International Immunology, Vol. 14, No. 2, 111-119,
February 2002
© 2002 Japanese Society for Immunology
A quantitative model for neutrophil response and delayed-type hypersensitivity reaction in rats orally inoculated with various doses of Salmonella Enteritidis
Microbiological Laboratory for Health Protection, and
1 Laboratory for Pathology and Immunobiology, National Institute of Public Health and the Environment, PO Box 1, 3720 BA Bilthoven, The Netherlands
Correspondence to: K. Takumi; E-mail: katsuhisa.Takumi{at}rivm.nl
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Abstract |
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Our aim was to investigate the quantitative relationship between inoculation doses and physiological responses to infection by Salmonella enterica serovar Enteritidis. Rats were orally inoculated with 10–109 c.f.u. of S. Enteritidis and monitored for 6 days. Neutrophil and delayed-type hypersensitivity (DTH) responses were assessed, and the spleens were analyzed for the pathogen. The experimental data were analyzed by a mathematical model for the host response to salmonella infection, which is based on the assumptions that: (i) the number of pathogens in the inoculum is Poisson distributed, (ii) any cell that is inoculated can multiply and form a clone to infect the animal, (iii) the probability of infection by any cell of the pathogen is independent of the number of cells ingested, and (iv) the magnitude of the immune response increases with dose, but eventually saturates to a maximum level. The probability of infection assessed by the DTH response is 7.5 x 10–3/c.f.u. of the inoculum (confidence interval 5.1 x 10–5, 1.2 x 10–2). When five S. Enteritidis independently initiated the infection, the DTH response to the resulting clones of the salmonellae saturated to the maximum level. The probability of infection assessed by the neutrophil response is 3.4 x 10–4/c.f.u. (1.0 x 10–4, 6.8 x 10–4). The response saturated when six S. Enteritidis independently initiated the infection. The probability of infection assessed by the analysis of spleens is 1.2 x 10–3/c.f.u. (4.1 x 10–4, 2.6 x 10–3). We conclude that at low inocula, infections are initiated by very small numbers of bacteria. The magnitude of the immune responses is similar whether only a few or a larger number of bacteria initiated the infection.
Keywords: bacteria, dose, response, infectious immunity, in vivo animal models, mathematical model
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Introduction |
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Salmonella spp. are facultative intracellular pathogens (1). In the small intestine, viable salmonellae invade the host via M cells and epithelial cells (2). In response to bacterial entry, epithelial cells secrete IL-8, which is a chemoattractant for neutrophils (3,4). Other pro-inflammatory cytokines are also expressed and secreted by epithelial cells upon bacterial entry (5). Intestinal dendritic cells can take up and process salmonellae, and migrate to draining lymph nodes to present antigens to T cells (6). Virulent strains of salmonella are capable of persisting and multiplying inside macrophages (1,7,8). Host-specific virulence may correspond to in vitro differential persistence in murine and in human macrophages (9).
Following an oral administration of a well-mixed inoculum, one or more salmonellae may survive the non-immune host defense. These surviving pathogens may find a niche on the mucosal surface where they may multiply, causing cell or tissue damage, and triggering a host response (10). Why some orally administered pathogens survive to cause an infection, while others in the same inoculum do not, is incompletely understood. However, random selection seems to be important, apart from molecular- or cellular-based reasons. Earlier studies of lethal salmonella infection in rodent models indicated that a single c.f.u. of salmonella has a very small but non-zero probability of causing infection (single-hit hypothesis) (11). In the absence of cooperating action between pathogens, the probability of lethal infection by a single cell may be considered constant, i.e. the hypothesis of independent action. Meynell and Stocker investigated and supported the hypothesis of independent action of microorganisms (12), by i.p. injecting a mixture of flagella variants of S. paratyphi B into mice. They reasoned that, if the hypothesis of independent action holds, salmonellae isolated from dying rats following exposure to a low dose should be dominated by a monoculture because the probability of two salmonellae simultaneously infecting the rodent is vanishingly small. Moxon and Murphy repeated similar experiments by infecting infant rats via the intranasal route with a mixture of streptomycin-sensitive and -resistant variants of Haemophilus influenzae type b (13). They also found that the majority of blood cultures was dominated by a single variant, even for a very high dose. Based on the hypothesis of independent action, a mathematical model has been derived, which relates the probability of infection to inoculated doses of a pathogen (14–16). To date, the dose–response model has been applied to experimental salmonella infection in rodents (15) and Escherichia coli O157 infection in rabbits (14,17), as well as to infections by a variety of intestinal pathogens in human volunteer studies (18).
