Citation: O. Roger Anderson. Marine and estuarine natural microbial biofilms: ecological and biogeochemical dimensions[J]. AIMS Microbiology, 2016, 2(3): 304-331. doi: 10.3934/microbiol.2016.3.304
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Theory of m-subharmonic functions was recently developed by many mathematicians such as Li [20], Błocki [9], Dinew and Kołodziej [14,15], Lu [21,22], Sadullaev and Abdullaev [30], Nguyen [23,24], Åhag, Czyż and Hed [3,4] and many others. The notion of m-subharmonicity appears naturally in generalization of subharmonicity and plurisubharmonicity. For the similarities and the differences between these notions, we refer the readers to the paper [15].
A bounded domain Ω⊂Cn is called m-hyperconvex if there exists an m-subharmonic function ρ:Ω→(−∞,0) such that the closure of the set {z∈Ω:ρ(z)<c} is compact in Ω for every c∈(−∞,0). In what follows we will always assume that Ω is an m-hyperconvex domain. Denote by SHm(Ω) the set of all m-subharmonic functions in Ω. Let the cones E0,m,Ep,m,Fm be defined in the similar way as in [21,25]:
E0,m={u∈SHm(Ω)∩L∞(Ω):limz→∂Ωu(z)=0 and ∫ΩHm(u)<∞},Ep,m={u∈SHm(Ω):∃ {uj}⊂E0,m,uj↓u,supj∫Ω(−uj)pHm(uj)<∞},Fm={u∈SHm(Ω):∃ {uj}⊂E0,m,uj↓u and supj∫ΩHm(uj)<∞}. |
For the properties and applications of these classes, see [1,21,22,25,26,27].
We use the notation δK=K=K for K be one of the classes E0,m,Ep,m,Fm. Define
||u||p,m=infu=u1−u2u1,u2∈Ep,m{(∫Ω(−u1−u2)pHm(u1+u2))1m+p}, | (1.1) |
with the convention that (−u1−u2)p=1 if p=0. For the reason why this quasi-norm is effective, please see [2,13,16,22,29]. It was proved in [25] that (δEp,m,||⋅||p,m) is a quasi-Banach space for p>0,p≠1 and it is a Banach space if p=1. Moreover in [17] it was proved that (δFm,||⋅||0,m) is a Banach space. The authors in [12] show that (δEp,m,||⋅||p,m) can not be a Banach space. These facts are counterparts of [5,6,10,18] in m-subharmonic setting.
In Section 2, we shall show that E0,m and δE0,m are closed neither in (δEp,m,||⋅||p,m) nor in (δFm,||⋅||0,m). Moreover we prove that the inclusions E0,m⊆Fm,δE0,m⊆δFm are proper in the space (δFm,||⋅||0,m).
In Section 3, we prove that the convergence in δEp,m implies the convergence in m-capacity (Theorem 3). But the convergence in m-capacity is not a sufficient condition for the convergence in δEp,m (Example 3). Similar results in plurisubharmonic setting have been proved by Czyż in [11].
In plurisubharmonic case, the following proposition was proved in (see [11]). Let B=B(0,1)⊂Cn be the unit ball in Cn. Then the cones E0,m(B) and δE0,m(B) are not closed respectively in (δFm(B),||⋅||0,m) and (δEp,m(B),||⋅||p,m).
Proof. We define
v(z)={ln|z|if m=n,1−|z|2−2nmif 1≤m<n. |
We obtain that Hm(v):=ddc(v)∧βn−m=c(n,m)δ0, where c(n,m) is a constant depending only on n and m, δ0 is the Dirac measure at the origin 0 (see [28]). For each j∈N, define the function vj:B→R∪{−∞} by
vj(z)=max(ajv(z),−bj), |
where aj=12j,bj=1j.
