Horizontal transfer of genetic elements in nature

 

Horizontal transfer of genetic elements in nature has been linked to bacterial adaptation and evolution, thus giving rise to a range of important phenomena, in some cases benefi- cial, e.g., acquired or enhanced biodegradation capabilities by a bacterial strain, but in other instances potentially hazardous, for example, the development of antibiotic resistance by pathogens, and gene flow from genetically modified organisms to native soil microfauna (Miller and Levy, 1989). The main known transfer processes are transformation (uptake of DNA from the environ- ment), transduction (DNA transfer mediated by a bacteriophage), and conjugation (cell-to-cell DNA transfer requiring contact). Conjugation is of particular interest, as it is possibly one of the major mechanisms of transfer of genetic information in the envi- ronment (Yin and Stotzky, 1997). Although the mechanisms at play have been elucidated, the processes controlling rates of con- jugative gene transfer are currently incompletely identified, and associated expressions for kinetic rates of gene transfer have been

Department of Civil & Environmental Engineering, 1 Shields Ave., Univ. of California, Davis, CA 95616. Received 10 May 2006. *Corresponding author (trginn@ucdavis.edu).

 

Vadose Zone J. 6:306–315 doi:10.2136/vzj.2006.0069

© Soil Science Society of America

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established only for particular isolated microcosm studies, such as solutions or biofilms in batch. Because conjugation frequency depends on local cell number densities, when bacteria move through multiphase environments such as subsurface porous media, conjugative gene transfer rates will depend on bacterial transport and rates of attachment and detachment to surfaces.

Planktonic cells, biofilm pieces, and cell clumps in perme- able porous media (aquifer materials) may undergo advection, dispersion, motile transport, attachment, adhesion, and detach- ment processes, which may or may not lead to biofilm forma- tion depending on multiple abiotic and biotic factors, including aqueous chemistry and nutrient availability, physiological state of microbes, chemotactic activity, quorum sensing, and other community dynamics (e.g., Lappin-Scott and Bass, 2001; Ginn et al., 2005). Biofilm formation is a sequential process with five developmental stages: reversible attachment, irreversible attach- ment, sessile community, climax community, and mature biofilm (e.g., Jenkinson and Lappin-Scott, 2001). Biofilms are foci for the study of conjugative gene transfer (Beaudoin et al., 1998a; Lilley and Bailey, 2002), as microbes are in close proximity in the biofilm, arranged in a variety of architectural and functional phenotypes (Molin and Tolker-Nielsen, 2003). The focus of this study was on preliminary model development for conjuga- tive gene transfer within the first three developmental stages of biofilms, i.e., before the formation of a climax community or a mature biofilm. Thus, our interest lies with the conjugative pro- cess that can occur on surfaces during the transport of individual microorganisms through porous media and their attachment to solid surfaces.




We begin with a summary review of gene transfer processes with primary emphasis on conjugation as performed by the F- plasmid in Escherichiae coli, the first and most studied mecha- nism (Birge, 1994). As we are interested in viewing conjugative gene transfer in the context of soil science and hydrogeological applications, we maintain a focus on kinetics of these processes in multiphase systems. Developing our conceptual model from the current knowledge reviewed, we introduce a novel modeling framework for kinetics of horizontal gene transfer on surfaces that honors lags observed in conjugation kinetics studies by use of the exposure-time approach (Ginn, 2000). We also describe how to integrate the novel kinetics of gene transfer by conjuga- tion with bacterial fate and transport processes including advec- tion, motility, and filtration.

Horizontal Gene Transfer

 

The following review is limited to kinetics, with a general introduction to horizontal genetic transfer processes in prokary- otes, within a soil science context. Vertical gene transfer among unicellular organisms involves the inheritance of a copy of the parent cell genetic material by the “daughter” cell during rep- lication. Horizontal gene transfer processes allow genetic mate- rial to move among cells and their environment, independent of reproduction. As horizontal transfer involves organisms of multiple species, it is of concern for (unintended) spread of anti- biotic resistance, and transfer of engineered genes and virulence properties. Processes and rates of horizontal transfer also affect potential beneficial applications, such as conveyance of xeno- biotic degradation ability in bioremediation of organic com- pounds or metal tolerance in engineered reductive precipitation. Understanding the kinetics of horizontal transfer is crucial to quantify these impacts and estimate related risks, and to pro- vide insights into the evolution of microorganisms (Birge, 1994; Maloy et al., 1994; Davison, 1999).

Three main types of horizontal gene transfer mechanisms are known so far in bacteria. Transformation is the uptake of free DNA from the environment and was first observed in the 1920s in Streptococcus pneumoniae, during an experiment pro- viding the first direct evidence that DNA is genetic material (Avery et al., 1944; Magasanik, 1999; Madigan et al., 2003). Transduction is the transfer of genetic material via a bacterio- phage, i.e., a virus attacking a bacterial cell, and was discovered in 1952 in Salmonella typhimurium (Zinder and Lederberg, 1952; Lederberg, 1994; Magasanik 1999). Conjugation is the transfer of DNA, usually in the form of plasmids, via direct cell-to-cell contact (Salyers et al., 1998; Davison, 1999), and was reported as early as 1946 (Lederberg and Tatum, 1946). Gene transfer by these processes takes place despite the presence of what are effec- tively defense measures of the bacterial cell to prevent the entry of foreign DNA, such as endonucleases in the periplasm, hydro- phobic membranes, and negatively charged lipopolysaccharides in the outer membrane of Gram-negative bacteria (Kado and Syvanen, personal communication, 2005). We discuss here only conjugative gene transfer mechanisms.

