Pattern formation during Caenorhabditis Elegans vulval development

Pattern formation during animal development involves at least three processes: establishment of the competence of precursor cells to respond to intercellular signals, formation of a pattern of different cell fates adopted by precursor cells, and execution of the cell fate by generating a pattern of distinct descendants from precursor cells. I have analyzed the fundamental mechanisms of pattern formation by studying the development of Caenorhabditis elegans vulva.

In C. elegans, six multipotential vulval precursor cells (VPCs) are competent to respond to an inductive signal LIN-3 (EGF) mediated by LET- 23 (RTK) and a lateral signal via LIN-12 (Notch) to form a fixed pattern of 3°-3°-2°-1°-2°-3°. Results from expressing LIN-3 as a function of time in animals lacking endogenous LIN-3 indicate that both VPCs and VPC daughters are competent to respond to LIN-3. Although the daughters of VPCs specified to be 2° or 3° can be redirected to adopt the 1°fate, the decision to adopt the 1° fate is irreversible. Coupling of VPC competence to cell cycle progression reveals that VPC competence may be periodic during each cell cycle and involve LIN-39 (HOM-C). These mechanisms are essential to ensure a bias towards the 1° fate, while preventing an excessive response.

After adopting the 1° fate, the VPC executes its fate by dividing three rounds to form a fixed pattern of four inner vulF and four outer vulE descendants. These two types of descendants can be distinguished by a molecular marker zmp-1::GFP. A short-range signal from the anchor cell (AC), along with signaling between the inner and outer 1° VPC descendants and intrinsic polarity of 1° VPC daughters, patterns the 1° lineage. The Ras and the Wnt signaling pathways may be involved in these mechanisms.

The temporal expression pattern of egl-17::GFP, another marker ofthe 1° fate, correlates with three different steps of 1° fate execution: the commitment to the 1° fate, as well as later steps before and after establishment of the uterine-vulval connection. Six transcription factors, including LIN-1(ETS), LIN-39 (HOM-C), LIN-11(LIM), LIN-29 (zinc finger), COG-1 (homeobox) and EGL-38 (PAX2/5/8), are involved in different steps during 1° fate execution.

Experimental and theoretical studies of Notch signaling-mediated spatial pattern

Notch signaling acts in many diverse developmental spatial patterning processes. To better understand why this particular pathway is employed where it is and how downstream feedbacks interact with the signaling system to drive patterning, we have pursued three aims: (i) to quantitatively measure the Notch system's signal input/output (I/O) relationship in cell culture, (ii) to use the quantitative I/O relationship to computationally predict patterning outcomes of downstream feedbacks, and (iii) to reconstitute a Notch-mediated lateral induction feedback (in which Notch signaling upregulates the expression of Delta) in cell culture. The quantitative Notch I/O relationship revealed that in addition to the trans-activation between Notch and Delta on neighboring cells there is also a strong, mutual cis-inactivation between Notch and Delta on the same cell. This feature tends to amplify small differences between cells. Incorporating our improved understanding of the signaling system into simulations of different types of downstream feedbacks and boundary conditions lent us several insights into their function. The Notch system converts a shallow gradient of Delta expression into a sharp band of Notch signaling without any sort of feedback at all, in a system motivated by the Drosophila wing vein. It also improves the robustness of lateral inhibition patterning, where signal downregulates ligand expression, by removing the requirement for explicit cooperativity in the feedback and permitting an exceptionally simple mechanism for the pattern. When coupled to a downstream lateral induction feedback, the Notch system supports the propagation of a signaling front across a tissue to convert a large area from one state to another with only a local source of initial stimulation. It is also capable of converting a slowly-varying gradient in parameters into a sharp delineation between high- and low-ligand populations of cells, a pattern reminiscent of smooth muscle specification around artery walls. Finally, by implementing a version of the lateral induction feedback architecture modified with the addition of an autoregulatory positive feedback loop, we were able to generate cells that produce enough cis ligand when stimulated by trans ligand to themselves transmit signal to neighboring cells, which is the hallmark of lateral induction.

