Recent developments and future perspectives in aging and macrophage immunometabolism

Brandt D. Pence; Brandt D. Pence

doi:10.3934/molsci.2021015

AIMS Molecular Science

2021, Volume 8, Issue 3: 193-201. doi: 10.3934/molsci.2021015

Previous Article Next Article

Review

Recent developments and future perspectives in aging and macrophage immunometabolism

Brandt D. Pence ^{1,2
,
,}

1.
College of Health Sciences, University of Memphis, Memphis, TN, USA
2.
Center for Nutraceutical and Dietary Supplement Research, University of Memphis, Memphis, TN, USA

Received: 14 July 2021 Accepted: 24 August 2021 Published: 26 August 2021

Aging is the strongest contributor to the development and severity of many chronic and infectious diseases, primarily through age-related increases in low-grade inflammation (inflammaging) and decreases in immune function (immunosenescence). Metabolic reprogramming in immune cells is a significant contributor to functional and phenotypic changes in these cells, but little is known about the direct effect of aging on immunometabolism. This review highlights several recent advances in this field, focusing on mitochondrial dysfunction, NAD+ metabolism, and therapeutic reprogramming in aged monocytes and macrophages. Perspectives on opportunities for future research in this area are also provided. Targeting immunometabolism is a promising strategy for designing therapeutics for a wide variety of age-related diseases.

Keywords:

Citation: Brandt D. Pence. Recent developments and future perspectives in aging and macrophage immunometabolism[J]. AIMS Molecular Science, 2021, 8(3): 193-201. doi: 10.3934/molsci.2021015

Related Papers:

[1]	M. Mossa Al-Sawalha, Safyan Mukhtar, Azzh Saad Alshehry, Mohammad Alqudah, Musaad S. Aldhabani . Chaotic perturbations of solitons in complex conformable Maccari system. AIMS Mathematics, 2025, 10(3): 6664-6693. doi: 10.3934/math.2025305
[2]	M. B. Almatrafi, Mahmoud A. E. Abdelrahman . The novel stochastic structure of solitary waves to the stochastic Maccari's system via Wiener process. AIMS Mathematics, 2025, 10(1): 1183-1200. doi: 10.3934/math.2025056
[3]	Naseem Abbas, Amjad Hussain, Mohsen Bakouri, Thoraya N. Alharthi, Ilyas Khan . A study of dynamical features and novel soliton structures of complex-coupled Maccari's system. AIMS Mathematics, 2025, 10(2): 3025-3040. doi: 10.3934/math.2025141
[4]	Mohammad Alqudah, Manoj Singh . Applications of soliton solutions of the two-dimensional nonlinear complex coupled Maccari equations. AIMS Mathematics, 2024, 9(11): 31636-31657. doi: 10.3934/math.20241521
[5]	Mahmoud A. E. Abdelrahman, S. Z. Hassan, R. A. Alomair, D. M. Alsaleh . Fundamental solutions for the conformable time fractional Phi-4 and space-time fractional simplified MCH equations. AIMS Mathematics, 2021, 6(6): 6555-6568. doi: 10.3934/math.2021386
[6]	Hammad Alotaibi . Solitary waves of the generalized Zakharov equations via integration algorithms. AIMS Mathematics, 2024, 9(5): 12650-12677. doi: 10.3934/math.2024619
[7]	E. S. Aly, Mahmoud A. E. Abdelrahman, S. Bourazza, Abdullah Ali H. Ahmadini, Ahmed Hussein Msmali, Nadia A. Askar . New solutions for perturbed chiral nonlinear Schrödinger equation. AIMS Mathematics, 2022, 7(7): 12289-12302. doi: 10.3934/math.2022682
[8]	Jamshad Ahmad, Zulaikha Mustafa, Mehjabeen Anwar, Marouan Kouki, Nehad Ali Shah . Exploring solitonic wave dynamics in the context of nonlinear conformable Kairat-X equation via unified method. AIMS Mathematics, 2025, 10(5): 10898-10916. doi: 10.3934/math.2025495
[9]	Azzh Saad Alshehry, Safyan Mukhtar, Ali M. Mahnashi . Optical fractals and Hump soliton structures in integrable Kuralay-Ⅱ system. AIMS Mathematics, 2024, 9(10): 28058-28078. doi: 10.3934/math.20241361
[10]	Yousef F. Alharbi, E. K. El-Shewy, Mahmoud A. E. Abdelrahman . New and effective solitary applications in Schrödinger equation via Brownian motion process with physical coefficients of fiber optics. AIMS Mathematics, 2023, 8(2): 4126-4140. doi: 10.3934/math.2023205

Abstract

1. Introduction

Nonlinear evolution equations (NLEEs) are utilized in order to display many complex phenomena arising in various fields of applied sciences, such as superfluid, chemical engineering, thermal engineering, plasma physics, optical fibers and so on ^{[1,2,3,4,5,6,7,8]}. There are many scientists in various fields of natural sciences are interested in investigation of the nonlinear phenomena. Various vital analytical methods have been proposed and developed to extract the solutions of different kinds of NLEEs, see ^{[9,10,11,12,13,14,15,16,17,18]}. Moreover, there are recent development in studying the dynamics of soliton solutions and analytical closed-form solutions ^{[19,20,21,22,23,24,25,26,27,28,29,30]}.

The Maccari (MS) system, derived by Maccari in 1996 with a reduction technique based on spatio-temporal rescaling, from the Kadomtsev-Petviashvili equation ^[31]. This system is a kind of NLEEs that are often introduced to prescribe the motion of the isolated waves, localized in a small part of space, in various fields such as plasma physics, quantum mechanics, Bose-Einstein condensates, optical fiber communications and so on ^{[32,33,34,35,36,37,38,39]}. Recently, some investigations presented new novel concepts in wave motions and pulses in the study of nonlinear unforeseen critical behaviors such as the electrostatic noise in auroura, the acoustics wave in fluid and telltales wiggle electric fields ^{[40,41,42,43]}.

In this article, we consider the coupled MS ^[32,35,44], given as follows:

$\begin{equation} \begin{array}{l} iQ_t+Q_{xx}+RQ = 0, \\ R_{t}+R_{y}+(\mid Q \mid^2)_{x} = 0, \end{array} \end{equation}$

(1.1)

where $Q = Q(x, y, t)$ denotes the complex scalar field and $R = R(x, y, t)$ denotes the real scalar field. The independent variables are $x, y$ and $t$ denotes the temporal variable.

Also, we can consider the coupled nonlinear MS ^[45], given as follows:

$\begin{equation} \begin{array}{l} iQ_t+Q_{xx}+RQ = 0, \\ i\, S_{t}+S_{xx}+RS = 0, \\ R_{t}+R_{y}+(\mid Q+S \mid^2)_{x} = 0, \end{array} \end{equation}$

(1.2)

where $Q = Q(x, y, t)$ and $S = S(x, y, t)$ denote the complex scalar fields and $R = R(x, y, t)$ denotes the real scalar field.

Moreover, we consider the coupled nonlinear MS ^[34], described as follows:

$\begin{equation} \begin{array}{l} i\, Q_t+Q_{xx}+RQ = 0, \\ i\, S_{t}+S_{xx}+RS = 0, \\ i\, N_{t}+N_{xx}+RN = 0, \\ R_{t}+R_{y}+(\mid Q+S+N \mid^2)_{x} = 0, \end{array} \end{equation}$

(1.3)

where $Q = Q(x, y, t)$ , $S = S(x, y, t)$ , $N = N(x, y, t)$ denote the complex scalar fields and $R = R(x, y, t)$ denotes the real scalar field.

Our study is motivated to grasp some new solutions for the three coupled models of MS by using the unified solver method. This solver introduces some families of solutions in explicit way with free physical parameters. These solutions admit pivotal applications in plasma environments, superfluid, plasma physics, nonlinear optic^[46,47]. The proposed solver will be utilized as a box solver for solving many other nonlinear models arising in applied science and new physics. In contrast to other methods, this solver preserves several advantages, such as, it avoids complex and tedious calculations and presents pivotal solutions in an explicit way. Moreover, this solver is simple, robust, well ordered and efficacious. The proposed solver will be significant for mathematicians, engineers and physicists. To the best of our knowledge, no previous work has been done using the proposed solver for solving the MS systems.