We can see that vj∈E0,m(B), for each j. Therefore, the function uk:=∑kj=1vj belongs to E0,m(B). For k>l we can compute
||uk−ul||m0,m=||k∑j=l+1vj||m=∫BHm(k∑j=l+1vj)=c(n,m)(k∑j=l+1aj)m, | (2.1) |
and
||uk−ul||p+mp,m=||k∑j=l+1vj||p+mp+m=ep,m(k∑j=l+1vj)=∫B(−k∑j=l+1vj)pHm(k∑j=l+1vj)=c(n,m)k∑j1,⋯,jm=l+1[−k∑r=l+1vr(max(tj1,⋯,tjm))]paj1⋯ajm≤c(n,m)k∑j1,⋯,jm=l+1[−uk(max(tj1,⋯,tjm))]paj1⋯ajm≤c(n,m)[k∑j=l+1(−uk(tj))pmaj]m, |
where
tj={(1+bjaj)m2(m−n),if 1≤m<n,e−bjaj,if m=n. |
The last inequality is a consequence of the fact that vj is increasing function for each j. Since
vl(tj)={−1l,if 1≤l≤j,−2jj2l,if l>j, |
we have
−uk(tj)=j∑l=11l+2jjk∑l=j+112l≤j+1. |
Hence
||uk−ul||p+mp,m≤c(n,m)(k∑j=l+1(j+1)pm2j)m. | (2.2) |
Let u:B→R∪{−∞} be defined by u=limk→∞uk. Observe that u is the limit of a decreasing sequence of m-subharmonic functions and u(z)>−∞ on the boundary of the ball B(0,12). Hence u is m-subharmonic. Moreover u∉E0,m(B) since it is not bounded on B, its value is not bounded below at the origin. Equality (2.1) shows that {uk} is a Cauchy sequence in the space δFm(B). Thus the cone E0,m(B) and the space δE0,m(B) are not closed in (δFm(B),||⋅||0,m).
The series ∑∞j=1(j+1)pm2j is convergent by the ratio test. Therefore {uk} is a Cauchy sequence in δEp,m by (2.2). We have proved that the cone E0,m(B) and the space δE0,m(B) are not closed in (δEp,m(B),||⋅||p,m).
The following proposition shows that the closure of the cone E0,m (resp. δE0,m) is strictly smaller than Fm (resp. δFm) in the space (δFm,||⋅||0,m). We have ¯E0,m⊊Fm and ¯δE0,m⊊δFm in the space (δFm,||⋅||0,m).
Proof. The definition of the m-Lelong number of a function v∈SHm(Ω) at a∈Ω is the following
νm,a(v)=limr→0+∫|z−a|≤rddcv∧[ddc(−|z−a|2−2nm)]m−1∧βn−m |
It is easy to see that m-Lelong number is a linear functional on δFm. Moreover, as in [7, Remark 1], for a function φ∈Fm then
νm,a(φ)≤(Hm(φ)({a}))1m≤(Hm(φ)(Ω))1m. |
Hence, for any representation u=u1−u2 of u∈δFm we have
|νm,a(u)|≤(Hm(u1+u2)(Ω))1m. |
This implies that m-Lelong number is a bounded functional on the space δFm. We have shown that m-Lelong number is continuous on the Banach space (δFm,||⋅||0,m). We recall the definition of m-Green function with pole at a
gm,Ω,a(z)=sup{v∈SH−m(Ω):u(z)+|z−a|2−2nm≤O(1) as z→a}. |
The readers can find more properties of m-Green function in [31]. Assume that ¯E0,m=Fm. Then there exists a sequence {uj} in E0,m that converges to gm,Ω,a in the space δFm as j→∞. The m-Lelong number of all uj at a vanishes since uj is bounded, but the m-Lelong number of gm,Ω,a at a is 1. Hence we get a contradiction. Thus, ¯E0,m⊊Fm. By the same argument, if ¯δE0,m=δFm, then there exists a sequence {uj} in E0,m that converges to gm,Ω,a in the space δFm as j→∞, but this is impossible since νm,a(uj)=0.
We are going to recall a Błocki type inequality (see [8]) for the class Ep,m. Similar results for the class Fm were proved by Hung and Phu in [19, Proposition 5.3] (see also [1]) and for locally bounded functions were proved by Wan and Wang [31]. Assume that v∈Ep,m and h∈SHm is such that −1≤h≤0. Then
∫Ω(−v)m+pHm(h)≤m!∫Ω(−v)pHm(v). |
Proof. See the proof of [19, Proposition 5.3].
Recall that the relative m-capacity of a Borel set E⊂Ω with respect to Ω is defined by
capm,Ω(E)=sup{∫EHm(u):u∈SHm(Ω),−1≤u≤0}. |
We are going to recall the convergence in m-capacity. We say that a sequence {uj}⊂SHm(Ω) converges to u∈SHm(Ω) in m-capacity if for any ϵ>0 and K⋐Ω then we have
limj→∞capm,Ω(K∩{|uj−u|>ϵ})=0. |
Let {uj}⊂δEp,m be a sequence that converges to a function u∈δEp,m as j tends to ∞. Then {uj} converges to u in m-capacity.
