Two-Dimensional Magnetic Resonance Tomographic Microscopy using Ferromagnetic Probes

We introduce the concept of computerized tomographic microscopy in magnetic resonance imaging using the magnetic fields and field gradients from a ferromagnetic probe. We investigate a configuration where a two-dimensional sample is under the influence of a large static polarizing field, a small perpendicular radio-frequency field, and a magnetic field from a ferromagnetic sphere. We demonstrate that, despite the non-uniform and non-linear nature of the fields from a microscopic magnetic sphere, the concepts of computerized tomography can be applied to obtain proper image reconstruction from the original spectral data by sequentially varying the relative sample-sphere angular orientation. The analysis shows that the recent proposal for atomic resolution magnetic resonance imaging of discrete periodic crystal lattice planes using ferromagnetic probes can also be extended to two-dimensional imaging of non-crystalline samples with resolution ranging from micrometer to Angstrom scales.Comment: 9 pages, 11 figure

Metabolic engineering of Saccharomyces cerevisiae to produce a reduced viscosity oil from lignocellulose

Citation: Tran, T. N. T., Breuer, R. J., Narasimhan, R. A., Parreiras, L. S., Zhang, Y. P., Sato, T. K., & Durrett, T. P. (2017). Metabolic engineering of Saccharomyces cerevisiae to produce a reduced viscosity oil from lignocellulose. Biotechnology for Biofuels, 10, 12. doi:10.1186/s13068-017-0751-yBackground: Acetyl-triacylglycerols (acetyl-TAGs) are unusual triacylglycerol (TAG) molecules that contain an sn-3 acetate group. Compared to typical triacylglycerol molecules (here referred to as long chain TAGs; lcTAGs), acetyl-TAGs possess reduced viscosity and improved cold temperature properties, which may allow direct use as a drop-in diesel fuel. Their different chemical and physical properties also make acetyl-TAGs useful for other applications such as lubricants and plasticizers. Acetyl-TAGs can be synthesized by EaDAcT, a diacylglycerol acetyltransferase enzyme originally isolated from Euonymus alatus (Burning Bush). The heterologous expression of EaDAcT in different organisms, including Saccharomyces cerevisiae, resulted in the accumulation of acetyl-TAGs in storage lipids. Microbial conversion of lignocellulose into acetyl-TAGs could allow biorefinery production of versatile molecules for biofuel and bioproducts. Results: In order to produce acetyl-TAGs from abundant lignocellulose feedstocks, we expressed EaDAcT in S. cerevisiae previously engineered to utilize xylose as a carbon source. The resulting strains were capable of producing acetyl-TAGs when grown on different media. The highest levels of acetyl-TAG production were observed with growth on synthetic lab media containing glucose or xylose. Importantly, acetyl-TAGs were also synthesized by this strain in ammonia fiber expansion (AFEX)-pretreated corn stover hydrolysate (ACSH) at higher volumetric titers than previously published strains. The deletion of the four endogenous enzymes known to contribute to lcTAG production increased the proportion of acetyl-TAGs in the total storage lipids beyond that in existing strains, which will make purification of these useful lipids easier. Surprisingly, the strains containing the four deletions were still capable of synthesizing lcTAG, suggesting that the particular strain used in this study possesses additional undetermined diacylglycerol acyltransferase activity. Additionally, the carbon source used for growth influenced the accumulation of these residual lcTAGs, with higher levels in strains cultured on xylose containing media. Conclusion: Our results demonstrate that S. cerevisiae can be metabolically engineered to produce acetyl-TAGs when grown on different carbon sources, including hydrolysate derived from lignocellulose. Deletion of four endogenous acyltransferases enabled a higher purity of acetyl-TAGs to be achieved, but lcTAGs were still synthesized. Longer incubation times also decreased the levels of acetyl-TAGs produced. Therefore, additional work is needed to further manipulate acetyl-TAG production in this strain of S. cerevisiae, including the identification of other TAG biosynthetic and lipolytic enzymes and a better understanding of the regulation of the synthesis and degradation of storage lipids

A Carleman type theorem for proper holomorphic embeddings

In 1927, Carleman showed that a continuous, complex-valued function on the real line can be approximated in the Whitney topology by an entire function restricted to the real line. In this paper, we prove a similar result for proper holomorphic embeddings. Namely, we show that a proper \cC^r embedding of the real line into \C^n can be approximated in the strong \cC^r topology by a proper holomorphic embedding of \C into \C^n

The instanton contributions to Yang-Mills theory on the torus: localization, Wilson loops and the perturbative expansion