Conjugation

Conjugation is thought to be the most frequent and effi- cient of all mechanisms of horizontal gene transfer in the envi-



ronment (Kado and Syvanen, personal communication, 2005). The process involves cell-to-cell contact and formation of a “mat- ing bridge,” followed by the transfer of horizontally mobile ele- ments (HMEs) of genetic material, typically plasmids or trans- posons. Plasmids are double-stranded extrachromosomal genetic elements, mostly circular in shape and ranging from 300 to 2 400 000 base pairs long. They exist inside prokaryotic and also a few eukaryotic organisms, and are capable of replication inde- pendently from the main DNA filament, as well as of insertion into the main filament. They are present in a cell in specific copy numbers, varying from one to >100 depending on the plasmid, while different plasmid types may coexist in one cell (Madigan et al., 2003). Transposons, originally called “jumping genes,” are mobile DNA segments that can frequently move from one loca- tion to another on the bacterial chromosome, and also to and from plasmids, but cannot replicate independently. They can be conjugative and, once in the cell genome, are reproduced by the normal cell duplication processes (Maloy et al., 1994; Roberts et al., 2001, Madigan et al., 2003). The distinguishing characteris- tic of HMEs is this peculiar ability of being transferred horizon- tally, in addition to vertically, while the chromosome can usually be transferred only from parent cell to daughter (Heinemann, 1998).

Plasmids and transposons can carry a variety of traits, including resistance to antibiotics or heavy metals, toxin pro- duction ability, virulence factors, ability to biodegrade a sub- strate, and plasmids encoding for the conjugative machinery itself (Maloy et al., 1994; Madigan et al., 2003). Nonconjugative plasmids can use the same mating bridge created by conjugative plasmids (Davison, 1999), but the resulting transfer is relatively rare. A distinction can be made between Gram-negative bac- teria, which among other characteristics can express a mating pilus, and Gram-positive, which come into contact without a pilus. The specific conjugation mechanisms vary for each plas- mid, but in most Gram-negative bacteria they follow that of the

E. coli “fertility” (F) plasmid, while in Gram-positive bacteria they are more diverse (Birge, 1994; Madigan et al., 2003). The transfer of genetic material from the recipient back to the donor has also been observed, even though the frequencies of such ret- rotransfer are lower than “forward” conjugation (Heinemann and Ankenbauer, 1993; Sia et al., 1996; Blanco et al., 1991). Conjugative transposons follow a similar scheme of transfer, but with some important differences. Normally integrated into the host genome, a transposon can excise itself with great preci- sion, and give origin to a covalently closed circular intermediate, which is then transferred to another cell by conjugation. The transposon also carries within itself integrase enzymes, which allow its integration into the genome of the new host. Due to the precision of the excision, the recipient cell receives all the genes needed for the transposon to transfer again, and is therefore fully functional as a donor if the transposon genes are expressed. Some other transposons are not self-transmissible, but can be mobilized by conjugative transposons (Salyers et al., 1998).

It has been observed that many plasmids and transpo- sons have a wide host range, in that they can be transferred to and expressed in bacterial cells of different species and genera. Moreover, conjugative transfer can cross the border between kingdoms, i.e., the transfer can happen from bacteria to yeasts, or to plants (Heinemann and Sprague 1989; Davison, 1999;

Roberts et al., 2001; Madigan et al., 2003). From a DNA-centric point of view, conjugation has also been viewed as an infectious process, through which a “selfish” DNA segment, such as a plas- mid or a transposon, exploits a host cell and assures its survival and spread, while at the same time it may provide useful traits to the host (Doolittle and Sapienze, 1980; Orgel and Crick, 1980; Rensing et al., 2002). Similarly, plasmid behavior has also been interpreted as the migration of a “population” from a patch of resources (a bacterial cell) to another to ensure its survival and multiplication (Landis et al., 2000). Another aspect of plasmid interaction with the host cell and among themselves is that plas- mids can affect the success of other plasmids in entering or resid- ing in a host cell (Birge, 1994).

Conjugative transfer data arise from either the observations in cell culture (macroscale) or confocal microscopy (cytoscale). Conjugation begins when donor and recipient come in contact, either by collision or via a conjugative pilus that may sense recip- ient cells. In the case of E.coli, the ability of a potential donor cell to initiate conjugation is dependent on its possession of the F or other conjugative plasmid. A physiologically active state of donors and recipients is a prerequisite as well. The F-plasmid in the donor directs the expression of one to three pili, rigid pilin fibers sticking out from the cell wall. Cell contact is followed by pilus retraction (or not, Lawley et al., 2004), and the forma- tion of a mating bridge by the fusion of a portion of cell mem- branes (Achtman et al., 1978). In the donor cell, DNA transfer is initiated at the oriT region of the plasmid, where one of the DNA strands is cleaved, and then gradually separated from the complementary strand while being transferred to the recipient through the mating bridge. When the single strand enters the recipient cell, a complementary strand is synthesized, and the DNA string reassumes the circular shape of a plasmid. While the single strand of DNA is being transferred to the recipient, this transferred strand is simultaneously replaced in the donor via a “rolling circle” mechanism. As the donor and recipient part, both cells own a complete copy of the plasmid (Madigan et al., 2003). The recipient develops thus into a potential donor, although the frequency of this happening is still debated (Sorensen et al., 2005) and is also dependent on inhibition mechanisms (Shi et al., 2005; Perez-Mendoza et al., 2005) or chromosomal integra- tion of the plasmid (Birge, 1994; Madigan et al., 2003).