Proof. Replacing uj by uj−u, we can assume that u=0. By the definition of δEp,m, there exist functions vj,wj∈Ep,m such that uj=vj−wj and ep(vj+wj)→0 as j→∞. By [25],
max(ep,m(vi),ep,m(wj))≤ep,m(vj+wj), |
which implies that ep,m(vj),ep,m(wj) tend to 0 as j→∞. Given ϵ>0 and K⋐Ω. For a function φ∈SHm(Ω), −1≤φ≤0, we have
∫{|vj|>ϵ}∩KHm(φ)≤1ϵp+m∫Ω(−vj)p+mHm(φ)≤m!ϵp+mep,m(vj). | (3.1) |
The last inequality comes from Lemma 3. Hence, by taking the supremum over all functions φ in inequality (3.1), we get
capm,Ω({|vj|>ϵ}∩K)≤m!ϵm+pep,m(vj). | (3.2) |
Similarly,
capm,Ω({|wj|>ϵ}∩K)≤m!ϵm+pep,m(wj). | (3.3) |
From (3.2), (3.3) we obtain
capm,Ω({|uj|>ϵ}∩K)≤capm,Ω({|vj|>ϵ2}∩K)+capm,Ω({|wj|>ϵ2}∩K)≤m!2m+pϵm+p(ep,m(vj)+ep,m(wj))→0 as j→∞. |
Hence the sequence {uj} tends to 0 in m-capacity and the proof is finished.
A similar result for the space δFm is proved in [17]. But the convergence in m-capacity is not a sufficient condition for the convergence in the space δEp,m. The following example shows that convergence in m-capacity is strictly weaker than convergences in both δEp,m and δFm. The case m=n has been showed in [11, Example 3.3]. Let v(z) be the function defined in the unit ball in Cn as in the proof of Proposition 2. We define
uj(z)=max(jpmv(z),−1j), vj(z)=max(v(z),−1j) |
Then we have uj,vj∈E0,m(B) for every j, and ep,m(uj)=c(n,m),e0,m(vj)=1. These show that the sequence {uj} and {vj} do not converge to 0 in δEp,m(B) and δFm(B) respectively as j→∞. Moreover, for fixed ϵ>0 and K⋐B there exists j0 such that for all j≥j0 we have
uj=vj=−1j on K. |
This infers that both sets K∩{uj<−ϵ} and K∩{vj<−ϵ} are empty. Hence uj and vj tend to 0 in m-capacity.
The authors would like to thank Rafał Czyż for many valuable comments and suggestions for this manuscript. We are grateful to the referee whose remarks and comments helped to improve the paper.
The authors declare no conflict of interest.
[1] | Costerton JW (2007) The Biofilm Primer, Berlin: Springer. |
[2] |
Costerton JW, Lewandowski Z, Caldwell DE, et al. (1995) Microbial Biofilms. Annu Rev Microbiol 49: 711–745. doi: 10.1146/annurev.mi.49.100195.003431
![]() |
[3] | Lappin-Scott, HM, Costerton JW (1995) Microbial biofilms, Cambridge: Cambridge Univ. Press. |
[4] | Stoodley P, Boyle JD, Dodds I, et al. (1997) Consensus model of biofilm structure, In: Wimpenny JWT, Handley PS, Gilbert, P et al. Authors, Biofilms: community interactions and control, Cardiff, UK.: BioLine, 1–9. |
[5] | Anderson OR (2016) Natural Freshwater Biofilms: Structure and Function with Attention to the Biogeochemical Carbon Cycle, In: Biofilms: Characterization, Applications and Recent Advances, New York: Nova Scientific Publishers, [in press]. |
[6] |
Cooksey KE, Wigglesworth-Cooksey B (1995) Adhesion of bacteria and diatoms to surfaces in the sea-a review. Aquat Microb Ecol 9: 87–96. doi: 10.3354/ame009087
![]() |
[7] | Evans LV (2000) Biofilms: recent advances in their study and control, Amsterdam: Harwood Academic Publ. |
[8] | Maki JS (1999) The influence of marine microbes on biofouling, In: Fingerman M, Nagabhushanam R, Thompson M-F Authors, Recent advances in marine biotechnology, vol 3. Biofilms, bioadhesion, corrosion and biofouling. Enfield: Science Publ., 141–171. |
[9] | Railkin AI (2004) Marine biofouling: colonization processes and defences. Boca Raton: CRC Press. |
[10] | Salta M, Wharton J, Blache Y, et al. (2013) Marine biofilms on man-made surfaces: structure and dynamics. Environ Microbiol 15: 2879–2893. |
[11] | Wahl M (1989) Marine epibiosis.1. Fouling and antifouling – some basic aspects. Mar Ecol Prog Ser 58:175–189. |
[12] | Callow JA, Callow ME (2006) Biofilms, In: Fusetani N, Clare AS Authors, Antifouling Compounds, Berlin: Springer-Verlag, 141–169. |
[13] |
