THE PATCH DYNAMICS OF HORIZONTAL GENE TRANSFER AND IMPLICATIONS FOR THE RISK ASSESSMENT OF PLASMIDS

Wayne G. Landis and Julann A. Spromberg

Institute of Environmental Toxicology and Chemistry, Huxley College of Environmental Studies, Western Washington University, Bellingham, WA 98225-9180, fax (360)650-7284, landis@lilypad.ietc.wwu.edu

SUMMARY

Horizontal and vertical gene transfer using a plasmid as the mobile element are important considerations in the spread and impacts of introduced gene sequences. This example of cytoplasmic population genetics can be thought of as the population biology of the plasmid using bacterial populations as resource patches. In our models we characterize the growth and infection of two bacterial populations, patches, along with calculating the total number of infected bacteria within each patch. We use discrete values instead of continuous for variables such as population growth and plasmid infection. The use of discrete values allows a wider and perhaps more accurate representation of the population dynamics of the plasmid-bacteria complex.

Infection using the parameters of a typical simulation occurs rapidly. There is a lag between the growth of the bacterial population and the infection by the plasmid. Because of the loss rate, 100 percent infection does not occur. At low rates of reproduction the population dynamics of the bacteria and plasmid oscillate around the carrying capacity of both patches. If the plasmid containing host has a higher fitness, a population curve can exhibit a bifurcation to more complex dynamics. The stochastic nature of conjugation can also lead to variation in the rate of infection of a plasmid. An increase in conjugation distance does not apparently result in a proportional change in infection rate.

The implications for risk assessment are manyfold. An impact of the introduction of a new genetic element can change the timing of population cycles. The introduction of a plasmid can change the dynamics of the host population, even increasing the complexity of the population dynamics. Since genetic exchange is almost certain under the parameters of the model, it is unlikely that new genetic information can be contained among procaryotes. Lastly, due to the stochastic nature of conjugation and the contagious distribution of bacteria, a variety of results are likely to be obtained from identical experiments.

INTRODUCTION

Quantification of exposure is a critical component of ecological risk assessment (Suter, 1993). In the prediction of the potential risks of transgenic organisms or introduced plasmids with novel traits, the estimation of exposure and potential risks must be addressed. Traditionally, the prediction of the frequency of genetic elements and their fitness in populations has been the purview of population genetics. Unlike most conventional population genetics, the prediction of the transmission of plasmid borne elements must consider both vertical and horizontal gene transfer.

It has become apparent that genetic information can be transferred between distantly related types of bacteria (Mazodier and Davies, 1991; Amabile-Cuevas and Chicurel, 1993). There are even cases of likely procaryotic to eucaryotic (Heinemann and Sprague, 1989), eucaryotic to eucaryotic (Houck et al., 1991), and eucaryotic to procaryotic horizontal transfer (Smith et al., 1992). Antibiotic resistance is perhaps a classical case of horizontal transfer, and horizontal transfer is likely the mechanism for the rapid spread of resistance in procaryotic populations (Amabile-Cuevas and Chicurel 1993). Introduction of novel sequences by horizontal transfer into various genetic backgrounds may be an important mechanism for the formation of novel traits. An example of horizontal transfer related to pesticide degradation is the case of the opd gene.

As described by Harper et al. (1988), dissimilar plasmids isolated from Pseudomonas diminuta MG and Flavobacterium sp. (ATCC 27551) contain identical opd genes. The opd gene product is an organophosphate acid anhydrolase able to degrade several types of organophosphates, including potent mammalian acetylcholinesterase inhibitors. Strict conservation of the base sequence also indicates either a recent transfer event or strong selective pressure for the ability to degrade organophosphates and related materials. The opd OPA anhydrolase is encoded by a plasmid borne gene of 1079 base pairs in length (McDaniel et al., 1988). The gene sequence is identical in both Flavobacterium and P. diminuta although the plasmids bearing this gene are not. Strong selection for the ability to degrade organophosphates or relatively recent transfer into the host plasmid are indicated by this strict conservation of sequence.