As the transfer process can be very efficient, the spread of

a plasmid in a bacterial population can potentially convert all the cells to plasmid-positive. On the other hand, a plasmid can be lost by a cell population, especially when there is no selec- tive pressure to justify its retention; this phenomenon is termed “curing,” and consists in the progressive dilution of a plasmid in a population, as the plasmid doesn’t replicate together with the cell (Madigan et al., 2003). Also, in some studies on bio- films it was observed that when transconjugants had competitive advantage in selective conditions, after some initial conjugative transfer they tended to transfer the acquired plasmid vertically as their population grew (Christensen et al., 1998; Haagensen et al., 2002).

Conjugation has been observed both in controlled and natural environments, including the rhizosphere, water, soil and subsurface ecosystems, the leaf surface, and the animal intestine, in many cases with different kinetics and efficiencies, so that extrapolation from one case to the other is not reliable (Dröge



et al., 1999; Davison, 1999). In such natural environments, the frequencies of plasmid transfer seem to be dependent on the physiological status (e.g., growth rate) of the donor (Smets et al., 1993; Sudarshana and Knudsen, 1995), but not significantly on the status of the recipient (Arana et al., 1997; Muela et al., 1994). Nutrient-rich environments have been observed to lead to an increase in transfer frequency (Sandt and Herson, 1991; Clerc and Simonet, 1996; Götz and Smalla, 1997), even though gene transfer has been detected in oligotrophic environments, or after bacteria had undergone starvation (Goodman et al., 1993; Davison, 1999). On the contrary, Hausner and Wuertz (1999) reported transfer rates in biofilms to be independent of the concentration of nutrients; similar observations were made by Ehlers and Bouwer (1999). In biofilms, biomass surface has an influence on the efficiency of plasmid transfer, with high sur- face-to-volume ratios favoring the transfer (Molin and Tolker- Nielsen, 2003). There seems to be an optimal temperature for plasmid transfer, defined by the characteristics of both the spe- cific plasmid and its host; out of the optimal region, the transfer still happens, but at lower frequencies (Dröge et al., 1999). In general, conjugation can occur under a vast range of conditions, and the effect of environmental variables on its efficiency and extent are under active investigation.

It has been demonstrated that cell culture and micros- copy lead to substantially different conclusions about conjuga- tion extent. The kinetics results presented below and elsewhere should be evaluated considering that the quantification methods used are, in general, different from one study to another, and most trials to date have used cell culture assays (Sorensen et al., 2005).

 

Kinetics and Modeling of Conjugative Gene Transfer

Different Approaches to the Quantification of Plasmid Transfer

  Levin et al. (1979) measured F- and R-plasmid transfer rates among different strains of E. coli in batch cultures and in che- mostat, and developed a model of transfer kinetics, with assump- tions including: (i) mating is a random process and mating fre- quency is proportional to the concentrations of plasmid-free and plasmid-bearing cells; (ii) plasmid loss due to cell replication is negligible; (iii) transconjugants, cells originally free of a specific plasmid that have received it by conjugation, become potential donors without any delay; (iv) the plasmid transfer rate is the same for the original donors as well as transconjugants, and (v) all bacterial clones have the same growth rate. The result is a mass-action kinetics, with rate proportional to the product of the local number densities of donor and recipient cells:

r = k  [F+] [F-]                                                  [1]

where k is the rate coefficient [in units of ([F]2)1/2 T-1], [F+] is the local number density of F-plasmid-bearing cells and [F-] is the local number density of F-plasmid-free cells, where local number density is defined as the cell number per local volume (Levin et al., 1979). This model performs well in the laboratory setting for active planktonic cells. In natural environments, how- ever, donors, recipients, and transconjugants will not in general be homogeneously mixed and Eq. [1] should not work (Levin et al., 1979). Also, the form of Eq. [1] does not accommodate delays or lags observed in horizontal gene transfer. We address these two limitations below by structuring the model on space and including in the kinetics a measure of the mixing of donor and recipients on surfaces, and by accommodating lags. The mass action model does not perform well where recipients far outnumber donors (“donor saturation,” Cullum et al., 1978), and it is not recommended for measuring relatively low transfer rates (Levin et al., 1979; Andrup et al., 1998; Simonsen et al., 1990). Fernandez-Astorga et al. (1992) found that cell number density and donor/recipient ratio had a significant effect on con- jugation among E.coli strains. Simonsen et al. (1990) observed that the number of transconjugants formed on surfaces was strongly influenced by initial cell density, but the same did not hold for liquid cultures. Similar results are reported in Knudsen et al. (1988), studying conjugation on leaf surfaces.


