Loading [MathJax]/jax/output/SVG/jax.js
Research article

In vitro antifungal activity of pelgipeptins against human pathogenic fungi and Candida albicans biofilms

  • Systemic mycoses have become a major cause of morbidity and mortality, particularly among immunocompromised hosts and long-term hospitalized patients. Conventional antifungal agents are limited because of not only their costs and toxicity but also the rise of resistant strains. Lipopeptides from Paenibacillus species exhibit antimicrobial activity against a wide range of human and plant bacterial pathogens. However, the antifungal potential of these compounds against important human pathogens has not yet been fully evaluated, except for Candida albicans. Paenibacillus elgii produces a family of lipopeptides named pelgipeptins, which are synthesized by a non-ribosomal pathway, such as polymyxin. The present study aimed to evaluate the activity of pelgipeptins produced by P. elgii AC13 against Cryptococcus neoformans, Paracoccidioides brasiliensis, and Candida spp. Pelgipeptins were purified from P. elgii AC13 cultures and characterized by high-performance liquid chromatography (HPLC) and mass spectrometry (MALDI-TOF MS). The in vitro antifugal activity of pelgipeptins was evaluated against C. neoformans H99, P. brasiliensis PB18, C. albicans SC 5314, Candida glabrata ATCC 90030, and C. albicans biofilms. Furthermore, the minimal inhibitory concentration (MIC) was determined according to the CLSI microdilution method. Fluconazole and amphotericin B were also used as a positive control. Pelgipeptins A to D inhibited the formation and development of C. albicans biofilms and presented activity against all tested microorganisms. The minimum inhibitory concentration values ranged from 4 to 64 µg/mL, which are in the same range as fluconazole MICs. These results highlight the potential of pelgipeptins not only as antimicrobials against pathogenic fungi that cause systemic mycoses but also as coating agents to prevent biofilm formation on medical devices.

    Citation: Débora Luíza Albano Fulgêncio, Rosiane Andrade da Costa, Fernanda Guilhelmelli, Calliandra Maria de Souza Silva, Daniel Barros Ortega, Thiago Fellipe de Araujo, Philippe Spezia Silva, Ildinete Silva-Pereira, Patrícia Albuquerque, Cristine Chaves Barreto. In vitro antifungal activity of pelgipeptins against human pathogenic fungi and Candida albicans biofilms[J]. AIMS Microbiology, 2021, 7(1): 28-39. doi: 10.3934/microbiol.2021003

    Related Papers:

    [1] Shuhai Li, Lina Ma, Huo Tang . Meromorphic harmonic univalent functions related with generalized (p, q)-post quantum calculus operators. AIMS Mathematics, 2021, 6(1): 223-234. doi: 10.3934/math.2021015
    [2] Bakhtiar Ahmad, Muhammad Ghaffar Khan, Basem Aref Frasin, Mohamed Kamal Aouf, Thabet Abdeljawad, Wali Khan Mashwani, Muhammad Arif . On $ q $-analogue of meromorphic multivalent functions in lemniscate of Bernoulli domain. AIMS Mathematics, 2021, 6(4): 3037-3052. doi: 10.3934/math.2021185
    [3] Ying Yang, Jin-Lin Liu . Some geometric properties of certain meromorphically multivalent functions associated with the first-order differential subordination. AIMS Mathematics, 2021, 6(4): 4197-4210. doi: 10.3934/math.2021248
    [4] Hari Mohan Srivastava, Muhammad Arif, Mohsan Raza . Convolution properties of meromorphically harmonic functions defined by a generalized convolution $ q $-derivative operator. AIMS Mathematics, 2021, 6(6): 5869-5885. doi: 10.3934/math.2021347
    [5] Tao He, Shu-Hai Li, Li-Na Ma, Huo Tang . Closure properties of generalized $\lambda$-Hadamard product for a class of meromorphic Janowski functions. AIMS Mathematics, 2021, 6(2): 1715-1726. doi: 10.3934/math.2021102
    [6] Zhuo Wang, Weichuan Lin . The uniqueness of meromorphic function shared values with meromorphic solutions of a class of q-difference equations. AIMS Mathematics, 2024, 9(3): 5501-5522. doi: 10.3934/math.2024267
    [7] Pinhong Long, Xing Li, Gangadharan Murugusundaramoorthy, Wenshuai Wang . The Fekete-Szegö type inequalities for certain subclasses analytic functions associated with petal shaped region. AIMS Mathematics, 2021, 6(6): 6087-6106. doi: 10.3934/math.2021357
    [8] Ekram E. Ali, Nicoleta Breaz, Rabha M. El-Ashwah . Subordinations and superordinations studies using $ q $-difference operator. AIMS Mathematics, 2024, 9(7): 18143-18162. doi: 10.3934/math.2024886
    [9] Erhan Deniz, Hatice Tuǧba Yolcu . Faber polynomial coefficients for meromorphic bi-subordinate functions of complex order. AIMS Mathematics, 2020, 5(1): 640-649. doi: 10.3934/math.2020043
    [10] Huo Tang, Muhammad Arif, Khalil Ullah, Nazar Khan, Bilal Khan . Majorization results for non vanishing analytic functions in different domains. AIMS Mathematics, 2022, 7(11): 19727-19738. doi: 10.3934/math.20221081
  • Systemic mycoses have become a major cause of morbidity and mortality, particularly among immunocompromised hosts and long-term hospitalized patients. Conventional antifungal agents are limited because of not only their costs and toxicity but also the rise of resistant strains. Lipopeptides from Paenibacillus species exhibit antimicrobial activity against a wide range of human and plant bacterial pathogens. However, the antifungal potential of these compounds against important human pathogens has not yet been fully evaluated, except for Candida albicans. Paenibacillus elgii produces a family of lipopeptides named pelgipeptins, which are synthesized by a non-ribosomal pathway, such as polymyxin. The present study aimed to evaluate the activity of pelgipeptins produced by P. elgii AC13 against Cryptococcus neoformans, Paracoccidioides brasiliensis, and Candida spp. Pelgipeptins were purified from P. elgii AC13 cultures and characterized by high-performance liquid chromatography (HPLC) and mass spectrometry (MALDI-TOF MS). The in vitro antifugal activity of pelgipeptins was evaluated against C. neoformans H99, P. brasiliensis PB18, C. albicans SC 5314, Candida glabrata ATCC 90030, and C. albicans biofilms. Furthermore, the minimal inhibitory concentration (MIC) was determined according to the CLSI microdilution method. Fluconazole and amphotericin B were also used as a positive control. Pelgipeptins A to D inhibited the formation and development of C. albicans biofilms and presented activity against all tested microorganisms. The minimum inhibitory concentration values ranged from 4 to 64 µg/mL, which are in the same range as fluconazole MICs. These results highlight the potential of pelgipeptins not only as antimicrobials against pathogenic fungi that cause systemic mycoses but also as coating agents to prevent biofilm formation on medical devices.