The population genetics of cytoplasmically inherited traits has previously been modelled for the killer trait in the Paramecium aurelia complex (Landis, 1987) and CO₂ sensitivity in Drosophila (L'Heritier, 1970). In both instances it was found that infection due to cytoplasmic transfer could be high enough to maintain the cytoplasmically inherited trait even in the face of natural selection. The models used to study these factors did not include environmental heterogeneity.

Horizontal and vertical transfer of cytoplasmically inherited traits borne on plasmids or symbiotic procaryotes are important considerations in the spread and impacts of introduced gene sequences. Cytoplasmic population genetics can be thought of as the population biology of the plasmid using heterogeneous bacterial populations as resource patches. In this manner the dynamics resemble that of metapopulations. Metapopulations are groups of populations linked by migration. Bacterial populations are the resaource patch and the plasmids are the populations of interest.

This paper presents a selection of output from our preliminary modelling of plasmid population genetics. The research described below uses the basic premises of metapopulation genetics to describe the spread of plasmids and their influence on the dynamics of the host bacterial populations. Using the parameters of the model, the plasmids rapidly spread throughout the potential host populations. As natural selection alters the growth rate of a population due to the presence of the plasmid, populations can vary dynamics, from stable points to chaos.

MODEL DEVELOPMENT

Our research is based on the metapopulation dynamic models of Wu et al. (1993). Metapopulations are populations that occupy different patches but are connected by migration. In examining population genetics of movable genetic elements metapopulation type models are particularly useful. The metapopulations themselves are the populations of the same type of plasmid or other genetic element and the bacterial hosts represent the various environmental patches. Migration rates between patches are not set by geographic distance but by the compatibility of the two host populations to exchange genetic information. In conventional metapopulation dynamics, the patch does not grow or shrink but is taken as a constant. In the models developed here, the patch can grow and is dependent upon the growth rate of the host bacteria, the carrying capacity of the environment, and the fitness of the host. In the case of movable genetic elements, the new genetic sequence has the potential to alter the fitness of the host. In these models we attempt to simulate the growth and infection of two bacterial populations (patches) along with calculating the total number of infected bacteria within each patch.

We use the object oriented modelling program Stella II for the construction of our modelling programs. Table 1 lists some of the variables included in the model. Stella allows programming of the model using a graphical user interface and the incorporation of distributions and rates from graphical inputs. A graphical representation of the two-patch model is presented in Figure 1. Unlike the models of Wu et al. (1993), we use discrete values instead of continuous for variables such as population growth and plasmid infection. Genetic elements are discrete units, as are individual organisms. This use of discrete values allows a wider and perhaps more accurate representation of the population dynamics of the plasmid-bacteria complex . Work pioneered by May (1973) and May and Oster (1976) have demonstrated that the use of discrete models for the description of population models can lead to a variety of dynamics, from stable equilibrium to chaotic but deterministic. A variety of pathogen populations have demonstrated chaotic dynamics (Schaeffer and Kot, 1985).

Conjugation is assumed to be the principal mode of genetic exchange in these models, and processes, such as transduction and transformation, are not treated separately. The frequency of conjugation is treated as a Poisson distribution, one that is discrete and contagious compared to a normal distribution. Migration between patches is modelled by a distance function, the longer the distance the slower the rate of infection from other patches. This value is more a term of conjugative compatibility since the bacterial populations may be co-located, but the rate of conjugation and henceforth transfer of the plasmid may be very low. A low rate of conjugation corresponds to a long distance in the model. Typically, a new plasmid is introduced to one of the populations and the changes in the total number of bacteria and the number of bacteria infected are plotted over time. A partial list of the variables included in the model are listed in Table 1. Diagrams demonstrating the relationships among the variables for the two and three-patch case are depicted in Figures 1 and 2 respectively. The Stella line code representing the three-patch model can be found in Appendix 1.

RESULTS

Our preliminary results demonstrate a variety of dynamics. The Appendix lists the typical values for a model simulation. In the next sections we will examine the rate of infection, the change in dynamics due to selection and the effect of the stochastic nature of transfer due to conjugation.