The instanton contributions to the partition function and to homologically trivial Wilson loops for a U(N) Yang-Mills theory on a torus $T^2$ are analyzed. An exact expression for the partition function is obtained as a sum of contributions localized around the classical solutions of Yang-Mills equations, that appear according to the general classification of Atiyah and Bott. Explicit expressions for the exact Wilson loop averages are obtained when N=2, N=3. For general $N$ the contribution of the zero-instanton sector has been carefully derived in the decompactification limit, reproducing the sum of the perturbative series on the plane, in which the light-cone gauge Yang-Mills propagator is prescribed according to Wu-Mandelstam-Leibbrandt (WML). Agreement with the results coming from $S^2$ is therefore obtained, confirming the truly perturbative nature of the WML computations.Comment: 28 pages, revtex, no figure

Spontaneous Interlayer Charge Transfer near the Magnetic Quantum Limit

Experiments reveal that a confined electron system with two equally-populated layers at zero magnetic field can spontaneously break this symmetry through an interlayer charge transfer near the magnetic quantum limit. New fractional quantum Hall states at unusual total filling factors such as \nu = 11/15 (= 1/3 + 2/5) stabilize as signatures that the system deforms itself, at substantial electrostatic energy cost, in order to gain crucial correlation energy by "locking in" separate incompressible liquid phases at unequal fillings in the two layers (e.g., layered 1/3 and 2/5 states in the case of \nu = 11/15).Comment: 4 pages, 4 figures (1 color) included in text. Related papers at http://www.ee.princeton.edu/~hari/papers.htm

Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups

In this paper, we construct a Lagrangian submanifold of the moduli space associated to the fundamental group of a punctured Riemann surface (the space of representations of this fundamental group into a compact connected Lie group). This Lagrangian submanifold is obtained as the fixed-point set of an anti-symplectic involution defined on the moduli space. The notion of decomposable representation provides a geometric interpretation of this Lagrangian submanifold

A natural Finsler--Laplace operator

We give a new definition of a Laplace operator for Finsler metric as an average with regard to an angle measure of the second directional derivatives. This definition uses a dynamical approach due to Foulon that does not require the use of connections nor local coordinates. We show using 1-parameter families of Katok--Ziller metrics that this Finsler--Laplace operator admits explicit representations and computations of spectral data.Comment: 25 pages, v2: minor modifications, changed the introductio

Real-time non-equilibrium dynamics of quantum glassy systems

We develop a systematic analytic approach to aging effects in quantum disordered systems in contact with an environment. Within the closed-time path-integral formalism we include dissipation by coupling the system to a set of independent harmonic oscillators that mimic a quantum thermal bath. After integrating over the bath variables and averaging over disorder we obtain an effective action that determines the real-time dynamics of the system. The classical limit yields the Martin-Siggia-Rose generating functional associated to a colored noise. We apply this general formalism to a prototype model related to the $p$ spin-glass. We show that the model has a dynamic phase transition separating the paramagnetic from the spin-glass phase and that quantum fluctuations depress the transition temperature until a quantum critical point is reached. We show that the dynamics in the paramagnetic phase is stationary but presents an interesting crossover from a region controlled by the classical critical point to another one controlled by the quantum critical point. The most characteristic property of the dynamics in a glassy phase, namely aging, survives the quantum fluctuations. In the sub-critical region the quantum fluctuation-dissipation theorem is modified in a way that is consistent with the notion of effective temperatures introduced for the classical case. We discuss these results in connection with recent experiments in dipolar quantum spin-glasses and the relevance of the effective temperatures with respect to the understanding of the low temperature dynamics.Comment: 56 pages, Revtex, 17 figures include

Time-dependent single molecule spectral lines

A general conceptual problem of time-dependent single molecule spectra is discussed theoretically in the framework of recently developed intensity-time-frequency correlation spectroscopy. It is shown that the new method is closely related to a "gedanken" three-pulse photon echo experiment done on an ensemble of identical molecules interacting with statistically identical microscopic environments. The correlation function is an integral transform (under certain conditions a Fourier transform) of the echo amplitude as a function of the delay between the first and the second pulses. [S0163-1829(99)10907-X]

SU(2) WZW Theory at Higher Genera

We compute, by free field techniques, the scalar product of the SU(2) Chern-Simons states on genus > 1 surfaces. The result is a finite-dimensional integral over positions of ``screening charges'' and one complex modular parameter. It uses an effective description of the CS states closely related to the one worked out by Bertram. The scalar product formula allows to express the higher genus partition functions of the WZW conformal field theory by finite-dimensional integrals. It should provide the hermitian metric preserved by the Knizhnik-Zamolodchikov-Bernard connection describing the variations of the CS states under the change of the complex structure of the surface.Comment: 44 pages, IHES/P/94/10, Latex fil