    Let denote the class of meromorphic function of the form:

    λ(ω)=1ω+t=0atωt, (1.1)

    which are analytic in the punctured open unit disc U={ω:ωC and 0<|ω|<1}=U{0}, where U=U{0}. Let δ(ω), be given by

    δ(ω)=1ω+t=0btωt, (1.2)

    then the Convolution (Hadamard product) of λ(ω) and δ(ω) is denoted and defined as:

    (λδ)(ω)=1ω+t=0atbtωt.

    In 1967, MacGregor [17] introduced the concept of majorization as follows.

    Definition 1. Let λ and δ be analytic in U. We say that λ is majorized by δ in U and written as λ(ω)δ(ω)ωU, if there exists a function φ(ω), analytic in U, satisfying

    |φ(ω)|1,  and  λ(ω)=φ(ω)δ(ω), ωU. (1.3)

    In 1970, Robertson [19] gave the idea of quasi-subordination as:

    Definition 2. A function λ(ω) is subordinate to δ(ω) in U and written as: λ(ω)δ(ω), if there exists a Schwarz function k(ω), which is holomorphic in U with |k(ω)|<1, such that λ(ω)=δ(k(ω)). Furthermore, if the function δ(ω) is univalent in U, then we have the following equivalence (see [16]):

    λ(ω)δ(ω)andλ(U)δ(U). (1.4)

    Further, λ(ω) is quasi-subordinate to δ(ω) in U and written is

    λ(ω)qδ(ω)  ( ωU),

    if there exist two analytic functions φ(ω) and k(ω) in U such that λ(ω)φ(ω) is analytic in U and

    |φ(ω)|1 and k(ω)|ω|<1  ωU,

    satisfying

      λ(ω)=φ(ω)δ(k(ω))  ωU. (1.5)

    (ⅰ) For φ(ω)=1 in (1.5), we have

      λ(ω)=δ(k(ω))  ωU,

    and we say that the λ function is subordinate to δ in U, denoted by (see [20])

    λ(ω)δ(ω)  ( ωU).

    (ⅱ) If k(ω)=ω, the quasi-subordination (1.5) becomes the majorization given in (1.3). For related work on majorization see [1,4,9,21].

    Let us consider the second order linear homogenous differential equation (see, Baricz [6]):

    ω2k(ω)+αωk(ω)+[βω2ν2+(1α)]k(ω)=0. (1.6)

    The function kν,α,β(ω), is known as generalized Bessel's function of first kind and is the solution of differential equation given in (1.6)

    kν,α,β(ω)=t=0(β)tΓ(t+1)Γ(t+ν+1+α+12)(ω2)2t+ν. (1.7)

    Let us denote

    Lν,α,βλ(ω)=2νΓ(ν+α+12)ων2+1kν,α,β(ω12),  =1ω+t=0(β)t+1Γ(ν+α+12)4t+1Γ(t+2)Γ(t+ν+1+α+12)(ω)t,

    where ν,α and β are positive real numbers. The operator Lν,α,β is a variation of the operator introduced by Deniz [7] (see also Baricz et al. [5]) for analytic functions. By using the convolution, we define the operator Lν,α,β as follows:

    ( Lν,α,βλ)(ω)=Lν,α,β(ω)λ(ω),=1ω+t=0(β)t+1Γ(ν+α+12)4t+1Γ(t+2)Γ(t+ν+1+α+12)at(ω)t. (1.8)

    The operator Lν,α,β was introduced and studied by Mostafa et al. [15] (see also [2]). From (1.8), we have

    ω(Lν,α,βλ(ω))j+1=(ν1+α+12)(Lν1,α,βλ(ω))j(ν+α+12)(Lν,α,βλ(ω))j. (1.9)

    By taking α=β=1, the above operator reduces to ( Lνλ)(ω) studied by Aouf et al. [2].

