Dynamic Ligand Discrimination in the Notch Signaling Pathway

The Notch signaling pathway comprises multiple ligands that are used in distinct biological contexts. In principle, different ligands could activate distinct target programs in signal-receiving cells, but it is unclear how such ligand discrimination could occur. Here, we show that cells use dynamics to discriminate signaling by the ligands Dll1 and Dll4 through the Notch1 receptor. Quantitative single-cell imaging revealed that Dll1 activates Notch1 in discrete, frequency-modulated pulses that specifically upregulate the Notch target gene Hes1. By contrast, Dll4 activates Notch1 in a sustained, amplitude-modulated manner that predominantly upregulates Hey1 and HeyL. Ectopic expression of Dll1 or Dll4 in chick neural crest produced opposite effects on myogenic differentiation, showing that ligand discrimination can occur in vivo. Finally, analysis of chimeric ligands suggests that ligand-receptor clustering underlies dynamic encoding of ligand identity. The ability of the pathway to utilize ligands as distinct communication channels has implications for diverse Notch-dependent processes

Storage Qubits and Their Potential Implementation Through a Semiconductor Double Quantum Dot

In the context of a semiconductor based implementation of a quantum computer the idea of a quantum storage bit is presented and a possible implementation using a double quantum dot structure is considered. A measurement scheme using a stimulated Raman adiabatic passage is discussed.Comment: Revised version accepted for publication in Phys.Rev. B. 19 pages, 4 eps figure

An Electronic Mach-Zehnder Interferometer

Double-slit electron interferometers, fabricated in high mobility two-dimensional electron gas (2DEG), proved to be very powerful tools in studying coherent wave-like phenomena in mesoscopic systems. However, they suffer from small fringe visibility due to the many channels in each slit and poor sensitivity to small currents due to their open geometry. Moreover, the interferometers do not function in a high magnetic field, namely, in the quantum Hall effect (QHE) regime, since it destroys the symmetry between left and right slits. Here, we report on the fabrication and operation of a novel, single channel, two-path electron interferometer that functions in a high magnetic field. It is the first electronic analog of the well-known optical Mach-Zehnder (MZ) interferometer. Based on single edge state and closed geometry transport in the QHE regime the interferometer is highly sensitive and exhibits very high visibility (62%). However, the interference pattern decays precipitously with increasing electron temperature or energy. While we do not understand the reason for the dephasing we show, via shot noise measurement, that it is not a decoherence process that results from inelastic scattering events.Comment: to appear in Natur

Cis-interactions between Notch and Delta generate mutually exclusive signalling states

The Notch–Delta signalling pathway allows communication between neighbouring cells during development^1. It has a critical role in the formation of ‘fine-grained’ patterns, generating distinct cell fates among groups of initially equivalent neighbouring cells and sharply delineating neighbouring regions in developing tissues. The Delta ligand has been shown to have two activities: it transactivates Notch in neighbouring cells and cis-inhibits Notch in its own cell. However, it remains unclear how Notch integrates these two activities and how the resulting system facilitates pattern formation. Here we report the development of a quantitative time-lapse microscopy platform for analysing Notch–Delta signalling dynamics in individual mammalian cells, with the aim of addressing these issues. By controlling both cis- and trans-Delta concentrations, and monitoring the dynamics of a Notch reporter, we measured the combined cis–trans input–output relationship in the Notch–Delta system. The data revealed a striking difference between the responses of Notch to trans- and cis-Delta: whereas the response to trans-Delta is graded, the response to cis-Delta is sharp and occurs at a fixed threshold, independent of trans-Delta. We developed a simple mathematical model that shows how these behaviours emerge from the mutual inactivation of Notch and Delta proteins in the same cell. This interaction generates an ultrasensitive switch between mutually exclusive sending (high Delta/low Notch) and receiving (high Notch/low Delta) signalling states. At the multicellular level, this switch can amplify small differences between neighbouring cells even without transcription-mediated feedback. This Notch–Delta signalling switch facilitates the formation of sharp boundaries and lateral-inhibition patterns in models of development, and provides insight into previously unexplained mutant behaviours

