Microbiological Laboratory for Health Protection and 1 Laboratory for Toxicology, Pathology and Genetics, National Institute for Public Health and Environment, P.O. Box 1, 3720 BA, Bilthoven, The Netherlands
2 Current address: Numico-Research B.V. Headquarters, Bosrandweg 20, P.O. Box 7005, 6700 CA Wageningen, The Netherlands
Correspondence to: K. Takumi; E-mail: Katsuhisa.Takumi{at}rivm.nl
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Abstract |
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Keywords: mathematical model, Peyer's patch, rodent, Salmonella enteritidis, spleen
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Introduction |
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Studying Salmonella infection in mice, Meynell and Stocker postulated that a single Salmonella cell could cause infection (8), albeit with a low probability. To support the idea, they infected mice with a mixture of flagella variants and demonstrated that Salmonella isolated from the dying mice following exposure to a low dose were dominated by a monoculture, because the probability of two Salmonella cells simultaneously infecting a mouse is vanishingly small. This experiment supported two hypotheses. First, the probability of infection by a single micro-organism is very small but non-zero (single-hit hypothesis). Second, micro-organisms act independently to infect a host. These hypotheses lead to development of a mathematical model relating the probability of infection to ingested doses of a pathogen (911). In experimental infection of rats with Salmonella enteritidis, we estimated that 1 per 1000 c.f.u. of ingested micro-organism causes infection (12). Surviving Salmonella cells multiply to form a clone in the host body. The doubling time of Salmonella in mice ranges between 1 to 37 h, depending on the hostpathogen combination (13,14).
The influx of neutrophils is bacterial-burden dependent (15). Therefore, the kinetics of neutrophil and monocyte responses should be dependent on the dose and the rate of growth of Salmonella that determine the bacterial burden in beginning infection. To understand quantitatively the dynamics of hostpathogen interactions in the early phase of infection, we performed a series of doseresponse experiments and estimated the probability of infection and the rate of growth of Salmonella in rodents. Using these estimates, and mathematically modeling neutrophil and monocyte responses, we predict numbers of neutrophils and monocytes in the blood up to a week after inoculation of a low or a high dose of Salmonella via the oral route.
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Methods |
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All other husbandry conditions were maintained according to all applicable provisions of the national laws; Experiments on Animals Decree and Experiments on Animals Act. In accordance with Section 14 of this Act, an officer was appointed to supervise the welfare of laboratory animals. All experiments were discussed and approved by an independent ethical committee prior to the study.
Bacterial strains
Salmonella enterica subsp. enterica serovar Enteritidis strain 97-198, a patient isolate (origin RIVM); and Escherichia coli WG5, a nalidixic acid resistant derivative of E. coli C was used as a negative control (16). From all strains, a stock collection was made by pure culturing on brain heart infusion (BHI) agar (1820 h at 37°C) and inoculating a single colony in BHI, incubated for 1820 h at 37°C. After incubation, 0.7 ml of the culture was added to cryotubes filled with glass beads and 0.1 ml of glycerol (82% w/v). Directly after adding the cultures the cryotubes were thoroughly mixed and placed in a 70°C freezer.
Inoculum cultures
Both strains were inoculated by placing one glass bead from the stock collection in 10 ml BHI and incubated at 37°C for 6 ± 2 h. Subsequently, 5 µl of the culture was added to 100 ml BHI and further incubated at 37°C for 18 ± 2 h. After incubation, 50 ml of each culture was centrifuged at 5000 g for 10 min at room temperature. The supernatant was discarded and the pellet was resuspended in 50 ml physiological saline (PS, 9 g/l NaCl), followed by recentrifugation. Again, the supernatant was discarded and the pellet was resuspended in a volume of 50 ml PS. Then 0.5 ml of the culture was added to 100 ml of PS. The cell suspension and serial dilutions in PS were delivered at the animal department on melting ice. Directly before administration to the animals, 4 ml of each bacterial suspension was mixed with 4 ml of a solution of 6% (w/v) NaHCO3. After administration, the remainder of the inoculum cultures was transported to the microbiological laboratory on melting ice for plate counts on sheep-blood agar (incubated as above) after appropriate dilution in PS plus 1% peptone (PPS).
The plate counts of different dilutions of the inoculum cultures, used as oral doses for different animals, were 1.1 x 102, 9.5 x 102, 8.5 x 103 and 9.8 x 104 per ml for S. Enteritidis and 4.9 x 104 per ml for E. coli WG5.
Experimental design
On arrival (day 14), the animals were weighed, randomized and housed individually. On day 1, the animals were starved overnight (water ad libitum). Five treatment groups (n = 20 per group) were evaluated for determination of the kinetics of the S. Enteritidis infection and the innate immune response. On day 0, groups 14 received 1 ml of different dilutions of S. enteritidis per animal. Group 5 received 1 ml of E. coli WG5 per animal. The bacterial suspensions were orally administered by gavage. Directly after gavage, food and water was provided ad libitum. On days 26 after the oral infection, four animals of each group were sacrificed and various parameters were evaluated.