In these dose–response models, the outcome of infection is binary, e.g. the pathogen was isolated or not isolated from feces. However, for many physiological responses to infection such as immune responses, it is unreasonable to regard them as a yes/no type of response. This severely limits applicability of the binary-outcome dose–response model to experimental models of infection. To overcome this difficulty, we developed a novel dose–response model in which continuous outcome variables may be used. The continuous-outcome dose–response model is based on the single-hit hypothesis and the hypothesis of independent action. An additional assumption is that the magnitude of the immune responses increases with the dose but saturates to a maximum level. In this report, we present the continuous-outcome dose–response model and apply it to analyze immune responses to experimental S. Enteritidis infection in rats.
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Methods |
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Bacterial strains
S. enterica serovar Enteritidis 97-198, patient isolate (origin RIVM); E. coli WG5, a nalidixic acid resistant derivative of E. coli C (19) was used as a negative control. From these strains a stock collection was made by pure culturing on brain heart infusion (BHI) agar (18–20 h at 37°C) and inoculating a single colony in BHI, incubated for 18–20 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 BHI and incubating at 37°C for 18 h. After incubation, 100 ml of each culture was centrifuged at 5000 g for 10 min at 4°C. The supernatant was discarded and the pellet was re-suspended in 100 ml physiological saline (PS), followed by re-centrifugation. Again, the supernatant was discarded and the pellet was re-suspended in 4 ml 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).
Animals
Specific pathogen-free male Wistar-Unilever rats were obtained from the breeding colony at the National Institute of Public Health and the Environment (Bilthoven, The Netherlands). The animals, 6–9 weeks of age, were housed individually in macrolon cages, 1–2 weeks prior to inoculation. Drinking water and conventional diet (RMH-B; Hope Farms, Woerden, The Netherlands) were provided ad libitum. The breeding colony of the animals was pre-screened/monitored for endogenous pathogenic viruses and bacteria, and was found negative.
Experimental design
The Central Animal Laboratory of RIVM possesses a license under the Dutch `Animal Experiments Act'. In accordance with Section 14 of this Act, an officer has been appointed to supervise the welfare of laboratory animals. All experiments were discussed and approved by an independent ethical committee prior to the study. After 1–2 weeks of rest (i.e. acclimatization), the animals were starved overnight (water ad libitum). After 16 h of starvation, 1 ml of the bacterial suspensions was orally administered by gavage (three to five animals per dose group). Directly after gavage (day 0) food and water was provided ad libitum. Blood samples were taken via orbita plexus puncture using a capillary under light ether anesthesia 10–14 days before and 5 days after oral inoculation just before administration of heat-killed S. Enteritidis into the pinnae of both ears (see below). Daily clinical observations were made with reference to the status of general health of the animals. The animals were sacrificed on day 6 after oral inoculation, by bleeding from the abdominal aorta under KRA anesthesia [i.m. injection of 100 µl of a cocktail consisting of 7 ml ketalar (50 mg/ml; Parke Davis, Barcelona, Spain), 3 ml rompun (20 mg/ml; Bayer, Leverkusen, Germany) and 1 ml of atropin (1 mg/ml; OPG, Utrecht, The Netherlands)]. Gastrointestinal tract, mesenteric lymph nodes, spleen and, in some experiments, other organs were removed aseptically.