Infection of the host bacteria within a patch using the parameters of a typical run of a two-patch model occurs rapidly (Figure 3). Using the baseline parameters, the bacterial population fluctuates around the carrying capacity in a simple oscillation. There is a lag between the growth of the bacterial population and the infection of the plasmid. Within 100 generations (fissions), the plasmid is at an equilibrium within the population and the total number of infected bacteria fluctuates only with the total number in the patch. Because of the loss rate, 100 percent infection does not occur, and under the conditions of the two-patch model, an equilibrium is formed.

In the second example a three-patch model is used and a slight selective advantage for the plasmid containing bacteria is introduced (Figure 4). The distance between patches in this example is 1.0 for all combinations. The period of time that it takes for a plasmid to reach a high proportion of the population is substantially longer in a three-patch model, as the plasmid is now being diluted among three and not two patches. Also note that the dynamics of the host population changes as the mean fitness of the population is increased due to the plasmid. With the plasmid at a low level, the population dynamics of the host are regular (Fissions 50-75). As the frequency of the plasmid increases, the population dynamics of the host change into a two-period oscillation (Fission 100-200). Given a sufficient increase in fitness to the host due to containing a plasmid, the dynamics can be driven to chaos. As with the two-patch equal fitness model output presented above, the plasmid does not infect 100 percent of the population.

The final example (Figure 5) is from a three-patch model that compares the difference that distance between patches makes in the infection of a plasmid. In this instance, the model is run ten times to provide a representation of the variability between runs due to the stochastic nature of infection and conjugation. Patch 2 is one unit from the source Patch 1, and Patch 3 is thirty units from the source patch. There are several important dynamics that can be observed in the plot. First, there is a great deal of variability among the ten outputs as to when infection of the patch occurs and the rate of increase of the plasmid within a population. Although Patch 3 is thirty times more distant than Patch 2, it does not take thirty times longer for infection to occur. There is overlap between the outputs. Simply put, sometimes due to chance the population of bacteria farthest away from the patch infected with the plasmid may be infected before the closer patch. Second, the rate of increase observed in the number of infected bacteria is different between runs. Part of this is due to the number of bacteria within the patch, and some of the variability is due to the stochastic nature of conjugation. In some instances, the increase in the number of plasmid-containing bacteria within a population increases rapidly, at other times there is a substantial lag period.

DISCUSSION

The examples presented above have important implications for the estimation of exposure and impacts due to the introduction of a novel plasmid into a host population. The output from these models demonstrates that plasmids can spread rapidly, can change the population dynamics of the host, and will demonstrate highly variable rates of infection.

Plasmid borne traits can be readily transmitted throughout a population. In the outputs from our models, less than one hundred fissions can result in an equilibrium being reached in which the plasmid containing bacteria are over ninety percent of the population. Genetic exchange between patches can also be rapid, and once infection occurs plasmid containing bacteria reach a high proportion of the population.

Infection of a population by a plasmid can alter the population dynamics of that population. In the example presented above, the increase in fitness due to the plasmid of an individual bacterium altered the dynamics from a one-cycle equilibrium through a bifurcation to a two-cycle oscillation about the carrying capacity. It is likely that a further increase in fitness could result in chaotic dynamics. Conversely, a decrease in fitness due to the carrying of a plasmid could produce regularity in population dynamics. A change in the intrinsic dynamics of a population would likely be a fundamental shift in the ecological role of that population and would have implications for other species dependent upon the infected organism.

The stochastic nature of the conjugation process and the transmission of the new genetic elements means that a wide variation in transmission rates would be observed. Without sufficient modelling and a critical review of experimental design, chance events in the transmission of genetic material may be seen as significant events. Since genetic exchange is almost certain under the parameters of the model, it is unlikely that new genetic information can be contained among procaryotes.

REFERENCES

Amabile-Cuevas, C.F. and M.E. Chicurel. (1993) Horizontal gene transfer. American Scientist 81:332-341.

Harper, L.L., C.S. McDaniel, C.E. Miller and J.R. Wild. (1988) Dissimilar plasmids isolated from Pseudomonas diminuta MB and Flavobacterium sp. (ATCC 27551) contain identical opd genes. Applied Environmental Microbiology 54:2586.

Heinemann, J.A. and G.F. Sprague, Jr. (1989) Bacterial conjugative plasmids mobilize DNA transfer between bacteria and yeast. Nature 340:205-209.