Muia AW, Bretschko G, Herndi GJ (2011) An overview of the structure and function of microbial biofilms, with special emphasis on heterotrophic aquatic microbial communities. Afr J Aquat Sci 36: 1–10. doi: 10.2989/16085914.2011.562279
![]() |
[14] |
Petrova OE, Sauer K (2012) Sticky situations: key components that control bacterial surface attachment. J Bacteriol 194: 2413–2425. doi: 10.1128/JB.00003-12
![]() |
[15] |
Callow ME, Fletcher RL (1994) The influence of low surface energy materials on bioadhesion – a review. Int Biodeter Biodegr 34: 333–348. doi: 10.1016/0964-8305(94)90092-2
![]() |
[16] |
Ista LK, Callow ME, Finlay JA, et al. (2004) Effect of substratum surface chemistry and surface energy on attachment of marine bacteria and algal spores. Appl Environ Microbiol 70: 4151–4157. doi: 10.1128/AEM.70.7.4151-4157.2004
![]() |
[17] | Chamberlain AHL (1992) The role of adsorbed layers in bacterial adhesion, In: Melo LF, Bott TR, Fletcher M, et al. Authors, Biofilms – Science and Technology, Dordrecht: JKluwer Academic, 59–67. |
[18] | Absolom DR, Lamberti FV, Policova, Z, et al. (1983) Surface thermodynamics of bacterial adhesion. Appl Environ Microbiol 46: 90–97. |
[19] |
Grasland B, Mitalane J, Briandet R, et al. (2003) Bacterial biofilm in seawater: cell surface properties of early-attached marine bacteria. Biofouling 19: 307–313. doi: 10.1080/0892701031000121041
![]() |
[20] |
Dalton HM, Goodman AE, Marshall KC (1996) Diversity in surface colonization behavior in marine bacteria. J Ind Microbiol Biotechnol 17: 228–234. doi: 10.1007/BF01574697
![]() |
[21] |
Marshall KC, Stout R, Mitchell R (1971) Selective sorption of bacteria from seawater. Can J Microbiol 17: 1413–1416. doi: 10.1139/m71-225
![]() |
[22] |
O’Toole GA, Kolter R (1998) Flagellar and twitching motility are necessary for Pseudomonas aeruginosa biofilm development. Mol Microbiol 30: 295–304. doi: 10.1046/j.1365-2958.1998.01062.x
![]() |
[23] | Belas R (2014) Biofilms, flagella, and mechanosensing of surfaces by bacteria. Trends Microbiol 22: 518–527. |
[24] |
Marshall KC, Stout R, Mithcell R (1971) Mechanism of the initial events in the sorption of marine bacteria to surfaces. J Gen Microbiol 68: 337–348. doi: 10.1099/00221287-68-3-337
![]() |
[25] |
Witt V, Wild C, Uthicke S (2011) Effect of substrate type on bacterial community composition in biofilms from the Great Barrier Reef. FEMS Microbiol Lett 323: 188–195. doi: 10.1111/j.1574-6968.2011.02374.x
![]() |
[26] |
Siboni N, Lidor M, Kramarsky-Winter E, et al. (2007) Conditioning film and initial biofilm formation on ceramics tiles in the marine environment. FEMS Microbiol Lett 274: 24–29. doi: 10.1111/j.1574-6968.2007.00809.x
![]() |
[27] |
Patrauchan MA, Sarkisova S, Sauer K, et al. (2005) Calcium influences cellular and extracellular product formation during biofilm-associated growth of a marine Pseudoalteromonas sp. Microbiology 151: 2885–2897. doi: 10.1099/mic.0.28041-0
![]() |
[28] |
Dang H, Li T, Chen M, et al. (2008) Cross-ocean distribution of Rhodobacterales bacteria as primary surface colonizers in temperate coastal marine waters. Appl Environ Microbiol 74: 52–60. doi: 10.1128/AEM.01400-07
![]() |
[29] |
Lee, JW, Nam JH, Kim YH, et al. (2008) Bacterial communities in the initial stage of marine biofilm formation on artificial surfaces. J Microbiol 46: 174–182. doi: 10.1007/s12275-008-0032-3
![]() |
[30] | Satheesh S, Wesley SG (2010) Biofilm development on acrylic coupons during the initial 24 hour period of submersion in a tropical coastal environment. Int J Oceanogr Hydrobiol 39: 27–38. |
[31] | Rao TS (2010) Comparative effect of temperature on biofilm formation in natural and modified marine environment. Aquat Ecol 44: 463–478. |
[32] |
Witt V, Wild C, Kenneth RN, et al. (2011) Effects of ocean acidification on microbial communit composition of, and oxygen fluxes through, biofilms from the Great Barrier Reef. Environ Microbiol 13: 2976–2989. doi: 10.1111/j.1462-2920.2011.02571.x