The present article is organized as follows. Section 2 describes the unified solver technique. Section 3 presents the solutions for three coupled of the Maccari's systems. Section 4 gives the physical interpretation of the presented results. Moreover, some graphs of some acquired solutions are depicted. Conclusions and future directions for research are all reported in Section 5.

2. Unified solver method

We give the unified solver for the widely used NLEEs arising in the nonlinear science. For a given NLEE with some physical field $\Psi(x, y, t)$

$\begin{equation} F(\Psi , \Psi _{t}, \Psi _{x}, \Psi _{tt}, \Psi _{xx}, ....) = 0, \end{equation}$

(2.1)

we construct its explicit solutions in the form:

$\begin{equation} \Psi (x, y, t) = \Psi (\xi ), \ \xi = k_1 x+k_2 y+k_3t, \end{equation}$

(2.2)

where $k_1$ , $k_2$ and $k_3$ are constants. Consequently the nonlinear evolution Eq (2.1) transformed to the following ordinary differential equation (ODE):

$\begin{equation} G(\Psi , \Psi ^{\prime }, \Psi ^{\prime \prime }, \Psi ^{\prime \prime \prime}, ...) = 0. \end{equation}$

(2.3)

Based on He's semi-inverse method ^[48,49,50], if possible, integrate (2.3) term by term one or more times. The variational model for the differential Eq (2.3) can be obtained by the semi-inverse method ^[51] which reads:

$\begin{equation} J(\Psi) = \underset{0}{\overset{\infty}{\int}}L\, d\xi, \end{equation}$

(2.4)

where $L$ is the Lagrangian function, of the problem described by the Eq (2.3), depending on $\Psi$ and its derivatives given in the form:

$\begin{equation} L = \frac{1}{2}\Psi^{^{\prime}2}-V, \end{equation}$

(2.5)

where $V$ is the potential function. By a Ritz method, we can find different forms of solitary wave solutions, such as $\Psi(x, y, t) = \alpha$ $\mbox{sech}(\beta \xi)$ , $\Psi(x, y, t) = \alpha$ $\mbox{csch}(\beta \xi)$ , $\Psi(x, y, t) = \alpha$ $\mbox{tanh}(\beta \xi)$ , $\Psi(x, y, t) = \alpha$ $\mbox{cotch}(\beta \xi)$ and $\Psi(x, y, t) = \alpha$ $\mbox{sech}^2(\beta \xi)$ where $\alpha$ and $\beta$ are constants determined later.

We look for a solitary wave solution in the form

$\begin{equation} \Psi(x, y, t) = \alpha, \mbox{sech}(\beta \xi), \Psi(x, y, t) = \alpha, \mbox{sech}^2(\beta \xi), \Psi(x, y, t) = \alpha, \tanh(\beta \xi). \end{equation}$

(2.6)

In this section we give the unified solver for the widely used NLEEs arising in the nonlinear science. Suppose a system of equations can be reduced to the form:

$\begin{equation} L_{1}\Psi^{\prime\prime}+L_{2}\Psi^{3}+L_{3}\Psi = 0, \end{equation}$

(2.7)

where $L_{i}, i = 1, 2, 3$ are constants. Multiplying (2.7) by $\Psi^{^{\prime}}$ and integrating with respect to $\Psi$ we get the equation:

$\begin{equation} \frac{1}{2}\Psi^{^{\prime}2}+\frac{L_2}{4L_1} \Psi^{4}+\frac{L_3}{2L_1} \Psi^{2}+L_{0} = 0 \end{equation}$

(2.8)

and $L_{0}$ is a constant of integration. Thus the Eq (2.7) can be written in the form:

$\begin{equation} \Psi^{\prime\prime} = -\frac{\partial V}{\partial\Psi}, \; V = -(\gamma_{2}\Psi ^{4}+\gamma_{1}\psi^{2}+\gamma _{0}), \end{equation}$

(2.9)

where

$\begin{equation} \gamma_2 = -\frac{L_2}{4L_1}, \gamma_1 = -\frac{L_3}{2L_1}, \gamma_{0} = - L_0 \end{equation}$

(2.10)

and $V$ is the potential function (Sagadev potential).

We apply He's semi-inverse technique^[48,49,50] for solving Eq (2.7), which construct the following variational formulation from Eq (2.8)

$\begin{equation} J = \int_{0}^{\infty}\left[\frac{1}{2}\Psi^{\prime2}+\gamma_{2}\Psi^{4}+\gamma_{1}\Psi^{2}+\gamma_{0}\right] d\xi. \end{equation}$

(2.11)

By Ritz-like method, we look for a solitary wave solution in the form given by Eq (2.6). Substituting from Eq (2.6) into Eq (2.11) and making $J$ stationary with respect to $\alpha$ and $\beta$ we obtain:

$\begin{equation} \frac{\partial J}{\partial \alpha} = 0;\; \frac{\partial J}{\partial \beta} = 0. \end{equation}$

(2.12)

Solving simultaneously the system of equations given by (2.12) we obtain $\alpha$ and $\beta$ . Consequently the solitary wave solution given by Eq (2.6) is well determined.

2.1. The first family

The first family of solutions takes the form:

$\begin{equation} \Psi(\xi) = \alpha\, \mbox{sech}^{{}}\theta, \; \theta = \beta\xi. \end{equation}$

(2.13)

Substituting from Eq (2.13) in Eq (2.11), we get

$\begin{align*} J & = \frac{1}{\beta}\int_{0}^{\infty}[\frac{1}{2}\alpha^{2}\beta^{2}, \mbox{sech}^{2}, \theta\; \mbox{tanh}^{2}\theta+ \gamma_2, \alpha^{4} \mbox{sech}^{4}\theta+\gamma_1 , \alpha^{2}\mbox{sech}^{2}\theta+\gamma_{0}]d\theta. \end{align*}$

Since $\gamma_{0}$ is a constant of integration we can let $\gamma_{0} = 0$ and consequently:

$\begin{align} J = \frac{\alpha}{12 \beta}\left[ 2\alpha \beta^{2}+8\gamma_{2}\alpha^{3}+12 \gamma_{1}\alpha\right]. \end{align}$

(2.14)

Making $J$ stationary with respect to $\alpha$ and $\beta$ leads to

$\begin{equation} \frac{\partial J}{\partial \alpha} = \frac{1}{12\beta}\left[ 32\gamma_{2}\alpha^{3}+24\gamma_{1}\alpha+4\alpha\beta^2\right] = 0, \end{equation}$

(2.15)

$\begin{equation} \frac{\partial J}{\partial \beta} = -\frac{\alpha}{12\beta^{2}}\left[ 8\gamma_{2}\alpha^{3}+12\gamma_{1}\alpha-2\alpha\beta^{2}\right] = 0. \end{equation}$

(2.16)

Solving these equations and using (2.13), the solutions of Eq (2.9) take the form:

$\begin{equation} \Psi(\xi) = \pm\sqrt{\frac{-\gamma_1}{\gamma_2}}, \mbox{sech}\left(\pm\sqrt{2\gamma_{1}}\xi\right). \end{equation}$

(2.17)

Consequently by using (2.10) the first family of solutions takes the form:

$\begin{equation} \Psi(\xi) = \pm \sqrt{\frac{-2L_3}{L_2}}, \mbox{sech}\left( \pm \sqrt{-\frac{L_3}{L_1}}\xi\right). \end{equation}$

(2.18)

2.2. The second family

The second family of solutions takes the form:

$\begin{equation} \psi(\xi) = \alpha\, \mbox{sech}^{2}\theta\; ;\theta = \beta\xi. \end{equation}$

(2.19)

The substitution from Eq (2.19) in Eq (2.11) leads to

$\begin{align*} J & = \frac{\alpha}{\beta}\int_{0}^{\infty}[2\alpha \beta^{2}\mbox{sech}^{4}\theta\; \mbox{tanh}^{2}\theta+\gamma_{2}\alpha^{3} \mbox{sech}^{8}\theta+ \gamma_{1} \alpha\, \mbox{sech}^{4}\theta+\frac{\gamma_{0}}{\alpha}] d\theta. \end{align*}$

Assuming that $\gamma_{0} = 0$ we find that

$\begin{equation} J = \frac{2\alpha^{2}}{105\beta}\left[ 14\alpha \beta^{2}+24\gamma_{2}\alpha^{3}+35 \gamma_{1}\alpha\right]. \end{equation}$

(2.20)

Making $J$ stationary with respect to $\alpha$ and $\beta$ leads to

$\begin{align} 14\alpha \beta^{2}+48\gamma_{2}\alpha^{3}+35\gamma_{1}\alpha & = 0, \end{align}$

(2.21)

$\begin{align} 14\alpha \beta^{2}-24\gamma_{2} \alpha^{3}-35\gamma_{1}\alpha & = 0. \end{align}$

(2.22)

Solving these equations and using (2.19), the second family of solutions of Eqs (2.9) and (2.7) take the form:

$\begin{equation} \Psi(\xi) = \pm \sqrt{\frac{-35\gamma_{1}}{36\gamma_{2}}}\, \mbox{sech}^{2}\left( \pm \sqrt{\frac{5}{6}\gamma_{1}} \, \xi\right) \end{equation}$

(2.23)

and

$\begin{equation} \Psi(\xi) = \pm\sqrt{\frac{-35\, L_{3}}{18\, L_{2}}} \mbox{sech}^{2}\left( \pm \sqrt{-\frac{5\, L_{3}}{12\, L_{1}}} \, \xi\right), \end{equation}$

(2.24)

respectively.