Houck, M.A., J.B. Clark, K.R. Peterson and M.G. Kidwell. (1991) Possible horizontal transfer of Drosophila genes by the mite Proctolaelaps regalis. Science 253:1125-1129.

Landis, W.G. (1987) Factors determining the frequency of the killer trait within populations of the Paramecium aurelia complex. Genetics 115:197-205.

L'Heritier, P. (1970) Drosophila viruses and their role as evolutionary factors. Evolutionary Biology 4:185-209.

May, R.M. and G.F. Oster. (1976) Bifurcations and dynamic complexity in simple ecological models. American Naturalist. 110:573-599.

Mazodier, P. and J. Davies. (1991) Gene transfer between distantly related bacteria. Annual Review of Genetics 25:147-171.

McDaniel, C.S., L.L. Harper and J.R. Wild. (1988) Cloning and sequencing of a plasmid-borne gene (opd) encoding a phosphotriesterase. Journal of Bacteriology 170, pp. 2306-2311.

Schaffer, W. M. and M. Kot. (1985) Do strange attractors govern ecological systems? Bioscience 35: 342-350.

Smith, M.W., D.F. Feng and R.F. Doolittle. (1992) Evolution by acquisition: the case for horizontal gene transfers. Trends in Biochemical Sciences 17(12):489-493.

Suter, G.W (1993) Ecological risk assessment. Lewis Publishers, Michigan.

Wu, J., J.L. Vankat and Y. Barlas. (1993) Effects of patch connectivity and arrangement on animal metapopulation dynamics: A simulation study. Ecological Modelling, 65:221-254.

Figure 1. Two-patch plasmid model using Stella.

Figure 2. Three-patch Stella model with conjugation and distance between patches.

Figure 3. Dynamics of the populations: two-patch model. Note that the number of infected bacteria never reaches the same level as the total number of bacteria within the population.

Figure 4. Dynamics of a bacterial population and its infection from a three-patch model. Note that as the number of infected bacteria increase that the dynamics of the total populations changes to a series of bifurcations. Given a large enough change in fitness due to the plasmid it would be possible to obtain chaotic population dynamics.

Figure 5. Increase in infected bacteria within two populations of a three-patch model. Note the overlap between Patch 2 and Patch 3 populations although there is a great deal of difference in their relative distances from the originally infected patch.

APPENDIX 1

Line Code for a three-patch plasmid model with Poisson conjugation and varying patch distance using Stella.

Bacteria Metapopulation & plasmid infection
Bacteria1(t) = Bacteria1(t - dt) + (ImRt21 + NetGR_1 - ImRt12) * dt
INIT Bacteria1 = 10000

INFLOWS:
ImRt21 = IF(ImRt_Test*PCImRt_2<=1) THEN INT(ImRt_Test*PCImRt_2*Bacteria2 *Habitat_Avail_1/distance21)ELSE INT(Bacteria2*Habitat_Avail_1/distance21)
NetGR_1 = INT(ActPCNGR1*(Bacteria1-BactInfect1)*Fitnesswo)+INT(ActPCNGR1*
BactInfect1*Fitnesswith)

OUTFLOWS:
ImRt12 = IF (ImRt_Test*PCImRt_1<=1) THEN INT(ImRt_Test*PCImRt_1*Bacteria1*
Habitat_Avail_2/distance12)ELSE INT(Bacteria1*Habitat_Avail_2/distance12)
Bacteria2(t) = Bacteria2(t - dt) + (ImRt12 + ImRt32 + NetGR_2 - ImRt21 - ImRt23) * dt
INIT Bacteria2 = 50000

INFLOWS:
ImRt12 = IF(ImRt_Test*PCImRt_1<=1)THEN INT(ImRt_Test*PCImRt_1*Bacteria1* Habitat_Avail_2/distance12)ELSE INT(Bacteria1*Habitat_Avail_2/distance12)
ImRt32 = IF(ImRt_Test*PCImRt_3<=1) THEN INT(ImRt_Test*PCImRt_3*Bacteria3* Habitat_Avail_2/distance32) ELSE INT(Bacteria3*Habitat_Avail_2/distance32)
NetGR_2 = INT((Bacteria2-BactInfect2)*ActPCNGR2*Fitnesswo)+INT(ActPCNGR2* BactInfect2*Fitnesswith)