![]() |
[33] |
Hudon C, Bourget E (1981) Initial colonization of artificial substrate: community development and structure studied by scanning electron microscopy. Can J Fish Aquat Sci 38: 1371–1384. doi: 10.1139/f81-184
![]() |
[34] | Doiron K, Linossier I, Fay F, et al. (2012) Dynamic approaches of mixed species biofilm formation using modern technologies. Mar Environ Res 30: 1–8. |
[35] |
Pan LA, Zhang J, Zhang LH (2007) Picophytoplankton, nanophytoplankton, heterotrophic bacteria and viruses in the Changjang Estuary and adjacent coastal waters. J Plankton Res 29: 187–197. doi: 10.1093/plankt/fbm006
![]() |
[36] | Wang M, Liang Y, Bai X, et al. (2010) Distribution of microbial populations and their relationship with environmental parameters in the coastal waters of Qingdao, China. Environ Microbiol 12: 1926–1939. |
[37] |
Nayar S, Goh, BPL, Chou LM (2005) Settlement of marine periphytic algae in a tropical estuary. Estuar Coast Shelf Sci 64: 241–248. doi: 10.1016/j.ecss.2005.01.016
![]() |
[38] | Mitbavkar S, Raghu C, Rajaneesh KM, et al. (2012) Picophytoplankton community from tropical marine biofilms. J Exp Mar Biol Ecol 426–427: 88–96. |
[39] |
McDougald D, Rice SA, Kjelleberg S (2007) Bacterial quorum sensing and interference by naturally occurring biomimics. Anal Bioanal Chem 387: 445–453. doi: 10.1007/s00216-006-0761-2
![]() |
[40] |
Kjelleberg S, Molin S (2002) Is there a role for quorum sensing signals in bacterial biofilms? Curr Opin Microbiol 5: 254–258. doi: 10.1016/S1369-5274(02)00325-9
![]() |
[41] |
Joint I, Tait K, Callow ME (2002) Cell-to-cell communication across the prokaryote-eukaryote boundary. Science 298: 1207. doi: 10.1126/science.1077075
![]() |
[42] |
Tait K, Williamson H, Atkinson S (2009) Turnover of quorum sensing signal molecules modulates cross-kingdom signaling. Environ Microbiol 11: 1792–1802. doi: 10.1111/j.1462-2920.2009.01904.x
![]() |
[43] | Zhou J, Lyu Y, Richlen ML, et al. (2016) Quorum sensing is a language of chemical signals and plays an ecological role in algal-bacterial interactions. Crit Rev Plant Sci. doi: 1080/07352689.2016.1172461. |
[44] |
Yang C, Fang S, Chen D, et al. (2016) The possible role of bacterial signal molecules N-acyl homoserine lactones in the formation of diatom-biofilm (Cylindrotheca sp.). Mar Pollut Bull 107: 118–124. doi: 10.1016/j.marpolbul.2016.04.010
![]() |
[45] | Walker DI, Keevil CW (2015) Low-concentration diffusible molecules affect the formation of biofilms by mixed marine communities. Cogent Biol 1: 1103830. |
[46] |
Dusane DH, Damare SR, Nancharaiah YV, et al. (2013) Disruption of microbial biofilms by an extracellular protein isolated from epibiotic tropical marine strain of Bacillus licheniformis. PLoS ONE 8: e64501. doi:10.1371/journal.pone.0064501. doi: 10.1371/journal.pone.0064501
![]() |
[47] |
Kiemle SN, Domozych DS, Gretz, MR (2007) The extracellular polymeric substances of desmids (Conjugatophyceae, Streptophyta): chemistry, structural analyses and implications in wetland biofilms. Phycologia 46: 617–627. doi: 10.2216/06-97.1
![]() |
[48] |
Anderson OR (2013) Naked amoebae in biofilms collected from a temperate freshwater pond. J Eukaryot Microbiol 60: 429–431. doi: 10.1111/jeu.12042
![]() |
[49] |
Jones PR, Cottrell, MT, Kirchman DL, et al. (2007) Bacterial community structure on artificial surfaces in an estuary. Microb Ecol 53: 153–162. doi: 10.1007/s00248-006-9154-5
![]() |
[50] |
Lau S, Thiyagarajan V, Cheung S et al. (2005) Roles of bacterial community composition in biofilms as a mediator for larval settlement of three marine invertebrates. Aquat Microbiol Ecol 38: 41–51. doi: 10.3354/ame038041
![]() |
[51] |
Lee JW, Nam JH, Kim YH, et al. (2008) Bacterial communities in the initial stage of marine biofilm formation on artificial surfaces. J Microbiol 46: 174–182. doi: 10.1007/s12275-008-0032-3