The mass action model of Levin et al. (1979) has been used to compute conjugation rates, coupled with microbial growth and decay, in Knudsen et al. (1988) studying rhizosphere and phyllosphere environments, in Clewlow et al. (1990) and Simonsen et al. (1990) studying liquid cultures, and in Smets et al. (1994) and Beaudoin et al. (1998a, 1998b) studying bio- films. In particular, Beaudoin et al. (1998b) enrolled mass action kinetics with dynamic growth and decay in biofilm to quantify the transfer of mobilizable plasmid pDLB101 from Pseudomonas putida to a pure culture biofilm of Bacillus azotoformans. The biofilm model AQUASIM was modified to accommodate con- jugation kinetics and plasmid loss and used to model data from a parallel study of Beaudoin et al. (1998a).

An alternative approach that treats bacterial conjugation as a classical enzyme catalysis type reaction was proposed in Andrup et al. (1998) and in Andrup and Andersen (1999), where donors and recipients are analogous to (catalyzing) enzymes and reactant, respectively. Thus a mating is viewed as an activated complex, and a transconjugant as a product, with a Michaelis–Menten kinetic governing the rate of bacterial conjugation. Assumptions include: (i) recipient cells vastly outnumber donors; (ii) trans- conjugants do not become donors with significant frequency; and (iii) plasmid loss is negligible. This Michaelis–Menten- analogous model predicts that, at low recipient concentrations, the conjugation rate is proportional to recipient concentration, whereas at high recipient concentrations the donors are satu- rated, thus a maximal conjugation rate is attained.

An ecological modeling approach was presented in Lagido et al. (2003), who described conjugative transfer on solid sur- faces as a result of the contact between growing colonies of donors and of recipients. The model assumes that donor and recipient colonies grow exponentially until nutrient exhaustion and that, when donors and recipients come into contact, trans- conjugants are formed instantaneously, converting all the recipi- ents to transconjugants at the same instant. Although this model incorporates the role of surfaces, it has limited applicability because of the required number of novel parameter values and because it does not account for any cell mobility in either aque- ous or surface phases (Lagido et al., 2003). Another ecological approach, rooted in population dynamics, appeared in Landis et al. (2000), who simulated individual microbial generations as “resources” on which plasmid “infection” proceeds under a set of



rules. While absent of a physical setting (neither liquid culture nor surfaces defined), the model includes selective pressure and an assumed Poisson distribution of conjugation rates.

Time Lags in the Plasmid Transfer Kinetics


Here we provide a brief summary of some relevant experi- mental observations of time lags and conjugation rates, consider- ing in turn the conjugation event, post-conjugation recovery of the donor, and transconjugant maturation time. Although many researchers have modeled conjugative transfer, we are unaware of any attempt to date to include time lags in conjugation kinetics, despite the fact that such lags are consistently indicated.

Conjugation Event

 

In the study of plasmid transfer in E. coli by Andrup et al. (1998), the minimum time required for a single transfer event (including transconjugant formation evinced by gene expres- sion) was 3.5 to 4.0 min. Similarly, Michel-Briand and Laporte (1985), while studying transfer of plasmid RP4 in E. coli, reported formation of transconjugant in ?5 min. These times certainly depend on the mating strains and experimental condi- tions.

Recovery Period

 

The recovery period for Bti encoded by the plasmid pXO16 was reported as approximately 10 min (Andrup et al., 1998). It was estimated that a transfer from a donor to recipient takes place every 15 min on average (calculated from the maximal con- jugation rate) and, in view of the time required for a single trans- fer event, it was deduced that ?10 min is required for recovery and mating initiation (Andrup et al., 1998). In Cullum et al. (1978), however, the lag period between two rounds of transfer for the F-plasmid in E. coli was reported as 30 min, about three times as that of Bti. This disparity may be attributed to the dif- ference in the ratio of donors to recipients at which the maximal rate of conjugation takes place, as well as the mating conditions (Andrup and Andersen, 1999).

Transconjugant Maturation Time

 

The maturation time of a transconjugant can be defined as the time it takes to achieve donor capability. Andrup and Andersen (1999) report maturation times for E. coli receiving the F-plasmid of ?80 min, and for Ent. fecalis receiving the pCF10 plasmid of ?100 min. These times were estimated by observing, in plots of transconjugants formed vs. time, dramatic increases in the number of transconjugants formed at 80 min for E. coli and at 100 min for Ent. fecalis. It was inferred that the increase results from the lag time needed for transconjugants to become donors. A similar maturation time of ?90 min was reported for the F-plasmid-mediated conjugation in E. coli by Cullum et al. (1978). The maturation time of Bti (pXO16) was studied by Andrup et al. (1998), who found that ?40 min are required for transfer from newly formed transconjugants.

The relevant data regarding kinetics and lag times in conju- gative gene transfer is summarized in Table 1. The processes rep- resented in this table include duration of: (i) conjugation events,

(ii) donor resting (recovery) state after conjugation, (iii) time to transconjugant joining the donor pool, and (iv) maximum con- jugation rate.

In summary, plasmid trans- fer rate was originally expressed in terms of cell densities and ratios of donor, recipient, or transcon-



TABLE 1. Compilation of mean times associated with conjugative gene transfer processes.

