On the Origins of Life — Modelling the Initial Stages of Complex Coacervate Droplet Formation

Coacervate droplets are considered a plausible model for protocells due to their spontaneous formation and ability to compartmentalize macromolecules such as nucleic acid and peptides. Although experimental studies have observed and synthesized coacervates under different laboratory conditions, little is known about their structure. Here we present atomistic molecular dynamic simulations of the interactions between water and oppositely charged proteins that cluster together in a salt-dependent process. Observing such liquid-liquid phase separation on an atomic level would serve as a model for the initial stages of complex coacervate formation. Molecular Dynamics was used to compute diagnostics of the structure at different NaCl concentrations. Limitation of this study are the time constraint and cell size. Modelling coacervate formation is not only important to the origins of life research, but it would also deepen our understanding of membraneless organelles, their role in diseases, and many other fields such as material sciences

Highly accurate operator factorization methods for the integral fractional Laplacian and its generalization

In this paper, we propose a new class of operator factorization methods to discretize the integral fractional Laplacian $(-\Delta)^\frac{\alpha}{2}$ for $\alpha \in (0, 2)$. The main advantage of our method is to easily increase numerical accuracy by using high-degree Lagrange basis functions, but remain the scheme structure and computer implementation unchanged. Moreover, our discretization of the fractional Laplacian results in a symmetric (multilevel) Toeplitz differentiation matrix, which not only saves memory cost in simulations but enables efficient computations via the fast Fourier transforms. The performance of our method in both approximating the fractional Laplacian and solving the fractional Poisson problems was detailedly examined. It shows that our method has an optimal accuracy of ${\mathcal O}(h^2)$ for constant or linear basis functions, while ${\mathcal O}(h^4)$ if quadratic basis functions are used, with $h$ a small mesh size. Note that this accuracy holds for any $\alpha \in (0, 2)$ and can be further increased if higher-degree basis functions are used. If the solution of fractional Poisson problem satisfies $u \in C^{m, l}(\bar{\Omega})$ for $m \in {\mathbb N}$ and $0 < l < 1$, then our method has an accuracy of ${\mathcal O}\big(h^{\min\{m+l,\, 2\}}\big)$ for constant and linear basis functions, while ${\mathcal O}\big(h^{\min\{m+l,\, 4\}}\big)$ for quadratic basis functions. Additionally, our method can be readily applied to study generalized fractional Laplacians with a symmetric kernel function, and numerical study on the tempered fractional Poisson problem demonstrates its efficiency.Comment: 21 pages, 7 figure

Adipocyte Liver Kinase b1 Suppresses Beige Adipocyte Renaissance Through Class IIa Histone Deacetylase 4.

Uncoupling protein 1+ beige adipocytes are dynamically regulated by environment in rodents and humans; cold induces formation of beige adipocytes, whereas warm temperature and nutrient excess lead to their disappearance. Beige adipocytes can form through de novo adipogenesis; however, how "beiging" characteristics are maintained afterward is largely unknown. In this study, we show that beige adipocytes formed postnatally in subcutaneous inguinal white adipose tissue lost thermogenic gene expression and multilocular morphology at the adult stage, but cold restored their beiging characteristics, a phenomenon termed beige adipocyte renaissance. Ablation of these postnatal beige adipocytes inhibited cold-induced beige adipocyte formation in adult mice. Furthermore, we demonstrated that beige adipocyte renaissance was governed by liver kinase b1 and histone deacetylase 4 in white adipocytes. Although neither presence nor thermogenic function of uncoupling protein 1+ beige adipocytes contributed to metabolic fitness in adipocyte liver kinase b1-deficient mice, our results reveal an unexpected role of white adipocytes in maintaining properties of preexisting beige adipocytes

Information-Coupled Turbo Codes for LTE Systems

We propose a new class of information-coupled (IC) Turbo codes to improve the transport block (TB) error rate performance for long-term evolution (LTE) systems, while keeping the hybrid automatic repeat request protocol and the Turbo decoder for each code block (CB) unchanged. In the proposed codes, every two consecutive CBs in a TB are coupled together by sharing a few common information bits. We propose a feed-forward and feed-back decoding scheme and a windowed (WD) decoding scheme for decoding the whole TB by exploiting the coupled information between CBs. Both decoding schemes achieve a considerable signal-to-noise-ratio (SNR) gain compared to the LTE Turbo codes. We construct the extrinsic information transfer (EXIT) functions for the LTE Turbo codes and our proposed IC Turbo codes from the EXIT functions of underlying convolutional codes. An SNR gain upper bound of our proposed codes over the LTE Turbo codes is derived and calculated by the constructed EXIT charts. Numerical results show that the proposed codes achieve an SNR gain of 0.25 dB to 0.72 dB for various code parameters at a TB error rate level of $10^{-2}$, which complies with the derived SNR gain upper bound.Comment: 13 pages, 12 figure

