Structural Implementation of Unsatured Systems Driven by Electrophilic Nitrogen-Containing Functional Groups.

The present thesis can be divided into four chapters. The first chapter reports an efficient synthesis of conjugated nitrotrienes and benzothiaziones. The second chapter describes a new simple synthesis of unsymmetrical bisindoylmethanes and their anti-cancer activity test. The third chapter reports the biological tests between soy protein isolate and stilbene representatives. The fourth chapter lists the references and 1H NMR 13C NMR spectra. CHAPTER ONE: Efficient Synthesis of Conjugated Nitrotrienes and Benzothiaziones Nitro-containing compounds are excellent scaffolds for synthesizing small molecules and heterocyclic systems that can be used in pharmaceuticals, agrochemicals, and materials science. β-Nitroenones (1, Figure 1) and β-nitroacrylates (2, Figure 1) can be considered as good starting materials for various targets. This chapter reports a brief overview of the chemistry of nitro-containing compounds and the efficient synthesis of conjugated nitrotrienes and benzothiaziones. For the synthesis of conjugated nitrotrienes, -nitroenones 1 can be allylated with allylboronic pinacol ester 3 to give tertiary homoallylic alcohols 4. Subsequently, 4 can eliminate water to generate the corresponding conjugated nitrotrienes in the presence of the Lewis acid boron trifluoride etherate (Scheme 1). The successful application of this route with a wide range of substituents and the excellent yield obtained demonstrate its versatility. The nitrotrienes are obtained as a mixture of two isomers. However, this procedure can prevent the elimination of the nitro group which is retained in the triene molecule. The critical situation caused by the increasing number of tuberculosis and the synergetic effect between tuberculosis and human immunodeficiency virus or multidrug-resistance makes the discovery of a drug with the structure of benzothiazinone an emergency. Considering the drawbacks of previous studies, such as long reaction times, limited substituents or pretreatment before reaction, a sustainable, convenient one-pot synthesis of benzothiazinones was proposed. The synthesis can be carried out in three steps: (i) Michael addition of -nitroacrylates 2 and aminothiophenols 5 to form adducts 6 under neat condition; (ii) elimination of nitrous acid to afford 7; (iii) intramolecular cyclization to obtain benzothiazinones 8 (Scheme 2). Since solid promoters (carbonate on polymer and Amberlyst-15) were used in the last two steps, the whole three steps can be combined in one-pot procedure by simple filtration and final flash column chromatography. This synthetic method can produce a series of benzothiazinones with good overall yields, in addition, products with different substituents can be prepared. CHAPTER TWO: Synthesis of Unsymmetrical Bisindolylmethanes and Their Anti-cancer Activity Test Bisindolylmethanes, widely distributed in various vegetables, have the ability to regulate plant growth and prevent cancer. Several studies on the synthesis of symmetrical bisindoylmethanes are currently available. However, the development of synthetic protocols for unsymmetrical bisindoylmethanes is limited by the use of harmful Lewis acid or Brønsted acid catalysts and plagued by the formation of by-products or low yield of targets. In this chapter, a new, mild procedure was proposed to obtain unsymmetrical bisindoylmethanes from sulfonyl indoles. Sulfonyl indoles (Lg = SO2Ar) 9 can afford a weakly electrophilic alkylideneindolenine 10 upon basic promoted elimination of arylsulfinic acids. Reaction of intermediate 10 with a rather strong, stabilized nucleophilic indole 11, otained by metalation of indoles with Grignard reagents, can generate the unsymmetrical bisindoylmethanes 12 by a Michael-type process (Scheme 3). The target products with different substituents can be prepared in moderate to excellent yields, and the reaction of pyrrolylmagnesium bromides with sulfonyl indoles under un-optimized conditions showed the wide boundaries of this route. In addition, the anti-cancer activity of five selected compounds was tested and compared with cisplatin. The results indicate that unsymmetrical bisindoylmethanes have anti-cancer activity and can be considered as good anti-cancer reagents. CHAPTER THREE: Effect of the Binding of Piceatannol and Oxyresveratrol to Soybean Protein Isolate on the Structural and Functional Properties Piceatannol (PIC, 13, Figure 2), oxyresveratrol (OXY, 14, Figure 2), and soy protein isolate (SPI) are essential nutritional molecules for a human’s daily life. In this chapter, the interaction between PIC/OXY and SPI was investigated using multiple spectroscopic techniques and molecular docking simulations. Steady-state fluorescence, Förster resonance energy transfer and time-resolved fluorescence spectroscopy confirmed the static quenching mechanism. In addition, the binding affinity of PIC to SPI was stronger than that of OXY, and the interactions were spontaneous and exothermic. The surface hydrophobicity, sulfhydryl group content, particle size, zeta potential, and -helical contents can determine the subtle change in the secondary structure of SPI after binding. The emulsifying and foaming properties of SPI were improved after complexing with PIC or OXY. The molecular docking results and thermodynamic parameters showed that PIC and OXY were bound to SPI at the same sites, van der Waals forces and hydrogen bonds were the main interaction forces. The results also showed that the encapsulation of SPI can enhance the antioxidant activity of PIC and OXY. The in vitro gastrointestinal digestion of PIC and OXY in the presence of SPI helps patients with stomach problems. CHAPTER FOUR: References and 1H NMR 13C NMR Spectra This chapter displays the references and 1H NMR 13C NMR Spectra