 

Donor      Transconjugant

Ref.†            Species          Plasmid     Medium     Duration‡ recovery§ maturation time¶ Maximal conjugation rate#

 

———————— min ————————         no. donor-1 min-1

jugant populations, but later the	I.	Bti††	pXO16	liquid	3.5–4	10	40	0.05
transfer kinetics was cast as mass		E.coli	F	liquid		5	80	0.15
action and thus bilinear kinetics	II.	Ent. fecalis	pCF10	liquid			100, 80‡‡	0.29
(e.g., Levin et al., 1979; Smets et	III.§§	P. fluorescens	RP4	surface	3.5–4	5–30
al., 1994; Simonsen et al., 1990).	IV.	E. coli	RP4		5

Alternatively, conjugation has been represented by analogy to Michaelis–Menten enzyme catal- ysis (e.g., Cullum et al., 1978; Andrup et al., 1998; Andrup and Andersen, 1999). None of these models have accounted for the time lags, and most of the studies have not considered one or more of the following aspects of conju-

V.                   E.coli                                                                  30                90¶¶

 

† References: I. Andrup et al. (1998); II. Andrup and Andersen (1999); III. Lagido et al. (2003); IV. Michael-Briand and Laporte (1985); V. Cullum et al. (1978).

‡ The time at which the first transconjugant was observed.

§ Minimum time for donor recovery from its transfer activity to become a potential donor again.

¶ Time lag between recipient receipt of plasmid and recipient becoming a donor.

# Measured as the number of transconjugants per donor per minute during 15 min in broth matings.

†† Bacillus thuringiensis subsp. israelensis (Bti).

‡‡ For pheromone-induced matings.

§§ Results adapted from Andrup et al. (1998) and Cullum et al. (1978).

¶¶ Most cells became potential donors after 90 min; low levels of transfer detected within 40 min.

 

simplicity, the model assumes that capture and release of bac-


gative gene transfer: (i) spatial distribution and spatial separation of cells; (ii) population dynamics including growth and decay (with several important exceptions); or (iii) cell mobility in the case of conjugation on surfaces. We hypothesized that the ubiq- uitously poor fit of any kinetics to conjugative gene transfer data is due to these omissions. The lags especially often correspond to the lower bound on time intervals for a process to occur, thus limiting the applicability of bilinear and other forms that rep- resent the transfer classically as a Markovian stochastic process with Poisson distribution. Thus we applied a non-Markovian approach that expresses rate coefficients as dependent on time in a given state (e.g., transconjugant).

Most efforts to measure conjugative kinetics were con- ducted for liquid cultures (Levin et al., 1979; Simonsen, 1990; Andrup and Andersen, 1999; Andrup et al., 1998), and few studies have taken place investigating plasmid transfer rates on surfaces (Simonsen, 1990; Lagido et al., 2003). Most of the environments where gene transfer takes place can be considered porous in nature; examples are human and animal tissues, the



teria to and from the solid surface of the porous medium can be explained using linear sorption kinetics. We also assumed a locally homogeneous concentration of bacteria on the solid surface. Although in reality the local concentration of captured bacteria is not uniform, due to differences in the geometrical (Nelson et al., 2007; Yoon et al., 2006) and mineralogical (Sun et al., 2001; Seeboonruang and Ginn, 2006) accessibility of vari- ous sites on the surface, and therefore bacterial populations may concentrate in some, here we assumed that the effect of such heterogeneities can be accounted for using modified conjugation rate coefficients for the attached bacteria. As explained above, during conjugation, genetic material is transferred from a donor (F+) to a recipient (F-); following that, the recipient becomes a transconjugant (T), and the donor becomes a temporarily “exhausted” bacterium (X) (Andrup and Andersen, 1999). Both T and X return to F+ donor pool after their lag times.

Using the above assumption, the transport–conjugation equation describing the behavior of mobile donors (F+) and recipients (F-) in the aqueous phase can be written as follows




phyllosphere, all soil environments (e.g., the rhizosphere), and

biofilms formed in all environments. Hence, most of the model- ing approaches developed so far have only limited applications

∂F ⁺

a

∂t

+ v x

∂F ⁺

a

=∂x

to natural environments. To overcome these constraints, our approach also accommodates processes of bacterial attachment– detachment between the aqueous solution and the solid surface

∂ ⎛⎜            ∂F ⁺ ⎞⎟

⎜D    a ⎟ − rac + rarT + rarX −

∂x ⎜⎝                    ∂x ⎠⎟

S (k F ⁺ − k F ⁺ )

θ    f   a               r s

[2]

⎜            ⎟     ac

of a porous medium, thus keeping track of the surface number

∂F ⁻

 

∂F⁻

 

∂ ⎛⎜

 

∂F⁻ ⎞⎟

S         −                  −

density of cells on surfaces, and models conjugation within both

planktonic and sessile communities.

a     + v x           a =

∂t                ∂x

D ^a − r −

∂x ⎜⎝       ∂x  ⎠⎟            θ

(kf Fa

− kr Fs )

[3]

 

Conjugation Kinetics with Lags Modeled via the Exposure Time Concept

and for the immobile (or captured) bacteria on the solid sur- face:

∂

∂F ⁺                                       _{+          +}

Building on the conceptual framework of conjugation processes outlined above, particularly of the E. coli F plasmid, we developed a mathematical model of bacterial transport and

      s   = −rsc + rsrT  + rsrX  + kf Fa t

∂

∂F ⁻                           _{−             −}

−  kr Fs

[4]

conjugation in a one-dimensional porous medium. The model takes into account the following processes: advective–dispersive

      s     = −rsc  + kf Fa t

−  kr Fs

[5]

transport of bacteria, reversible attachment–detachment of bac- teria from bulk solution to the surface of the porous medium, and conjugation in the aqueous phase and on the surfaces. For



where F+ and F- are concentrations of donor and recipient bac-

teria, which are functions of space (x) and time (t); subscripts

a and s indicates aqueous (in cells per aqueous volume) and

attached (in cells per colonizeable surface area) phases, respec- tively; D is the diffusion coefficient for bacteria; S is the colo- nizable surface area of the solid phase per unit bulk volume of the porous medium; q is the porosity; vx is the flow velocity; kf

