserved elements. We made point mutations within these elements and found that most of them affect splicing efficiency in vivo and in vitro, usually by inhibiting spliceosome assembly.

To study trans -acting splicing factors we generated and screened a bank of temperature- sensitive (ts) mutants. Eleven new complementation groups (prp17 to prp27) were isolated. The four phenotypic classes obtained affect different steps in splicing and accumulate either: 1) pre-mRNA, 2) lariat intermediate, 3) excised intron or 4) both pre-mRNA and intron. The latter three classes represent novel phenotypes. The excised intron observed in one mutant: prp26 is stabilized due to protection in a snRNP containing particle. Extracts from another mutant: prpl8 are heat labile and accumulate lariat intermediate and exon 1. This is especially interesting as it allows analysis of the second splicing reaction. In vitro complementation of inactivated prp18 extracts does not require intact snRNPs. These studies have also shown the mutation to be in a previously unknown splicing protein. A specific requirement for A TP is also observed for the second step of splicing. The PRP 18 gene has been cloned and its polyadenylated transcript identified.

Singularities and horizons in the collisions of gravitational waves

This thesis presents a study of the dynamical, nonlinear interaction of colliding gravitational waves, as described by classical general relativity. It is focused mainly on two fundamental questions: First, what is the general structure of the singularities and Killing-Cauchy horizons produced in the collisions of exactly plane-symmetric gravitational waves? Second, under what conditions will the collisions of almost-plane gravitational waves (waves with large but finite transverse sizes) produce singularities?

In the work on the collisions of exactly-plane waves, it is shown that Killing horizons in any plane-symmetric spacetime are unstable against small plane-symmetric perturbations. It is thus concluded that the Killing-Cauchy horizons produced by the collisions of some exactly plane gravitational waves are nongeneric, and that generic initial data for the colliding plane waves always produce "pure" spacetime singularities without such horizons. This conclusion is later proved rigorously (using the full nonlinear theory rather than perturbation theory), in connection with an analysis of the asymptotic singularity structure of a general colliding plane-wave spacetime. This analysis also proves that asymptotically the singularities created by colliding plane waves are of inhomogeneous-Kasner type; the asymptotic Kasner axes and exponents of these singularities in general depend on the spatial coordinate that runs tangentially to the singularity in the non-plane-symmetric direction.

In the work on collisions of almost-plane gravitational waves, first some general properties of single almost-plane gravitational-wave spacetimes are explored. It is shown that, by contrast with an exact plane wave, an almost-plane gravitational wave cannot have a propagation direction that is Killing; i.e., it must diffract and disperse as it propagates. It is also shown that an almost-plane wave cannot be precisely sandwiched between two null wavefronts; i.e., it must leave behind tails in the spacetime region through which it passes. Next, the occurrence of spacetime singularities in the collisions of almost-plane waves is investigated. It is proved that if two colliding, almost-plane gravitational waves are initially exactly plane-symmetric across a central region of sufficiently large but finite transverse dimensions, then their collision produces a spacetime singularity with the same local structure as in the exact-plane-wave collision. Finally, it is shown that a singularity still forms when the central regions are only approximately plane-symmetric initially. Stated more precisely, it is proved that if the colliding almost-plane waves are initially sufficiently close to being exactly plane-symmetric across a bounded central region of sufficiently large transverse dimensions, then their collision necessarily produces spacetime singularities. In this case, nothing is now known about the local and global structures of the singularities.

The structure and petrology of the Johnny Lyon Hills area, Cochise County, Arizona

The Johnny Lyon Hills area is located in Cochise County in southeastern Arizona. The rocks of the area include a central core of Lower pre-Cambrian igneous and metamorphic rocks surrounded by a complexly faulted and tilted section of Upper pre-Cambrian and Paleozoic strata. Limited exposures of Mesozoic and Tertiary sedimentary and volcanic rocks are present at the north end of the map area. Late Tertiary and Quaternary alluvium almost completely surrounds and overlaps upon the older rocks.

The older pre-Cambrian rocks include a section of more than 9000 feet of generally moderately metamorphosed graywackes, slates and conglomerates of the Pinal schist injected in zones by somewhat younger rnyolite sheets. The original sediments were deposited in a geosyncline whose extent probably included large parts of Arizona, New Mexico and west Texas. During the Mazatzal Revolution the Pinal schist was deformed into northeast-trending, steeply dipping and plunging structures and the entire local section was overturned steeply toward the northwest. The pre-Cambrian Johnny Lyon granodiorite was emplaced as a large epi-tectonic pluton which modified the metamorphic character of part of the Pinal schist. Larsen method determinations indicate an age of about 715 million years for this rock, which is about the minimum age compatible with the geologic relations.