2.3. The third family

The third family of solutions takes the form:

$\begin{equation} \psi (\xi ) = \alpha, \tanh (\beta\xi ). \end{equation}$

(2.25)

Substituting from Eq (2.25) into Eq (2.11), we have

$\begin{align*} J & = \frac{1}{\beta}\int_{0}^{\infty}[\frac{1}{2}\alpha^{2}\, \beta^{2}\, \mbox{sech}^{4}\theta +\gamma_{2}\alpha^{4}\tanh^{4}\theta+ \gamma_{1}\, \alpha^{2}\tanh^{2}\theta+ \gamma_{0}]d\theta \\ & = \frac{1}{\beta}\int_{0}^{\infty}[\alpha^{2}( \gamma_{2}\alpha^{2}+\frac{1}{2} \beta^{2})\, \mbox{sech}^{4}\theta-\alpha^{2}(2 \gamma_{2} \alpha^{2}+\gamma_{1})\, \mbox{sech}^{2}\theta ]d\theta \\& +\frac{1}{\beta}(\gamma_{2}\alpha^{4}+ \gamma_{1}\alpha^{2}+\gamma_{0})\int_{0}^{\infty }d\theta \notag. \end{align*}$

Under the condition

$\begin{equation} \gamma_{0} = -\alpha^{2}(\gamma_{2} \alpha^{2}+\gamma_{1}), \end{equation}$

(2.26)

we find that

$\begin{align} J & = \frac{-\alpha^{2}}{3\beta}\left[ 4\gamma_{2}\alpha^{2}+3\gamma _{1}-\beta^{2}\right]. \end{align}$

(2.27)

The values of $\alpha$ and $\beta$ which makes $J$ stationary with respect to $\alpha$ and $\beta$ are obtained by solving the two conditions

$\begin{align} \frac{\partial J}{\partial \alpha} & = \frac{-\alpha}{3\beta}\left[ 16\gamma_{2}\alpha^{2}+6\gamma_{1}-2\beta^{2}\right] = 0, \end{align}$

(2.28)

$\begin{align} \frac{\partial J}{\partial \beta} & = \frac{\alpha^{2}}{3\beta^{2}}\left[ 4\gamma_{2}\alpha^{2}+3\gamma_{1}+\beta^{2}\right] = 0. \end{align}$

(2.29)

Solving these equations and using (2.25), the solutions of Eq (2.9) take the form:

$\begin{equation} \Psi(\xi) = \pm\sqrt{\frac{-\gamma_{1}}{2\, \gamma_{2}}} \tanh\left( \pm \sqrt{-\gamma_{1}}\xi\right). \end{equation}$

(2.30)

Consequently the third family of solutions of (2.7) take the form:

$\begin{equation} \Psi(\xi) = \pm\sqrt{\frac{-L_{3}}{L_{2}}} \tanh\left( \pm \sqrt{\frac{L_3}{2L_1}}\xi\right). \end{equation}$

(2.31)

3. Applications

In this section we introduce the solutions for the coupled nonlinear Maccari's systems.

3.1. Solutions of system (1.1)

Utilizing the wave transformation:

$\begin{equation} \begin{split} Q(x, y, t) = &e^{i(kx+\alpha\, y+\lambda\, t)}u(\zeta), \; \; \; R(x, y, t) = R(\zeta), \zeta = x + \beta y -2k t, \end{split} \end{equation}$

(3.1)

$k, \alpha, \lambda$ and $\beta$ are constants. Then the system of Eq (1.1) is converted to the following system

$\begin{equation} \begin{array}{l} u''+u R-(\lambda+k^2)u = 0, \\ (u^2)'-(2k-\beta)R' = 0. \end{array} \end{equation}$

(3.2)

Integrating second equation of Eq (3.2) and taking integration constant as zero, gives

$\begin{equation} R = \left(\frac{1}{2k-\beta}\right)u^2. \end{equation}$

(3.3)

Substituting Eq (3.3) into first equation of system (3.2), yields

$\begin{equation} L_{1} u''+L_{2}u^3+L_{3}u = 0, \end{equation}$

(3.4)

where

$\begin{equation} L_{1} = 1, L_{2} = \frac{1}{2k-\beta}, L_{3} = -(\lambda+k^2). \end{equation}$

(3.5)

Applying the unified solver method described in Section 2, three families of solutions of Eq (1.1) are given as follows:

3.1.1. The first family of solutions

$\begin{equation} u_{1, 2}(\zeta) = \pm \sqrt{2 (2k-\beta)(\lambda+k^2)}\, \mbox{sech}\left( \pm \sqrt{\lambda+k^2}\, \zeta\right). \end{equation}$

(3.6)

Thus,

$\begin{equation} Q_{1, 2}(x, y, t) = \pm e^{i(kx+\alpha\, y+\lambda\, t)}\sqrt{2 (2k-\beta)(\lambda+k^2)}\, \mbox{sech}\left( \pm \sqrt{\lambda+k^2}\, \zeta\right). \end{equation}$

(3.7)

$\begin{equation} R_{1, 2}(x, y, t) = 2(\lambda+k^2)\, \mbox{sech}^{2}\left( \pm \sqrt{\lambda+k^2}\, \zeta\right), \; \; \; \lambda+k^2 > 0. \end{equation}$

(3.8)

3.1.2. The second family of solutions

$\begin{equation} u_{3, 4}(\zeta) = \pm \sqrt{\frac{35(\lambda+k^2)(2k-\beta)}{18}}\, \mbox{sech}^{2}\left( \pm \sqrt{\frac{5(\lambda+k^2)}{12}} \, \zeta\right). \end{equation}$

(3.9)

Thus,

$\begin{equation} Q_{3, 4}(x, y, t) = \pm e^{i(kx+\alpha\, y+\lambda\, t)} \sqrt{\frac{35(\lambda+k^2)(2k-\beta)}{18}}\, \mbox{sech}^{2}\left( \pm \sqrt{\frac{5(\lambda+k^2)}{12}} \, \zeta\right). \end{equation}$

(3.10)

$\begin{equation} R_{3, 4}(x, y, t) = \frac{35(\lambda+k^2)}{18}\, \mbox{sech}^{4}\left( \pm\sqrt{ \frac{5(\lambda+k^2)}{12}} \, \zeta\right) , \; \; \; \lambda+k^2 > 0. \end{equation}$

(3.11)

3.1.3. The third family of solutions

$\begin{equation} u_{5, 6}(\zeta) = \pm\sqrt{(\lambda+k^2)(2k-\beta)} \tanh\left( \pm \sqrt{-\frac{(\lambda+k^2)}{2}}\zeta\right). \end{equation}$

(3.12)

Thus,

$\begin{equation} Q_{5, 6}(x, y, t) = \pm\, e^{i(k+\alpha\, y+\lambda\, t)}\sqrt{(\lambda+k^2)(2k-\beta)} \tanh\left( \pm \sqrt{-\frac{\lambda+k^2}{2}}\zeta\right). \end{equation}$

(3.13)

$\begin{equation} R_{5, 6}(x, y, t) = (\lambda+k^2) \tanh^{2}\left( \pm \sqrt{-\frac{\lambda+k^2}{2}}\zeta\right), \; \; \lambda+k^2 < 0. \end{equation}$

(3.14)

3.2. Solutions of system (1.2)

Consider the wave transformation:

$\begin{equation} \begin{split} Q(x, y, t)& = e^{i(kx+\alpha\, y+\lambda\, t)}u(\zeta), \\ S(x, y, t)& = e^{i(kx+\alpha\, y+\lambda\, t)}v(\zeta), \\ R(x, y, t)& = R(\xi), \zeta = x + \beta y -2k t, \end{split} \end{equation}$

(3.15)

where $k, \alpha, \lambda$ and $\beta$ are constants. By applying this transformation to the system (1.2) we get

$\begin{equation} \begin{array}{l} u''-(\lambda+k^2) u + u R = 0, \\ v''-(\lambda+k^2) v + v R = 0, \\ ((u+v)^2)'-(2k-\beta)R' = 0. \end{array} \end{equation}$

(3.16)

Integrating third equation of the system of Eq (3.16) and taking integration constant as zero, gives

$\begin{equation} R = \left(\frac{1}{2k-\beta}\right)(u+v)^2. \end{equation}$

(3.17)

Substituting Eq (3.17) into first two equations of (3.16), yields

$\begin{equation} \begin{array}{l} u''+ \frac{1}{2k-\beta}u(u+v)^2-(\lambda+k^2)u = 0, \\ v''+ \frac{1}{2k-\beta}v(u+v)^2-(\lambda+k^2)v = 0. \end{array} \end{equation}$

(3.18)

In order to solve the last system of equations, we use a simple relation between $u$ and $v$ , as follows:

$\begin{equation} v = r\, u, \end{equation}$

(3.19)

where $r$ is an arbitrary constant. Substituting (3.19) into the system (3.18), gives

$\begin{equation} \Gamma_{1} u''+\Gamma_{2}u^3+\Gamma_{3}u = 0, \end{equation}$

(3.20)

where $\Gamma_{1} = 1, \Gamma_{2} = \frac{(1+r)^2}{2k-\beta}, \Gamma_{3} = -(\lambda+k^2)$ .

In view of the unified solver illustrated in Section 2 solutions of Eq (1.2) can be given in the following formulas:

3.2.1. The first family of solutions

$\begin{equation} u_{1, 2}(\zeta) = \pm \sqrt{\frac{2(\lambda+k^2)(2k-\beta)}{(1+r)^2}}\, \mbox{sech}\left( \pm \sqrt{\lambda+k^2}\zeta\right). \end{equation}$

(3.21)

Thus,

$\begin{equation} v_{1, 2}(\zeta) = \pm r \sqrt{\frac{2(\lambda+k^2)(2k-\beta)}{(1+r)^2}}\, \mbox{sech}\left( \pm \sqrt{\lambda+k^2}\zeta\right). \end{equation}$

(3.22)

$\begin{equation} Q_{1, 2}(x, y, t) = \pm e^{i(kx+\alpha\, y+\lambda\, t)}\sqrt{\frac{2(\lambda+k^2)(2k-\beta)}{(1+r)^2}}\, \mbox{sech}\left( \pm \sqrt{\lambda+k^2}\zeta\right). \end{equation}$

(3.23)

$\begin{equation} S_{1, 2}(x, y, t) = \pm r e^{i(kx+\alpha\, y+\lambda\, t)}\sqrt{\frac{2(\lambda+k^2)(\beta-2k)}{(1+r)^2}}\, \mbox{sech}\left( \pm \sqrt{\lambda+k^2}\zeta\right). \end{equation}$

(3.24)

$\begin{equation} R_{1, 2}(x, y, t) = 2(\lambda+k^2)\mbox{sech}^2\left( \pm \sqrt{\lambda+k^2}\xi\right), \lambda+k^2 > 0. \end{equation}$

(3.25)

3.2.2. The second family of solutions

$\begin{equation} u_{3, 4}(\zeta) = \pm \sqrt{\frac{35(\lambda+k^2)(2k-\beta)}{18(1+r)^2}}\, \mbox{sech}^2\left( \pm \sqrt{\frac{5}{12}(\lambda+k^2)}\zeta\right). \end{equation}$

(3.26)

Thus,

$\begin{equation} v_{3, 4}(\zeta) = \pm r \sqrt{\frac{35(\lambda+k^2)(2k-\beta)}{18(1+r)^2}}\, \mbox{sech}^2\left( \pm \sqrt{\frac{5}{12}(\lambda+k^2)}\zeta\right). \end{equation}$

(3.27)

$\begin{equation} Q_{3, 4}(x, y, t) = \pm e^{i(kx+\alpha\, y+\lambda\, t)}\sqrt{\frac{35(\lambda+k^2)(2k-\beta)}{18(1+r)^2}}\, \mbox{sech}^2\left( \pm \sqrt{\frac{5}{12}(\lambda+k^2)}\zeta\right). \end{equation}$

(3.28)

$\begin{equation} S_{3, 4}(x, y, t) = \pm r e^{i(kx+\alpha\, y+\lambda\, t)}\sqrt{\frac{35(\lambda+k^2)(2k-\beta)}{18(1+r)^2}}\, \mbox{sech}^2\left( \pm \sqrt{\frac{5}{12}(\lambda+k^2)}\zeta\right). \end{equation}$

(3.29)

$\begin{equation} R_{3, 4}(x, y, t) = \frac{35}{18}(\lambda+k^2)\mbox{sech}^4\left( \pm \sqrt{\frac{5}{12}(\lambda+k^2)}\xi\right), \; \; \lambda+k^2 > 0. \end{equation}$

(3.30)

3.2.3. The third family of solutions

$\begin{equation} u_{5, 6}(\zeta) = \pm \sqrt{\frac{(\lambda+k^2)(2k-\beta)}{(1+r)^2}}\, \tanh\left( \pm \sqrt{-\frac{\lambda+k^2}{2}}\zeta\right). \end{equation}$

(3.31)

Thus,

$\begin{equation} v_{5, 6}(\zeta) = \pm r\sqrt{\frac{(\lambda+k^2)(2k-\beta)}{(1+r)^2}}\, \tanh\left( \pm \sqrt{-\frac{\lambda+k^2}{2}}\zeta\right). \end{equation}$

(3.32)

$\begin{equation} Q_{5, 6}(x, y, t) = \pm e^{i(kx+\alpha\, y+\lambda\, t)} \sqrt{\frac{(\lambda+k^2)(2k-\beta)}{(1+r)^2}}\, \tanh\left( \pm \sqrt{-\frac{\lambda+k^2}{2}}\zeta\right). \end{equation}$

(3.33)

$\begin{equation} S_{5, 6}(x, y, t) = \pm re^{i(kx+\alpha\, y+\lambda\, t)} \sqrt{\frac{(\lambda+k^2)(2k-\beta)}{(1+r)^2}}\, \tanh\left( \pm \sqrt{-\frac{\lambda+k^2}{2}}\zeta\right). \end{equation}$

(3.34)

$\begin{equation} R_{5, 6}(x, y, t) = (\lambda+k^2)\tanh^2\left( \pm \sqrt{-\frac{\lambda+k^2}{2}}\zeta\right), \; \; \lambda+k^2 < 0. \end{equation}$

(3.35)

3.3. Solutions of system (1.3)

In order to solve the system of Eq (1.3), we first consider the following wave transformation:

$\begin{equation} \begin{split} Q(x, y, t)& = e^{i(kx+\alpha\, y+\lambda\, t)}u(\zeta), \\ S(x, y, t)& = e^{i(kx+\alpha\, y+\lambda\, t)}v(\zeta), \\ N(x, y, t)& = e^{i(kx+\alpha\, y+\lambda\, t)}w(\zeta), \\ R(x, y, t)& = R(\zeta), \; \zeta = x + \beta y -2k t, \end{split} \end{equation}$

(3.36)

where $k, \alpha, \lambda$ and $\beta$ are constants. Substituting this transformation to system (1.3) gives

$\begin{equation} \begin{array}{l} u''-(\lambda+k^2) u + u R = 0, \\ v''-(\lambda+k^2) v + v R = 0, \\ w''-(\lambda+k^2) w + w R = 0, \\ ((u+v+w)^2)' -(2k-\beta)R' = 0. \end{array} \end{equation}$

(3.37)

As illustrated before, we integrate the third equation of (3.37) with assuming the integration constant to be zero and this gives

$\begin{equation} R = \left(\frac{1}{2k-\beta}\right)(u+v+w)^2. \end{equation}$

(3.38)

Substituting Eq (3.38) into first three equation of (3.37), implies

$\begin{equation} \begin{array}{l} u''+ \frac{1}{2k-\beta}u(u+v+w)^2-(\lambda+k^2)u = 0, \\ v''+ \frac{1}{2k-\beta}v(u+v)^2-(\lambda+k^2)v = 0, \\ w''+ \frac{1}{2k-\beta}w(u+v+w)^2-(\lambda+k^2)w = 0. \end{array} \end{equation}$

(3.39)

To solve these equations, we use a simple relations between $v, w$ and $u$ , as follows

$\begin{equation} v = r_{1}\, u, \; \; \; w = r_{2}\, u, \end{equation}$

(3.40)

where $r_{1}, r_{2}$ are arbitrary constants. Substituting (3.40) into the Eq (3.39), gives

$\begin{equation} \Gamma_{1} u''+\Gamma_{2}u^3+\Gamma_{3}u = 0, \end{equation}$

(3.41)

where $\Gamma_{1} = 1, \Gamma_{2} = \frac{(1+r_{1}+r_{2})^2}{2k-\beta}, \Gamma_{3} = -(\lambda+k^2)$ .