Blood samples were taken via orbita plexus puncture using a capillary under light ether anaesthesia on day 10 to obtain a reference value of each individual animal, and 24 h before autopsy. Part of the blood was used to obtain pre-treatment serum samples.
Daily clinical observations were made with reference to the status of general health of the animals. Special attention was paid to the consistency of the faeces. The animals were weighed each day (early in the morning) starting on day 1 prior to the oral inoculation. Each morning, faeces were obtained from each rat in each group. The faeces were macroscopically evaluated and tested for microbiology the same day.
Animals were sacrificed by bleeding from the abdominal aorta under KRA anaesthesia [intramuscular injection of 100 µl of a cocktail consisting of 7 ml of ketalar (50 mg/ml, Parke Davis, Barcelona, Spain], 3 ml of rompun (20 mg/ml, Bayer, Leverkusen, FRG) and 1 ml of atropin (1mg/ml, OPG, Utrecht, The Netherlands). The following organs were removed aseptically: jejunum, ileum, coecum, colon and the spleen. Peyer's patches were removed from the jejunum and ileum.
Haematology
Haematology for each rat was performed in blood samples, anticoagulated with K3EDTA, obtained on days 10 and 6. The haematological analyses were performed using the H1-E, a multi-species haematology analyser (Bayer B.V., Mijdrecht, The Netherlands) with multi-species software, version 3.0, as published previously (16).
Microbiology
Internal organs were weighted and homogenized in PPS by using an Ultra Thurrax. For counting S. Enteritidis, we used brilliant green agar (Oxoid) after appropriate 10-fold serial dilutions in PPS. Escherichia coli was counted on tryptone (10 g/l) yeast extract (1 g/l) NaCl (8 g/l) agar plates containing 100 µg/ml nalidixin acid. For identification, colonies were checked for indole production.
Mathematical model
Probability of infection.
The exponential dose response model relates dose D to the probability that the host is infected.
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The parameter p is the probability of infection per Salmonella cell in inoculum of size D. The model is based on the single-hit hypothesis and the independent action of micro-organisms (8). Derivation of the formula can be found in (12).
Neutrophils.
The following set of equations describe two cell-populations, blood neutrophils Nblood and tissue neutrophils Ntissue. A schematic presentation of neutrophil turnover is shown in Fig. 1(A).
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Monocytes.
The following set of equations describe three cell populations, blood monocytes Mblood, resting tissue macrophages Mtissue and activated tissue macrophages Mactivated. A schematic presentation of monocyte turnover is shown in Fig. 1(B).
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The baseline release from the bone marrow is equal to s3 monocytes per day. Circulating monocytes spontaneously enter body tissues at the migration rate k2 per day. In tissue, monocytes differentiate into macrophages (17,18) or dendritic cells (19,20). In the model, we consider monocytes in tissue as one population and call it tissue macrophages. Resting tissue macrophages die at the rate d4 per day. Setting B = 0 and solving the equations d/dt Mblood = 0 and d/dt Mtissue = 0, we obtain the steady state numbers of blood and tissue macrophages prior to infection, Mblood(0) and Mtissue(0). On day 0, tissue macrophages are exclusively in a resting state, i.e. Mactivated(0) = 0.
In infection, the bone marrow releases more monocytes into the blood, with the maximum release of s4 monocytes per day and the half-maximum constant h3. Circulating monocytes enter the tissue at the maximum migration rate k3 and the half-maximum constant h4. The presence of Salmonella in the Peyer's patches activates resting tissue macrophages. The activation rate is c per day. Activated tissue macrophages die at the rate d5.
Salmonella.
The following equations describe the population of Salmonella B in the Peyer's patches.
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The number of Salmonella cells surviving follows a binomial process with probability of infection p. When inoculum of the dose D is given to an animal, the mean pD of the binomial process is assumed to be the number of Salmonella cells in Peyer's patches of the animal on day 0 immediately after exposure.
Parameter estimates.
The present experiments were designed to estimate the probability of infection and the rate of growth of Salmonella. Estimates for many of the rate parameters of neutrophil and monocyte response were based on published experimental studies. How we incorporated the results of these studies into our mathematical model is outlined below. References to the experimental studies are listed in Table 2. For other parameters of neutrophil and monocyte response, no independent studies could be found. These were treated as free parameters of the mathematical model.
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Release of neutrophils and monocytes into the blood (s1, s2, s3, s4).
In mice, 1.575 x 106 neutrophils per ml per day enter the bloodstream (21). Injection of G-CSF increases the release to 13.8 x 106 neutrophils per ml per day (21).