Rules for biological regulation based on error minimization

The control of gene expression involves complex mechanisms that show large variation in design. For example, genes can be turned on either by the binding of an activator (positive control) or the unbinding of a repressor (negative control). What determines the choice of mode of control for each gene? This study proposes rules for gene regulation based on the assumption that free regulatory sites are exposed to nonspecific binding errors, whereas sites bound to their cognate regulators are protected from errors. Hence, the selected mechanisms keep the sites bound to their designated regulators for most of the time, thus minimizing fitness-reducing errors. This offers an explanation of the empirically demonstrated Savageau demand rule: Genes that are needed often in the natural environment tend to be regulated by activators, and rarely needed genes tend to be regulated by repressors; in both cases, sites are bound for most of the time, and errors are minimized. The fitness advantage of error minimization appears to be readily selectable. The present approach can also generate rules for multi-regulator systems. The error-minimization framework raises several experimentally testable hypotheses. It may also apply to other biological regulation systems, such as those involving protein-protein interactions.Comment: biological physics, complex networks, systems biology, transcriptional regulation http://www.weizmann.ac.il/complex/tlusty/papers/PNAS2006.pdf http://www.pnas.org/content/103/11/3999.ful

Continuous weak measurement of quantum coherent oscillations

We consider the problem of continuous quantum measurement of coherent oscillations between two quantum states of an individual two-state system. It is shown that the interplay between the information acquisition and the backaction dephasing of the oscillations by the detector imposes a fundamental limit, equal to 4, on the signal-to-noise ratio of the measurement. The limit is universal, e.g., independent of the coupling strength between the detector and system, and results from the tendency of quantum measurement to localize the system in one of the measured eigenstates

Theory of weak continuous measurements in a strongly driven quantum bit

Continuous spectroscopic measurements of a strongly driven superconducting qubit by means of a high-quality tank circuit (a linear detector) are under study. Output functions of the detector, namely, a spectrum of voltage fluctuations and an impedance, are expressed in terms of the qubit spectrum and magnetic susceptibility. The nonequilibrium spectrum of the current fluctuations in the qubit loop and the linear response function of the driven qubit coupled to a heat bath are calculated with Bloch-Redfield and rotating wave approximations. Backaction effects of the qubit on the tank and the tank on the qubit are analyzed quantitatively. We show that the voltage spectrum of the tank provides detailed information about a frequency and a decay rate of Rabi oscillations in the qubit. It is found that both an efficiency of spectroscopic measurement and measurement-induced decoherence of the qubit demonstrate a resonant behaviour as the Rabi frequency approaches the resonant frequency of the tank. We determine conditions when the spectroscopic observation of the Rabi oscillations in the flux qubit with the tank circuit can be considered as a weak continuous quantum measurement.Comment: 28 page

Quantum-Limited Measurement and Information in Mesoscopic Detectors

We formulate general conditions necessary for a linear-response detector to reach the quantum limit of measurement efficiency, where the measurement-induced dephasing rate takes on its minimum possible value. These conditions are applicable to both non-interacting and interacting systems. We assess the status of these requirements in an arbitrary non-interacting scattering based detector, identifying the symmetries of the scattering matrix needed to reach the quantum limit. We show that these conditions are necessary to prevent the existence of information in the detector which is not extracted in the measurement process.Comment: 13 pages, 1 figur

Dephasing and Measurement Efficiency via a Quantum Dot Detector

We study charge detection and controlled dephasing of a mesoscopic system via a quantum dot detector (QDD), where the mesoscopic system and the QDD are capacitively coupled. The QDD is considered to have coherent resonant tunnelling via a single level. It is found that the dephasing rate is proportional to the square of the conductance of the QDD for the Breit-Wigner model, showing that the dephasing is completely different from the shot noise of the detector. The measurement rate, on the other hand, shows a dip near the resonance. Our findings are peculiar especially for a symmetric detector in the following aspect: The dephasing rate is maximum at resonance of the QDD where the detector conductance is insensitive to the charge state of the mesoscopic system. As a result, the efficiency of the detector shows a dip and vanishes at resonance, in contrast to the single-channel symmetric non-resonant detector that has always a maximum efficiency. We find that this difference originates from a very general property of the scattering matrix: The abrupt phase change exists in the scattering amplitudes in the presence of the symmetry, which is insensitive to the detector current but {\em stores} the information of the quantum state of the mesoscopic system.Comment: 7 pages, 3 figure