Squeezing and Dual Recycling in Laser Interferometric Gravitational Wave Detectors

We calculate the response of an ideal Michelson interferometer incorporating both dual recycling and squeezed light to gravitational waves. The photon counting noise has contributions from the light which is sent in through the input ports as well as the vacuum modes at sideband frequencies generated by the gravitational waves. The minimum detectable gravity wave amplitude depends on the frequency of the wave as well as the squeezing and recycling parameters. Both squeezing and the broadband operation of dual recycling reduce the photon counting noise and hence the two techniques can be used together to make more accurate phase measurements. The variance of photon number is found to be time-dependent, oscillating at the gravity wave frequency but of much lower order than the constant part.Comment: Plain tex, 11 pages, 1 figure available on request from [email protected]

A Computational Model for Understanding Stem Cell, Trophectoderm and Endoderm Lineage Determination

Background: Recent studies have associated the transcription factors, Oct4, Sox2 and Nanog as parts of a self-regulating network which is responsible for maintaining embryonic stem cell properties: self renewal and pluripotency. In addition, mutual antagonism between two of these and other master regulators have been shown to regulate lineage determination. In particular, an excess of Cdx2 over Oct4 determines the trophectoderm lineage whereas an excess of Gata-6 over Nanog determines differentiation into the endoderm lineage. Also, under/over-expression studies of the master regulator Oct4 have revealed that some self-renewal/pluripotency as well as differentiation genes are expressed in a biphasic manner with respect to the concentration of Oct4. Methodology/Principal Findings: We construct a dynamical model of a minimalistic network, extracted from ChIP-on-chip and microarray data as well as literature studies. The model is based upon differential equations and makes two plausible assumptions; activation of Gata-6 by Oct4 and repression of Nanog by an Oct4–Gata-6 heterodimer. With these assumptions, the results of simulations successfully describe the biphasic behavior as well as lineage commitment. The model also predicts that reprogramming the network from a differentiated state, in particular the endoderm state, into a stem cell state, is best achieved by over-expressing Nanog, rather than by suppression of differentiation genes such as Gata-6. Conclusions: The computational model provides a mechanistic understanding of how different lineages arise from the dynamics of the underlying regulatory network. It provides a framework to explore strategies of reprogramming a cell from a differentiated state to a stem cell state through directed perturbations. Such an approach is highly relevant to regenerative medicine since it allows for a rapid search over the host of possibilities for reprogramming to a stem cell state

Bifurcation discovery tool

Motivation: Biochemical networks often yield interesting behavior such as switching, oscillation and chaotic dynamics. This article describes a tool that is capable of searching for bifurcation points in arbitrary ODE-based reaction networks by directing the user to regions in the parameter space, where such interesting dynamical behavior can be observed. Results: We have implemented a genetic algorithm that searches for Hopf bifurcations, turning points and bistable switches. The software is implemented as a Systems Biology Workbench (SBW) enabled module and accepts the standard SBML model format. The interface permits a user to choose the parameters to be searched, admissible parameter ranges, and the nature of the bifurcation to be sought. The tool will return the parameter values for the model for which the particular behavior is observed. Availability: The software, tutorial manual and test models are available for download at the following website: http:/www.sys-bio.org/ under the bifurcation link. The software is an open source and licensed under BSD

Probing the role of stochasticity in a model of the embryonic stem cell – heterogeneous gene expression and reprogramming efficiency

Background: Embryonic stem cells (ESC) have the capacity to self-renew and remain pluripotent, while continuously providing a source of a variety of differentiated cell types. Understanding what governs these properties at the molecular level is crucial for stem cell biology and its application to regenerative medicine. Of particular relevance is to elucidate those molecular interactions which govern the reprogramming of somatic cells into ESC. A computational approach can be used as a framework to explore the dynamics of a simplified network of the ESC with the aim to understand how stem cells differentiate and also how they can be reprogrammed from somatic cells. Results: We propose a computational model of the embryonic stem cell network, in which a core set of transcription factors (TFs) interact with each other and are induced by external factors. A stochastic treatment of the network dynamics suggests that NANOG heterogeneity is the deciding factor for the stem cell fate. In particular, our results show that the decision of staying in the ground state or commitment to a differentiated state is fundamentally stochastic, and can be modulated by the addition of external factors (2i/3i media), which have the effect of reducing fluctuations in NANOG expression. Our model also hosts reprogramming of a committed cell into an ESC by over-expressing OCT4. In this context, we recapitulate the important experimental result that reprogramming efficiency peaks when OCT4 is over-expressed within a specific range of values. Conclusions: We have demonstrated how a stochastic computational model based upon a simplified network of TFs in ESCs can elucidate several key observed dynamical features. It accounts for (i) the observed heterogeneity of key regulators, (ii) characterizes the ESC under certain external stimuli conditions and (iii) describes the occurrence of transitions from the ESC to the differentiated state. Furthermore, the model (iv) provides a framework for reprogramming from somatic cells and conveys an understanding of reprogramming efficiency as a function of OCT4 over-expression

Homodyne locking of a squeezer

We report on the successful implementation of a new approach to locking the frequencies of an OPO-based squeezed-vacuum source and its driving laser. The technique allows the simultaneous measurement of the phase-shifts induced by a cavity, which may be used for the purposes of frequency-locking, as well as the simultaneous measurement of the sub-quantum-noise-limited (sub-QNL) phase quadrature output of the OPO. The homodyne locking technique is cheap, easy to implement and has the distinct advantage that subsequent homodyne measurements are automatically phase-locked. The homodyne locking technique is also unique in that it is a sub-QNL frequency discriminator.Comment: Accepted to Optics Letter