Translating Solutions of a Generalized Mean Curvature Flow in a Cylinder: I. Constant Boundary Angles

We study a generalized mean curvature flow involving a positive power of the mean curvature and a driving force. In this paper, we first construct all kinds of radially symmetric translating solutions, and then select one of them to satisfy a prescribed boundary angle in a cylinder. We then consider the flow starting at an initial hypersurface: showing the a priori estimates (especially the uniform-in-time bounds for the mean curvature which guarantee the uniform parabolicity of the corresponding fully nonlinear equation), giving the global existence for the solution of the initial boundary value problem, and proving its convergence to the corresponding translating solution. Our study provides a complete exposition on the influence of the dimension, the power of the mean curvature, the driving force and the boundary angles on the existence and stability of radially symmetric translating solutions.Comment: 29 page

A Mean Curvature Flow Propagating in a Cylinder at Exponential Speed

In this paper, we study the long time behaviour of mean curvature flow in a cylinder with Robin boundary conditions. Such a boundary condition can force the solution to have a singular behaviour at the boundary when $t\to \infty$. The planar version of this problem has been investigated in an existing literature, where the curve shortening flow in $2$-dimensional band with Robin boundary conditions is shown to converge to a translating Grim Reaper with finite speed and fixed profile. By considering a radially symmetric mean curvature flow, denoted by $u(|x|,t)$, in $(N+1)$-dimensional cylinder ($N\geq 2$), we find in the present paper a new feature of the flow: both the interior gradients and the propagating speed of the flow increase to infinity exponentially, $Du/u\sim x$ and $u\sim C_0 e^{(N-1)t}e^{\frac{|x|^2}{2}}$ as $t\to \infty$ for some $C_0>0$, which is completely different from the 2-dimensional case

Convergence to the Grim Reaper for a Curvature Flow with Unbounded Boundary Slopes

We consider a curvature flow $V=H$ in the band domain $\Omega :=[-1,1]\times \R$, where, for a graphic curve $\Gamma_t$, $V$ denotes its normal velocity and $H$ denotes its curvature. If $\Gamma_t$ contacts the two boundaries $\partial_\pm \Omega$ of $\Omega$ with constant slopes, in 1993, Altschular and Wu \cite{AW1} proved that $\Gamma_t$ converges to a {\it grim reaper} contacting $\partial_\pm \Omega$ with the same prescribed slopes. In this paper we consider the case where $\Gamma_t$ contacts $\partial_\pm \Omega$ with slopes equaling to $\pm 1$ times of its height. When the curve moves to infinity, the global gradient estimate is impossible due to the unbounded boundary slopes. We first consider a special symmetric curve and derive its uniform interior gradient estimates by using the zero number argument, and then use these estimates to present uniform interior gradient estimates for general non-symmetric curves, which lead to the convergence of the curve in $C^{2,1}_{loc} ((-1,1)\times \R)$ topology to the {\it grim reaper} with span $(-1,1)$