The Evolution of Measurement Methods of Comparative Advantage and New Trends in IntraProduct International Specialization

In the development and the evolution of international trade theory, comparative advantage has always been a core concept. A great deal of research pertains to the calculation methods of comparative advantage. However, most previous research on measurement methods of comparative advantage is mainly based on a country's import/export volume of a specific industry or product. Under the circumstances of contemporary intra-product international specialization, previous measurement methods are not appropriate. It is imperative to improve original measure methods of comparative advantage through stripping overseas contents of exports, and putting forward a new measurement index reflecting the domestic contents of export

A unified meshfree pseudospectral method for solving both classical and fractional PDEs

In this paper, we propose a meshfree method based on the Gaussian radial basis function (RBF) to solve both classical and fractional PDEs. The proposed method takes advantage of the analytical Laplacian of Gaussian functions so as to accommodate the discretization of the classical and fractional Laplacian in a single framework and avoid the large computational cost for numerical evaluation of the fractional derivatives. These important merits distinguish it from other numerical methods for fractional PDEs. Moreover, our method is simple and easy to handle complex geometry and local refinement, and its computer program implementation remains the same for any dimension $d \ge 1$. Extensive numerical experiments are provided to study the performance of our method in both approximating the Dirichlet Laplace operators and solving PDE problems. Compared to the recently proposed Wendland RBF method, our method exactly incorporates the Dirichlet boundary conditions into the scheme and is free of the Gibbs phenomenon as observed in the literature. Our studies suggest that to obtain good accuracy the shape parameter cannot be too small or too big, and the optimal shape parameter might depend on the RBF center points and the solution properties.Comment: 24 pages; 15 figure

Structural Studies of the Integrator Complex -- pre-UsnRNA 3'-end Processing Machinery

The Integrator complex (INT) is a metazoan-specific group of proteins associated with RNA polymerase II (Pol II) that has important functions in the 3'-end processing of noncodng RNAs, including uridine-rich small nuclear RNA (UsnRNA) and enhancer RNA (eRNA). Recently, INT has also been reported to be involved in Pol II transcriptional regulation of protein-encoding genes. INT contains at least 14 subunits, but the function of each subunit is difficult to predicted, because most subunits lack identifiable domains and display little similarity with other proteins. The endonuclease activity of INT is carried out by its subunit 11 (IntS11), which belongs to the metallo--lactamase superfamily and is a paralog of CPSF-73, the endonuclease for pre-mRNA 3'-end processing. IntS11 forms a stable complex with INT subunit 9 (IntS9) through their C-terminal domains (CTDs). This dissertation describes the crystal structure of the IntS9-IntS11 CTD complex at 2.1-Å resolution and summaries the structure-based biochemical and functional studies. The complex is composed of a continuous nine-stranded -sheet with four strands from IntS9 CTD and five from IntS11 CTD. Highly conserved residues are located in the interface between the two CTDs. The structural observations on the complex are confirmed by yeast two-hybrid assays and coimmunoprecipitation experiments. Functional studies demonstrate that the Int9-IntS11 interaction is crucial for proper INT function in snRNA 3'-end processing. The dissertation also presents the structural studies of a newly found mammalian mRNA deNADding enzyme, Nudt12. We determined the crystal structure of mouse Nudt12 in complex with the deNADding product AMP and three Mg2+ ions at 1.6-Å resolution. The structure provides exquisite insights into the molecular basis of the deNADding activity within the NAD pyrophosphate. Previous studies have reported that NAD-capped mRNAs in mammalian cells are hydrolyzed by the DXO deNADding enzyme. Together with biochemical and functional studies, we demonstrate that Nudt12 is a second mammalian deNADding enzyme structurally and mechanistically distinct from DXO and targets different RNAs