Dynamic Resonance of Light in Fabry-Perot Cavities

The dynamics of light in Fabry-Perot cavities with varying length and input laser frequency are analyzed and the exact condition for resonance is derived. This dynamic resonance depends on the light transit time in the cavity and the Doppler effect due to the mirror motions. The response of the cavity to length variations is very different from its response to laser frequency variations. If the frequency of these variations is equal to multiples of the cavity free spectral range, the response to length is maximized while the response to the laser frequency is zero. Implications of these results for the detection of gravitational waves using kilometer-scale Fabry-Perot cavities are discussed

Simulating the Mammalian Blastocyst - Molecular and Mechanical Interactions Pattern the Embryo

Mammalian embryogenesis is a dynamic process involving gene expression and mechanical forces between proliferating cells. The exact nature of these interactions, which determine the lineage patterning of the trophectoderm and endoderm tissues occurring in a highly regulated manner at precise periods during the embryonic development, is an area of debate. We have developed a computational modeling framework for studying this process, by which the combined effects of mechanical and genetic interactions are analyzed within the context of proliferating cells. At a purely mechanical level, we demonstrate that the perpendicular alignment of the animal-vegetal (a-v) and embryonic-abembryonic (eb-ab) axes is a result of minimizing the total elastic conformational energy of the entire collection of cells, which are constrained by the zona pellucida. The coupling of gene expression with the mechanics of cell movement is important for formation of both the trophectoderm and the endoderm. In studying the formation of the trophectoderm, we contrast and compare quantitatively two hypotheses: (1) The position determines gene expression, and (2) the gene expression determines the position. Our model, which couples gene expression with mechanics, suggests that differential adhesion between different cell types is a critical determinant in the robust endoderm formation. In addition to differential adhesion, two different testable hypotheses emerge when considering endoderm formation: (1) A directional force acts on certain cells and moves them into forming the endoderm layer, which separates the blastocoel and the cells of the inner cell mass (ICM). In this case the blastocoel simply acts as a static boundary. (2) The blastocoel dynamically applies pressure upon the cells in contact with it, such that cell segregation in the presence of differential adhesion leads to the endoderm formation. To our knowledge, this is the first attempt to combine cell-based spatial mechanical simulations with genetic networks to explain mammalian embryogenesis. Such a framework provides the means to test hypotheses in a controlled in silico environment

Transcriptional Dynamics of the Embryonic Stem Cell Switch

Recent ChIP experiments of human and mouse embryonic stem cells have elucidated the architecture of the transcriptional regulatory circuitry responsible for cell determination, which involves the transcription factors OCT4, SOX2, and NANOG. In addition to regulating each other through feedback loops, these genes also regulate downstream target genes involved in the maintenance and differentiation of embryonic stem cells. A search for the OCT4–SOX2–NANOG network motif in other species reveals that it is unique to mammals. With a kinetic modeling approach, we ascribe function to the observed OCT4–SOX2–NANOG network by making plausible assumptions about the interactions between the transcription factors at the gene promoter binding sites and RNA polymerase (RNAP), at each of the three genes as well as at the target genes. We identify a bistable switch in the network, which arises due to several positive feedback loops, and is switched on/off by input environmental signals. The switch stabilizes the expression levels of the three genes, and through their regulatory roles on the downstream target genes, leads to a binary decision: when OCT4, SOX2, and NANOG are expressed and the switch is on, the self-renewal genes are on and the differentiation genes are off. The opposite holds when the switch is off. The model is extremely robust to parameter changes. In addition to providing a self-consistent picture of the transcriptional circuit, the model generates several predictions. Increasing the binding strength of NANOG to OCT4 and SOX2, or increasing its basal transcriptional rate, leads to an irreversible bistable switch: the switch remains on even when the activating signal is removed. Hence, the stem cell can be manipulated to be self-renewing without the requirement of input signals. We also suggest tests that could discriminate between a variety of feedforward regulation architectures of the target genes by OCT4, SOX2, and NANOG

Squeezed Light for the Interferometric Detection of High Frequency Gravitational Waves

The quantum noise of the light field is a fundamental noise source in interferometric gravitational wave detectors. Injected squeezed light is capable of reducing the quantum noise contribution to the detector noise floor to values that surpass the so-called Standard-Quantum-Limit (SQL). In particular, squeezed light is useful for the detection of gravitational waves at high frequencies where interferometers are typically shot-noise limited, although the SQL might not be beaten in this case. We theoretically analyze the quantum noise of the signal-recycled laser interferometric gravitational-wave detector GEO600 with additional input and output optics, namely frequency-dependent squeezing of the vacuum state of light entering the dark port and frequency-dependent homodyne detection. We focus on the frequency range between 1 kHz and 10 kHz, where, although signal recycled, the detector is still shot-noise limited. It is found that the GEO600 detector with present design parameters will benefit from frequency dependent squeezed light. Assuming a squeezing strength of -6 dB in quantum noise variance, the interferometer will become thermal noise limited up to 4 kHz without further reduction of bandwidth. At higher frequencies the linear noise spectral density of GEO600 will still be dominated by shot-noise and improved by a factor of 10^{6dB/20dB}~2 according to the squeezing strength assumed. The interferometer might reach a strain sensitivity of 6x10^{-23} above 1 kHz (tunable) with a bandwidth of around 350 Hz. We propose a scheme to implement the desired frequency dependent squeezing by introducing an additional optical component to GEO600s signal-recycling cavity.Comment: Presentation at AMALDI Conference 2003 in Pis