(in units of aqueous volume per colonizeable surface area per



Here we assumed that all exhausted and transconjugant bac- teria return to the donor state after lag time intervals tT and tX, respectively. Thus the rate of return to the donor state equals the flux in age dimension at age equal to the respective lag time, as




time) and kr (in units of 1/time) are attachment and detachment rates to the solid surface, respectively. The rates rac and rsc are conjugation rates in aqueous and attached phases respectively; rrT is the rate of transition from the transconjugant state T to a

new donor state F+, and rrX is the rate of return from exhausted

rarT = Ta (τT )v τ

rarX = Xa (τ X )v τ

[12a]

 

[12b]

state X to donor state F+. The rate of conjugation is assumed to be proportional to the product of the concentrations of donors and recipients:

rsrT = Ts(τ T )v τ

[12c]

az   a       a

rac = k F + F −

[6]

rsrX = Xs (τ X )v τ

[12d]

 

sz   s        s

rsc = k F + F −

[7]

The flux of transconjugants at t = 0 is equal to the rate of production of transconjugants, therefore the boundary condi- tion for Eq. [8] to [11] can be written as

where kaz and ksz are conjugation rate coefficients in aqueous (in units of aqueous volume per cell per time) and attached (in units of colonizeable surface area per cell per time) phase, respec- tively.

The rate of conversion of exhausted and transconjugant bacteria into donor bacteria depends on the continuous time

Ta (0)v τ = Xa (0)v τ = rac = k F ⁺F ⁻

az   a       a

and similarly:

sz   s        s

Ts(0)v τ = Xs(0)v τ = rsc = k F ⁺F ⁻

[13a]

 

 

[13b]

bacteria have spent in exhausted or transconjugant states, or “age” within the state. The distributions of transconjugant and exhausted bacteria concentrations within this age are denoted by T and X, respectively. Thus T = T(x,t,t) and X = X(x,t,t). For simplicity of notation these will be expressed without the x,t



∫



dependency. For example, the concentration of transconjugants



The set of Eq. [2] to [5] and [8] to [11], along with the boundary conditions in Eq. [13] and [14], is solved using a hybrid numerical method. The age distribution of transconju- gants and exhausted bacteria is discretized into age intervals. The equations governing the fate and transport of F+, F-, T, and X

bacteria at each time interval is solved using a Crank–Nicholson

between ages t1

and t2

will be equal to

τ2 T (τ)dτ . The distri-

τ

implicit finite difference scheme. To model the evolution of age

bution T at a certain point along the col1umn changes due to fluxes in both the physical dimension and the aging dimension. Using the exposure-time approach of Ginn (2000), the mass bal- ance of transconjugants T can be expressed with fluxes in both physical and age directions as (see Appendix):

distribution in time, the advective operator in age is imposed by shifting the concentration distribution over age to the next age step at each time step. To use such a shift operator, it is neces- sary that an age interval equal to the time step used in the finite difference scheme be chosen. This approach will reduce the

∂T (τ)

+ v τ

∂T (τ)

+ v x

∂T (τ) =

∂  ⎡     ∂T (τ)⎤

⎥

⎢D

                

computational effort significantly and also eliminate numerical

diffusion error that a numerical solver can cause on the purely

∂t                   ∂τ                  ∂x

∂x ⎢⎣

∂x ⎥⎦

advective transport in the age direction.

Including attachment and detachment of bacteria to the surfaces, the governing equations for the aqueous and attached transconjugants and exhausted bacteria can be written as:

Simplification for Aqueous Batch Systems

To interpret the results from typical horizontal gene transfer

∂T (τ)

∂T (τ)

∂T (τ)

batch experiments (no transport and no solid phase present), it

         a          + v τ             a          + v x             a         

∂t                    ∂τ                   ∂x

is worthwhile to study the form of governing equations describ- ing the kinetics in such systems. For a batch system with no

∂ ⎡

=      ⎢D

∂Ta (τ)⎤

[k_fT_a (τ) + k_rT_s(τ)]

[8]

transport and no solid phase and with aging velocity vt = 1, the

concentration  of  transconjugants  and  exhausted  cells  can  be

⎥ −

S

∂x ⎢⎣              ∂x   ⎥⎦           θ

expressed as

∂Xa (τ) + v

∂t              ^τ

∂Xa (τ) + v

∂τ             ^x

∂Xa (τ)

∂x

T (t , τ) = T (t − τ, 0)

[14]

∂ ⎡

=      ⎢D

∂Xa (τ)⎤

[k_f X_a (τ) + k_r X_s(τ)]

[9]

and

⎥ −

S

∂x ⎢⎣              ∂x      ⎥⎦        θ

∂Ts(τ) + v

 

∂Ts(τ) = k T (τ) − k T (τ)

 

[10]

X(t , τ) = X(t − τ, 0)

[15]

∂t             ^τ     ∂τ

f   a                    r s

Substituting Eq. [14] and [15] (through Eq. [12]) into Eq.

