Karyopherin alpha subtypes and porcine early stage embryo development

Intracellular communication between the nucleus and cytoplasm is critically important for coordinating cellular events during embryogenesis. The karyopherin α/β heterodimer is an intracellular nuclear trafficking system that mediates nuclear import of proteins that bear classical nuclear localization signals (NLSs). Seven karyopherin α subtypes have been identified in the domestic pig, and while each of these karyopherin α subtypes is able to bind to a nuclear localization signal, individual karyopherin α subtypes have been shown to transport specific NLS-bearing proteins. The objective of this study was to determine the developmental requirements of karyopherin α subtypes (KPNAs) during cleavage development in porcine embryos. The purpose of this dissertation was to test the hypothesis that the karyopherin α/β heterodimer-mediated nuclear trafficking pathway serves regulatory roles during cleavage development by selectively partitioning intracellular cargoes, thereby affecting epigenetic modifications, transcription, and embryo developmental potential. We tested our hypothesis via a combination of a series of in vivo and in vitro assays. Our microinjection assay revealed that POU domain, class 3, transcription factor 2 (BRN2, also referred to as POU3F2) adopts a nuclear localization in all nuclei through the 4-cell stage of development, while only a subset of blastomeres in 8-cell stage embryos possess nuclear BRN2. Octamer-binding transcription factor 4 (OCT4) adopts a nuclear localization in all nuclei prior to the 2-cell stage of development, whereas OCT4 is undetectable in nuclei at the 4-cell stage. In vitro binding assays showed that both BRN2 and OCT4 are able to bind with multiple porcine karyopherin α subtypes. Moreover, we tested the impact of KPNA1-depletion in the intracellular localization of BRN2 and the embryo developmental competence via a series of co-microinjection assays. Our results showed that GFP-BRN2 accumulation was significantly reduced in the nuclei of KPNA1-depleted embryos, and KPNA1-depleted embryos possessed significantly fewer nuclei as well as a reduced proportion with the capacity to develop to the 8-cell stage and beyond as compared with the control embryos.^ In summary, the data discussed in this dissertation provide more evidence to support the conclusion that discrete classes of NLS-bearing nuclear proteins may be preferentially imported by individual karyopherin α subtypes. Our data also indicate that KPNA1 might be involved in the transport of transcription factor BRN2 in 4-cell stage embryos. Furthermore, the data suggest that KPNA1 may serve a critical role of partitioning intracellular cargoes that are directly involved in zygotic genome activation, or that direct development immediately after zygotic genome activation, hence affecting early cleavage embryo development

Robust piecewise adaptive control for an uncertain semilinear parabolic distributed parameter systems

In this study, we focus on designing a robust piecewise adaptive controller to globally asymptotically stabilize a semilinear parabolic distributed parameter systems (DPSs) with external disturbance, whose nonlinearities are bounded by unknown functions. Firstly, a robust piecewise adaptive control is designed against the unknown nonlinearity and the external disturbance. Then, by constructing an appropriate Lyapunov–Krasovskii functional candidate (LKFC) and using the Wiritinger’s inequality and a variant of the Agmon’s inequality, it is shown that the proposed robust piecewise adaptive controller not only ensures the globally asymptotic stability of the closed-loop system, but also guarantees a given performance. Finally, two simulation examples are given to verify the validity of the design method

Ground state solutions to a coupled nonlinear logarithmic Hartree system

In this paper, we study the following coupled nonlinear logarithmic Hartree system \begin{align*} \left\{ \displaystyle \begin{array}{ll} \displaystyle -\Delta u+ \lambda_1 u =\mu_1\left( -\frac{1}{2\pi}\ln(|x|) \ast u^2 \right)u+\beta \left( -\frac{1}{2\pi}\ln(|x|) \ast v^2 \right)u, & x \in ~ \mathbb R^2, \vspace{.4cm}\\ -\Delta v+ \lambda_2 v =\mu_2\left( -\frac{1}{2\pi}\ln(|x|) \ast v^2 \right)v +\beta\left( -\frac{1}{2\pi}\ln(|x|) \ast u^2 \right)v, & x \in ~ \mathbb R^2, \end{array} \right.\hspace{1cm} \end{align*} where $\beta, \mu_i, \lambda_i \ (i=1,2)$ are positive constants, $\ast$ denotes the convolution in $\mathbb R^2$. By considering the constraint minimum problem on the Nehari manifold, we prove the existence of ground state solutions for $\beta>0$ large enough. Moreover, we also show that every positive solution is radially symmetric and decays exponentially