Similarly, solutions of system (1.3) can be obtained using the unified solver, presented in Section 2, and are described in the following:

3.3.1. The first family of solutions

$\begin{equation} u_{1, 2}(\zeta) = \pm \sqrt{\frac{2(\lambda+k^2)(2k-\beta)}{(1+r_1+r_2)^2}}\, \mbox{sech}\left( \pm \sqrt{\lambda+k^2}\zeta\right). \end{equation}$

(3.42)

Thus,

$\begin{equation} v_{1, 2}(\zeta) = \pm r_1 \sqrt{\frac{2(\lambda+k^2)(2k-\beta)}{(1+r_1+r_2)^2}}\, \mbox{sech}\left( \pm \sqrt{\lambda+k^2}\zeta\right). \end{equation}$

(3.43)

$\begin{equation} w_{1, 2}(\zeta) = \pm r_2 \sqrt{\frac{2(\lambda+k^2)(2k-\beta)}{(1+r_1+r_2)^2}}\, \mbox{sech}\left( \pm \sqrt{\lambda+k^2}\zeta\right). \end{equation}$

(3.44)

$\begin{equation} Q_{1, 2}(x, y, t) = \pm e^{i(kx+\alpha\, y+\lambda\, t)}\sqrt{\frac{2(\lambda+k^2)(2k-\beta)}{(1+r_1+r_2)^2}}\, \mbox{sech}\left( \pm \sqrt{\lambda+k^2}\zeta\right). \end{equation}$

(3.45)

$\begin{equation} S_{1, 2}(x, y, t) = \pm r_1 e^{i(kx+\alpha\, y+\lambda\, t)}\sqrt{\frac{2(\lambda+k^2)(2k-\beta)}{(1+r_1+r_2)^2}}\, \mbox{sech}\left( \pm \sqrt{\lambda+k^2}\zeta\right). \end{equation}$

(3.46)

$\begin{equation} N_{1, 2}(x, y, t) = \pm r_2 e^{i(kx+\alpha\, y+\lambda\, t)}\sqrt{\frac{2(\lambda+k^2)(2k-\beta)}{(1+r_1+r_2)^2}}\, \mbox{sech}\left( \pm \sqrt{\lambda+k^2}\zeta\right). \end{equation}$

(3.47)

$\begin{equation} R_{1, 2}(x, y, t) = 2(\lambda+k^2)\, \mbox{sech}^2\left( \pm \sqrt{\lambda+k^2}\zeta\right), \; \; \lambda+k^2 > 0. \end{equation}$

(3.48)

3.3.2. The second family of solutions

$\begin{equation} u_{3, 4}(\zeta) = \pm \sqrt{\frac{35(\lambda+k^2)(2k-\beta)}{18(1+r_1+r_2)^2}}\, \mbox{sech}^2\left( \pm \sqrt{\frac{5}{12}(\lambda+k^2)}\zeta\right). \end{equation}$

(3.49)

Thus,

$\begin{equation} v_{3, 4}(\zeta) = \pm r_1 \sqrt{\frac{35(\lambda+k^2)(2k-\beta)}{18(1+r_1+r_2)^2}}\, \mbox{sech}^2\left( \pm \sqrt{\frac{5}{12}(\lambda+k^2)}\zeta\right). \end{equation}$

(3.50)

$\begin{equation} w_{3, 4}(\zeta) = \pm r_2 \sqrt{\frac{35(\lambda+k^2)(2k-\beta)}{18(1+r_1+r_2)^2}}\, \mbox{sech}^2\left( \pm \sqrt{\frac{5}{12}(\lambda+k^2)}\zeta\right). \end{equation}$

(3.51)

$\begin{equation} Q_{3, 4}(x, y, t) = \pm e^{i(kx+\alpha\, y+\lambda\, t)}\sqrt{\frac{35(\lambda+k^2)(2k-\beta)}{18(1+r_1+r_2)^2}}\, \mbox{sech}^2\left( \pm \sqrt{\frac{5}{12}(\lambda+k^2)}\zeta\right). \end{equation}$

(3.52)

$\begin{equation} S_{3, 4}(x, y, t) = \pm r_1 e^{i(kx+\alpha\, y+\lambda\, t)}\sqrt{\frac{35(\lambda+k^2)(2k-\beta)}{18(1+r_1+r_2)^2}}\, \mbox{sech}^2\left( \pm \sqrt{\frac{5}{12}(\lambda+k^2)}\zeta\right). \end{equation}$

(3.53)

$\begin{equation} N_{3, 4}(x, y, t) = \pm r_2 e^{i(kx+\alpha\, y+\lambda\, t)}\sqrt{\frac{35(\lambda+k^2)(2k-\beta)}{18(1+r_1+r_2)^2}}\, \mbox{sech}^2\left( \pm \sqrt{\frac{5}{12}(\lambda+k^2)}\zeta\right). \end{equation}$

(3.54)

$\begin{equation} R_{3, 4}(x, y, t) = \frac{35}{18}(\lambda+k^2)\mbox{sech}^4\left(\pm \sqrt{\frac{5}{12}(\lambda+k^2)}\zeta\right), \; \; \lambda+k^2 > 0. \end{equation}$

(3.55)

3.3.3. The third family of solutions

$\begin{equation} u_{5, 6}(\zeta) = \pm \sqrt{\frac{(\lambda+k^2)(2k-\beta)}{(1+r_1+r_2)^2}}\, \tanh\left( \pm \sqrt{-\frac{\lambda+k^2}{2}}\zeta\right). \end{equation}$

(3.56)

Thus,

$\begin{equation} v_{5, 6}(\zeta) = \pm r_1 \sqrt{\frac{(\lambda+k^2)(2k-\beta)}{(1+r_1+r_2)^2}}\, \tanh\left( \pm \sqrt{-\frac{\lambda+k^2}{2}}\zeta\right). \end{equation}$

(3.57)

$\begin{equation} w_{5, 6}(\zeta) = \pm r_2 \sqrt{\frac{(\lambda+k^2)(2k-\beta)}{(1+r_1+r_2)^2}}\, \tanh\left( \pm \sqrt{ -\frac{\lambda+k^2}{2}}\zeta\right). \end{equation}$

(3.58)

$\begin{equation} Q_{5, 6}(x, y, t) = \pm\, e^{i(kx+\alpha\, y+\lambda\, t)}\sqrt{\frac{(\lambda+k^2)(2k-\beta)}{(1+r_1+r_2)^2}}\, \tanh\left( \pm \sqrt{-\frac{\lambda+k^2}{2}}\zeta\right). \end{equation}$

(3.59)

$\begin{equation} S_{5, 6}(x, y, t) = \pm r_1 e^{i(kx+\alpha\, y+\lambda\, t)}\sqrt{\frac{(\lambda+k^2)(2k-\beta)}{(1+r_1+r_2)^2}}\, \tanh\left( \pm \sqrt{-\frac{\lambda+k^2}{2}}\zeta\right). \end{equation}$

(3.60)

$\begin{equation} N_{5, 6}(x, y, t) = \pm r_2 e^{i(kx+\alpha\, y+\lambda\, t)}\sqrt{\frac{(\lambda+k^2)(2k-\beta)}{(1+r_1+r_2)^2}}\, \tanh\left( \pm \sqrt{-\frac{\lambda+k^2}{2}}\zeta\right). \end{equation}$

(3.61)

$\begin{equation} R_{5, 6}(x, y, t) = (\lambda+k^2) \tanh^{2}\left( \pm \sqrt{-\frac{\lambda+k^2}{2}}\zeta\right), \; \; \lambda+k^2 < 0. \end{equation}$

(3.62)

4. Results and discussions

Some new solutions for three coupled nonlinear Maccari's systems were achieved in explicit form. These systems are the complex nonlinear models that characteristic the dynamics of isolated waves, confined in a small part of space, in some fields such as plasma physics, superfluid and optical fiber communications ^[35,45]. The acquired solutions are hyperbolic function solutions. These solutions explain some interesting physical phenomena in applied science and new physics. E.g., the hyperbolic secant arises in the profile of a laminar jet whereas the hyperbolic tangent emerges in the study of magnetic moment and special relativity. Indeed, the presented solutions included bright and dark and soliton solutions of the nonlinear Maccari's systems.