Delayed-type hypersensitivity (DTH) reaction
Five days after oral infection with S. Enteritidis the thickness of both ears of each animal in each group was assessed in duplicate using an engineering micrometer (193-10; Mitutoyo, Veenendaal, The Netherlands). For this purpose, the animals were anesthetized by i.m. injection of 100 µl of a KRA solution. Directly after the ear measurements 25 µl of a heat-killed suspension of S. Enteritidis (~5x108 c.f.u./ml) was s.c. injected into the ear pinnae of each rat (also into the control animals receiving E. coli WG5). The increase in ear thickness was assessed 24 h after challenge under ether anesthesia. Because the assessments of ear thickness performed in duplicate were always consistent, we expressed ear thickness as the average of the duplicate. Finally, the DTH reaction is expressed as 100x(ear thickness 24 h following the DTH test)/(ear thickness prior to the DTH test performed on day 5). The reason for percent instead of absolute change is that change may be dependent on an initial value, i.e. a thicker ear swells more in absolute value than does a thinner ear.
Hematology
As an indicator for (systemic) infection, hematology for each rat was performed in blood samples, anticoagulated with K3EDTA, obtained at day –10 and 5. The hematological analyses were performed using the H1-E, a multi-species hematology analyzer (Bayer, Mijdrecht, The Netherlands) with multi-species software, version 3.0. Like the DTH reaction, neutrophil response is expressed as 100x(cell count 5 days following the inoculation)/(cell count 2 weeks prior to the inoculation).
Microbiology
Internal organs were homogenized with 1:10 (w/v) in peptone-PS using an Ultra Turrax (Janke und Kunkel, Breisgau, Germany). Then 0.1-ml volumes of serial 10-fold dilutions were spread-plated on brilliant green agar (BGA) for S. Enteritidis and on tryptone yeast extract glucose agar with nalidix acid 100 µg/ml (TYGnal) for E. coli WG5. The BGA and TYGnal were incubated at 37°C for 22–26 and 18–20 h respectively. Blood samples were analyzed by spread-plating 0.1 ml volumes on the same media.
Model and parameter estimation
The binary-outcome dose–response model is derived based on the assumptions (16):
(i)The number of pathogens in the inoculum follows the Poisson distribution.
(ii)Any cell that is inoculated can multiply and form a clone to infect the animal (single-hit hypothesis).
(iii)The probability of infection by any cell of the pathogen is independent of the number of cells ingested (hypothesis of independent action).
The first means that the inoculum is well mixed. The last two have been investigated and supported by a series of experimental studies (12,13), as discussed in the Introduction.
The outcome variable of the model is the fraction of the animals that did not respond to a dose of S. Enteritidis. The model has only one parameter, the probability of infection per c.f.u. of the inoculum (r in Table 1
). The parameter must be estimated from experimental data. This model is difficult to apply to outcome variables for which no clear threshold exists, e.g. blood cell counts following a low-dose challenge. The outcome variable of the continuous-outcome dose–response model that overcomes this difficulty is a set of measured physiological responses to salmonellae (e.g. DTH and neutrophil response). The continuous-outcome dose–response model is based on the preceding three and one additional assumption.
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(iv)The magnitude of the immune response initially increases with dose but eventually saturates to a maximum level.
The continuous-outcome dose–response model has six parameters (Table 1
). Some parameters of the model can directly be measured in the experiments. These are the median of the baseline response µ and the standard deviation 
. All other parameters must be estimated from the experimental data. The set of all measured responses to various inoculation doses is used to determine the best-fit estimates for the model parameters.
We now discuss the equation of the binary-outcome dose–response model. A rat is given an inoculum of average size D. The number (in c.f.u.) of salmonellae actually present in the inoculum is most likely equal to D but may be zero, one, and in fact any positive integer. The probability that it is j is equal to
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 | (Eq. 1) |
We now discuss the equation for the continuous-outcome dose–response model. In the absence of salmonella infection, we model a set of measured responses of a group of rats (i.e. baseline responses) by the log-normal distribution Y with median µ and standard deviation on the linear scale. If exactly one of the inoculated salmonellae did infect a rat, the immune response to the resulting clone of this cell is assumed to increase proportionally to the baseline response. The factor of the proportional increase varies between the animals because, for example, salmonellae grow slightly differently from one rat to another or individual rats respond differently to infection. We model the factor of proportional increase by the log-normal distribution Z with median 
and standard deviation 
on the linear scale. Thus, for a group of rats each infected by exactly 1 c.f.u. of salmonella, the immune responses are distributed according to the product of two log-normal distributions YZ. If two salmonellae independently initiate infection, the immune response is distributed according to YZ2, YZ3 for three and so on.