    Definition 3. Let 1B<A1,ηC{0},jW and ν,α,β>0. A function λ is said to be in the class Mν,jα,β(η,ϰ;A,B) of meromorphic functions of complex order η0 in U if and only if

    11η(ω(Lν,α,βλ(ω))j+1(Lν,α,βλ(ω))j+ν+j)ϰ|1η(ω(Lν,α,βλ(ω))j+1(Lν,α,βλ(ω))j+ν+j)|1+Aω1+Bω. (1.10)

    Remark 1.

    (i). For A=1,B=1 and ϰ=0, we denote the class

    Mν,jα,β(η,0;1,1)=Mν,jα,β(η).

    So, λMν,jα,β(η,ϰ;A,B) if and only if

    [11η(ω(Lν,α,βλ(ω))j+1(Lν,α,βλ(ω))j+ν+j)]>0.

    (ii). For α=1,β=1, Mν,j1,1(η,0;1,1) reduces to the class Mν,j(η).

    [11η(ω(Lνλ(ω))j+1(Lνλ(ω))j+ν+j)]>0.

    Definition 4. A function λ is said to be in the class  Nν,jα,β(θ,b;A,B) of meromorphic spirllike functions of complex order b0 in U, if and only if

    1eiθbcosθ(ω(Lν,α,βλ(ω))j+1(Lν,α,βλ(ω))j+j+1)1+Aω1+Bω, (1.11)

    where,

    (π2<θ<π2, 1β<A1,ηC{0}, jW, ν,α,β>0andωU ).

    (i). For A=1 and B=1, we set

    Nν,jα,β(θ,b;1,1)=Nν,jα,β(θ,b),

    where Nν,jα,β(θ,b) denote the class of functions λ satisfying the following inequality:

    [eiθbcosθ(ω(Lν,α,βλ(ω))j+1(Lν,α,βλ(ω))j+j+1)]<1.

    (ii). For θ=0 and α=β=1 we write

    Nν,j1,1(0,b;1,1)=Nν,j(b),

    where Nν,j(b) denote the class of functions λ satisfying the following inequality:

    [1b(ω(Lνλ(ω))j+1(Lνλ(ω))j+j+1)]<1.

    A majorization problem for the normalized class of starlike functions has been examined by MacGregor [17] and Altintas et al. [3,4]. Recently, Eljamal et al. [8], Goyal et al. [12,13], Goswami et al. [10,11], Li et al. [14], Tang et al. [21,22] and Prajapat and Aouf [18] generalized these results for different classes of analytic functions.

    The objective of this paper is to examined the problems of majorization for the classes Mν,jα,β(η,ϰ;A,B) and Nν,jα,β(θ,b;A,B).

    In Theorem 1, we prove majorization property for the class Mν,jα,β(η,ϰ;A,B).

    Theorem 1. Let the function λ and suppose that δMν,jα,β(η,ϰ;A,B). If  (Lν,α,βλ(ω))j is majorized by (Lν,α,βδ(ω))j in U, then

    |(Lν,α,βλ(ω))j+1||(Lν,α,βδ(ω))j+1|,(|ω|<r0), (2.1)

    where r0=r0(η,ϰ,ν,α,β,A,B) is the smallest positive roots of the equation

    ρ(ν1+α+12)[(AB)|η|1ϰ(α+12)|B|]r3(ν1+α+12)[ρ(α+12)+ρ2|B||B|]r2(ν1+α+12)[(AB)|η|1ϰ(α+12)|B|+ρ2|B|1]r+ρ(ν1+α+12)(α+12)=0. (2.2)

    Proof. Since δMν,jα,β(η,ϰ;A,B), we have

    11η(ω(Lν,α,βδ(ω))j+1(Lν,α,βδ(ω))j+ν+j)ϰ|1η(ω(Lν,α,βδ(ω))j+1(Lν,α,βδ(ω))j+ν+j)|=1+Ak(ω)1+Bk(ω), (2.3)

    where k(ω)=c1ω+c2ω2+..., is analytic and bounded functions in U with

     |k(ω)||ω|  (ωU). (2.4)

    Taking

    §(ω)=11η(ω(Lν,α,βδ(ω))j+1(Lν,α,βδ(ω))j+ν+j), (2.5)

    In (2.3), we have

    §(ω)ϰ|§(ω)1|=1+Ak(ω)1+Bk(ω),

    which implies

    §(ω)=1+(ABϰeiθ1ϰeiθ)k(ω)1+Bk(ω). (2.6)

    Using (2.6) in (2.5), we get

    ω(Lν,α,βδ(ω))j+1(Lν,α,βδ(ω))j=ν+j+[(AB)η1ϰeiθ+(ν+j)B]k(ω)1+Bk(ω). (2.7)

    Application of Leibnitz's Theorem on (1.9) gives

    ω(Lν,α,βδ(ω))j+1=(ν1+α+12)(Lν1,α,βδ(ω))j(ν+j+α+12)(Lν,α,βδ(ω))j. (2.8)

    By using (2.8) in (2.7) and making simple calculations, we have

    (Lν1,α,βδ(ω))j(Lν,α,βδ(ω))j=α+12[(AB)η1ϰeiθ(α+12)B]k(ω)(1+Bk(ω))(ν1+α+12). (2.9)

    Or, equivalently

    (Lν,α,βδ(ω))j=(1+Bk(ω))(ν1+α+12)α+12[(AB)η1ϰeiθ(α+12)B]k(ω)(Lν1,α,βδ(ω))j. (2.10)

