Relationship between promoter sequence and its strength in gene expression

In this study, through various tests one theoretical model is presented to describe the relationship between promoter strength and its nucleotide sequence. Our analysis shows that, promoter strength is greatly influenced by nucleotide groups with three adjacent nucleotides in its sequence. Meanwhile, nucleotides in different regions of promoter sequence have different effects on promoter strength. Based on experimental data for {\it E. coli} promoters, our calculations indicate, nucleotides in -10 region, -35 region, and the discriminator region of promoter sequence are more important than those in spacing region for determining promoter strength. With model parameter values obtained by fitting to experimental data, four promoter libraries are theoretically built for the corresponding experimental environments under which data for promoter strength in gene expression has been measured previously

Existence and uniqueness of solution of the differential equation describing the TASEP-LK coupled transport process

In this paper, the existence and uniqueness of solution of a specific differential equation is studied. This equation originates from the description of a coupled process by totally asymmetric simple exclusion process (TASEP) and Langmuir kinetics (LK). In the fields of physics and biology, the properties of the TASEP-LK coupled process have been extensively studied by Monte Carlo simulations and numerical calculations, as well as detailed experiments. However, so far, no rigorous mathematical analysis has been given to the corresponding differential equations, especially their existence and uniqueness of solution. In this paper, using the upper and lower solution method, the existence of solution of the steady state equation is obtained. Then using a generalized maximum principle, we show that the solution constructed from the upper and lower solution method is actually the unique solution in C∞ space. Moreover, the existence and uniqueness of solution of the time dependent differential equation are also obtained in one specific space X\b{eta}. Our results imply that the previous results obtained by numerical calculations and Monte Carlo simulations are theoretically correct, especially the most important phase diagram of particle density along the travel track under different model parameters. The study in this paper provides theoretical foundations for the analysis of TASEP-LK coupled process. At the same time, the methods used in this paper may be instructive for studies about the more general cases of the TASEP-LK process, such as the one with multiple travel tracks or the one with multiple particle species.Comment: This paper has been thoroughly modified and submited again to arXiv by my coauther Jingwei Li. So I think it is betetr for me to withdraw from my account. see arXiv:1905.12235v

Choosing the proper link function for binary data

textSince generalized linear model (GLM) with binary response variable is widely used in many disciplines, many efforts have been made to construct a fit model. However, little attention is paid to the link functions, which play a critical role in GLM model. In this article, we compared three link functions and evaluated different model selection methods based on these three link functions. Also, we provided some suggestions on how to choose the proper link function for binary data.Statistic

Asymptotic-preserving exponential methods for the quantum Boltzmann equation with high-order accuracy

In this paper we develop high-order asymptotic-preserving methods for the spatially inhomogeneous quantum Boltzmann equation. We follow the work in Li and Pareschi, where asymptotic preserving exponential Runge-Kutta methods for the classical inhomogeneous Boltzmann equation were constructed. A major difficulty here is related to the non Gaussian steady states characterizing the quantum kinetic behavior. We show that the proposed schemes work with high-order accuracy uniformly in time for all Planck constants ranging from classical regime to quantum regime, and all Knudsen numbers ranging from kinetic regime to fluid regime. Computational results are presented for both Bose gas and Fermi gas

The coordination chemistry of a chelating tricyclic bisamidine and a new synthetic route to a C(2)-symmetric tricyclic bisamidine

This thesis presents the synthesis of a novel tricyclic bisamidine, 3,2,3-BisAm 9 (2,3,4,6,7,9,10,11-octahydro-pyrazino[1,2-a:4,3-a\u27] dipyrimidine) and its coordination chemistry with transition metals. By comparison with its analogue 2,2,2-BisAm, which has diverse coordination modes including both symmetrical and unsymmetrical chelating as well as metal-bridging coordination modes, 3,2,3-BisAm, with a substantially larger ideal bite angle, only exhibits the chelating mode. The preparation and characterization of its complexes with W(0), Cu(II), Pd(II), Zn(II), Cd(II), Hg(II), Ag(I), and Eu(III) will be discussed in detail. This thesis also describes the completion of a novel multi-step synthesis from S-valine of a C2 symmetric chiral 2,2,2-BisAm 71 (2,9-diisopropyl-2,3,5,6,8,9-hexa hydro-diimidazo [1,2-a;2\u27,1\u27-c] pyrazine, which can potentially serve as a chiral ligand in asymmetric catalysis. In addition, the synthesis of a C 2 symmetric chiral 3,2,3-BisAm 74 was initiated by adopting the same synthetic strategy. On the basis of these studies, a general synthetic route can be developed to prepare C2-symmetric tricyclic bisamidines from chiral amino acids.*