The number of salmonellae independently initiating infection follows a binomial process with the probability of infection r per c.f.u. (assumption 3). Thus, on average, 1 c.f.u. of salmonella initiates infection if a rat is given a dose approximately equal to 1/r. Given a dose of 2/r, on average two salmonellae initiate infection, 3/r for three and so on. Because the immune response cannot indefinitely increase with dose, we assume that the immune response saturates when the dose is equal to c/r, i.e. when the average number of salmonellae independently initiating infection is equal to c. We model the saturating response by introducing the hyperbolic tangent function ctanh(rD/c). For a low dose, the function closely approximates the average number of salmonellae initiating infection, rD. For a large dose, the function approaches the maximum number c.
The overall response (denoted by X) of a group of rats is a mixture of the baseline response and the immune response, weighted by the binary-outcome dose–response model.
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) and Z ~ log-normal(,). We performed parameter estimates based on the method of maximum likelihood. Briefly, the formalism links measured data and a probability model in the form of a mathematical function and postulates that we should choose parameter values so that the measurements become the most likely outcome of the proposed probability model. The link is called a likelihood function. It is essential to consider the experimental measurements as samples of a statistical distribution. For the microbiological data, i.e. salmonella isolated/not isolated, the binomial distribution is a natural choice. For the hematological and DTH data, we chose the log-normal distribution because the variance of the data increases with the mean response. A sufficiently large amount of data is also essential for reliable parameter estimation.
For the response assessed by the isolation of salmonella, the number of animals free of salmonella follows the binomial distribution, the probability of no-isolation being equal to e–rD. We obtain the following log-likelihood function:
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The best estimate for the parameter r, which maximizes the log likelihood l, is the solution of the equation
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is the solution, an ~95% confidence interval for the parameter r consists of all r values satisfying the equation
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2 distribution with 1 d.f.
For the DTH and neutrophil responses, the log-likelihood function is:
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We estimated parameter values by repeatedly running a Markov Chain Monte-Carlo algorithm that we adopted from Gilks et al. (20). Initial conditions were randomly sampled from a wide area of the parameter space. We take as the best-fit estimate the set of parameter values, for which l is the largest at the end of a simulation (subsequently verified to be close to the maximum of the log-likelihood function obtained using the Newton's method). All computation is done using Mathematica software (21).
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Results |
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Invasion into the spleen
Isolation of S. Enteritidis from post-mortem samples of the spleens indicated an extraordinary ability of S. Enteritidis to invade this secondary lymphoid organ at day 6 following inoculation. With increasing dose, S. Enteritidis was more frequently isolated from the spleens. This dose-dependent decrease in the percentage of salmonella-free rats was most simply accommodated by the binary-outcome dose–response model (Fig. 1
). The probability of infection (or, perhaps more appropriately for this outcome variable, the probability of invasion) assessed by the analysis of spleens was estimated to be r = 1.2x10–3/c.f.u. of the inoculum. This is equivalent to an ED50 of 580 c.f.u.
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The precision in the parameter estimate depends on the doses tested and the numbers of animals per dose group. A larger number of animals given a medium dose (i.e. ~ED50) usually result in a more precise estimate.
DTH reaction
The measured percent change in the ear thickness of the control animals is approximately normally distributed (Fig. 2). Initial ear thickness before the injection of heat-killed salmonellae was between 420 and 600 µm, with a mean equal to 510 µm and a standard deviation equal to 60 µm. One day following the injection, ear thickness of the control animals increased up to 120% of the initial thickness. This background swelling is probably induced by non-specific inflammatory reactions at the sites of injection.