The Laramide orogeny produced numerous major thrust faults in the area involving all rocks older than and including the Lower Cretaceous Bisbee group. Major compression from the southwest and subsequent superimposed thrusting from the southeast and east are indicated. Minimum thrust displacements of more than a mile are clear and the probable displacements are of much greater magnitude. The crystalline core behaved as a single structural unit and probably caused important local divergences from the regional pattern of northeast-trending compressive forces. The massif was rotated as a unit 40 degrees or more about a northwest-trending axis overturning the pre-Cambrian fold axes in the Pinal schist.

Swarms of Late Cretaceous(?) or Early Tertiary(?) lamprophyric dikes cross the Laramide structures and are probably related to the large Texas Canyon stock several miles southeast of the map area. Intermittent high angle faulting, both older and younger than the dikes, has continued since the Laramide orogeny and has been superimposed on the older structures. This steep faulting combined with the fundamental northwesterly Laramide structural grain to produce the northwesterly trends characteristic of the mountain ridges and valleys of the area.

Studies on photoblastic germination in lettuce seed

It was shown, with the aid of osmotic inhibition of germination, that the action of the far-red-absorbing form of phytochrome (Pf) in promoting germination can be completed even if the seed is held under conditions where germination is not possible. An effect of the continuing action of Pf beyond the point of complete germination promotion was demonstrated by enhancement of germination rate after removal of the osmotically active solute.

Previous reports that the rate of growth in water of seeds freed from the expansion-restricting endosperm is independent of the state of phytochrome were confirmed. However, a marked, phytochrome-mediated enhancement of the growth potential of such seeds was demonstrated through restricting water uptake by incubation in an osmoticum.

An experimental system, utilizing the appearance of a geotropic curvature in the radicle of the excised axial portion of the seed, was developed for more detailed studies of the phytochrome-enhanced growth potential. It was possible to demonstrate the light effect in water as well as in osmotica; this apparently is not possible with de-endospermed entire seeds. As in intact seeds, the effect of the continuing action of Pf is to enhance the rate of the response. Secretion of a chemical inhibitor of growth by the endosperm as a possible mechanism of induction of light sensitivity has been ruled out.

The phytochrome-dependent rate of appearance of geotropic curvature in osmotica is paralleled in time by a similar dependence of the rate of early extension growth of the embryonic axis. Only the first small increment of growth is a differentially responsive to red (R) and far-red (F); the rate of later increase in length is independent of the light regime.

It was shown that the high concentrations of gibberellic acid required for germination promotion in the intact seed are due at least in part to a diffusion barrier in the endosperm, and that the occasional reports in the literature of the ineffectiveness of kinetin are probably due to the same phenomenon. It was shown that gibberellin, like red light, enhances the growth potential of the axis, but kinetin does not. The difference in rates of response obtained after R-irradiation or gibberellin treatment, together with other results reported in the literature, strongly suggests that gibberellic acid and red light promote germination by different means. The idea that kinetin promotes germination by yet another mechanism, probably operating in the cotyledons, was supported through two different experimental approaches.

The phenomenon of temperature-dependent dark germination was examined in detail, using a wide range of both temperatures and incubation times. With the aid of the half-seed system, it was demonstrated that the promotive effect of low temperature on germination could not be due to a low optimum temperature for early growth of the radicle, since the rate of that process increased with increasing temperature, up to the highest temperature used.

It was shown that phytochrome does not function at high temperatures. This fact is of considerable importance in interpreting the phenomenon of thermodormancy, since in the literature only a small part of the effect of high temperature has been ascribed to an effect on phytochrome, and at that, only to an acceleration of dark reversion of Pf to the red-absorbing form of phytochrome (Pr). Partial denaturation of phytochrome may also make some contribution.

It was shown that the germination-promoting effect of low temperature depends on the presence of Pf, and concluded that low temperatures act by delaying or preventing transformation of Pf. Support for the assumption that Pf, not Pr, is the active form of phytochrome in lettuce seeds was drawn from the same evidence.

Attempts to stimulate germination by repeated irradiation with F over relatively prolonged incubation times resulted in failure, as have similar attempts reported in the literature. However, an enhancement of growth potential in the half-seed system by the maintenance of a small amount of Pf over long periods at ordinary temperatures by repeated irradiation with F was demonstrated.