OUTFLOWS:
ImRt21 = IF(ImRt_Test*PCImRt_2<=1)THEN INT(ImRt_Test*PCImRt_2*Bacteria2*Habitat_Avail_1/distance21)ELSE INT(Bacteria2*Habitat_Avail_1/distance21)
ImRt23 = IF(ImRt_Test*PCImRt_2<=1) THEN INT(ImRt_Test*PCImRt_2*Bacteria2 *Habitat_Avail_3/distance23) ELSE INT(Bacteria2*Habitat_Avail_3/distance23)
Bacteria3(t) = Bacteria3(t - dt) + (NetGR_3 + ImRt23 - ImRt32) * dt
INIT Bacteria3 = 5000

INFLOWS:
NetGR_3 = INT(ActPCNGR3*(Bacteria3-BactInfect3)*Fitnesswo)+INT(ActPCNGR3*
Fitnesswith*BactInfect3)
ImRt23 = IF(ImRt_Test*PCImRt_2<=1) THEN INT(ImRt_Test*PCImRt_2*Bacteria2 *Habitat_Avail_3/distance23) ELSE INT(Bacteria2*Habitat_Avail_3/distance23)

OUTFLOWS:
ImRt32 = IF(ImRt_Test*PCImRt_3<=1) THEN INT(ImRt_Test*PCImRt_3*Bacteria3 *Habitat_Avail_2/distance32) ELSE INT(Bacteria3*Habitat_Avail_2/distance32)
BactInfect1(t) = BactInfect1(t - dt) + (NGInf1) * dt
INIT BactInfect1 = 0

INFLOWS:
NGInf1 = INT(BactInfect1*Fitnesswith*ActPCNGR1)+ConjInf1+InfectedIm21-
InfectedIm12 -INT(Lossrate*BactInfect1)
BactInfect2(t) = BactInfect2(t - dt) + (NGinf2) * dt
INIT BactInfect2 = 10

INFLOWS:
NGinf2 = INT(BactInfect2*Fitnesswith*ActPCNGR2)+ConjInf2+InfectedIm12+
InfectedIm32-InfectedIm21-InfectedIm23-INT(Lossrate*BactInfect2)
BactInfect3(t) = BactInfect3(t - dt) + (NGInf3) * dt
INIT BactInfect3 = 0