∂Xs(τ) + v

 

∂Xs(τ) = k X (τ) − k X (τ)

 

[11]

[2] and [3] and ignoring sorption leads to

∂t             ^τ      ∂τ

f     a                    r s

 

F                     + −

∂ +

a = −kaz Fa Fa

∂t

+ T (t − τ_T , 0) + X (t −τ_X , 0)

[16]

10 min, respectively. The model matches reasonably well with the experimental data.

To perform the simulations of conjugative gene transfer among bacteria undergoing advective–dispersive transport in a

Considering the boundary conditions given in Eq. [13], the above equation can be written as

∂F +                   +   −                      +                   −

 

one-dimensional porous medium, with kinetically controlled attachment–detachment, rate values of conjugation for the bac- teria on the solid surface are also required. Under the assumption

a = −kaz Fa Fa

∂t

+ kaz Fa

(t − τT )Fa

(t − τT )

that this rate is intrinsically the same as the aqueous rate, but in

units of surface area per cell per time, ksz, can be derived as:

+k F ⁺(t −τ

)F ⁻(t −τ )

[17]

k = S k

az   a                     X       a                    X

 

and the governing equation for recipients can be obtained by eliminating transport and sorption terms from Eq. [3]:

∂F ⁻                   _{+ −}

 

sz            θ az

This is a reasonable assumption considering the lack of experimental data on bacterial conjugation on surfaces without biofilms. This assumption needs to be refined, however, by fur-

a = −kaz Fa Fa

∂t

[18]

ther studies on bacterial conjugation on surfaces, both without

and with biofilms, since the kinetics of conjugation on surfaces

Equations [17] and [18] were used to obtain the parameters that best agree with kinetics results in the batch experiments by Andrup and Andersen (1999).

Demonstration Calculations

A demonstration computation is performed to present the performance of the model in a one-dimensional porous medium. First, data reported by Andrup and Andersen (1999) represent- ing the kinetics of conjugation of E. coli were used to estimate the conjugation parameters, including the lags and the conjuga- tion rate coefficient. In this study, E. coli strain MC1000 (F-, StrR) was used as recipient and strain XL-1 Blue (F+:Tn10, TetR NalR) as donor. Since the experiment was performed in a batch system, batch model Eq. [17] and [18] were used to estimate the parameters by minimizing the mean squared error between the transconjugant concentration calculated by the model and the transconjugant concentration measured by Andrup and Andersen. Figure 1 presents measured along with simulated transconjugant concentration vs. time. Rates kaz, tT, and tX were

estimated to be 10-6 min-1 (cell concentration)-1, 34 min, and

FIG. 1. Observed vs. simulated transconjugant concentration in E. coli for donors initial concentration F+ = 4.1 ´ 103 cell mL-1, recipi-

can be quite different from that in bulk water in many aspects.

Concentration profiles in a simulated column, with bacteria at various conjugative states both on solid and in aqueous phases at steady-state conditions, are presented in Fig. 2. Attachment and detachment rates were found by fitting a single rate model

 

0

ent initial concentration F-

= 7.6 ´

0

106 cell mL-1, (lag) time spent in

FIG. 2. Simulated (a) mobile and (b) immobile concentration profiles

exhausted state (te) = 10 min, (lag) time spent in transconjugant state (tT) = 34 min, and transconjugation rate kaz = 10-6 min-1 bacterium-1.

for donor (F+), recipient (F-), exhausted (E), and transconjugant (T) bacteria.

to the data presented by Li et al. (2004). Inflow concentrations adopted were from Andrup and Andersen (1999). Parameters used for this simulation are listed in Table 2.

In both phases, concentration profiles show that at the end of the 30-cm column, almost all F- bacteria are converted to transconjugants T. A fraction of transconjugants is still present at the end of the column, whereas almost all of the exhausted bac- teria are converted back to F+. For mobile bacteria, conjugation rate is low at the beginning of the column due to the lower avail- ability of donors, whereas in the middle of the column the rate increases due to the increase in the number of donors, which also produces a high concentration of exhausted and transconjugant bacteria. Further downstream in the column, transconjugant and exhausted bacteria gradually overcome their lag time and convert into donors. In the immobile phase, due to the smaller num- ber of bacteria per surface area, the overall process takes place at a slower pace. Bacteria on the surfaces have a longer residence time, however, which affords more return to donor state of the transconjugant and exhausted cells. The low concentration of F- in the attached state at all locations along the column indicates that the rate of attachment of bacteria to the surface is signifi- cantly smaller than the rate of conjugation, which means that most recipients partake in conjugation soon after their attach- ment to the solid surface. Also, the decreasing concentration of exhausted and transconjugant bacteria with distance can be explained by the smaller number of F- bacteria remaining at the end of the column. These results are, of course, a consequence of the assumed experimental conditions; however, they demon- strate how transport, attachment–detachment, and conjugative gene transfer dynamics are coupled together.

Implications for the Vadose Zone

The foregoing conceptual and mathematical models focus on the conjugative gene transfer reactions among aqueous- and attached-phase microbes, and were developed mainly with satu- rated conditions in mind. There is some basis, however, for spec- ulations about the behavior in the vadose zone. The gene transfer process in the aqueous phase requires bacterial transport across macroscopic scales and mixing of cells at the microscopic scale, and these processes slow down with decreasing water content. On the contrary, richer nutrient and electron acceptor (starting with O2) conditions in the shallow vadose zone and capillary

fringe may lead more frequently to the occurrence of robust ses-

sile communities, i.e., biofilms that could support gene transfer rates above that in the saturated zone. In either case, the results

TABLE 2. Parameter values used in the demonstration simulation.