Applications of frequency modulation interference cancellers to multiaccess communications systems

Cancellation of interfering frequency-modulated (FM) signals is investigated with emphasis towards applications on the cellular telephone channel as an important example of a multiple access communications system. In order to fairly evaluate analog FM multiaccess systems with respect to more complex digital multiaccess systems, a serious attempt to mitigate interference in the FM systems must be made. Information-theoretic results in the field of interference channels are shown to motivate the estimation and subtraction of undesired interfering signals. This thesis briefly examines the relative optimality of the current FM techniques in known interference channels, before pursuing the estimation and subtracting of interfering FM signals.

The capture-effect phenomenon of FM reception is exploited to produce simple interference-cancelling receivers with a cross-coupled topology. The use of phase-locked loop receivers cross-coupled with amplitude-tracking loops to estimate the FM signals is explored. The theory and function of these cross-coupled phase-locked loop (CCPLL) interference cancellers are examined. New interference cancellers inspired by optimal estimation and the CCPLL topology are developed, resulting in simpler receivers than those in prior art. Signal acquisition and capture effects in these complex dynamical systems are explained using the relationship of the dynamical systems to adaptive noise cancellers.

FM interference-cancelling receivers are considered for increasing the frequency reuse in a cellular telephone system. Interference mitigation in the cellular environment is seen to require tracking of the desired signal during time intervals when it is not the strongest signal present. Use of interference cancelling in conjunction with dynamic frequency-allocation algorithms is viewed as a way of improving spectrum efficiency. Performance of interference cancellers indicates possibilities for greatly increased frequency reuse. The economics of receiver improvements in the cellular system is considered, including both the mobile subscriber equipment and the provider's tower (base station) equipment.

The thesis is divided into four major parts and a summary: the introduction, motivations for the use of interference cancellation, examination of the CCPLL interference canceller, and applications to the cellular channel. The parts are dependent on each other and are meant to be read as a whole.

Investigations of noise and of quantum interference in proximity effect bridges

This work reports investigations upon weakly superconducting proximity effect bridges. These bridges, which exhibit the Josephson effects, are produced by bisecting a superconductor with a short (<1µ) region of material whose superconducting transition temperature is below that of the adjacent superconductors. These bridges are fabricated from layered refractory metal thin films whose transition temperature will depend upon the thickness ratio of the materials involved. The thickness ratio is changed in the area of the bridge to lower its transition temperature. This is done through novel photolithographic techniques described in the text, Chapter 2.

If two such proximity effect bridges are connected in parallel, they form a quantum interferometer. The maximum zero voltage current through this circuit is periodically modulated by the magnetic flux through the circuit. At a constant bias current, the modulation of the critical current produces a modulation in the dc voltage across the bridge. This change in dc voltage has been found to be the result of a change in the internal dissipation in the device. A simple model using lumped circuit theory and treating the bridges as quantum oscillators of frequency ω = 2eV/h, where V is the time average voltage across the device, has been found to adequately describe the observed voltage modulation.

The quantum interferometers have been converted to a galvanometer through the inclusion of an integral thin film current path which couples magnetic flux through the interferometer. Thus a change in signal current produces a change in the voltage across the interferometer at a constant bias current. This work is described in Chapter 3 of the text.

The sensitivity of any device incorporating proximity effect bridges will ultimately be determined by the fluctuations in their electrical parameters. He have measured the spectral power density of the voltage fluctuations in proximity effect bridges using a room temperature electronics and a liquid helium temperature transformer to match the very low (~ 0.1 Ω) impedances characteristic of these devices.

We find the voltage noise to agree quite well with that predicted by phonon noise in the normal conduction through the bridge plus a contribution from the superconducting pair current through the bridge which is proportional to the ratios of this current to the time average voltage across the bridge. The total voltage fluctuations are given by <V^2(f ) > = 4kTR^2_d I/V where R_d is the dynamic resistance, I the total current, and V the voltage across the bridge . An additional noise source appears with a strong 1/f^(n) dependence , 1.5 < n < 2, if the bridges are fabricated upon a glass substrate. This excess noise, attributed to thermodynamic temperature fluctuations in the volume of the bridge, increases dramatically on a glass substrate due to the greatly diminished thermal diffusivity of the glass as compared to sapphire.

