EVOLUTION OF PROTEIN COMPLEXES IN BACTERIAL SPECIES

Protein complexes are composed of two or more associated polypeptide chains that may have different functions. Protein complexes play a critical role for all processes in life and are considered as highly conserved in evolution. In previous studies, protein complexes from E. coli or Mycoplasma pneumoniae have been characterized experimentally, revealing that a typical bacterial cell has on the order of 500 protein complexes. Using gene homology (orthology), these experimentally-observed complexes can be used to predict protein complexes across many species of bacteria. Surprisingly, the majority of protein complexes is not conserved, demonstrating an unexpected evolutionary flexibility. The current research investigates the evolution of 174 well-characterized (“reference”) protein complexes from E. coli that have three or more subunits. More specifically, we study the evolutionary flexibility by using evidence and patterns of the presence or absence of the subunits across a range of 894 bacterial species and to interpret whether the evolution is due to the loss or gain of a subunit in the protein complex. The purpose of this study is to determine how the presence or absence of a subunit affects the protein complexes’ functionality. We discuss the functional changes observed in a protein complex due to the presence or absence of a particular subunit by using a statistical approach and by confirming its significance.https://scholarscompass.vcu.edu/uresposters/1253/thumbnail.jp

Groundstate asymptotics for a class of singularly perturbed p-Laplacian problems in RN{{\mathbb {R}}}^N

We study the asymptotic behavior of positive groundstate solutions to the quasilinear elliptic equation in the whole space; we give a characterisation of asymptotic regimes as a function of the parameters and show that the behavior of the groundstates is sensitive to the relation of the growth on the nonlinearities and the critical Sobolev exponent

Mixed Chebyshev and Legendre polynomials differentiation matrices for solving initial-boundary value problems

A new form of basis functions structures has been constructed. These basis functions constitute a mix of Chebyshev polynomials and Legendre polynomials. The main purpose of these structures is to present several forms of differentiation matrices. These matrices were built from the perspective of pseudospectral approximation. Also, an investigation of the error analysis for the proposed expansion has been done. Then, we showed the presented matrices' efficiency and accuracy with several test functions. Consequently, the correctness of our matrices is demonstrated by solving ordinary differential equations and some initial boundary value problems. Finally, some comparisons between the presented approximations, exact solutions, and other methods ensured the efficiency and accuracy of the proposed matrices

Existence criteria for fractional differential equations using the topological degree method

In this work, we analyze the fractional order by using the Caputo-Hadamard fractional derivative under the Robin boundary condition. The topological degree method combined with the fixed point methodology produces the desired results. Finally to show how the key findings may be utilized, applications are presented

A new discussion concerning to exact controllability for fractional mixed Volterra-Fredholm integrodifferential equations of order r∈(1,2) with impulses

In this article, we look into the important requirements for exact controllability of fractional impulsive differential systems of order 1<r<2. Definitions of mild solutions are given for fractional integrodifferential equations with impulses. In addition, applying fixed point methods, fractional derivatives, essential conditions, mixed Volterra-Fredholm integrodifferential type, for exact controllability of the solutions are produced. Lastly, a case study is supplied to show the illustration of the primary theorems

Analytical modelling of Tm-doped tellurite glass including cross-relaxation process

In this paper, we present a comprehensive analytical model of Tm able to take into account direct cross-relaxation process. We show that by using an appropriate set of parameters the model is able to properly fit the first part of the fluorescence decay of Tm-doped tellurite glasses for different dopant concentration values. We also compare the model with a full numerical model to investigate its limitations. We assess the model is a valid tool to fit fluorescence properties but for precisely predicting population inversion is limited to doping level up to about 1%. In fact, we show the reverse cross-relaxation process becomes significant in case of higher doping level

Electron-Acoustic (Un)Modulated Structures in a Plasma Having (r, q)-Distributed Electrons: Solitons, Super Rogue Waves, and Breathers