It was observed that cold storage of the dry seed prevents or delays loss of dark dormancy during post-harvest storage. No change in the response of the half-seed in osmoticum to R and F was observed in seeds that has lost dark dormancy; that is, no internal change took place to measurably increase the growth potential of the embryonic axis. This suggests that the endosperm is the seat of changes responsible for after-ripening of photoblastic lettuce seed.

A generalized Hausdorff dimension for functions and sets

Let E be a compact subset of the n-dimensional unit cube, 1_n, and let C be a collection of convex bodies, all of positive n-dimensional Lebesgue measure, such that C contains bodies with arbitrarily small measure. The dimension of E with respect to the covering class C is defined to be the number

d_C(E) = sup(β:H_{β, C}(E) > 0),

where H_{β, C} is the outer measure

inf(Ʃm(C_i)^β:UC_i Ↄ E, C_i ϵ C) .

Only the one and two-dimensional cases are studied. Moreover, the covering classes considered are those consisting of intervals and rectangles, parallel to the coordinate axes, and those closed under translations. A covering class is identified with a set of points in the left-open portion, 1’_n, of 1_n, whose closure intersects 1_n - 1’_n. For n = 2, the outer measure H_{β, C} is adopted in place of the usual:

Inf(Ʃ(diam. (C_i))^β: UC_i Ↄ E, C_i ϵ C),

for the purpose of studying the influence of the shape of the covering sets on the dimension d_C(E).

If E is a closed set in 1₁, let M(E) be the class of all non-decreasing functions μ(x), supported on E with μ(x) = 0, x ≤ 0 and μ(x) = 1, x ≥ 1. Define for each μ ϵ M(E),

d_C(μ) = lim/c → inf/0 log ∆μ(c)/log c , (c ϵ C)

where ∆μ(c) = v/x (μ(x+c) – μ(x)). It is shown that

d_C(E) = sup (d_C(μ):μ ϵ M(E)).

This notion of dimension is extended to a certain class Ӻ of sub-additive functions, and the problem of studying the behavior of d_C(E) as a function of the covering class C is reduced to the study of d_C(f) where f ϵ Ӻ. Specifically, the set of points in 1₁,

(*) {d_B(F), d_C(f)): f ϵ Ӻ}

is characterized by a comparison of the relative positions of the points of B and C. A region of the form (*) is always closed and doubly-starred with respect to the points (0, 0) and (1, 1). Conversely, given any closed region in 1₂, doubly-starred with respect to (0, 0) and (1, 1), there are covering classes B and C such that (*) is exactly that region. All of the results are shown to apply to the dimension of closed sets E. Similar results can be obtained when a finite number of covering classes are considered.

In two dimensions, the notion of dimension is extended to the class M, of functions f(x, y), non-decreasing in x and y, supported on 1₂ with f(x, y) = 0 for x · y = 0 and f(1, 1) = 1, by the formula

d_C(f) = lim/s · t → inf/0 log ∆f(s, t)/log s · t , (s, t) ϵ C

where

∆f(s, t) = V/x, y (f(x+s, y+t) – f(x+s, y) – f(x, y+t) + f(x, t)).

A characterization of the equivalence d_C1(f) = d_C2(f) for all f ϵ M, is given by comparison of the gaps in the sets of products s · t and quotients s/t, (s, t) ϵ C_i (I = 1, 2).

I. The crystal structure of potassium bis(tricyanovinyl)amine. II. Nuclear magnetic resonance studies of alkali halide solutions. III. Elucidation of the intramolecular hydrogen bond in acetylacetone by the deuterium isotope effect on the chemical shift of the bridge hydrogen

Part I

Potassium bis-(tricyanovinyl) amine, K⁺N[C(CN)=C(CN)₂]₂^-, crystallizes in the monoclinic system with the space group Cc and lattice constants, a = 13.346 ± 0.003 Å, c = 8.992 ± 0.003 Å, B = 114.42 ± 0.02°, and Z = 4. Three dimensional intensity data were collected by layers perpendicular to b* and c* axes. The crystal structure was refined by the least squares method with anisotropic temperature factor to an R value of 0.064.

The average carbon-carbon and carbon-nitrogen bond distances in –C-CΞN are 1.441 ± 0.016 Å and 1.146 ± 0.014 Å respectively. The bis-(tricyanovinyl) amine anion is approximately planar. The coordination number of the potassium ion is eight with bond distances from 2.890 Å to 3.408 Å. The bond angle C-N-C of the amine nitrogen is 132.4 ± 1.9°. Among six cyano groups in the molecule, two of them are bent by what appear to be significant amounts (5.0° and 7.2°). The remaining four are linear within the experimental error. The bending can probably be explained by molecular packing forces in the crystals.

