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ISSNOO27-1314

Moscow University

Chemistry

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Bulletin
(Vestnik Moskovskogo Universiteta. Khimiya)
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Vol.

57,

No.6
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Mo.cow Uni..er.ity Chemi.try Bulletin Vol. 57, No.6, pp. 75-78, 2002

Ve.tnik Mo.ko...ko90 Uni..er.iteta. Khimiya UDC 579.088;577.158.54

DEVELOPMENT OF A PHENOMENOLOGICAL MODEL OF THE KINETICS OF BACTERIAL ADSORPTION ON LOW-ENERGY SURFACES
V. V. Fedorovich, S. V. Kalyuzhnyi, P. van der Meeren., and W. Verstraete..

A mathematical model of the kinetics of bacterial adsorption on polymeric materials with various hydrophobicity is developed. The model describing the bacteria-liquid phase-polymer surface system is capable of predicting the amount of bacteria adsorbed on the surface within a certain period of time. The model is based on the resolution of the motive f?rce of adsorption into two components. The first component characterizes the interactions based on the hydrophobic properties of bacteria and polymers and is expressed in terms of interphase tensions. The second component describes the remaining types of interactions, which cannot be represented in a similar way.

Our work was dedicated to the establishment of a quantitative relation between the rate of adsorption of a certain class of microorganisms on polymeric materials and their adhesion to the latter. The results of an analysis of the free energy of adhesion of microorganisms to various polymeric materials and the experimentally found amounts of microorganisms adsorbed on polymers per unit time [1] are a direct corroboration of the existence of this relation. The simplest physicochemical approach widely employed in describing the adhesion processis the one based on classical thermodynamics [2]. At present, this approach is extensively used in many works to describe the bacterial adhesion process [1, 3-6]. Based on these papers, we may conclude that two main factors affect the adhesion process: the hydrophobicity of the bacterial wall and the adsorbing surface on the one hand and their charges, on the other. In some special problems concerning granulation processesand the development of biofilms, the key factor is the rate of bacterial adsorption. Various attempts have been made in this field [7, 8]. As a rule, these works deal with the time dependenceof the number of bacteria adsorbed on unit area determined by statistical methods. However, no description of the kinetics of this processin terms of energy parameters, as, for example, in the Arrhenius law for the kinetics of a chemical reaction, has been made until now. One of the possibilities for finding this relationship resides in representing the rate of the adsorption process as a sum of the rates of processeshaving different origin. In this case the kinetics of bacterial adsorption can partly be expressedon the basis of thermodynamic propositions. A similar approach was used for establishing the relationship between the free energy of adhesion and the number of adsorbed bacteria [9, 10]. Unfortunately, the resultant relationships describe only the final equilibrium states of the liquid-bacteria-adsorbing surface system; it is not possible to obtain any expressionsfor the kinetics of the process. Nevertheless,it is clear that this approach may be useful in the development of the fundamentals of the kinetics. .

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Interphase TechnologiesTeam. . Laboratory of Microbial Ecology, Department of Applied BiQlogic.alSciencesand Agriculture, Ghent

University,Ghent B-90000, Belgium. @ 2003 by Allerton Press,Inc.

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Cherni.try

Bulletin

Vol. 57, No.6

In this article we consider adsorption of hydrophilic microorganisms on low-energyuncharged surfaces. In this case, we may expect that the motive force of the adsorption process is based on hydrophobic interactions. Moreover, the well-known equation of state for calculating the adhesion energy in terms of surface tensions can be employed in the analysis of the kinetics of bacterial adsorption. The choiceof the system in question is not accidental. As wasshown [11], it is not always possible to find a clear-cut correlation between the electrophoretic mobility of bacteria and their adhesionto materials with different surface properties. Thus, by selecting the required experimental conditions, we may expect that the contribution of electrostatic interactions will be low. The contribution of other interactions (including electrostatic) to the adhesion processcan be taken into account by using an additional parameter. THE DEVELOPMENT OF A MODEL