In mice, 13.6 x 105 monocytes enter the bloodstream in 48 h (18). Assuming 2 ml blood per mouse weighing 30 g (in proportion to 5 litres blood per 75 kg man), we obtain 3 x 105 monocytes per ml per day. In an acute inflammation reaction in mice provoked by injecting new born calf serum, 27.2 x 105 monocytes enter the bloodstream in 48 h (18). This is equivalent to 8 x 105 monocytes per ml per day.
Migration from the blood to tissues (k2).
In mice in a steady state, circulating monocytes spontaneously enter the body tissue at a rate of 0.03974 per hour, an equivalent of 0.95 per day for the rate of spontaneous migration (18).
Death of neutrophils and monocytes (d1, d2, d3, d4, d5).
Neutrophils are short-lived cells with t1/2 of 610 h in the circulation, after which they undergo apoptosis (22,23). Assuming t1/2 of 8 h (0.33 day), the rate of death is equal to ln(2)/0.33 2.1 per day. Lifespans potentially differ in tissue compartments, but we assume them to be the same because relevant in vivo data are unavailable (d1 = d2). Tissue macrophages are generally considered to be long lived cells. In a normal mouse, there are 106 blood monocytes and 2.4 x 106 peritoneal-cavity macrophages (18). At least 7.6% of all monocytes that leave the bloodstream arrive in the peritoneal cavity (18). These data give
3 x 107 tissue macrophages per mouse. To maintain the total body count in a steady state while new monocytes continuously enter the body tissue, macrophages must die at the rate of 0.03 per day (the total monocyte release into the bloodstream divided by the number of tissue macrophages = 106/3 x 107). The equivalent t1/2 is about 30 days. Lifespans potentially differ in resting and activated states, but we assume them to be the same because relevant in vivo data are unavailable (d3 = d4 = d5).
Removal rates (z1, z3).
Intracellular killing of Salmonella by blood granulocytes was estimated using C57/BL and CBA mice. The rates of intracellular killing were 0.007 (C57/BL) and 0.017 (CBA) per min per (5 x 106 granulocytes/ml) (24). A similar study reported the rates of intracellular killing of Salmonella by resident peritoneal macrophages (likely to be in an activated state) as being 0.03 (C57/BL) and 0.05 (CBA) per min per (5 x 106 macrophages/ml) (25). Judged by the fit of the mathematical model to our data, the estimates for C57/BL were just as good as the estimates for CBA mice. The estimates for C57/BL mice expressed in ml per blood cell per day were used in this study.
Half saturation constants (h1, h2, h3, h4), exponents (n1, n2, n3, n4), migration rates due to infection (k1, k3), activation rate (c) and removal rates (z2).
No independent studies could be found for these parameters, and they are treated as free parameters of the mathematical model. Estimates were based on the data presented in this study, the number of blood neutrophils, blood monocytes and Salmonella cells in the Peyer's patches. The data from all dose groups were used. All data were assumed to be log-normally distributed. We minimize the log likelihood function (l): the sum of squared differences between the data and the model, using a numerical optimization function (NMinimize) in Mathematica version 5 (Wolfram Research). At each optimization step, the system of ODEs was solved numerically using the Mathematica ODE solver (NDSolve). To determine a credible range of values for each parameter, we numerically determined the two roots of the equation, where
is the minimum value for the log likelihood function l and
is the 95th percentile of the Chi square distribution with 1 degree of freedom.
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Results |
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Neutrophil and monocyte responses to growing bacteria
In our mathematical model, the number of neutrophils and macrophages in Peyer's patches increases with the bacterial burden. The killing by the phagocytes eventually exceeds the growth of bacteria, resulting in the decrease in bacterial burden on day 3 to day 4 (Fig. 3A). Neutrophil and monocyte responses in high-dose infection are characterized by three time periods (Figs 4A and 5A). In the first period, neutrophils and monocytes in the blood circulation migrate massively into the infected tissue and their numbers drop, reaching the lowest on day 1 after inoculation. Density-dependent migration of neutrophils and monocytes cannot be established based on our data, i.e. both constants h2 and h4 can be zero. In the second period, the release of neutrophils and monocytes from the bone marrow exceeds the loss by migration and the pool of blood neutrophils and monocytes increases gradually in number to the highest on day 4. This is when the bacterial burden was the highest and started to decrease (Fig. 3A). The release of neutrophils and monocytes into the blood is a density-dependent response, i.e. both constants h1 and h3 are greater than zero. Furthermore, the release-response significantly differs from MichaelisMenten type, i.e. both exponents n1 and n3 are greater than one, indicating a positive feedback mechanism in the responding bone marrow. In the third period, the release from the bone marrow decreases with the bacterial burden. Beyond day 7, the bacterial burden decreases very slowly but not completely. Long term dynamics of bacterial burden exhibited a damped oscillation to the equilibrium 105 c.f.u./g.
