Kinetic theory of normal quantum fluids

Close to equilibrium, a normal Bose or Fermi fluid can be described by an exact kinetic equation whose kernel is nonlocal in space and time. The general expression derived for the kernel is evaluated to second order in the interparticle potential. The result is a wavevector- and frequency-dependent generalization of the linear Uehling-Uhlenbeck kernel with the Born approximation cross section.

The theory is formulated in terms of second-quantized phase space operators whose equilibrium averages are the n-particle Wigner distribution functions. Convenient expressions for the commutators and anticommutators of the phase space operators are obtained. The two-particle equilibrium distribution function is analyzed in terms of momentum-dependent quantum generalizations of the classical pair distribution function h(k) and direct correlation function c(k). The kinetic equation is presented as the equation of motion of a two -particle correlation function, the phase space density-density anticommutator, and is derived by a formal closure of the quantum BBGKY hierarchy. An alternative derivation using a projection operator is also given. It is shown that the method used for approximating the kernel by a second order expansion preserves all the sum rules to the same order, and that the second-order kernel satisfies the appropriate positivity and symmetry conditions.

Synthetic regulation of eukaryotic gene expression by noncoding RNA

Synthetic biological systems promise to combine the spectacular diversity of biological functionality with engineering principles to design new life to address many pressing needs. As these engineered systems advance in sophistication, there is ever-greater need for customizable, situation-specific expression of desired genes. However, existing gene control platforms are generally not modular, or do not display performance requirements required for robust phenotypic responses to input signals. This work expands the capabilities of eukaryotic gene control in two important directions.

For development of greater modularity, we extend the use of synthetic self-cleaving ribozyme switches to detect changes in input protein levels and convey that information into programmed gene expression in eukaryotic cells. We demonstrate both up- and down-regulation of levels of an output transgene by more than 4-fold in response to rising input protein levels, with maximal output gene expression approaching the highest levels observed in yeast. In vitro experiments demonstrate protein-dependent ribozyme activity modulation. We further demonstrate the platform in mammalian cells. Our switch devices do not depend on special input protein activity, and can be tailored to respond to any input protein to which a suitable RNA aptamer can be developed. This platform can potentially be employed to regulate the expression of any transgene or any endogenous gene by 3’ UTR replacement, allowing for more complex cell state-specific reprogramming.

We also address an important concern with ribozyme switches, and riboswitch performance in general, their dynamic range. While riboswitches have generally allowed for versatile and modular regulation, so far their dynamic ranges of output gene modulation have been modest, generally at most 10-fold. We address this shortcoming by developing a modular genetic amplifier for near-digital control of eukaryotic gene expression. We combine ribozyme switch-mediated regulation of a synthetic TF with TF-mediated regulation of an output gene. The amplifier platform allows for as much as 20-fold regulation of output gene expression in response to input signal, with maximal expression approaching the highest levels observed in yeast, yet being tunable to intermediate and lower expression levels. EC50 values are more than 4 times lower than in previously best-performing non-amplifier ribozyme switches. The system design retains the modular-input architecture of the ribozyme switch platform, and the near-digital dynamic ranges of TF-based gene control.

Together, these developments suggest great potential for the wide applicability of these platforms for better-performing eukaryotic gene regulation, and more sophisticated, customizable reprogramming of cellular activity.