Quantum Interference and Entanglement of Surface Plasmons

Surface plasma waves arise from the collective oscillations of billions of electrons at the surface of a metal in unison. The simplest way to quantize these waves is by direct analogy to electromagnetic fields in free space, with the surface plasmon, the quantum of the surface plasma wave, playing the same role as the photon. It follows that surface plasmons should exhibit all of the same quantum phenomena that photons do, including quantum interference and entanglement.

Unlike photons, however, surface plasmons suffer strong losses that arise from the scattering of free electrons from other electrons, phonons, and surfaces. Under some circumstances, these interactions might also cause “pure dephasing,” which entails a loss of coherence without absorption. Quantum descriptions of plasmons usually do not account for these effects explicitly, and sometimes ignore them altogether. In light of this extra microscopic complexity, it is necessary for experiments to test quantum models of surface plasmons.

In this thesis, I describe two such tests that my collaborators and I performed. The first was a plasmonic version of the Hong-Ou-Mandel experiment, in which we observed two-particle quantum interference between plasmons with a visibility of 93 ± 1%. This measurement confirms that surface plasmons faithfully reproduce this effect with the same visibility and mutual coherence time, to within measurement error, as in the photonic case.

The second experiment demonstrated path entanglement between surface plasmons with a visibility of 95 ± 2%, confirming that a path-entangled state can indeed survive without measurable decoherence. This measurement suggests that elastic scattering mechanisms of the type that might cause pure dephasing must have been weak enough not to significantly perturb the state of the metal under the experimental conditions we investigated.

These two experiments add quantum interference and path entanglement to a growing list of quantum phenomena that surface plasmons appear to exhibit just as clearly as photons, confirming the predictions of the simplest quantum models.

Nonclassical excitation and quantum interference in a three level atom

Non-classical properties and quantum interference (QI) in two-photon excitation of a three level atom (|1〉), |2〉, |3〉) in a ladder configuration, illuminated by multiple fields in non-classical (squeezed) and/or classical (coherent) states, is studied. Fundamentally new effects associated with quantum correlations in the squeezed fields and QI due to multiple excitation pathways have been observed. Theoretical studies and extrapolations of these findings have revealed possible applications which are far beyond any current capabilities, including ultrafast nonlinear mixing, ultrafast homodyne detection and frequency metrology. The atom used throughout the experiments was Cesium, which was magneto-optically trapped in a vapor cell to produce a Doppler-free sample. For the first part of the work the |1〉 → |2〉 → |3〉 transition (corresponding to the 6S_1/2F = 4 → 6P_3/2F' = 5 → 6D_5/2F" = 6 transition) was excited by using the quantum-correlated signal (Ɛ_s) and idler (Ɛ_i) output fields of a subthreshold non-degenerate optical parametric oscillator, which was tuned so that the signal and idler fields were resonant with the |1〉 → |2〉 and |2〉 → |3〉 transitions, respectively. In contrast to excitation with classical fields for which the excitation rate as a function of intensity has always an exponent greater than or equal to two, excitation with squeezed-fields has been theoretically predicted to have an exponent that approaches unity for small enough intensities. This was verified experimentally by probing the exponent down to a slope of 1.3, demonstrating for the first time a purely non-classical effect associated with the interaction of squeezed fields and atoms. In the second part excitation of the two-photon transition by three phase coherent fields Ɛ₁ , Ɛ₂ and Ɛ₀, resonant with the dipole |1〉 → |2〉 and |2〉 → |3〉 and quadrupole |1〉 → |3〉 transitions, respectively, is studied. QI in the excited state population is observed due to two alternative excitation pathways. This is equivalent to nonlinear mixing of the three excitation fields by the atom. Realizing that in the experiment the three fields are spaced in frequency over a range of 25 THz, and extending this scheme to other energy triplets and atoms, leads to the discovery that ranges up to 100's of THz can be bridged in a single mixing step. Motivated by these results, a master equation model has been developed for the system and its properties have been extensively studied.