![]() |
[52] |
Patil J, Anil A (2005) Biofilm diatom community structure: influence of temporal and substratum variability. Biofouling 21: 189–206. doi: 10.1080/08927010500256757
![]() |
[53] | Dobretsov S (2009) Marine Biofilms, In: Dürr S, Thomason, JC Authors, Biofouling. Oxford: Wiley-Blackwell. doi: 10.1002/9781444315462.ch9. |
[54] |
Zargiel KA, Coogan JS, Swain GW (2011) Diatom community structure on commercially available ship hull coatings. Biofouling 27: 955–965. doi: 10.1080/08927014.2011.618268
![]() |
[55] | Salta M, Wharton JA, Blache Y, et al. (2013) Marine biofilms on artificial surfaces: structure and dynamics. Environ Microbiol 15: 2879–2893. |
[56] |
Fröls S (2013). Archaeal biofilms: widespread and complex. Biochem Soc Trans 41: 393–398. doi: 10.1042/BST20120304
![]() |
[57] |
Briggs BR, Pohlman JW, Torres M, et al. (2011) Macroscopic biofilms in fracture-dominated sediment that anaerobically oxidize methane. Appl Environ Microbiol 77: 6780–6787. doi: 10.1128/AEM.00288-11
![]() |
[58] |
Schrenk MO, Kelley DS, Delaney JR, et al. (2003) Incidence and diversity of microorganisms within the walls of an active deep-sea sulfide chimney. Appl Environ Microbiol 69: 3580–3592. doi: 10.1128/AEM.69.6.3580-3592.2003
![]() |
[59] |
Schrenk MO, Kelley DS, Bolton SA, et al. (2004) Low archaeal diversity linked to subseafloor geochemical processes at the Lost City Hydrothermal Field, Mid-Atlantic Ridge. Environ Microbiol 6: 1086–1095. doi: 10.1111/j.1462-2920.2004.00650.x
![]() |
[60] |
Webster NS, Negri AP (2006) Site-specific variation in Antarctic marine biofilms established on artificial surfaces. Environ. Microbiol 8: 1177–1190. doi: 10.1111/j.1462-2920.2006.01007.x
![]() |
[61] |
Ionescu D, Siebert C, Polerecky L, et al. (2012) Microbial and chemical characterization of underwater fresh water springs in the Dead Sea. PLoS ONE 7: e38319. doi: 10.1371/journal.pone.0038319
![]() |
[62] |
Fröls S, Dyall-Smith M, Pfeifer F (2012) Biofilm formation by haloarchaea. Environ Microbiol 14: 3159–3174. doi: 10.1111/j.1462-2920.2012.02895.x
![]() |
[63] | Schrenk MO, Kelley DS, Delaney JR, et al. (2003) Incidence and diversity of microorganisms within the walls of an active deep-sea sulfide chimney. Appl Environ Microbiol 69: 3580–3592. |
[64] |
Doghri I, Rodrigues S, Bazire A, et al. (2015) Marine bacteria from the French Atlantic coast displaying high forming-biofilm abilities and different biofilm 3D architectures. BMC Microbiol 15: 231. doi 10.1186/s12866-015-0568-4. doi: 10.1186/s12866-015-0568-4
![]() |
[65] |
Naraváez-Zapata J, Tebbe CC, Ortega-Morales BO (2005) Molecular diversity and biomass of epilithic biofilms from intertidal rocky shores of the Gulf of Mexico. Biofilms 2: 93–103. doi: 10.1017/S147905050500178X
![]() |
[66] | Moldoveanu AM (2012) Environmental factors influences on bacterial biofilms formation. Ann RSCB 17: 118–126. |
[67] | Chiu JMY, Thiyagarajan V, Tsoi MMY, et al. (2006) Qualitative and quantitative changes in marine biofilms as a function of temperature and salinity in summer and winter. Biofilms 2: 183–195. |
[68] |
Meyer-Reil L-A, Köster M (2000) Eutrophication of marine waters: effects on benthic microbial communities. Mar Poll Bull 41: 255–263. doi: 10.1016/S0025-326X(00)00114-4
![]() |
[69] | Underwood GJC (2010) Exopolymers (extracellular polymeric substances) in diatom-dominated marine sediments. In: Seckbach J, Oren A Authors, Microbial Mats: Modern and Ancient Microorganisms in Stratified Systems, Cellular Origin, Life in Extreme Habitats and Astrobiology Berlin: Springer. Science+Business Media B.V 14: 287–300. doi 10.1007/978-90-481-3799-2_15. |
[70] |
Steele DJ, Franklin DJ, Underwood GJC (2014) Protection of cells from salinity stress by extracellular polymeric substances in diatom biofilms. Biofouling 30: 987–998. doi: 10.1080/08927014.2014.960859