 

Parameter                                            Value

 

Inflow F+ concentration                     4.1 × 10-3 bacteria cm-3†

Inflow F- concentration                     7.6 × 10-6 bacteria cm-3†

Exhaustion lag time, tX                     34 min†

Transconjugant lag time, tT               10 min†

Conjugation rate                               10-6 min-1 bacterium-1†

Attachment rate, kf                                         88.34 × 10-9 cm min-1‡

Detachment rate, kr                                       0.0167 min-1‡

Specific surface area                        15 281 cm2 cm-3‡

Porosity                                          0.373‡

Column length                                  30 cm

Flow rate                                         0.277 cm min-1‡

of gene spread from introduced species requires either transport of introduced species across macroscales, or positive selection for the plasmid conveyed. The preliminary modeling developed here shows the coupling of transport and conjugative gene transfer through the attachment–detachment processes controlling the locally mixed cell number densities on surfaces. The air–water interface may play a role as a surface supporting communities among which gene transfer can occur. These questions are ripe for subsequent research steps, and the model proposed here may serve as a starting point for quantitative analyses of such observa- tions.

 

Conclusions

 

In this study, we developed a novel modeling approach for quantifying the conjugative transfer rates on surfaces in porous media, taking into account some of the key aspects of conjuga- tion in natural systems, including time lags and interactions of the bacteria in the bulk fluid with solid surfaces. Most of the transfer kinetics studies in the past did not account for impor- tant transfer-rate-determining factors such as time lags, spatial distribution of cell populations, etc., in their models. Moreover, most of the studies were performed in batch solution micro- cosms, which are not the ideal imitations of the natural environ- ment in which conjugation generally occurs. The natural envi- ronment on which we focused is a porous medium, with bacteria undergoing transport and the initial development stages of bio- film formation, consisting of reversible attachment, detachment, and irreversible adherence that leads to colony formation on the surfaces. Hence, a one-dimensional bacterial transport–conjuga- tion model was developed to estimate gene transfer rates of bac- teria attaching to surfaces during their transport through porous media. We have tested an “aqueous batch” reduced model refer- ring to the batch experiment data from Andrup and Andersen (1999), and obtained a reasonably good fit to their measured data. The obtained parameters were then used in an extrapo- lative modeling exercise to predict the distribution of donors and recipients in one-dimensional flow in porous media. This exercise is part of a premodeling effort to design small-scale experiments for observing the processes considered in the labo- ratory. As such, this model may be used to design flow rates and boundary concentrations for given porous medium physical and chemical characteristics and given microbial species. The model includes several far-reaching assumptions, one of which is the uniform distribution of attached microbes on surfaces. It is pos- sible to relax this assumption by using individual-based simula- tion of bacterial transport in the Happel sphere-in-cell model of a porous medium, to obtain better approximations of how attached bacteria are distributed on surfaces of granular porous media (Nelson et al., 2007).

Appendix

Here we provide a brief description of the basis for the mass balance of species, such as transconjugants and exhausted spe- cies, across physical and age dimensions. The physical and age fluxes, F and F , respectively, are shown schematically in Fig. 3,

Dispersion coefficient                        2.77 cm2 min-1‡                                                         x           t

† Andrup and Andersen (1999).

‡ Li et al. (2004).

and the corresponding mass balance of the distribution T at the

finite volume can be written as

ΔT ( x, t , τ)ΔxΔτ =

Δt Δτ ⎣⎡Fx ( x − Δx / 2, t , τ) − Fx ( x + Δx / 2, t , τ)⎤⎦

+ Δt Δx ⎣⎡Fτ ( x, t , τ − Δτ/ 2) − Fτ ( x, t , τ + Δτ / 2)⎤⎦   [A1]

Ft is the flux in the age dimension, which is equal to the rate of change of age with respect to time vt, termed the “aging veloc- ity,” multiplied by concentration at any point, or Ft = Tvt. The physical flux Fx is defined using the conventional advection and diffusion: Fx = vxT + D¶T/¶x. Substituting Ft and Fx into Eq. [A1], dividing both sides by ÄxÄtÄt and taking the limit when (Äx,Ät,Ät) ® 0 yields

∂T (τ)

+ v τ

∂T (τ)

+ v x

∂T (τ) =

∂  ⎡     ∂T (τ)⎤

⎥

⎢D

                

[A2]

∂t                   ∂τ                  ∂x

∂x ⎢⎣

∂x ⎥⎦

 

ACKNOWLEDGMENTS

This project research was supported by NSF Project Award nos. 0620966 and 0416194, “Collaborative Research: CMG: Toward Understanding the Transfer of Genetic Information in Subsurface Hydrology,” and NSF Project Award no. 0420374, “Biogeochemical Cycling of Heavy Metals in Lake Coeur d’Alene Sediments: The Role of Indigenous Microbial Communities,” as well as the UC CARE Project entitled “Exposure-time Approach in Modeling Dynamics of Subsurface Microbial Communities in Contaminated Aquifers: Horizontal Gene Transfer in Adaptive Bioremediation.”

 

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