The main dependences the model describing the number of bacteria adsorbed on unit surface as a of function of time are representedby Eqs. (1) and (3). Because the present paper we considershort-duration in experiments, the bacterial growth on the surfacesof materials is not taken into account. dN saccess(t) 8.Gh~ 0, dt =
(1) (2) (3)

dt = 0, saccess(t) = Stot(l- N(t)Stot).

dN

saccess (t)

As is seen in Eq. (1), the rate of bacterial adsorption is represented by the sum of two terms. The first term containing 8.Gh is the rate of adsorption determined by the hydrophobic properties of the wall of the bacterial cell and of the surface of the material. It is expressedthrough interphase tensions (type 1 interaction). III in Eqs. (1) and (2) describes the contribution of other interaction types to the process of adsorption (type 2 interaction). For this reason, the 8.Gh > 0 condition in Eq. (2) denotes the zero contribution of the hydrophobic component to the adsorption process. It is also assumedthat the adsorption rate is directly proportional to the number of cells in unit volume of the surroundings, Next, and to the portion of the surface {S(t)}jS that is accessiblefor the adsorption process. The absolute value of the accessiblesurface at any time is calculated from Eq. (3). The use of the resolution of motive forces of this type makesit possible to analyze both terms in the rate expressions independently of one another. It follows from thermodynamics that if only hydrophobic properties are to be analyzed, the process of bacterial adhesion will depend on the changesin the so-called free energy of adhesion or Gibbs' free energy (8.Gh) between the following phases: solid-liquid, bacterium-solid, and liquid-vapor. In this case the adhesionprocessoccurs if the adhesion energy of the system becomeslower. This energy can be found from Eq. (4). One of the main ideas of our work consistsin the use of 8.Gh for the description of the contribution of hydrophobic interactions to the adsorption process. In order to calculate the 8.Gh value, Eq. (4) should be supplementedby Eqs. (5)-(8). Equations (5) and (7) are the Young equations [2] for two systems: one system includes the surface of the polymer, liquid, and vapor, the second, the wall of the bacterial cell, liquid, and vapor. Using the equation of state [12, 13], we can supplement Eq. (5) with Eq. (6). This makes it possible to find in a unique fashion ")'Lv (and "YSL) the experimental data on the wetting angle 0SL and if on the surface tension of the liquid ")'Lvare known. Moreover, Eqs. (5) and (6) allow one to find "YSL any for value of the surface tension of the liquid basedon the "YsVvalue found earlier,

8.Gh "YBS"YBL - "YSL, = "Ysv

(4)
(5)
- "YSV)2) . (6)

-

"YSL

=

")'Lv

cos 0SL,

cos0SL = -1 + 2

fiii

exp (-0.0001247(")'LV

Vm 76


Mo.cow Uni1ler.ity Cherni.try Bulletin

Vol. 57, No.6

A similar approach can be used in finding 'YBv (and 'YBL)from Eqs. (7) and (8) on the condition that the experiment gives the values of the wetting angle 0BL and of the surface tension of the liquid 'YLv. In this caseEqs. (7) and (8) are used for determining 'YBLfor any 'YLVvalue from the 'YBv value found above, 'YBv
cos 0BL = -1 +2

-

'YBL

=

'YLv cos 0BL,
'YBV)2) .

(7)
(8) .

~ y-:r;;;