![]() |
[71] |
Krembs C, Eicken H, Junge K (2002) High concentrations of exopolymeric substances in Arctic winter sea ice: implications for the polar ocean carbon cycle and cryoprotection of diatoms. Deep-Sea Res I 49: 2163–2181. doi: 10.1016/S0967-0637(02)00122-X
![]() |
[72] |
Perkins RG, Lavaud J, Serôdio J, et al. (2010) Vertical cell movement is a primary response of intertidal benthic biofilms to increasing light dose. Mar Ecol Prog Ser 416: 93–103. doi: 10.3354/meps08787
![]() |
[73] | Paerl HW, Pinckney JL (1996) A mini-review of microbial consortia: their roles in aquatic production and biogeochemical cycling. Microb Ecol 31: 225–247. |
[74] | Newman DK, Banfield JF (2003) Geomicrobiology: how molecular-scale interactions underpin biogeochemical systems. Science 296: 1071–1077. |
[75] |
Lugomela C, Söderbäck E, Björk M (2005) Photosynthesis rates in cyanobacteria-dominated sub-tidal biofilms near Zanzibar, Tanzania. Estuar Coast Shelf Sci 63: 439–446. doi: 10.1016/j.ecss.2004.11.012
![]() |
[76] | Stal LJ (2000) Cyanobacterial mats and stromatolites. In: Whitton BA, Potts M Authors, The Ecology of Cyanobacteria: Their Diversity in Time and Space. Dordrecht: Kluwer Academic Publishers 61–120. |
[77] |
Johnstone RW, Koop K, Larkum AWD (1990) Physical aspects of coral reef lagoon sediments in relation to detritus processing and primary production. Mar Ecol Progress Ser 66: 273–283. doi: 10.3354/meps066273
![]() |
[78] |
Uthicke S, Klumpp DW (1998) Microphytobenthos community production at a near-shore coral reef: seasonal variations and response to ammonium recycled by holothurians. Mar Ecol Progress Ser 169: 1–11. doi: 10.3354/meps169001
![]() |
[79] |
Magalhães CA, Bordalo A, Wiebe WJ (2003) Intertidal biofilms on rocky substratum can play a major role in estuarine carbon nutrient dynamics. Mar Ecol Progress Ser 258: 275–281. doi: 10.3354/meps258275
![]() |
[80] |
Bellinger BJ, Underwood GJC., Ziegler SE, et al. (2009) Significance of diatom-derived polymers in carbon flow dynamics within estuarine biofilms determined through isotopic enrichment. Aquat Microb Ecol 55: 169–187. doi: 10.3354/ame01287
![]() |
[81] | Decho AW (1990) Microbial exopolymer secretions in ocean environments: their role(s) in food webs and marine processes. Oceanogr Mar Biol Ann Rev 28: 73–153. |
[82] | Bhaskar PV, Bhosle NB (2005) Microbial extracellular polymeric substances in marine biogeochemical processes. Current Sci India 88: 45–53. |
[83] | Orcutt BN, Sylvan JB, Rogers DR (2015) Carbon fixation by basalt–hosted microbial communities. Front Microbiol 6: 904. doi: 10.3389/fmicb.2015.00904. |
[84] |
Mislan KAS, Stock CA, Dunne JP, et al. (2014) Group behavior among model bacteria influence particulate carbon remineralization depths. J Mar Res 72: 183–218. doi: 10.1357/002224014814901985
![]() |
[85] | Jacobsen TR, Azam F (1984) Role of bacteria in copepod fecal pellet decomposition: Colonization, growth-rates and mineralization. Bull Mar Sci 35: 495–502. |
[86] | Magalhães CM, Wiebe W.J, Jove SB, et al. (2006). Inorganic nitrogen dynamics in the intertidal rocky biofilms and sediments of the Douro River Estuary (Portugal). Estuaries 28: 592–607. |
[87] |
Magalhães CM, Joye SB, Moreira RM, et al. (2005) Effect of salinity and inorganic nitrogen concentrations on nitrification and denitrification rates in intertidal sediments and rocky biofilms of the Douro River estuary, Portugal. Water Res 39: 1783–1794. doi: 10.1016/j.watres.2005.03.008
![]() |
[88] |
Rao TS (2003) Temporal variations in an estuarine biofilm: with emphasis on nitrate reduction. Estuar Coast Shelf S 58: 67–75. doi: 10.1016/S0272-7714(03)00060-X
![]() |
[89] |
Revsbech NP, Risgaard-Petersen N, Schramm A, et al. (2006) Nitrogen transformations in stratified aquatic microbial ecosystems. A van Leeuw 90: 361–375. doi: 10.1007/s10482-006-9087-5