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Discussion |
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In the mathematical model, resting tissue macrophages do not seem to be important to the extent that blocking phagocytosis by setting the parameter z2 to zero still resulted in a good fit to the experimental data. More surprisingly, blocking the activation of resting macrophages by setting the parameter c to zero did not result in an overgrowth of Salmonella. Therefore, the reduction in the number of Salmonella as shown in Fig. 3 is due to phagocytosis by tissue neutrophils. However, blocking phagocytosis activity of tissue neutrophils alone (by setting the parameter z1 to zero) resulted in an initial overgrowth of Salmonella that was later controlled by activated tissue macrophages that took over the role of neutrophils. This illustrates a complex interplay between neutrophils and macrophages that could be tested against the animal model.
The estimated doubling time of Salmonella (5 h) in the Peyer's patches is based on two assumptions. First, Salmonella is predominantly present in the Peyer's patches. In jejunum, ileum, coecum, colon and spleen, the number of Salmonella cells per gram of tissue are generally 10100 times lower than the number per gram of Peyer's patch. Only on days 5 and 6 in the highest dose group was Salmonella present in ileum, colon and Peyer's patches in a comparable density. Second, we assumed that Peyer's patches weigh 0.5 g per infected rat. We had to make the assumption because the weights per individual rat were not recorded following the measurements. We examined 410 of the largest Peyer's patches per infected rat, which weighted roughly between 0.1 and 0.5 g in total. The results should hold unless this assumption is grossly violated, e.g. by a factor 100, which we feel is unlikely. The estimated doubling time based on these assumptions lies within the range previously reported (14).
The numbers of Salmonella cells in the Peyer's patches in infected rats in the highest dose group tend to be higher than the simulation results using the mathematical model (Fig. 3A) whereas those in the lower dose groups tend to be lower (Fig. 3B). We regarded experimental noise as the source for the variability. However, alternative possibilities, such as a decision by a group of densely populated Salmonella cells in the intestine to turn on additional virulence mechanisms, cannot be excluded.
A protective role of B and T cell mediated immunity against Salmonella infection in mice was demonstrated in an adoptive transfer study (26). In the present experiment, Ag-specific T cell immunity was already detected from day 3 and onwards by ear swelling after injecting heat-killed Salmonella into the ears (unpublished observations). Although this read-out does indicate the presence of T cell dependent immune response, it does not by itself demonstrate T cell activity in the killing of Salmonella. In addition, Salmonella infections in nude rats that lack T cells and in which antibody production is diminished were not more severe than in normal rats during the first week of infection (our unpublished observations). So, in the mathematical model, we attributed the diminished growth of Salmonella entirely to tissue neutrophils and (activated) macrophages. In an experiment that lasted to 12 days following the challenge with the dose of 2.0 x 106 c.f.u. of S. Enteritidis, the bacterial load per gram of Peyer's patch on day 12 ranged between 4.6 x 104 and 7.4 x 104 c.f.u. (our unpublished observations). The simulated bacterial load on day 12 using the mathematical model was 2 x 105 c.f.u. per gram of Peyer's patches. This number is only marginally higher than the experimental data, despite the fact that T cell immunity is missing from the mathematical model.
In Peyer's patches or proximal gut tissues, Salmonella cell may enter the bloodstream and reach the liver and the spleen. Alternatively, cells of monocytemacrophage lineage may actively transport Salmonella cells into these organs. We observed in this study that Salmonella appears first in Peyer's patches and then in the spleen about a day later (Figs 3 and 6). Moreover, the appearance of Salmonella in the spleens of infected animals coincides with the appearance of a cell population in the model that we termed activated tissue macrophages. Although activated macrophages are not generally considered to be mobile, dendritic cells are. After taking up Salmonella in inflamed tissue, DC downregulate antigen uptake and migrate to a draining lymph node, where they activate Ag-specific T cells (19). The DC biology and the population dynamics of activated macrophages in our mathematical model substantiate the idea that Salmonella cells are actively transported to the spleen by a cell of monocytemacrophage lineage.
In conclusion, we estimated the in vivo growth rate of Salmonella in rats. The estimated doubling time is 5 h. The main strength of this estimate is that Salmonella is given via the oral route, which is the better route of infection to model food-borne infection compared to intra-peritoneal or other routes. We can predict the time course of neutrophil and monocyte responses up to a week in low and high dose infection. Predictions can be extended to a longer time period and to other altered situations, such as diminished/disabled neutrophil migration. Importantly, predictions can be tested quantitatively by experiments.
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Acknowledgements |
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Abbreviations |
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DC | dendritic cells |
BHI | brain heart infusion |
PS | physiological saline |
PPS | PS plus 1% peptone |
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Notes |
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Received 18 June 2003, accepted 26 October 2004.
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References |
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