The propagation of electron-acoustic waves (EAWs) in an unmagnetized plasma, comprising (r,q)-distributed hot electrons, cold inertial electrons, and stationary positive ions, is investigated. Both the unmodulated and modulated EAWs, such as solitary waves, rogue waves (RWs), and breathers are discussed. The Sagdeev potential approach is employed to determine the existence domain of electron acoustic solitary structures and study the perfectly symmetric planar nonlinear unmodulated structures. Moreover, the nonlinear Schrödinger equation (NLSE) is derived and its modulated solutions, including first order RWs (Peregrine soliton), higher-order RWs (super RWs), and breathers (Akhmediev breathers and Kuznetsov–Ma soliton) are presented. The effects of plasma parameters and, in particular, the effects of spectral indices r and q, of distribution functions on the characteristics of both unmodulated and modulated EAWs, are examined in detail. In a limited cases, the (r,q) distribution is compared with Maxwellian and kappa distributions. The present investigation may be beneficial to comprehend and predict the modulated and unmodulated electron acoustic structures in laboratory and space plasmas

Analyzing Both Fractional Porous Media and Heat Transfer Equations via Some Novel Techniques

It has been increasingly obvious in recent decades that fractional calculus (FC) plays a key role in many disciplines of applied sciences. Fractional partial differential equations (FPDEs) accurately model various natural physical phenomena and many engineering problems. For this reason, the analytical and numerical solutions to these issues are seriously considered, and different approaches and techniques have been presented to address them. In this work, the FC is applied to solve and analyze the time-fractional heat transfer equation as well as the nonlinear fractional porous media equation with cubic nonlinearity. The idea of solving these equations is based on the combination of the Yang transformation (YT), the homotopy perturbation method (HPM), and the Adomian decomposition method (ADM). These combinations give rise to two novel methodologies, known as the homotopy perturbation transform method (HPTM) and the Yang tranform decomposition method (YTDM). The obtained results show the significance of the accuracy of the suggested approaches. Solutions in various fractional orders are found and discussed. It is noted that solutions at various fractional orders lead to an integer-order solution. The application of the current methodologies to other nonlinear fractional issues in other branches of applied science is supported by their straightforward and efficient process. In addition, the proposed solution methods can help many plasma physics researchers in interpreting the theoretical and practical results

Synchronization Analysis of Multiple Integral Inequalities Driven by Steklov Operator

We construct a subclass of Copson’s integral inequality in this article. In order to achieve this goal, we attempt to use the Steklov operator for generalizing different inequalities of the Copson type relevant to the situations ρ&gt;1 as well as ρ&lt;1. We demonstrate the inequalities with the guidance of basic comparison, Holder’s inequality, and the integration by parts approach. Moreover, some new variations of Hardy’s integral inequality are also presented with the utilization of Steklov operator. We also formulate many remarks and two examples to show the novelty and authenticity of our results

New Localized and Periodic Solutions to a Korteweg–de Vries Equation with Power Law Nonlinearity: Applications to Some Plasma Models

Traveling wave solutions, including localized and periodic structures (e.g., solitary waves, cnoidal waves, and periodic waves), to a symmetry Korteweg–de Vries equation (KdV) with integer and rational power law nonlinearity are reported using several approaches. In the case of the localized wave solutions, i.e., solitary waves, to the evolution equation, two different methods are devoted for this purpose. In the first one, new hypotheses with Cole–Hopf transformation are employed to find general solitary wave solutions. In the second one, the ansatz method with hyperbolic sech algorithm are utilized to obtain a general solitary wave solution. The obtained solutions recover the solitary wave solutions to all one-dimensional KdV equations with a power law nonlinearity, such as the KdV equation with quadratic nonlinearity, the modified KdV (mKdV) equation with cubic nonlinearity, the super KdV equation with quartic nonlinearity, and so on. Furthermore, two different approaches with two different formulas for the Weierstrass elliptic functions (WSEFs) are adopted for deriving some general periodic wave solutions to the evolution equation. Additionally, in the form of Jacobi elliptic functions (JEFs), the cnoidal wave solutions to the KdV-, mKdV-, and SKdV equations are obtained. These results help many authors to understand the mystery of several nonlinear phenomena in different branches of sciences, such as plasma physics, fluid mechanics, nonlinear optics, Bose Einstein condensates, and so on