INFLOWS:
NGInf3 = INT(BactInfect3*ActPCNGR3*Fitnesswith)+ConjInf3+InfectedIm23-INT (Lossrate*BactInfect3)-InfectedIm32
ActPCNGR1 = IF(DLTNGR>0) THEN(SMDLTNGR1) ELSE(PCNGR_1)
ActPCNGR2 = IF(DLTNGR>0) THEN(SMDLTNGR2)ELSE(PCNGR2)
ActPCNGR3 = IF(DLTNGR>0) THEN(SMDLTNGR3) ELSE(PCNGR_3)
CarryingCap_1 = 10^5
CarryingCap_2 = 10^5
CarryingCap_3 = 10^5
ConjInf1 = IF(BactInfect1<(Bacteria1-BactInfect1)) THEN(INT((ConjRate*BactInfect1)*(Bacteria1-BactInfect1)/Bacteria1)) ELSE(INT((ConjRate*(Bacteria1-BactInfect1))*BactInfect1/Bacteria1))
ConjInf2 = IF(BactInfect2<(Bacteria2-BactInfect2)) THEN(INT((ConjRate*BactInfect2)*(Bacteria2-BactInfect2)/Bacteria2)) ELSE(INT(ConjRate*(Bacteria2-BactInfect2)*BactInfect2/Bacteria2))
ConjInf3 = IF(BactInfect3<(Bacteria3-BactInfect3)) THEN(INT((ConjRate*BactInfect3)*(Bacteria3-BactInfect3)/Bacteria3)) ELSE(INT((ConjRate*(Bacteria3-BactInfect3))*BactInfect3/Bacteria3))
ConjRate = pois/(pois+1)
Crowding_1 = Bacteria1/CarryingCap_1
Crowding_2 = Bacteria2/CarryingCap_2
Crowding_3 = Bacteria3/CarryingCap_3
distance12 = 1
distance21 = 1
distance23 = 30
distance32 = 30
DLTNGR = 0
Fitnesswith = .7
Fitnesswo = 1
ImRt_Test = 1
InfectedIm12 = INT(0.10*BactInfect1*Habitat_Avail_2/distance12)
InfectedIm21 = INT(0.10*BactInfect2*Habitat_Avail_1/distance21)
InfectedIm23 = INT(0.10*BactInfect2*Habitat_Avail_3/distance23)
InfectedIm32 = INT(0.10*BactInfect3*Habitat_Avail_2/distance32)
Lossrate = 0.01
MetapopInfected = BactInfect1+BactInfect2+BactInfect3
PCImRt_1 = 0.10
PCImRt_2 = 0.10
PCImRt_3 = 0.10
pois = POISSON(0.5)
SMDLTNGR1 = SMTH3(PCNGR_1,DLTNGR)
SMDLTNGR2 = SMTH3(PCNGR2,DLTNGR)
SMDLTNGR3 = SMTH3(PCNGR_3,DLTNGR)
Habitat_Avail_1 = GRAPH(Crowding_1)
(0.00, 1.00), (0.0833, 0.985), (0.167, 0.965), (0.25, 0.945), (0.333, 0.91), (0.417, 0.865), (0.5, 0.8), (0.583, 0.705), (0.667, 0.565), (0.75, 0.35), (0.833, 0.00), (0.917, 0.00), (1.00, 0.00)
Habitat_Avail_2 = GRAPH(Crowding_2)
(0.00, 1.00), (0.0833, 0.985), (0.167, 0.965), (0.25, 0.945), (0.333, 0.91), (0.417, 0.865), (0.5, 0.8), (0.583, 0.705), (0.667, 0.565), (0.75, 0.35), (0.833, 0.00), (0.917, 0.00), (1.00, 0.00)
Habitat_Avail_3 = GRAPH(Crowding_3)
(0.00, 1.00), (0.0833, 0.985), (0.167, 0.965), (0.25, 0.945), (0.333, 0.91), (0.417, 0.865), (0.5, 0.8), (0.583, 0.705), (0.667, 0.565), (0.75, 0.35), (0.833, 0.00), (0.917, 0.00), (1.00, 0.00)
PCNGR2 = GRAPH(Crowding_2)
(0.00, 0.074), (0.0789, 0.15), (0.158, 0.505), (0.237, 0.9), (0.316, 1.20), (0.395, 1.22), (0.474, 1.25), (0.553, 1.25), (0.632, 1.20), (0.711, 1.10), (0.789, 0.8), (0.868, 0.4), (0.947, 0.02), (1.03, -0.1), (1.11, -0.25), (1.18, -0.35), (1.26, -0.45), (1.34, -0.45), (1.42, -0.45), (1.50, -0.45)
PCNGR_1 = GRAPH(Crowding_1)
(0.00, 0.074), (0.0789, 0.15), (0.158, 0.505), (0.237, 0.9), (0.316, 1.20), (0.395, 1.22), (0.474, 1.25), (0.553, 1.25), (0.632, 1.20), (0.711, 1.10), (0.789, 0.8), (0.868, 0.4), (0.947, 0.02), (1.03, -0.1), (1.11, -0.25), (1.18, -0.35), (1.26, -0.45), (1.34, -0.45), (1.42, -0.45), (1.50, -0.45)
PCNGR_3 = GRAPH(Crowding_3)
(0.00, 0.074), (0.0789, 0.15), (0.158, 0.505), (0.237, 0.9), (0.316, 1.20), (0.395, 1.22), (0.474, 1.25), (0.553, 1.25), (0.632, 1.20), (0.711, 1.10), (0.789, 0.8), (0.868, 0.4), (0.947, 0.02), (1.03, -0.1), (1.11, -0.25), (1.18, -0.35), (1.26, -0.45), (1.34, -0.45), (1.42, -0.45), (1.50, -0.45)
Not in a sector
Metapop1 = Bacteria1+Bacteria2+Bacteria3