    Since |k(ω)||ω|, (2.10) gives us

    |(Lν,α,βδ(ω))j|[1+|B||ω|](ν1+α+12)α+12|(AB)η1ϰeiθ(α+12)B||ω||(Lν1,α,βδ(ω))j|[1+|B||ω|](ν1+α+12)α+12[(AB)|η|1ϰ(α+12)|B|]|ω||(Lν1,α,βδ(ω))j| (2.11)

    Since (Lν,α,βλ(ω))j is majorized by (Lν,α,βδ(ω))j in U. So from (1.3), we have

    (Lν,α,βλ(ω))j=φ(ω)(Lν,α,βδ(ω))j. (2.12)

    Differentiating (2.12) with respect to ω then multiplying with ω, we get

    (Lν,α,βλ(ω))j=ωφ(ω)(Lν,α,βδ(ω))j+ωφ(ω)(Lν,α,βδ(ω))j+1. (2.13)

    By using (2.8), (2.12) and (2.13), we have

    (Lν,α,βλ(ω))j+1=1(ν1+α+12)ωφ(ω)(Lν,α,βδ(ω))j+φ(ω)(Lν1,α,βδ(ω))j+1. (2.14)

    On the other hand, noticing that the Schwarz function φ satisfies the inequality

    |φ(ω)|1|φ(ω)|21|ω|2   (ωU). (2.15)

    Using (2.8) and (2.15) in (2.14), we get

    |(Lν,α,βλ(ω))j|[|φ(ω)|+ω(1|φ(ω)|2)[1+|B||ω|](ν1+α+12)(ν1+α+12)(1|ω|2)(α+12[(AB)|η|1ϰ(α+12)B]|ω|)]×|(Lν1,α,βδ(ω))j|,

    By taking

    |ω|=r,  |φ(ω)|=ρ    (0ρ1),

    reduces to the inequality

    |(Lν,α,βλ(ω))j|Φ1(ρ)(ν1+α+12)(1r2)(α+12[(AB)|η|1ϰ(α+12)B]r)|(Lν1,α,βδ(ω))j|,

    where

    Φ1(ρ)=[ρ(ν1+α+12)(1r2)(α+12[(AB)|η|1ϰ(α+12)B]r)+r(1ρ2)[1+|B|r](ν1+α+12)]=r[1+|B|r](ν1+α+12)ρ2+ρ(ν1+α+12)(1r2)(α+12[(AB)|η|1ϰ(α+12)B]r)+r[1+|B|r](ν1+α+12),           (2.16)

    takes in maximum value at ρ=1 with r0=r0(η,ϰ,ν,α,β,A,B) where r0 is the least positive root of the (2.2). Furthermore, if 0ξ0r0(η,ϰ,ν,α,β,A,B), then the function ψ1(ρ) defined by

    ψ1(ρ)=ξ0[1+|B|ξ0](ν1+α+12)ρ2+ρ(ν1+α+12)(1ξ20)(α+12[(AB)|η|1ϰ(α+12)B]ξ0)+ξ0[1+|B|ξ0](ν1+α+12),          (2.17)

    is an increasing function on the interval (0ρ1), so that

    ψ1(ρ)ψ1(1)=(ν1+α+12)(1ξ20)[α+12((AB)|η|1ϰ(α+12)B)ξ0](0ρ1, 0ξ0r0(η,ϰ,A,B)).

    Hence, upon setting ρ=1 in (2.17), we achieve (2.1).

    Special Cases: Let A=1 and B=1 in Theorem 1, we obtain the following corollary.

    Corollary 1. Let the function λ and suppose that δMν,jα,β(η,ϰ;A,B). If  (Lν,α,βλ(ω))j is majorized by (Lν,α,βδ(ω))j in U, then

    |(Lν,α,βλ(ω))j+1||(Lν,α,βδ(ω))j+1|,(|ω|<r1),

    where r1=r1(η,ϰ,ν,α,β) is the least positive roots of the equation

    ρ(ν1+α+12)[2|η|1ϰ(α+12)]r3(ν1+α+12)[ρ(α+12)+ρ21]r2(ν1+α+12)[ρ{2|η|1ϰ(α+12)}+ρ21]r+ρ(ν1+α+12)(α+12)=0. (2.18)

    Here, r=1 is one of the roots (2.18) and the other roots are given by

    r1=k0k204ρ2(ν1+α+12)[2|η|1ϰ(α+12)](ν1+α+12)(α+12)2ρ(ν1+α+12)[2|η|1ϰ(α+12)],

    where

    k0=(ν1+α+12)[ρ{2|η|1ϰ2(α+12)}+ρ21].

    Taking ϰ=0 in corollary 1, we state the following:

    Corollary 2. Let the function λ and suppose that δMν,jα,β(η,ϰ;A,B). If  (Lν,α,βλ(ω))j is majorized by (Lν,α,βδ(ω))j in U, then

    |(Lv,α,βλ(ω))j+1||(Lv,α,βδ(ω))j+1|,(|ω|<r2),

    where r2=r2(η,ν,α,β) is the lowest positive roots of the equation

    ρ(ν1+α+12)[2|η|(α+12)]r3(ν1+α+12)[ρ(α+12)+ρ21]r2(ν1+α+12)[ρ{2|η|(α+12)}+ρ21]r+ρ(ν1+α+12)(α+12)=0, (2.19)

    given by

    r2=k1k214ρ2(ν1+α+12)[2|η|(α+12)](ν1+α+12)(α+12)2ρ(ν1+α+12)[2|η|(α+12)],

    where

    k1=(ν1+α+12)[ρ{2|η|2(α+12)}+ρ21].