Part II

The nuclear magnetic resonance of ⁸¹Br and ¹²⁷I in aqueous solutions were studied. The cation-halide ion interactions were studied by studying the effect of the Li⁺, Na⁺, K⁺, Mg⁺⁺, Cs⁺ upon the line width of the halide ions. The solvent-halide ion interactions were studied by studying the effects of methanol, acetonitrile, and acetone upon the line width of ⁸¹Br and ¹²⁷I in the aqueous solutions. It was found that the viscosity plays a very important role upon the halide ions line width. There is no specific cation-halide ion interaction for those ions such as Mg⁺⁺, Di⁺, Na⁺, and K⁺, whereas the Cs⁺ - halide ion interaction is strong. The effect of organic solvents upon the halide ion line width in aqueous solutions is in the order acetone ˃ acetonitrile ˃ methanol. It is suggested that halide ions do form some stable complex with the solvent molecules and the reason Cs⁺ can replace one of the ligands in the solvent-halide ion complex.

Part III

An unusually large isotope effect on the bridge hydrogen chemical shift of the enol form of pentanedione-2, 4(acetylacetone) and 3-methylpentanedione-2, 4 has been observed. An attempt has been made to interpret this effect. It is suggested from the deuterium isotope effect studies, temperature dependence of the bridge hydrogen chemical shift studies, IR studies in the OH, OD, and C=O stretch regions, and the HMO calculations, that there may probably be two structures for the enol form of acetylacetone. The difference between these two structures arises mainly from the electronic structure of the π-system. The relative population of these two structures at various temperatures for normal acetylacetone and at room temperature for the deuterated acetylacetone were calculated.

Towards in situ Single Cell Systems Biology

Systems-level studies of biological systems rely on observations taken at a resolution lower than the essential unit of biology, the cell. Recent technical advances in DNA sequencing have enabled measurements of the transcriptomes in single cells excised from their environment, but it remains a daunting technical problem to reconstruct in situ gene expression patterns from sequencing data. In this thesis I develop methods for the routine, quantitative in situ measurement of gene expression using fluorescence microscopy.

The number of molecular species that can be measured simultaneously by fluorescence microscopy is limited by the pallet of spectrally distinct fluorophores. Thus, fluorescence microscopy is traditionally limited to the simultaneous measurement of only five labeled biomolecules at a time. The two methods described in this thesis, super-resolution barcoding and temporal barcoding, represent strategies for overcoming this limitation to monitor expression of many genes in a single cell. Super-resolution barcoding employs optical super-resolution microscopy (SRM) and combinatorial labeling via-smFISH (single molecule fluorescence in situ hybridization) to uniquely label individual mRNA species with distinct barcodes resolvable at nanometer resolution. This method dramatically increases the optical space in a cell, allowing a large numbers of barcodes to be visualized simultaneously. As a proof of principle this technology was used to study the S. cerevisiae calcium stress response. The second method, sequential barcoding, reads out a temporal barcode through multiple rounds of oligonucleotide hybridization to the same mRNA. The multiplexing capacity of sequential barcoding increases exponentially with the number of rounds of hybridization, allowing over a hundred genes to be profiled in only a few rounds of hybridization.

The utility of sequential barcoding was further demonstrated by adapting this method to study gene expression in mammalian tissues. Mammalian tissues suffer both from a large amount of auto-fluorescence and light scattering, making detection of smFISH probes on mRNA difficult. An amplified single molecule detection technology, smHCR (single molecule hairpin chain reaction), was developed to allow for the quantification of mRNA in tissue. This technology is demonstrated in combination with light sheet microscopy and background reducing tissue clearing technology, enabling whole-organ sequential barcoding to monitor in situ gene expression directly in intact mammalian tissue.

The methods presented in this thesis, specifically sequential barcoding and smHCR, enable multiplexed transcriptional observations in any tissue of interest. These technologies will serve as a general platform for future transcriptomic studies of complex tissues.

Control mechanisms in the human binocular oculomotor system

A study of human eye movements was made in order to elucidate the nature of the control mechanism in the binocular oculomotor system.

We first examined spontaneous eye movements during monocular and binocular fixation in order to determine the corrective roles of flicks and drifts. It was found that both types of motion correct fixational errors, although flicks are somewhat more active in this respect. Vergence error is a stimulus for correction by drifts but not by flicks, while binocular vertical discrepancy of the visual axes does not trigger corrective movements.