exp (-0.0001247('YLv

Formally, the equation of state can be applied to calculate cos0BS from 'YSVand 'YBv. Using the Young equation and the hypothetic value of the wetting angle, we can find 'YBS. Thus, Eqs. (4)-(8) allow us to calculate the changesin the adhesion energy between two states for an individual bacterium in the case where only hydrophobic interactions are taken into account. It should be noted that in the present work we used a new form of the relationship between the experimental values of the wetting angle and of the surface tension (Eqs. (6) and (8)). The main advantage of this form, which was derived earlier [13], is the absenceof singularity in the equation for the wetting angle. The process of bacterial accumulation on the surface of an inert material leads to a change in the averagedhydrophobic properties of the adsorbingsurface. This fact can be taken into account by introducing the effective wetting angle 0slf:(t), which can be J;neasured experimentally. As was shown earlier [14], the hydrophobicity of a bacterial mixture is the averageof the hydrophobicities of its components. Using this fact, we can calculate the effective hydrophobicity of the surface of the material as the average of the hydrophobicities of the portion that is occupied by the bacteria (1 - S(t)jS) and the portion that is free from the latter (S(t)jS), respectively,

cos 0slf:(t) (1- ~) =

cos + ~ C?s 0BL 0SL.

(9)

As the surface is covered with bacteria, the cos0slf:(t) function approachesin time the constant value 0BL. In our work the 0SL value, which dependsonly on the properties of the surface and liquid, will be used for calculating the 6.Gh value. This means that the bacteria will be fixed on the free portion of the surface rather than on bacteria adsorbed earlier; hence, the free energy of adhesionwill remain unchanged. Nevertheless,the rate of adsorption will decrease the available area is reduced. as Equations (4)-(8) are all that is necessary calculating the first component of the adsorption rate for based on the hydrophobic properties of the wall of the bacterial cell and on the properties of the surface of the inert material (type 1 interactions). The second term in Eqs. (1) and (2), lIt, characterizing the contribution of type 2 interactions to the adsorption rate can be determined from Eq. (2). In this case the rate of adsorption does not depend on 6.Gh. As in the present paper we consider adhesion to low-energy surfaces,the contribution made by the \If value may be assumed to be sufficiently low. Thus, if the experiment is designedin such a manner that it contains the area where 6.Gh > 0, the lIt term can be determined experimentally.

REFERENCES
1. D.R. Absolom, F. V. Lamberti, Z. Policova,W. Zingg, et al., Appl. Environ. Microbiol., vol. 46, p. 90, 1983. 2. A.W. Adamson, Physical Chemistry of Surfaces,p. 378, Wiley, New York, 1976. 3. D.F. Gerson, Biochim. Biophys. Acta, vol. 602, p. 269, 1980. 4. H.J. Busscher,A.H. Weerkamp, H.C. van der Mei, A.W.J. van Pelt, et al., Appl. Environ. Microbiol., vol. 48, p. 980, 1983. 5. M.C.M. van Loosdrecht and A.J.B. Zehnder, Experientia, vol. 46, p. 817, 1990. 6. J. T .C. Grotenhuis, Structure and Stability of Methanogenic Granular Sludge,Ph.D. Thesis, Agricultural University of Wageningen, the Netherlands, p. 27, 1992. 7. J.P. Robins and M.S. Switzenbaum, Environ. Technol., vol. 11, p. 521,1990. 8. M. Fletcher, Can. J. Microb., vol. 23, p. 1, 1977. 77


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9. I.H. Pratt-Terpstra, A.H. Weerkamp, and H.J. Busscher, Current Microb., vol. 16, p. 311, 1988. 10. I.H. Pratt-Terpstra, A.H. Weerkamp, and H.J. Busscher, J. Colloid Interface Sci., vol. 129, p. 568, 1989. 11. M.C.M. van Loosdrecht, Bacterial Adhesion, Ph.D. Thesis, Agricultural University of Wageningen, the Netherlands, p. 35, 1988. 12. A. W. Neumann, R.J. Good, C.J. Hope, and M. Sejpal, J. Colloid Interface Sci., vol. 49, p. 291, 1974. 13. D. Li and A. W. Neumann, J. Colloid Interface Sci., vol. 148, p. 190, 1992. 14. D. Daffonchio, J. Thaveesri, and W. Verstraete, Appl. Environ. Microbiol., vol. 61, p. 3676, 1995. 25 October 2002 Chair of Chemical Enzymology E-mail: vfedorovich@enz.chem.msu.ru

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