According to the presented results in Section 3 we found that

1) The last model generalize the first two models.

2) There is no change in the form of the real field $R(x, y, t)$ in the three models.

Remark 1. 1) The proposed solver in this study can be implemented for the wide classes of nonlinear stochastic partial differential equations (NSPDEs).

2) The proposed solver can be easily extended for solving nonlinear stochastic fractional partial differential equations (NSFPDEs) ^[52,53,54].

3) The proposed solver averts monotonous and complex computations and introduces vital solutions in an explicit form.

For certain values of the parameters in each three cases, Figures 1–6 display the nonlinear dynamical behaviour of the bright and dark soliton solutions.

Figure 1. 3D profile of bright soliton solution for Eq (1.1).

DownLoad: Full-Size Img PowerPoint

Figure 2. 3D profile of dark soliton solution for Eq (1.1).

DownLoad: Full-Size Img PowerPoint

Figure 3. 3D profile of bright soliton solution for Eq (1.2).

DownLoad: Full-Size Img PowerPoint

Figure 4. 3D profile of dark soliton solution for Eq (1.2).

DownLoad: Full-Size Img PowerPoint

Figure 5. 3D profile of bright soliton solution for Eq (1.3).

DownLoad: Full-Size Img PowerPoint

Figure 6. 3D profile of dark soliton solution for Eq (1.3).

DownLoad: Full-Size Img PowerPoint

5. Conclusions

In this article, three coupled nonlinear Maccari's systems were solved using the unified solver technique. Some vital soliton solutions are presented. These solutions have vital physical aspects in many fields such as nonlinear optics plasma physics, hydrodynamic. In the view of such information, it has been seen that the unified solver method has been influential for the analytical solutions of nonlinear Maccari's systems and it is highly effective and reliable in terms of finding new solutions. Moreover, our analysis shows that the proposed solver is simple, powerful and efficient. Some graphs are presented to prescribe the dynamical behaviour of selected solutions. Finally, the used solver can be applied for so many other models emerging in natural science.

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

BDP is funded by American Heart Association award 19TPA34910232 and a Collaborative Research Network (CORNET) award from the University of Memphis and the University of Tennessee Health Science Center.

Conflict of interest

The author declares no conflict of interest in this paper.