Second, we investigated the non-linearities of the oculomotor system by examining the eye movement responses to point targets moving in two dimensions in a subjectively unpredictable manner. Such motions consisted of hand-limited Gaussian random motion and also of the sum of several non-integrally related sinusoids. We found that there is no direct relationship between the phase and the gain of the oculomotor system. Delay of eye movements relative to target motion is determined by the necessity of generating a minimum afferent (input) signal at the retina in order to trigger corrective eye movements. The amplitude of the response is a function of the biological constraints of the efferent (output) portion of the system: for target motions of narrow bandwidth, the system responds preferentially to the highest frequency; for large bandwidth motions, the system distributes the available energy equally over all frequencies. Third, the power spectra of spontaneous eye movements were compared with the spectra of tracking eye movements for Gaussian random target motions of varying bandwidths. It was found that there is essentially no difference among the various curves. The oculomotor system tracks a target, not by increasing the mean rate of impulses along the motoneurons of the extra-ocular muscles, but rather by coordinating those spontaneous impulses which propagate along the motoneurons during stationary fixation. Thus, the system operates at full output at all times.

Fourth, we examined the relative magnitude and phase of motions of the left and the right visual axes during monocular and binocular viewing. We found that the two visual axes move vertically in perfect synchronization at all frequencies for any viewing condition. This is not true for horizontal motions: the amount of vergence noise is highest for stationary fixation and diminishes for tracking tasks as the bandwidth of the target motion increases. Furthermore, movements of the occluded eye are larger than those of the seeing eye in monocular viewing. This effect is more pronounced for horizontal motions, for stationary fixation, and for lower frequencies.

Finally, we have related our findings to previously known facts about the pertinent nerve pathways in order to postulate a model for the neurological binocular control of the visual axes.

The ionic basis of frequency selectivity in hair cells of the bullfrog's sacculus

Hair cells from the bull frog's sacculus, a vestibular organ responding to substrate-borne vibration, possess electrically resonant membrane properties which maximize the sensitivity of each cell to a particular frequency of mechanical input. The electrical resonance of these cells and its underlying ionic basis were studied by applying gigohm-seal recording techniques to solitary hair cells enzymatically dissociated from the sacculus. The contribution of electrical resonance to frequency selectivity was assessed from microelectrode recordings from hair cells in an excised preparation of the sacculus.

Electrical resonance in the hair cell is demonstrated by damped membrane-potential oscillations in response to extrinsic current pulses applied through the recording pipette. This response is analyzed as that of a damped harmonic oscillator. Oscillation frequency rises with membrane depolarization, from 80-160 Hz at resting potential to asymptotic values of 200-250 Hz. The sharpness of electrical tuning, denoted by the electrical quality factor, Q_e, is a bell-shaped function of membrane voltage, reaching a maximum value around eight at a membrane potential slightly positive to the resting potential.

In whole cells, three time-variant ionic currents are activated at voltages more positive than -60 to -50 mV; these are identified as a voltage-dependent, non-inactivating Ca current (I_ca), a voltage-dependent, transient K current (I_a), and a Ca-dependent K current (I_c). The C channel is identified in excised, inside-out membrane patches on the basis of its large conductance (130-200 pS), its selective permeability to Kover Na or Cl, and its activation by internal Ca ions and membrane depolarization. Analysis of open- and closed-lifetime distributions suggests that the C channel can assume at least two open and three closed kinetic states.

Exposing hair cells to external solutions that inhibit the Ca or C conductances degrades the electrical resonance properties measured under current-clamp conditions, while blocking the A conductance has no significant effect, providing evidence that only the Ca and C conductances participate in the resonance mechanism. To test the sufficiency of these two conductances to account for electrical resonance, a mathematical model is developed that describes I_ca, I_c, and intracellular Ca concentration during voltage-clamp steps. I_ca activation is approximated by a third-order Hodgkin-Huxley kinetic scheme. Ca entering the cell is assumed to be confined to a small submembrane compartment which contains an excess of Ca buffer; Ca leaves this space with first-order kinetics. The Ca- and voltage-dependent activation of C channels is described by a five-state kinetic scheme suggested by the results of single-channel observations. Parameter values in the model are adjusted to fit the waveforms of I_ca and I_c evoked by a series of voltage-clamp steps in a single cell. Having been thus constrained, the model correctly predicts the character of voltage oscillations produced by current-clamp steps, including the dependencies of oscillation frequency and Q_e on membrane voltage. The model shows quantitatively how the Ca and C conductances interact, via changes in intracellular Ca concentration, to produce electrical resonance in a vertebrate hair cell.