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Injection with heat-killed E. coli, Listeria monocytogenes or lipopolysaccharide failed to induce ear-swelling reactions in S. Enteritidis infected animals, indicating the antigen specificity of the response. The ear swelling was maximal 24–48 h after the ear challenge with heat-killed S. Enteritidis, and was characterized by a mononuclear infiltrate in the ears.
Rats orally inoculated 150 c.f.u. of S. Enteritidis did not exhibit an abnormal increase in ear thickness following the DTH test (Fig. 2). For a dose of 300 c.f.u. it is likely that all rats elicited an antigen-specific T cell response because the relative ear thickness fell outside of the range for the control animals inoculated with E. coli WG5. Among the five rats given this dose, we isolated S. Enteritidis from the spleens of two rats, but not from the remaining three rats (Table 2). The absence of S. Enteritidis may indicate that antigen-specific T cell responses already have contributed to eliminate the pathogen by the time the spleens were examined. Large increases in ear thickness following exposure to a dose of 49,000 c.f.u. are highly likely to be the result of antigen-specific T cell responses. We isolated S. Enteritidis from the spleens of all five rats given this dose.
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Overall, the data show that the higher the inoculation dose, the more pronounced the DTH response (Fig. 3
). The maximum responses in the range between 104 and 109 c.f.u. are approximately the same. Although this pattern is consistent with the saturating response, the minimum responses in the same range do increase, suggesting that a response without saturation might better account for the observed response. We tested an alternative model for the immune response without saturation. The likelihood ratio test supports the saturating response.
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The probability of infection assessed by the DTH response is estimated to be r = 7.5x10–3/c.f.u. of the inoculum. Although the confidence interval for the parameter r is wide, presumably due to the low responses ~104 c.f.u. and the high responses ~102 c.f.u. in Fig. 3
, the best estimate is close to the estimated probability of infection assessed by the analysis of spleens. When 5 (= c) c.f.u. of S. Enteritidis independently initiated the infection, the DTH response to the resulting clones of the salmonellae saturated (Table 3). For a larger inoculation dose, thus for a larger number of salmonellae initiating the infection, the variation between individual rats mostly accounts for the widely scattered data values.
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Peripheral neutrophil counts
A previous study indicated that S. Enteritidis especially affected the concentration of neutrophils in blood at day 5 (22). The relative cell counts of the control animals inoculated with E. coli WG5 varied between 50 and 160% of the absolute cell counts prior to the inoculation (Fig. 4
). The absolute cell counts prior to the inoculation varied between 360 and 1100 cell/µl, with a mean equal to 660 cell/µl and a standard deviation equal to 210 cell/µl. There was no evidence for neutrophil response in the group of rats given 10 c.f.u. of S. Enteritidis (Fig. 5). Following inoculation of 150 c.f.u., however, one rat had an absolute neutrophil count that was 260% of the count prior to the inoculation (Table 2). From the spleen of this rat, we isolated S. Enteritidis. The absolute counts for the other three rats given a dose of 150 c.f.u. did not abnormally increase and their spleens were free of S. Enteritidis. Two of the rats given a dose of 910 c.f.u. had high relative neutrophil counts (Fig. 4) and infected spleens (Table 2). The relative neutrophil counts of the animals given 4700 c.f.u. of S. Enteritidis were normal. Although this may indicate an absence of infection, a low level of neutrophil response to infection cannot be excluded (Fig. 4). At 26,000 c.f.u., all animals exhibited high relative neutrophil counts and infected spleens (Fig. 4).
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Neutrophil response to the salmonella infection quickly increases to the maximum level at the inoculum of 104 and larger (Fig. 5
). The saturation occurred when 6 (= c) c.f.u. of S. Enteritidis independently initiated the infection (Table 3). |
Discussion |
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We have shown considerable variation between outcome variables following an oral administration of S. Enteritidis to rodent hosts. Among the outcome variables presented, the DTH reaction and the presence of salmonella in the spleen most sensitively reacted to a low dose exposure. Because these are the responses of the same group of rats, we conclude that S. Enteritidis infects the rodent hosts at least as easily as is indicated by the DTH response. Our estimate regarding the probability of infection assessed by the DTH response translates approximately to infection by seven to eight per 1000 c.f.u. of the inoculum. These salmonellae must have survived non-specific host barriers, crossed the epithelial lining, multiplied to give rise to clones and damaged host tissues. Furthermore, because without antigen, T cell responses cannot be generated, intestinal dendritic cells apparently captured and processed the salmonellae and migrated to a draining lymph node to present the antigen to T cells.
Pamer and colleagues analyzed CD8 T cell responses to L. monocytogenes infection in relation to the amount and the duration of antigenic stimulation (23,24). The authors showed that the magnitude of the CD8 T cell responses was similar in mice i.v. receiving 1000 or larger doses of L. monocytogenes. Similarly, we showed that the magnitude of the DTH responses is similar in rats orally given 104 or larger doses of S. Enteritidis. Thus, both studies can be interpreted as showing full-blown T cell responses to a sufficiently large inoculum. Although it is difficult to compare the animal models with different routes of infection, the larger critical dose in the present study is consistent with an oral, as opposed to an i.v., route of administration.
The present analysis does not take time into account. All the measurements and parameter estimates refer to ~1 week following the inoculation. Systemic T cell immunity fully develops in a period of ~1 week. By taking measurements 6 days following the inoculation, our experimental set-up is probably optimized for detecting antigen-specific T cell responses. However, this may not be the case for the neutrophil response. We are currently performing experiments to assess neutrophil response in relation to time, to determine whether and to what extent the timing of the measurement influences the result and the parameter estimates.
The data on the DTH response and the continuous-outcome dose–response model do not agree well at high inocula (Fig. 3). This could reflect a conflict among the data points. Low DTH responses of ~104 c.f.u. are inconsistent with other data points that generally support the highly infectious nature of S. Enteritidis. The conflict could be resolved by further assessing the DTH responses.
The present parameter estimates might not be valid if ingested salmonella acted together to initiate the infection (i.e. if the hypothesis of independent action were violated). Communication between some bacterial pathogens by means of a chemical messenger (25) makes a case for a synergistic action of microorganisms. If these messenger molecules were produced in vitro, their concentration would strongly be reduced by the washing step in our procedure to prepare the inoculum. If these messenger molecules were produced in vivo, a large distance between the inoculated salmonellae would strongly limit their function. We therefore expect that a synergistic action among the inoculated bacteria has a negligible effect in the early stage of infection and may only be relevant after clones arising from the infecting cells have been established.
Inoculating distinguishable variants of salmonellae into mice, Meynell et al. obtained cultures of salmonella from the blood of the dying mice. Most cultures were dominated by a single variant up to several multiples of the ED50 dose (12). Translating this result to our rodent model, DTH or neutrophil responses would have been initiated by multiplication of single salmonella when the hosts were given doses up to several times the ED50. With a much higher dose, hundreds of salmonellae could indeed initiate infection independently, perhaps starting at different locations of the intestinal tract. A stronger host response might be suspected in such case. However, our estimates for the parameter c as described in Table 1 are relatively small. This indicates that the rodent host rapidly responds to multiplication of few salmonellae. Infection by a large number of salmonellae appears to have little additional effect on DTH and neutrophil responses beyond that initiated by only a few salmonellae.
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Acknowledgments |
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The experiments in this article involved the work of many persons in different laboratories. Hans Strootman, Mariska van Dijk, Dirk Elberts and Bert van Middelaar were responsible for the animal experiments. Coen Moolenbeek performed section of the animals. Lisete de la Fonteyne and Yvonne Wallbrink participated in hematological analysis. Ellen Delfgou-van Asch and Wilma Ritmeester were involved in the microbiological analysis. Wim Jansen and Nan van Leeuwen provided bacterial strains. Joseph Vos provided helpful advice on immunological aspects and Peter Teunis on statistical aspects of the work. We thank two anonymous referees for helpful and constructive comments.
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Abbreviations |
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| BGA brilliant green agar |
| BHI brain heart infusion |
| DTH delayed-type hypersensitivity |
| PS physiological saline |
| TYGnal tryptone yeast extract glucose agar with nalidix acid |
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