![]() |
[90] | Hamm RE, Thomoson TG (1941) Dissolved nitrogen in the seawater of the Northeast Pacific with notes on the total carbon dioxide and dissolved oxygen. J Mar Res 4: 11–27. |
[91] |
Li M, Gu J-D (2011) Advances in methods for detection of anaerobic ammonium oxidizing (anammox) bacteria. Appl Microbiol Biotechnol 90: 1241–1252. doi: 10.1007/s00253-011-3230-6
![]() |
[92] |
Awata T, Tanabe, K, Kindaichi T, et al. (2012) Influence of temperature and salinity on microbial structure of marine anammox bacteria. Water Sci Technol 66: 958–964. doi: 10.2166/wst.2012.234
![]() |
[93] |
Waite RD, Papakonstantinopoulou A, Littler E, et al. (2005) Transcriptome analysis of Pseudomonas aeruginosa growth: comparison of gene expression in planktonic cultures and developing and mature biofilms. J Bacteriol 187: 6571–6576. doi: 10.1128/JB.187.18.6571-6576.2005
![]() |
[94] |
Karatan E, Watnick P (2009) Signals, regulatory networks, and materials that build and break bacterial biofilms. Microbiol Mol Biol R 73: 310–347. doi: 10.1128/MMBR.00041-08
![]() |
[95] | Dötsch A, Eckweiler D, Schniederjans M, et al. (2011) The Pseudomonas aeruginosa transcriptome in planktonic cultures and static biofilms using RNA sequencing. PLoS ONE 7: e31092. doi:10.1371/journal.pone.0031092. |
[96] |
Dang H, Lovell CR (2016) Microbial surface colonization and biofilm development in marine environments. Microbiol Mol Biol R 80: 91–138. doi: 10.1128/MMBR.00037-15
![]() |
[97] |
Zimmermann-Timm H, Holst H, Müller S (1998) Seasonal dynamics of aggregates and their typical biocoenosis in the Elbe estuary. Estuaries 21: 613–621. doi: 10.2307/1353299
![]() |
[98] | Crump B, Baross J, Simenstad C (1998) Dominance of particle-attached bacteria in the Columbia River estuary, USA. Aquat Microb Ecol 14:7–18. |
[99] | Caron D (1987) Grazing of attached bacteria by heterotrophic microflagellates. Microb Ecol 13: 203–218. |
[100] |
Rogerson A, Anderson OR, Vogel C (2003) Are planktonic naked amoebae predominately floc associated or free in the water column. J Plankton Res 25: 1359–1365. doi: 10.1093/plankt/fbg102
![]() |
[101] |
Lesen AE, Juhl AR, Anderson OR (2010) Abundance and biomass of heterotrophic microplankton in the lower Hudson River Estuary, USA: Potential importance of naked, planktonic amebas for bacterivory and carbon flux. Aquat Microb Ecol 61: 45–56. doi: 10.3354/ame01434
![]() |
[102] | Anderson OR (2011) Particle-associated planktonic naked amoebae in the Hudson Estuary: size-fraction related densities, cell sizes and estimated carbon content. Acta Protozool 50: 15–22. |
[103] |
Juhl A, Anderson OR (2014) Geographic variability in amoeboid protists and other microbial groups in the water column of the lower Hudson River Estuary (New York, USA). Estuar Coast Shelf S 151: 45–53. doi: 10.1016/j.ecss.2014.09.020
![]() |
[104] |
Dupuy C, Agogué H, Guizien K, et al. (ed.) (2014) Trophic significance of microbial biofilm in tidal flats. J Sea Res 92: 1–178. doi: 10.1016/j.seares.2014.07.002
![]() |
[105] |
Dupuy C, Mallet C, Guizien K, et al. (2014) Sequential resuspension of biofilm components (viruses, prokaryotes and protists) as measured by erodimetry experiments in the Brouage mudflat (French Atlantic coast). J Sea Res 92: 56–65. doi: 10.1016/j.seares.2013.12.002
![]() |
[106] |
Montanié H, Ory P, Orvain F, et al. (2014) Microbial interactions in marine water amended by eroded benthic biofilm: A case study from an intertidal mudflat. J Sea Res 92: 74–85. doi: 10.1016/j.seares.2013.11.011
![]() |
[107] |
Saint-Béat B, Dupuy C, Agogué H, et al. (2014) How does the resuspension of the biofilm alter the functioning of the benthos-pelagos coupled food web of a bare mudflat in Marennes-Oléron Bay (NE Atlantic). J Sea Res 92: 144–157. doi: 10.1016/j.seares.2014.02.003
![]() |
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