    Taking α=β=1 in corollary 2, we get the following:

    Corollary 3. Let the function λ and suppose that δMν,jα,β(η,ϰ;A,B). If  (Lν,α,βλ(ω))j is majorized by (Lν,α,βδ(ω))j in U, then

    |(Lν,α,βλ(ω))j+1||(Lν,α,βδ(ω))j+1|,(|ω|<r3),

    where r3=r3(η,ν) is the lowest positive roots of the equation

    ρν[2|η|1]r3ν[ρ+ρ21]r2ν[ρ(2|η|1)+ρ21]r+ρν=0, (2.20)

    given by

    r3=k2k224ρ2ν[2|η|1]ν2ρν[2|η|1],

    where

    k2=ν[ρ{2|η|2}+ρ21].

    Secondly, we exam majorization property for the class Nν,jα,β(θ,b;A,B).

    Theorem 2. Let the function λ and suppose that δNν,jα,β(θ,b;A,B). If

    (Lν,α,βλ(ω))j(Lν,α,βδ(ω))j,(j0,1,2...),

    then

    |(Lν,α,βλ(ω))j+1||(Lν,α,βδ(ω))j+1|,(|ω|<r4), (3.1)

    where r4=r4(θ,b,ν,α,β,A,B) is the smallest positive roots of the equation

    ρ[|(BA)bcosθ+(ν+α+121)|B||]r3[ρ{ν+α+121}|B|(1ρ2)(ν1+α+12)]r2+[ρ{|(BA)bcosθ+(ν+α+121)|B||}+(1ρ2)(ν1+α+12)]r+ρ[ν+α+121]=0,(π2<θ<π2,1β<A1,ηC{0},ν,α,β>0,andωU). (3.2)

    Proof. Since δNν,jα,β(θ,b;A,B), so

    1eiθbcosθ(ω(Lν,α,βλ(ω))j+1(Lν,α,βλ(ω))j+j+1)=1+Aω1+Bω, (3.3)

    where, k(ω) is defined as (2.4).

    From (3.3), we have

    ω(Lν,α,βδ(ω))j+1(Lν,α,βδ(ω))j=[(BA)bcosθ(j+1)Beiθ]k(ω)(j+1)eiθeiθ(1+Bk(ω)). (3.4)

    Now, using (2.8) in (3.4) and making simple calculations, we obtain

    (Lν1,α,βδ(ω))j(Lν,α,βδ(ω))j=[(BA)bcosθ+(ν+α+121)Beiθ]k(ω)+[(ν+j+α+12)1]eiθeiθ(1+Bk(ω))(ν1+α+12), (3.5)

    which, in view of  |k(ω)||ω| (ωU), immediately yields the following inequality

    |(Lν,α,βδ(ω))j||eiθ|(1+|B||k(ω)|)(ν1+α+12)[|(BA)bcosθ+(ν+α+121)Beiθ|]|k(ω)|+[(ν+α+12)1]|eiθ|×|(Lν1,α,βδ(ω))j|. (3.6)

    Now, using (2.15) and (3.6) in (2.14) and working on the similar lines as in Theorem 1, we have

    |(Lν1,α,βλ(ω))j|[|φ(ω)|+|ω|(1|φ(ω)|2)(1+|B||ω|)(ν1+α+12)(1|ω|2)[{|(BA)bcosθ+(ν+α+121)B|}|ω|+[(ν+α+12)1]]]×|(Lν1,α,βδ(ω))j|.

    By setting |ω|=r,|φ(ω)|=ρ(0ρ1), leads us to the inequality

    |(Lν1,α,βλ(ω))j|[Φ2(ρ)(1r2)[{|(BA)bcosθ+(ν+α+121)B|}r+(ν+α+12)1]]×|(Lν1,α,βδ(ω))j|, (3.7)

    where the function Φ2(ρ) is given by

    Φ2(ρ)=ρ(1r2)[{|(BA)bcosθ+(ν+α+121)B|}r+(ν+α+12)1]+r(1ρ2)(1+Br)(ν1+α+12).

    Φ2(ρ) its maximum value at ρ=1 with r4=r4(θ,b,ν,α,β,A,B) given in (3.2). Moreover if 0ξ1r4(θ,b,ν,α,β,A,B), then the function.

    ψ2(ρ)=ρ(1ξ21)[{|(BA)bcosθ+(ν+α+121)B|}ξ1+(ν+α+12)1]+ξ1(1ρ2)(1+Bξ1)(ν1+α+12),

    increasing on the interval 0ρ1, so that ψ2(ρ) does not exceed

    ψ2(1)=(1ξ21)[{|(BA)bcosθ+(ν+α+121)B|}ξ1+(ν+α+12)1].

    Therefore, from this fact (3.7) gives the inequality (3.1). We complete the proof.

    Special Cases: Let A=1 and B=1 in Theorem 2, we obtain the following corollary.