References

[1]	Niccoli T, Partridge L (2012) Ageing as a risk factor for disease. Curr Biol 22: R741-R752. doi: 10.1016/j.cub.2012.07.024
[2]	Franceschi C, Garagnani P, Parini P, et al. (2018) Inflammaging: a new immune–metabolic viewpoint for age-related diseases. Nat Rev Endocrinol 14: 576-590. doi: 10.1038/s41574-018-0059-4
[3]	Williamson EJ, Walker AJ, Bhaskaran K, et al. (2020) Factors associated with COVID-19-related death using OpenSAFELY. Nature 584: 430-436. doi: 10.1038/s41586-020-2521-4
[4]	Pence BD (2020) Severe COVID-19 and aging: are monocytes the key? GeroScience 42: 1051-1061. doi: 10.1007/s11357-020-00213-0
[5]	Viboud C, Boëlle P, Cauchemez S, et al. (2004) Risk factors of influenza transmission in households. Br J Gen Pract 54: 684-689.
[6]	Hernandez-Vargas EA, Wilk E, Canini L, et al. (2014) Effects of aging on influenza virus infection dynamics. J Virol 88: 4123-4131. doi: 10.1128/JVI.03644-13
[7]	Falsey AR, Walsh EE (2000) Respiratory syncytial virus infection in adults. Clin Microbiol Rev 13: 371-384. doi: 10.1128/CMR.13.3.371
[8]	Franceschi C, Capri M, Monti D, et al. (2007) Inflammaging and anti-inflammaging: a systemic perspective on aging and longevity emerged from studies in humans. Mech Ageing Dev 128: 92-105. doi: 10.1016/j.mad.2006.11.016
[9]	Nikolich-Žugich J (2018) The twilight of immunity: Emerging concepts in aging of the immune system review-article. Nat Immunol 19: 10-19. doi: 10.1038/s41590-017-0006-x
[10]	O'Neill LAJ, Kishton RJ, Rathmell J (2016) A guide to immunometabolism for immunologists. Nat Rev Immunol 16: 553-565. doi: 10.1038/nri.2016.70
[11]	Mills EL, Kelly B, Logan A, et al. (2016) Succinate dehydrogenase supports metabolic repurposing of mitochondria to drive inflammatory macrophages. Cell 167: 457-470.e13. doi: 10.1016/j.cell.2016.08.064
[12]	Tannahill GM, Curtis AM, Adamik J, et al. (2013) Succinate is an inflammatory signal that induces IL-1β through HIF-1α. Nature 496: 238-242. doi: 10.1038/nature11986
[13]	Arts RJW, Novakovic B, Horst RT, et al. (2016) Glutaminolysis and fumarate accumulation integrate immunometabolic and epigenetic programs in trained immunity. Cell Metab 24: 807-819. doi: 10.1016/j.cmet.2016.10.008
[14]	Lampropoulou V, Sergushichev A, Bambouskova M, et al. (2016) Itaconate links inhibition of succinate dehydrogenase with macrophage metabolic remodeling and regulation of inflammation. Cell Metab 24: 158-166. doi: 10.1016/j.cmet.2016.06.004
[15]	Domínguez-Andrés J, Novakovic B, Li Y, et al. (2019) The itaconate pathway is a central regulatory node linking innate immune tolerance and trained immunity. Cell Metab 29: 211-220.e5. doi: 10.1016/j.cmet.2018.09.003
[16]	Yarbro JR, Emmons RS, Pence BD (2020) Macrophage immunometabolism and inflammaging: roles of mitochondrial dysfunction, cellular senescence, CD38, and NAD. Immunometabolism 2: e200026.
[17]	Zasłona Z, O'Neill LAJ (2020) Cytokine-like roles for metabolites in immunity. Mol Cell 78: 814-823. doi: 10.1016/j.molcel.2020.04.002
[18]	Makowski L, Chaib M, Rathmell JC (2020) Immunometabolism: from basic mechanisms to translation. Immunol Rev 295: 5-14. doi: 10.1111/imr.12858
[19]	Wang A, Luan HH, Medzhitov R (2019) An evolutionary perspective on immunometabolism. Science 363: eaar3932. doi: 10.1126/science.aar3932
[20]	Lee KA, Robbins PD, Camell CD (2021) Intersection of immunometabolism and immunosenescence during aging. Curr Opin Pharmacol 57: 107-116. doi: 10.1016/j.coph.2021.01.003
[21]	Murphy MP, O'Neill LAJ (2018) Krebs cycle reimagined: the emerging roles of succinate and itaconate as signal transducers. Cell 174: 780-784. doi: 10.1016/j.cell.2018.07.030
[22]	López-Otín C, Blasco MA, Partridge L, et al. (2013) The hallmarks of aging. Cell 153: 1194-1217. doi: 10.1016/j.cell.2013.05.039
[23]	Pence BD, Yarbro JR (2018) Aging impairs mitochondrial respiratory capacity in classical monocytes. Exp Gerontol 108: 112-117. doi: 10.1016/j.exger.2018.04.008
[24]	Saare M, Tserel L, Haljasmägi L, et al. (2020) Monocytes present age-related changes in phospholipid concentration and decreased energy metabolism. Aging Cell 19: e13127. doi: 10.1111/acel.13127
[25]	Gon Y, Hashimoto S, Hayashi S, et al. (1996) Lower serum concentrations of cytokines in elderly patients with pneumonia and the impaired production of cytokines by peripheral blood monocytes in the elderly. Clin Exp Immunol 106: 120-126.
[26]	McLachlan JA, Serkin CD, Morrey KM, et al. (1995) Antitumoral properties of aged human monocytes. J Immunol 154: 832-843.
[27]	Pence BD, Yarbro JR (2019) Classical monocytes maintain ex vivo glycolytic metabolism and early but not later inflammatory responses in older adults. Immun Ageing 16: 3. doi: 10.1186/s12979-019-0143-1
[28]	Renshaw M, Rockwell J, Engleman C, et al. (2002) Cutting edge: impaired toll-like receptor expression and function in aging. J Immunol 169: 4697-4701. doi: 10.4049/jimmunol.169.9.4697
[29]	Sinclair L V, Barthelemy C, Cantrell DA (2020) Single cell glucose uptake assays: a cautionary tale. Immunometabolism 2: e200029.
[30]	Reinfeld BI, Madden MZ, Wolf MM, et al. (2021) Cell-programmed nutrient partitioning in the tumour microenvironment. Nature 593: 282-288. doi: 10.1038/s41586-021-03442-1
[31]	Yoshino J, Baur JA, Imai S (2018) NAD+ intermediates: the biology and therapeutic potential of NMN and NR. Cell Metab 27: 513-528. doi: 10.1016/j.cmet.2017.11.002
[32]	Cameron AM, Castoldi A, Sanin DE, et al. (2019) Inflammatory macrophage dependence on NAD+ salvage is a consequence of reactive oxygen species–mediated DNA damage. Nat Immunol 20: 420-432. doi: 10.1038/s41590-019-0336-y
[33]	Verdin E (2015) NAD+ in aging, metabolism, and neurodegeneration. Science 350: 1208-1213. doi: 10.1126/science.aac4854
[34]	Minhas PS, Liu L, Moon PK, et al. (2019) Macrophage de novo NAD+ synthesis specifies immune function in aging and inflammation. Nat Immunol 20: 50-63. doi: 10.1038/s41590-018-0255-3
[35]	Covarrubias AJ, Kale A, Perrone R, et al. (2020) Senescent cells promote tissue NAD+ decline during ageing via the activation of CD38+ macrophages. Nat Metab 2: 1265-1283. doi: 10.1038/s42255-020-00305-3
[36]	Minhas PS, Latif-Hernandez A, McReynolds MR, et al. (2021) Restoring metabolism of myeloid cells reverses cognitive decline in ageing. Nature 590: 122-128. doi: 10.1038/s41586-020-03160-0
[37]	Vats D, Mukundan L, Odegaard JI, et al. (2006) Oxidative metabolism and PGC-1beta attenuate macrophage-mediated inflammation. Cell Metab 4: 13-24. doi: 10.1016/j.cmet.2006.05.011
[38]	Van den Bossche J, Baardman J, Otto NA, et al. (2016) Mitochondrial dysfunction prevents repolarization of inflammatory macrophages. Cell Rep 17: 684-696. doi: 10.1016/j.celrep.2016.09.008
[39]	Liang Y, Piao C, Beuschel CB, et al. (2021) eIF5A hypusination, boosted by dietary spermidine, protects from premature brain aging and mitochondrial dysfunction. Cell Rep 35: 108941. doi: 10.1016/j.celrep.2021.108941
[40]	Zhang H, Alsaleh G, Feltham J, et al. (2019) Polyamines control eIF5A hypusination, TFEB translation, and autophagy to reverse B cell senescence. Mol Cell 76: 110-125.e9. doi: 10.1016/j.molcel.2019.08.005
[41]	Puleston DJ, Buck MD, Klein Geltink RI, et al. (2019) Polyamines and eIF5A hypusination modulate mitochondrial respiration and macrophage activation. Cell Metab 30: 352-363.e8. doi: 10.1016/j.cmet.2019.05.003
[42]	Pence BD (2021) Aging and monocyte immunometabolism in COVID-19. Aging 13: 9154-9155. doi: 10.18632/aging.202918
[43]	Codo AC, Davanzo GG, de Brito Monteiro L, et al. (2020) Elevated glucose levels favor SARS-CoV-2 infection and monocyte response through a HIF-1α/glycolysis-dependent axis. Cell Metab 3: 437-446.e5. doi: 10.1016/j.cmet.2020.07.007
[44]	Ketelhuth DFJ, Lutgens E, Bäck M, et al. (2019) Immunometabolism and atherosclerosis: perspectives and clinical significance: a position paper from the Working Group on Atherosclerosis and Vascular Biology of the European Society of Cardiology. Cardiovasc Res 115: 1385-1392. doi: 10.1093/cvr/cvz166
[45]	Roy DG, Kaymak I, Williams KS, et al. (2020) Immunometabolism in the tumor microenvironment. Annu Rev Cancer Biol 5: 137-159.
[46]	O'Sullivan D, Sanin DE, Pearce EJ, et al. (2019) Metabolic interventions in the immune response to cancer. Nat Rev Immunol 19: 324-335. doi: 10.1038/s41577-019-0140-9
[47]	Hearps AC, Martin GE, Angelovich TA, et al. (2012) Aging is associated with chronic innate immune activation and dysregulation of monocyte phenotype and function. Aging Cell 11: 867-875. doi: 10.1111/j.1474-9726.2012.00851.x
[48]	Ong SM, Hadadi E, Dang T, et al. (2018) The pro-inflammatory phenotype of the human non-classical monocyte subset is attributed to senescence. Cell Death Dis 9: 266. doi: 10.1038/s41419-018-0327-1
[49]	Ma EH, Verway MJ, Johnson RM, et al. (2019) Metabolic profiling using stable isotope tracing reveals distinct patterns of glucose utilization by physiologically activated CD8+ T cells. Immunity 51: 856-870.e5. doi: 10.1016/j.immuni.2019.09.003
[50]	Artyomov MN, Van den Bossche J (2020) Immunometabolism in the single-cell era. Cell Metab 32: 710-725. doi: 10.1016/j.cmet.2020.09.013
[51]	Tabula Muris Consortium (2020) A single-cell transcriptomic atlas characterizes ageing tissues in the mouse. Nature 583: 590-595.
[52]	Wagner A, Wang C, Fessler J, et al. (2021) Metabolic modeling of single Th17 cells reveals regulators of autoimmunity. Cell 184: 4168-4185. doi: 10.1016/j.cell.2021.05.045
[53]	Argüello RJ, Combes AJ, Char R, et al. (2020) SCENITH: A flow cytometry-based method to functionally profile energy metabolism with single-cell resolution. Cell Metab 32: 1063-1075.e7. doi: 10.1016/j.cmet.2020.11.007
[54]	Rappez L, Stadler M, Triana S, et al. (2021) SpaceM reveals metabolic states of single cells. Nat Methods 18: 799-805. doi: 10.1038/s41592-021-01198-0
[55]	Zhang D, Tang Z, Huang H, et al. (2019) Metabolic regulation of gene expression by histone lactylation. Nature 574: 575-580. doi: 10.1038/s41586-019-1678-1
[56]	Tanaka T, Biancotto A, Moaddel R, et al. (2018) Plasma proteomic signature of age in healthy humans. Aging Cell 17: e12799. doi: 10.1111/acel.12799
[57]	Ackermann K, Bonaterra GA, Kinscherf R, et al. (2019) Growth differentiation factor-15 regulates oxLDL-induced lipid homeostasis and autophagy in human macrophages. Atherosclerosis 281: 128-136. doi: 10.1016/j.atherosclerosis.2018.12.009
[58]	Pence BD, Yarbro JR, Emmons RS (2021) Growth differentiation factor-15 is associated with age-related monocyte dysfunction. Aging Med 4: 47-52. doi: 10.1002/agm2.12128

This article has been cited by:

1.	R.A. Alomair, S.Z. Hassan, Mahmoud A.E. Abdelrahman, Ali H. Amin, E.K. El-Shewy, New solitary optical solutions for the NLSE with δ-potential through Brownian process, 2022, 40, 22113797, 105814, 10.1016/j.rinp.2022.105814
2.	Hanan A. Alkhidhr, Mahmoud A. E. Abdelrahman, Mohammad Mirzazadeh, Simulating New CKO as a Model of Seismic Sea Waves via Unified Solver, 2023, 2023, 1687-9139, 1, 10.1155/2023/2514899
3.	H. G. Abdelwahed, A. F. Alsarhana, E. K. El-Shewy, Mahmoud A. E. Abdelrahman, Higher-Order Dispersive and Nonlinearity Modulations on the Propagating Optical Solitary Breather and Super Huge Waves, 2023, 7, 2504-3110, 127, 10.3390/fractalfract7020127
4.	Mahmoud A.E. Abdelrahman, Hanan A. Alkhidhr, Ali H. Amin, E.K. El-Shewy, A new structure of solutions to the system of ISALWs via stochastic sense, 2022, 37, 22113797, 105473, 10.1016/j.rinp.2022.105473
5.	Mahmoud A.E. Abdelrahman, S.Z. Hassan, Munerah Almulhem, A new structure of optical solitons to the (n+1)-NLSE, 2022, 37, 22113797, 105535, 10.1016/j.rinp.2022.105535
6.	Hanan A. Alkhidhr, The new stochastic solutions for three models of non-linear Schrödinger’s equations in optical fiber communications via Itô sense, 2023, 11, 2296-424X, 10.3389/fphy.2023.1144704
7.	H. G. Abdelwahed, A. F. Alsarhana, E. K. El-Shewy, Mahmoud A. E. Abdelrahman, The Stochastic Structural Modulations in Collapsing Maccari’s Model Solitons, 2023, 7, 2504-3110, 290, 10.3390/fractalfract7040290
8.	H. G. Abdelwahed, A. F. Alsarhana, E. K. El-Shewy, Mahmoud A. E. Abdelrahman, Dynamical energy effects in subsonic collapsing electrostatic Langmuir soliton, 2023, 35, 1070-6631, 037129, 10.1063/5.0141228
9.	Emad K. El-Shewy, Noura F. Abdo, Mahmoud A. E. Abdelrahman, Modulations of Stochastic Modeling in the Structural and Energy Aspects of the Kundu–Mukherjee–Naskar System, 2023, 11, 2227-7390, 4881, 10.3390/math11244881
10.	Yousef F. Alharbi, Ahmed M. T. Abd El-Bar, Mahmoud A. E. Abdelrahman, Ahmed M. Gemeay, Arne Johannssen, A new statistical distribution via the Phi-4 equation with its wide-ranging applications, 2024, 19, 1932-6203, e0312458, 10.1371/journal.pone.0312458
11.	Munerah Almulhem, Samia Hassan, Alanwood Al-buainain, Mohammed Sohaly, Mahmoud Abdelrahman, Characteristics of Solitary Stochastic Structures for Heisenberg Ferromagnetic Spin Chain Equation, 2023, 15, 2073-8994, 927, 10.3390/sym15040927
12.	Maged A. Azzam, H. G. Abdelwahed, Emad K. El-Shewy, Mahmoud A. E. Abdelrahman, Langmuir Forcing and Collapsing Subsonic Density Cavitons via Random Modulations, 2023, 15, 2073-8994, 1558, 10.3390/sym15081558
13.	M. Mossa Al-Sawalha, Saima Noor, Mohammad Alqudah, Musaad S. Aldhabani, Rasool Shah, Formation of Optical Fractals by Chaotic Solitons in Coupled Nonlinear Helmholtz Equations, 2024, 8, 2504-3110, 594, 10.3390/fractalfract8100594
14.	Amira F. Daghistani, Ahmed M. T. Abd El-Bar, Ahmed M. Gemeay, Mahmoud A. E. Abdelrahman, Samia Z. Hassan, A Hyperbolic Secant-Squared Distribution via the Nonlinear Evolution Equation and Its Application, 2023, 11, 2227-7390, 4270, 10.3390/math11204270
15.	H. G. Abdelwahed, A. F. Alsarhana, E. K. El-Shewy, Mahmoud A. E. Abdelrahman, Characteristics of New Stochastic Solitonic Solutions for the Chiral Type of Nonlinear Schrödinger Equation, 2023, 7, 2504-3110, 461, 10.3390/fractalfract7060461
16.	Hadil Alhazmi, Sanaa A. Bajri, E. K. El-Shewy, Mahmoud A. E. Abdelrahman, Effect of random noise behavior on the properties of forcing nonlinear Maccari’s model structures, 2024, 14, 2158-3226, 10.1063/5.0228465
17.	Shan Zhao, Zhao Li, The analysis of traveling wave solutions and dynamical behavior for the stochastic coupled Maccari's system via Brownian motion, 2024, 15, 20904479, 103037, 10.1016/j.asej.2024.103037
18.	Jamil Abbas Haider, Abdullah M.S. Alhuthali, Mohamed Abdelghany Elkotb, Exploring novel applications of stochastic differential equations: Unraveling dynamics in plasma physics with the Tanh-Coth method, 2024, 60, 22113797, 107684, 10.1016/j.rinp.2024.107684
19.	Hesham G. Abdelwahed, Reem Alotaibi, Emad K. El-Shewy, Mahmoud A. E. Abdelrahman, Rajesh Sharma, An insight into the stochastic solitonic features of the Maccari model using the solver technique, 2024, 19, 1932-6203, e0312741, 10.1371/journal.pone.0312741
20.	S. Z. Hassan, D. M. Alsaleh, Munerah Almulhem, R. A. Alomair, A. F. Daghestani, Mahmoud A. E. Abdelrahman, Innovative solutions to the 2D nonlinear Schrödinger model in mathematical physics, 2025, 15, 2158-3226, 10.1063/5.0249246
21.	M. B. Almatrafi, Mahmoud A. E. Abdelrahman, The novel stochastic structure of solitary waves to the stochastic Maccari's system via Wiener process, 2025, 10, 2473-6988, 1183, 10.3934/math.2025056
22.	Mahmoud A. E. Abdelrahman, M. A. Sohaly, Yousef F. Alharbi, Optical random soliton solutions to conformable fractional NLSE via statistical distributions, 2025, 34, 0218-8635, 10.1142/S0218863523500911
23.	Zhimin Yan, Jinbo Li, Shoaib Barak, Salma Haque, Nabil Mlaiki, Delving into quasi-periodic type optical solitons in fully nonlinear complex structured perturbed Gerdjikov–Ivanov equation, 2025, 15, 2045-2322, 10.1038/s41598-025-91978-x
24.	Jin-Jin Mao, ∂̄-dressing method for the coupled third-order flow equation of the Kaup-Newell system, 2025, 10075704, 108841, 10.1016/j.cnsns.2025.108841

Reader Comments

Your name:*

Email:*
© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

AIMS Molecular Science

1.1

Metrics

Article views(2932) PDF downloads(154) Cited by(2)

Preview PDF

Download XML

Export Citation

Article outline

Show full outline

AIMS Molecular Science

Recent developments and future perspectives in aging and macrophage immunometabolism

Related Papers:

Abstract

1. Introduction

2. Unified solver method

2.1. The first family

2.2. The second family

2.3. The third family

3. Applications

3.1. Solutions of system (1.1)

3.1.1. The first family of solutions

3.1.2. The second family of solutions

3.1.3. The third family of solutions

3.2. Solutions of system (1.2)

3.2.1. The first family of solutions

3.2.2. The second family of solutions

3.2.3. The third family of solutions

3.3. Solutions of system (1.3)

3.3.1. The first family of solutions

3.3.2. The second family of solutions

3.3.3. The third family of solutions

4. Results and discussions

5. Conclusions

Conflict of interest

References

This article has been cited by:

Reader Comments

通讯作者: 陈斌, bchen63@163.com

Metrics

Other Articles By Authors

Related pages

Tools

Export File

Citation

Format

Content

Catalog

Abstract

1. Introduction

2. Unified solver method

2.1. The first family

2.2. The second family

2.3. The third family

3. Applications

3.1. Solutions of system (1.1)

3.1.1. The first family of solutions

3.1.2. The second family of solutions

3.1.3. The third family of solutions

3.2. Solutions of system (1.2)

3.2.1. The first family of solutions

3.2.2. The second family of solutions

3.2.3. The third family of solutions

3.3. Solutions of system (1.3)

3.3.1. The first family of solutions

3.3.2. The second family of solutions

3.3.3. The third family of solutions

4. Results and discussions

5. Conclusions

Conflict of interest

References