Steady surface wave pattern in a shear flow

The subject under investigation concerns the steady surface wave patterns created by small concentrated disturbances acting on a non-uniform flow of a heavy fluid. The initial value problem of a point disturbance in a primary flow having an arbitrary velocity distribution (U(y), 0, 0) in a direction parallel to the undisturbed free surface is formulated. A geometric optics method and the classical integral transformation method are employed as two different methods of solution for this problem. Whenever necessary, the special case of linear shear (i.e. U(y) = 1+ϵy)) is chosen for the purpose of facilitating the final integration of the solution.

The asymptotic form of the solution obtained by the method of integral transforms agrees with the leading terms of the solution obtained by geometric optics when the latter is expanded in powers of small ϵ r.

The overall effect of the shear is to confine the wave field on the downstream side of the disturbance to a region which is smaller than the wave region in the case of uniform flows. If U(y) vanishes, and changes sign at a critical plane y = y_cr (e.g. ϵy_cr = -1 for the case of linear shear), then the boundary of this asymmetric wave field approaches this critical vertical plane. On this boundary the wave crests are all perpendicular to the x-axis, indicating that waves are reflected at this boundary.

Inside the wave field, as in the case of a point disturbance in a uniform primary flow, there exist two wave systems. The loci of constant phases (such as the crests or troughs) of these wave systems are not symmetric with respect to the x-axis. The geometric optics method and the integral transform method yield the same result of these loci for the special case of U(y) = U_o(1 + ϵy) and for large Kr (ϵr ˂˂ 1 ˂˂ Kr).

An expression for the variation of the amplitude of the waves in the wave field is obtained by the integral transform method. This is in the form of an expansion in small ϵr. The zeroth order is identical to the expression for the uniform stream case and is thus not applicable near the boundary of the wave region because it becomes infinite in that neighborhood. Throughout this investigation the viscous terms in the equations of motion are neglected, a reasonable assumption which can be justified when the wavelengths of the resulting waves are sufficiently large.

Investigation of strong earthquake ground motion

The pattern of energy release during the Imperial Valley, California, earthquake of 1940 is studied by analysing the El Centro strong motion seismograph record and records from the Tinemaha seismograph station, 546 km from the epicenter. The earthquake was a multiple event sequence with at least 4 events recorded at El Centro in the first 25 seconds, followed by 9 events recorded in the next 5 minutes. Clear P, S and surface waves were observed on the strong motion record. Although the main part of the earthquake energy was released during the first 15 seconds, some of the later events were as large as M = 5.8 and thus are important for earthquake engineering studies. The moment calculated using Fourier analysis of surface waves agrees with the moment estimated from field measurements of fault offset after the earthquake. The earthquake engineering significance of the complex pattern of energy release is discussed. It is concluded that a cumulative increase in amplitudes of building vibration resulting from the present sequence of shocks would be significant only for structures with relatively long natural period of vibration. However, progressive weakening effects may also lead to greater damage for multiple event earthquakes.

The model with surface Love waves propagating through a single layer as a surface wave guide is studied. It is expected that the derived properties for this simple model illustrate well several phenomena associated with strong earthquake ground motion. First, it is shown that a surface layer, or several layers, will cause the main part of the high frequency energy, radiated from the nearby earthquake, to be confined to the layer as a wave guide. The existence of the surface layer will thus increase the rate of the energy transfer into the man-made structures on or near the surface of the layer. Secondly, the surface amplitude of the guided SH waves will decrease if the energy of the wave is essentially confined to the layer and if the wave propagates towards an increasing layer thickness. It is also shown that the constructive interference of SH waves will cause the zeroes and the peaks in the Fourier amplitude spectrum of the surface ground motion to be continuously displaced towards the longer periods as the distance from the source of the energy release increases.