    Corollary 4. Let the function λ and suppose that δNν,jα,β(θ,b;A,B). If

    (Lν,α,βλ(ω))j(Lν,α,βδ(ω))j,(j0,1,2,...),

    then

    |(Lν,α,βλ(ω))j+1||(Lν,α,βδ(ω))j+1|,(|ω|<r5),

    where r5=r5(θ,b,ν,α,β) is the lowest positive roots of the equation

    ρ[|2bcosθ+(ν+α+121)|]r3[ρ{ν+α+121}(1ρ2)(ν1+α+12)]r2+[ρ{|2bcosθ+(ν+α+121)|}+(1ρ2)(ν1+α+12)]r+ρ[ν+α+121]=0. (3.8)

    Where r=1 is first roots and the other two roots are given by

    r5=κ0κ20+4ρ2[|2bcosθ+(ν+α+121)|][ν+α+121]2ρ[|2bcosθ+(ν+α+121)|],

    and

    κ0=[(1ρ2)(ν1+α+12)ρ{|2bcosθ+2(ν+α+121)|}].

    Which reduces to Corollary 4 for θ=0.

    Corollary 5. Let the function λ and suppose that δNν,jα,β(θ,b;A,B). If

    (Lν,α,βλ(ω))j(Lν,α,βδ(ω))j,(j0,1,2,...),

    then

    |(Lν,α,βλ(ω))j+1||(Lν,α,βδ(ω))j+1|,(|ω|<r6),

    where r6=r6(b,ν,α,β) is the least positive roots of the equation

    ρ[|2b+(ν+α+121)|]r3[ρ{ν+α+121}(1ρ2)(ν1+α+12)]r2+[ρ{|2b+(ν+α+121)|}+(1ρ2)(ν1+α+12)]r+ρ[ν+α+121]=0, (3.9)

    given by

    r6=κ1κ21+4ρ2[|2b+(ν+α+121)|][ν+α+121]2ρ[|2b+(ν+α+121)|],

    and

    κ1=[(1ρ2)(ν1+α+12)ρ{|2b+2(ν+α+121)|}].

    Taking α=β=1 in corollary 5, we get.

    Corollary 6. Let the function λ and suppose that δNν,jα,β(θ,b;A,B). If

    (Lν,α,βλ(ω))j(Lν,α,βδ(ω))j,(j0,1,2,...),

    then

    |(Lν,α,βλ(ω))j+1||(Lν,α,βδ(ω))j+1|,(|ω|<r7),

    where r7=r7(b,ν) is the lowest positive roots of the equation

    ρ|2b+ν|r3[ρν(1ρ2)ν]r2+[ρ|2b+ν|+(1ρ2)ν]r+ρ[ν]=0, (3.10)

    given by

    r7=κ2κ22+4ρ2[|2b+ν|][ν]2ρ[|2b+ν|],

    and

    κ2=[(1ρ2)νρ{|2b+2ν|}].

    In this paper, we explore the problems of majorization for the classes Mν,jα,β(η,ϰ;A,B) and Nν,jα,β(θ,b;A,B) by using a convolution operator Lν,α,β. These results generalizes and unify the theory of majorization which is an active part of current ongoing research in Geometric Function Theory. By specializing different parameters like ν,η,ϰ,θ and b, we obtain a number of important corollaries in Geometric Function Theory.

    The work here is supported by GUP-2019-032.

    The authors agree with the contents of the manuscript, and there is no conflict of interest among the authors.


    Acknowledgments



    This study was financed in part by the Brazilian National Council for Scientific and Technological Development/Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Grant: 560915/2010-1. Daniel B. Ortega was supported by a Doctoral scholarship from CAPES (#88882.182971/2018-01 and #88887.363116/2019-00).

    Conflict of interest



    The authors declare that they have no conflicts of interest.

    [1] Calderone RA, Fonzi WA (2001) Virulence factors of Candida albicansTrends Microbiol 9: 327-335. doi: 10.1016/S0966-842X(01)02094-7
    [2] Shikanai-Yasuda MA (2015) Paracoccidioidomycosis treatment. Rev Inst Med Trop Sao Paulo 57: 31-37. doi: 10.1590/S0036-46652015000700007
    [3] Bongomin F, Gago S, Oladele RO, et al. (2017) Global and multi-national prevalence of fungal diseases—estimate precision. J Fungi 3: 57. doi: 10.3390/jof3040057
    [4] Sudbery PE (2011) Growth of Candida albicans hyphae. Nat Rev Microbiol 9: 737-748. doi: 10.1038/nrmicro2636
    [5] Horn DL, Neofytos D, Anaissie EJ, et al. (2009) Epidemiology and outcomes of candidemia in 2019 patients: data from the prospective antifungal therapy alliance registry. Clin Infect Dis 48: 1695-1703. doi: 10.1086/599039
    [6] Ramage G, Mowat E, Jones B, et al. (2009) Our current understanding of fungal biofilms. Crit Rev Microbiol 35: 340-355. doi: 10.3109/10408410903241436
    [7] Levitz SM (1991) The ecology of Cryptococcus neoformans and the epidemiology of cryptococcosis. Rev Infect Dis 13: 1163-1169. doi: 10.1093/clinids/13.6.1163
    [8] Idnurm A, Bahn YS, Nielsen K, et al. (2005) Deciphering the model pathogenic fungus Cryptococcus neoformansNat Rev Microbiol 3: 753-764. doi: 10.1038/nrmicro1245
    [9] Velagapudi R, Hsueh YP, Geunes-Boyer S, et al. (2009) Spores as infectious propagules of Cryptococcus neoformansInfect Immun 77: 4345-4355. doi: 10.1128/IAI.00542-09
    [10] Rajasingham R, Smith RM, Park BJ, et al. (2017) Global burden of disease of HIV-associated cryptococcal meningitis: an updated analysis. Lancet Infect Dis 17: 873-881. doi: 10.1016/S1473-3099(17)30243-8
    [11] San-Blas F, Cova LJ (1975) Growth curves of the yeast-like form of Paracocidioides brasiliensisSabouraudia 1: 22-29. doi: 10.1080/00362177585190041
    [12] San-Blas G (1985) Paracoccidioides brasiliensis: Cell Wall Glucans, Pathogenicity, and Dimorphism. Current Topics in Medical Mycology New York: Springer, 235-257. doi: 10.1007/978-1-4613-9547-8_9
    [13] Mendes RP, Cavalcante R de S, Marques SA, et al. (2017) Paracoccidioidomycosis: Current perspectives from Brazil. Open Microbiol J 11: 224-282. doi: 10.2174/1874285801711010224
    [14] da Costa MM, Marques da Silva SH (2014) Epidemiology, clinical, and therapeutic aspects of Paracoccidioidomycosis. Curr Trop Med Reports 1: 138-144.
    [15] Stein T (2005) Bacillus subtilis antibiotics: structures, syntheses and specific functions. Mol Microbiol 56: 845-857. doi: 10.1111/j.1365-2958.2005.04587.x
    [16] Cochrane SA, Vederas JC (2016) Lipopeptides from Bacillus and Paenibacillus spp.: a gold mine of antibiotic candidates. Med Res Rev 36: 4-31. doi: 10.1002/med.21321
    [17] Meena KR, Kanwar SS (2015) Lipopeptides as the antifungal and antibacterial agents: applications in food safety and therapeutics. Biomed Res Int 2015: 473050. doi: 10.1155/2015/473050
    [18] Olishevska S, Nickzad A, Déziel E (2019) Bacillus and Paenibacillus secreted polyketides and peptides involved in controlling human and plant pathogens. Appl Microbiol Biotechnol 103: 1189-1215. doi: 10.1007/s00253-018-9541-0
    [19] Velkov T, Roberts KD, Nation RL, et al. (2013) Pharmacology of polymyxins: new insights into an ‘old’ class of antibiotics. Future Microbiol 8: 711-724. doi: 10.2217/fmb.13.39
    [20] Wu XC, Shen XB, Ding R, et al. (2010) Isolation and partial characterization of antibiotics produced by Paenibacillus elgii B69. FEMS Microbiol Lett 310: 32-38. doi: 10.1111/j.1574-6968.2010.02040.x
    [21] Ding R, Wu XC, Qian CD, et al. (2011) Isolation and identification of lipopeptide antibiotics from Paenibacillus elgii B69 with inhibitory activity against methicillin-resistant Staphylococcus aureusJ Microbiol 49: 942-949. doi: 10.1007/s12275-011-1153-7
    [22] Costa R, Ortega D, Fulgêncio D, et al. (2019) Checkerboard testing method indicates synergic effect of pelgipeptins against multidrug resistant Klebsiella pneumoniaeBiotechnol Res Innov 3: 187-191. doi: 10.1016/j.biori.2018.12.001
    [23] Ortega DB, Costa RA, Pires AS, et al. (2018) Draft Genome sequence of the antimicrobial-producing strain Paenibacillus elgii AC13. Genome Announc 6: e00573-18. doi: 10.1128/genomeA.00573-18
    [24] Murphy JB, Kies MW (1960) Note on spectrophotometric determination of proteins in dilute solutions. Biochim Biophys Acta 45: 382-384. doi: 10.1016/0006-3002(60)91464-5
    [25] (2017) CLSIReference method for broth dilution antifungal susceptibility testing of yeasts CLSI Standard M27. Wayne, PA.
    [26] De-Souza-Silva CM, Guilhelmelli F, Zamith-Miranda D, et al. (2018) Broth microdilution in vitro screening: An easy and fast method to detect new antifungal compounds. J Vis Exp 132: 57127.
    [27] Pankey G, Ashcraft D, Kahn H, et al. (2014) Time-kill assay and etest evaluation for synergy with polymyxin B and fluconazole against Candida glabrataAntimicrob Agents Chemother 58: 5795-5800. doi: 10.1128/AAC.03035-14
    [28] Hsu LH, Wang HF, Sun PL, et al. (2017) The antibiotic polymyxin B exhibits novel antifungal activity against Fusarium species. Int J Antimicrob Agents 49: 740-748. doi: 10.1016/j.ijantimicag.2017.01.029
    [29] De Paula E Silva ACA, Oliveira HC, Silva JF, et al. (2013) Microplate alamarblue assay for paracoccidioides susceptibility testing. J Clin Microbiol 51: 1250-1252. doi: 10.1128/JCM.02914-12
    [30] Pierce CG, Uppuluri P, Tristan AR, et al. (2008) A simple and reproducible 96-well plate-based method for the formation of fungal biofilms and its application to antifungal susceptibility testing. Nat Protoc 3: 1494-1500. doi: 10.1038/nprot.2008.141
    [31] Pirri G, Giuliani A, Nicoletto SF, et al. (2009) Lipopeptides as anti-infectives: a practical perspective. Cent Eur J Biol 4: 258-273.
    [32] Trimble MJ, Mlynárčik P, Kolář M, et al. (2016) Polymyxin: Alternative mechanisms of action and resistance. Cold Spring Harb Perspect Med 6: 1-23. doi: 10.1101/cshperspect.a025288
    [33] Zhai B, Zhou H, Yang L, et al. (2010) Polymyxin B, in combination with fluconazole, exerts a potent fungicidal effect. J Antimicrob Chemother 65: 931-938. doi: 10.1093/jac/dkq046
    [34] Qian CD, Liu TZ, Zhou SL, et al. (2012) Identification and functional analysis of gene cluster involvement in biosynthesis of the cyclic lipopeptide antibiotic pelgipeptin produced by Paenibacillus elgiiBMC Microbiol 12: 197. doi: 10.1186/1471-2180-12-197
    [35] Campoy S, Adrio JL (2017) Antifungals. Biochem Pharmacol 133: 86-96. doi: 10.1016/j.bcp.2016.11.019
    [36] Kim J, Il Kim P, Bong KM, et al. (2018) Isolation and structural elucidation of pelgipeptin E, a novel pore-forming pelgipeptin analog from Paenibacillus elgii with low hemolytic activity. J Antibiot (Tokyo) 71: 1008-1017. doi: 10.1038/s41429-018-0095-2
    [37] Bachmann SP, VandeWalle K, Ramage G, et al. (2002) In vitro activity of caspofungin against Candida albicans biofilms. Antimicrob Agents Chemother 46: 3591-3596. doi: 10.1128/AAC.46.11.3591-3596.2002
    [38] Bruzual I, Riggle P, Hadley S, et al. (2007) Biofilm formation by fluconazole-resistant Candida albicans strains is inhibited by fluconazole. J Antimicrob Chemother 59: 441-450. doi: 10.1093/jac/dkl521
    [39] Ramage G, Vande Walle K, Wickes BL, et al. (2001) Standardized method for in vitro antifungal susceptibility testing of Candida albicans biofilms. Antimicrob Agents Chemother 45: 2475-2479. doi: 10.1128/AAC.45.9.2475-2479.2001
    [40] Ramage G, VandeWalle K, Lopez-Ribot J, et al. (2002) The filamentation pathway controlled by the Efg1 regulator protein is required for normal biofilm formation and development in Candida albicansFEMS Microbiol Lett 214: 95-100. doi: 10.1111/j.1574-6968.2002.tb11330.x
  • This article has been cited by:

    1. Syed Ghoos Ali Shah, Saqib Hussain, Akhter Rasheed, Zahid Shareef, Maslina Darus, Fanglei Wang, Application of Quasisubordination to Certain Classes of Meromorphic Functions, 2020, 2020, 2314-8888, 1, 10.1155/2020/4581926
    2. Syed Ghoos Ali Shah, Saima Noor, Saqib Hussain, Asifa Tasleem, Akhter Rasheed, Maslina Darus, Rashad Asharabi, Analytic Functions Related with Starlikeness, 2021, 2021, 1563-5147, 1, 10.1155/2021/9924434
    3. Syed Ghoos Ali Shah, Saqib Hussain, Saima Noor, Maslina Darus, Ibrar Ahmad, Teodor Bulboaca, Multivalent Functions Related with an Integral Operator, 2021, 2021, 1687-0425, 1, 10.1155/2021/5882343
    4. Syed Ghoos Ali Shah, Shahbaz Khan, Saqib Hussain, Maslina Darus, $ q $-Noor integral operator associated with starlike functions and $ q $-conic domains, 2022, 7, 2473-6988, 10842, 10.3934/math.2022606
    5. Neelam Khan, Muhammad Arif, Maslina Darus, Abdellatif Ben Makhlouf, Majorization Properties for Certain Subclasses of Meromorphic Function of Complex Order, 2022, 2022, 1099-0526, 1, 10.1155/2022/2385739
    6. Ibrar Ahmad, Syed Ghoos Ali Shah, Saqib Hussain, Maslina Darus, Babar Ahmad, Firdous A. Shah, Fekete-Szegö Functional for Bi-univalent Functions Related with Gegenbauer Polynomials, 2022, 2022, 2314-4785, 1, 10.1155/2022/2705203
    7. F. Müge SAKAR, Syed Ghoos Ali SHAH, Saqib HUSSAİN, Akhter RASHEED, Muhammad NAEEM, q-Meromorphic closed-to-convex functions related with Janowski function, 2022, 71, 1303-5991, 25, 10.31801/cfsuasmas.883970
    8. Syed Ghoos Ali Shah, Sa’ud Al-Sa’di, Saqib Hussain, Asifa Tasleem, Akhter Rasheed, Imran Zulfiqar Cheema, Maslina Darus, Fekete-Szegö functional for a class of non-Bazilevic functions related to quasi-subordination, 2023, 56, 2391-4661, 10.1515/dema-2022-0232
    9. Abdul Basir, Muhammad Adil Khan, Hidayat Ullah, Yahya Almalki, Saowaluck Chasreechai, Thanin Sitthiwirattham, Derivation of Bounds for Majorization Differences by a Novel Method and Its Applications in Information Theory, 2023, 12, 2075-1680, 885, 10.3390/axioms12090885
    10. Shatha S. Alhily, Alina Alb Lupas, Certain Class of Close-to-Convex Univalent Functions, 2023, 15, 2073-8994, 1789, 10.3390/sym15091789
  • Reader Comments
  • © 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

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(4292) PDF downloads(207) Cited by(5)

Figures and Tables

Figures(2)  /  Tables(3)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog