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Poult Sci 2007. 86:1336-1350
© 2007 Poultry Science Association
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IMMUNOLOGY, HEALTH, AND DISEASE

Modeling Immunocompetence Development and Immunoresponsiveness to Challenge in Chicks

B. Ask*,{dagger},1, E. H. van der Waaij{dagger}, E. J. Glass{ddagger} and S. C. Bishop{ddagger}

* Department of Farm Animal Health, Utrecht University, 3584 CL, the Netherlands; {dagger} Animal Breeding and Genetics Group, Wageningen University, 6700 AH, the Netherlands; and {ddagger} Division of Genetics and Genomics, Roslin Institute, Midlothian EH25 9PS, United Kingdom

1 Corresponding author: birgitteask{at}hotmail.com


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
The purpose of this study was 2-fold: 1) to develop a deterministic model that describes the development of immunocompetence and the kinetics of immunoresponsiveness to a pathogenic challenge in chicks and 2) to use this model to illustrate the importance of factors in experimental design, such as type of variable measured, measurement timing, and challenge age. Difficulties in evaluating immunological variables hinder attempts to improve animal health through selection on immunological variables. In young chicks, evaluating immunological variables is additionally complicated by immune system development and maternal immunity. The evaluation of immunocompetence and immunoresponsiveness and the definition of appropriate challenge and measurement strategies may be enabled through a mathematical model that captures the key components of the immune system and its development. Therefore, a model was developed that describes the development of immunocompetence as well as the kinetics of immunoresponsiveness to a pathogenic extracellular bacterial challenge in an individual chick from 0 to 56 d of age. The model consisted of 4 components describing immunocompetence (maternal and baseline immunity) and immunoresponsiveness (acute phase and antibody response). Individual component equations generally fit published data adequately. Four scenarios that represented combinations of challenge age and measurement timing were simulated. In each scenario, the immunoresponsiveness to a particular challenge was compared for 3 different levels of baseline immunity, representing 3 broiler genotypes. It was illustrated that experimental design (type of immunoresponsiveness measured, measurement timing, and challenge age) can have an important effect on the ranking of genotypes, groups, or individuals and on the reliability of extrapolations based on this ranking. It is concluded that this model is a potentially useful tool in the definition of appropriate challenge and measurement strategies when evaluating immunocompetence and immunoresponsiveness. Further, it may be used as a generator of hypotheses on global immunological relationships to be tested experimentally.

Key Words: breeding • chicken • experimental design • immunocompetence • immunoresponsiveness • mathematical modeling


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Selection for improved immunocompetence (ability to resist and recover from infection and disease; Owens and Wilson, 1999) and immunoresponsiveness (the ability to mount an immune response) has been suggested as a method to improve animal health. However, in selection experiments, expected improvements have not been achieved (Yunis et al., 2002), possibly because selected immunological variables were not indicative of the goal (Knap and Bishop, 2000). For example, different immunological variables are activated depending on whether a challenge is an extra- or intracellular pathogen, and selection is often based on 1 variable only (Pinard-van der Laan and Monvoisin, 2000; Adkins et al., 2004).

Alternatively, the failures may have been due to complications in the evaluation of individuals relative to other individuals based on any given variable. Complications in these evaluations are introduced by experimental design in combination with immune system development as well as maternal immunity in young animals, such as chicks (Cheema et al., 2003). These complications are due to, for example, challenge timing and the number of measurements over time but are also due to the (relative) timing of these measurements. For example, selection is often based on measurements from 1 time point only, but measurements from different time points may result in different or contradictory results. Therefore, experimental design in combination with immune system development and maternal immunity may explain why expected improvements in immunocompetence as a result of selection have not been achieved. Defining appropriate challenge and measurement strategies should, therefore, accommodate successful selection for improved animal health based on immunological variables.

The definition of appropriate challenge and measurement strategies for evaluation of immunocompetence and immunoresponsiveness for selection purposes may be assisted by a mathematical model that describes the development of the immune system. Such a model (currently not available) would allow many scenarios to be tested quickly before doing expensive and time-consuming experiments and thereby also minimize the use of laboratory animals.

The purpose of this study was 2-fold: 1) to develop a deterministic model that describes the development of immunocompetence and immunoresponsiveness kinetics in chicks challenged with an extracellular bacterial pathogen and 2) to use this model to illustrate the importance of factors in experimental design, such as type of variable measured, measurement timing, and challenge age.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Model Overview
A model was developed that describes the development of immunocompetence as well as the kinetics of immunoresponsiveness to a pathogenic extracellular bacterial challenge in an individual chick from 0 to 56 d of age. Immunocompetence was modeled as a combination of 2 components that are present irrespective of challenge, namely maternal immunity and baseline immunity, defined as the potential ability of the chick to recognize and respond to challenge. Immunoresponsiveness was modeled as a combination of 2 components that emerge only in response to a challenge, namely acute phase and antibody response. Each of the components was defined by an equation describing the development or kinetics of that component.

The cell-mediated immune response was not modeled, because the model was restricted to extracellular pathogens, for which the cell-mediated immune response is of relatively low importance (Janeway et al., 2005). Possible effects of immunological memory were not modeled, because for selection purposes, chicks are normally challenged once only, and immunoresponsiveness is therefore not affected by immunological memory. For simplicity, spatial effects of infection (e.g., routes of infection) and immune response were not modeled either.

The model input includes initial parameter values at 0 d of age for the immunocompetence equations, challenge age, and challenge pathogenicity. The parameter values at all subsequent ages (1 to 56 d of age) are based on the parameter values at the preceding age and possible effects of challenge. The model output is the immunocompetence and immunoresponsiveness at any particular age. The overall framework of the immunocompetence model is shown in Figure 1Go.


Figure 1
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Figure 1. An illustration of the overall framework of the model, which describes the development of the immunocompetence in and the immunoresponsiveness of an individual chick, depending on challenge from 0 to 56 d. The 3 polygonal boxes with dotted lines are indicative of the model input, model transitions across days, and model output, respectively. The solid arrows show the transitions of parameter values across days, thus the transitions of the initial level and degradation rate of the maternal immunity (mi0 and rmi) and the initial level, development rate, and expected mature level of the baseline immunity (bi0, kbi, and cbi). The open block arrow shows the transition of output parameter values into the equations defined for immunocompetence. The stippled arrows pointing from one box to another indicate an effect of the first box on the other box.

 
Model Components
Challenge.
The challenge was assumed to be an extracellular bacterial pathogen. The pathogenicity of a challenge is the disease-producing capacity of a pathogen. In this model, the pathogenicity of the challenge was defined as the capacity to cause an immune response (acute phase or antibody response). It was assumed that the pathogenicity could be reflected by the quantity of the pathogen in the host. Pathogen quantity in the host over time can be represented by a sigmoid pattern defined by the Gompertz curve, which traditionally describes population growth under control. Given a combination of initial

challenge load (chal0), proliferation rate (kchal), and proliferation limit (due to host environment; achal) of the challenge pathogen, the pathogen quantity (i.e., pathogenicity of the challenge) becomes:


Formula 1([1])

where i = a scaling parameter to make Chal(ageinf) {approx} chal0 (see Table 1Go); age = the age in days; and agechal = the age at challenge in days. The lower and upper limits of possible values of chal0, kchal, and achal are given in Table 2Go. The challenge was assumed to be given once in the lifetime of a chick (0 to 56 d of age) at a certain age, agechal, and rechallenge was not modeled.


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Table 1. The values of the scaling parameters for the immunoresponsiveness components, the acute phase and antibody response, as well as for the effect of challenge on the maternal immunity
 

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Table 2. The lower and upper limits of parameter values for the immunocompetence components, maternal immunity and baseline immunity, and the challenge
 
Maternal Immunity.
Maternal immunity consists of antibodies transferred from the dam through the yolk. The level of maternal antibodies increases during the first 2 to 4 d of age (as the yolk is absorbed; Kaleta et al., 1977; Kowalczyk et al., 1985; Shawky et al., 1994); whereafter, it decreases until 2 to 4 wk of age (Smith et al., 1994; Jeurissen et al., 2000; Ahmed and Akhter, 2003). The antibodies are degraded at an increasing rate over time in accordance with age-related metabolic changes (Stormont, 1972; Kaleta et al., 1977). Mathematically, the degradation can be described as exponential and expressed with a half-life constant (Kaleta et al., 1977; Sarvas et al., 1993; Sahin et al., 2001; Wilson et al., 2001; Müller et al., 2002, 2005; Tizard, 2002). Therefore, the kinetics of the maternal immunity (MI) were described with the following equation, which results in an exponential decrease of maternal immunity with increasing age, tending toward zero (Figure 2Go):


Figure 2
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Figure 2. Model prediction vs. published data ({blacktriangleup}, data; —, model) for the degradation of maternal immunity illustrated by data in panel A, R2 = 0.94 (Kaleta, 1972), and data in panel B, R2 = 0.99 (Islam et al., 2002). Kaleta (1972) measured Newcastle disease virus-specific maternal antibodies in 10 chicks by a so-called virus neutralization test and expressed as so-called neutralization indices. Islam et al. (2002) measured maternal antibodies, expressed as the absorbance, in the plasma of healthy broiler chicks by an ELISA.

 

Formula 2([2])

where mi0 = the initial level and rmi = the degradation rate. The lower and upper limits of mi0 and rmi are given in Table 2Go. The equation for MI (2) approaches the zero asymptote very slowly, which is not in agreement with the biological expectation that maternal antibodies have disappeared by 2 to 4 wk of age. Therefore, it was assumed that MI = 0 for MI < 0.001.

Baseline Immunity.
Baseline immunity is assumed to represent the potential ability of the chick to recognize and respond to challenge. It is assumed to consist of the basal levels of the innate immunity, natural antibodies, and lymphocytes. The innate immunity includes anatomical, chemical, and physiological barriers; cellular elements (endocytic, phagocytic, and antigen presenting cells, e.g., macrophages and dendritic cells); and soluble factors such as the complement system.

The pattern of development of baseline immunity should reflect the combined effect of all the above-mentioned elements and reflect immunocompetence, excluding maternal immunity. The immunocompetence of young and immature vertebrates, including chicken, has been described as gradually increasing with age until maturity, when a given plateau is reached (Siegrist, 2001; Reese et al., 2006). This has, for example, been demonstrated by age-dependent antibody responsiveness (Nadler et al., 1980; Siegrist, 2001), in which actual antibody responses are assumed to reflect the ability to mount an immune response. This may be related to, among others, a reduced capacity of dendritic cells to communicate with lymphocytes (Marshall-Clarke et al., 2000; Morein et al., 2002). A gradual increase with age is also seen for different elements of innate immunity. For example, age-dependent deficiencies have been demonstrated in macrophage and heterophil phagocytosis and killing (Kodama et al., 1976; Wells et al., 1998) as well as for natural antibodies (Kramer and Cebra, 1995; Parker et al., 1996; Parmentier et al., 2004) and the quantity and functionality of lymphocytes (Anderson and Stephens, 1970; Klinman, 1976; Van Benten et al., 2005).

The development of the baseline immunity with age has not previously been modeled. Based on the above-mentioned observations, the kinetics of baseline immunity (BI), were described with the following equation, which results in a curvilinear increase from some given initial level toward some given asymptotic mature level (Figure 3Go). This equation allows for relatively large flexibility in the development pattern of baseline immunity, enabling it to describe patterns differing among individuals as well as patterns differing among different underlying immunological variables. For example, the equation allows for an almost flat development to an exponential increase until the mature plateau is reached.


Figure 3
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Figure 3. Model prediction vs. published data (•, data; —, model) for the development of baseline immunity illustrated by data in panel A, R2 = 0.85 (Islam et al., 2002), and data in panel B, R2 = 0.77 (Okamura et al., 2004). Islam et al. (2002) measured total CD45+/CD3+ lymphocyte (T cells) count in the plasma of healthy broiler chicks. Okamura et al. (2004) measured serum interferon-{gamma} in healthy chickens.

 

Formula 3([3])

where bi0 = the initial level; kbi = the rate of increase; and cbi = a parameter, which in combination with bi0 prescribes the asymptote:


Formula 4([4])

The lower and upper limits of bi0, kbi, and cbi are given in Table 2Go.

Acute Phase Response.
The acute phase response consists of innate immune responses to antigenic stimulation, including releases of cytokines, acute phase proteins, complement system factors, fever, phagocytic and cytotoxic activity, and direct cell killing. The onset of the acute phase response occurs almost immediately after infection, and it normally lasts for a few days only (Stvrtinova et al., 1995). The response pattern is relatively similar, regardless of the pathogen or infection route, though differences may be observed in quantity and temporal characteristics (Nair, 1973). It is usually bell-shaped but sometimes skewed to either side (Hallquist and Klasing, 1994; Xie et al., 2002; Juul-Madsen et al., 2003; Kaiser et al., 2003) and has also previously been modeled as such (Antia and Koella, 1994; Faro et al., 1997; Morel, 1998). The acute phase response kinetics (APR) were therefore described by the following equation, resulting in an inverse parabolic pattern (Figure 4Go):


Figure 4
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Figure 4. Model prediction vs. published data ({blacksquare}, data; —, model) for the kinetics of the acute phase response illustrated by data in panel A, R2 = 0.82 (Okamura et al., 2004), and data in panel B, R2 = 0.57 (Jarosinski et al., 2002). Okamura et al. (2004) measured serum interferon-{gamma} in chickens vaccinated with a killed Salmonella at 4 wk. The model predictions were based on the assumption of a challenge at 4 wk. Jarosinski et al. (2002) measured plasma NO levels (as indicated by its by-product nitrite) in experimental specific-pathogen-free chicken lines challenged with Marek’s disease virus at 1 d. The model prediction was also based on a challenge at 1 d.

 

Formula 5([5])

where ageAPR = the age at which the acute phase response is initiated relative to the age at challenge; APRa and APRb = the dependence of the magnitude of the acute phase response on challenge and baseline immunity, as described in "Interrelations Among Model components" below (equations 11 and 12); and s1 and s2 = scaling parameters (Table 1Go).

The acute phase response was assumed to be initiated at a certain age after challenge (ageAPR), with the time lag between challenge and initiation of the acute phase response decreasing with increasing baseline immunity at the age of challenge. The ageAPR was defined by the following equation, resulting in an interval of 0 to 10 d postchallenge:


Formula 6([6])

Antibody Response.
The antibody response is a part of the acquired immune system, which is produced by B cells and mediated by Th2 cells in response to antigenic stimulation (Janeway et al., 2005). The antibody response in young chicks is immature, but a large range of responsiveness has been observed. Chicks generally respond faster and more strongly with increasing age (Hatkin et al., 1993), which is probably, among other factors, related to the development of the immune system (O’Neill et al., 2006). Antibody response kinetics can principally be described as having 4 phases, comprising a latent phase, a phase of exponential increase, a steady-state phase, and a reduction phase (Benjamini and Leskowitz, 1991). The latent phase varies from 0 to 3 d (Gross and Siegel, 1975; Leitner et al., 1992), and the peak is reached from 5 to 15 d postchallenge (Ubosi et al., 1985; Kreukniet and van der Zijpp, 1990; Leitner et al., 1992). The kinetics of antibody responses depend on the Ig isotype. A primary antibody response consists of mainly IgM rather than IgG (Glick, 1995; Tizard, 2002), and in the initial phase of a secondary response, IgM prevails as well. The IgM response is relatively short-lived and decreases more rapidly relative to the IgG response (Bacon et al., 1972). In infants, IgM is the predominant isotype in antibody responses, and therefore the kinetics of the antibody response (ABR) were described with the following gamma equation, which results in a sigmoid exponential pattern toward peak production, after which it gradually decreases toward zero (Figure 5Go). The absence of a true steady-state phase was assumed to be realistic because of the young age of the chicks.


Figure 5
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Figure 5. Model prediction vs. published data (•, data; —, model) for the kinetics of the antibody response illustrated by data in panel A, R2 = 0.94 (Parmentier et al., 1998), and data in panel B, R2 = 0.91 (Ubosi et al., 1985). Parmentier et al. (1998) measured the total antibody response in the serum to a combination of the 2 antigens, SRBC and BSA, in heavy, brown layer chicks inoculated at 35 d by an ELISA and expressed it as the base-2 logarithm of the greatest dilution giving a positive reaction. Ubosi et al. (1985) measured the antibody response to SRBC in chicks of the type White Leghorn inoculated at 35 d by the microtiter procedure and expressed it as the base-2 logarithm of the reciprocal of the greatest dilution giving visible agglutinin. The model predictions were based on a challenge at 35 d in both panels A and B.

 

Formula 7([7])

where ageABR = the age at which the antibody response is initiated; ABRa = the dependence of the antibody response on the challenge, maternal immunity, and acute phase response, as described in "Interrelations Among Model Components" below (equation 15); and s3 and s4 = scaling parameters (Table 1Go).

The antibody response was assumed to be initiated at a certain age after the challenge (ageABR), with the time lag between the challenge and initiation of the antibody response decreasing with a decreasing time lag between the challenge and initiation of the acute phase response. The ageABR was defined by the following equation:


Formula 8([8])

Interrelations Among Model Components.
The development of the immunocompetence, the challenge dynamics, and the kinetics of the immunoresponsiveness are interrelated. These interrelations taken into account in this model are illustrated in Figure 1Go as indicated by the dotted arrows.

The maternal immunity is affected by the challenge, because the encountering of pathogenic antigens results in an increased degradation rate of maternal antibodies (Kaleta et al., 1977; Siegrist, 2001). It was assumed that neither the baseline immunity nor the acute phase or the antibody response had an effect on the maternal immunity, because the maternal antibody is simply degraded in the same way that any other protein is degraded in the bodily fluids (Tizard, 2002). The increased rmi in the face of a challenge was described by an increase in the parameter rmi by multiplication of rmi with a factor (Frmi) at the age of challenge. The factor, Frmi, increases with increasing initial challenge dose and was defined as:


Formula 9([9])

where s5 = a scaling factor (Table 1Go). This factor reflects an increasing likelihood of the maternal antibodies encountering the antigens with increasing challenge dose. The likelihood of the maternal antibodies encountering antigens is likely to be a function of antigen concentration (Kulin et al., 2002) because of the distribution of antibodies and antigens in the bodily fluids.

There are indications that maternal antibodies can have a suppressing effect on the development of baseline immunity in the form of natural antibodies (Kramer and Cebra, 1995), and there are indications that maternal antibodies positively affect the development of lymphocytes (Lemke et al., 2000). However, no indications have been found that maternal antibodies affect the development of the innate immunity. Because of the opposing effect of maternal antibodies on natural antibodies and lymphocytes and the absence of an effect on innate immunity, for simplicity, it was assumed that maternal immunity did not affect baseline immunity. Pathogenic antigenic stimulation of the baseline immunity may result in an increased rate of development and an increased expected mature level. For example, the quantity of natural antibodies increases in response to pathogenic challenge, and the ability to respond to a secondary challenge increases, reflecting acquired memory. Moreover, the maturity of the immune system is increased in response to challenge (Tomer and Shoenfeld, 1988; Mast and Goddeeris, 1999). The increased development rate and mature level of baseline immunity in the face of a challenge was described by an increase in the parameters kbi and cbi by multiplication of both kbi and cbi with a factor (FBI) at the age at which the acute phase response reaches its peak (ageAPRmax; equation 13).

The effect of challenge on the baseline immunity is reflected in the elicitation of an acute phase response ("Acute Phase Response" above), and therefore, FBI is defined as a function of the acute phase response as:


Formula 10([10])

where APRmax = the peak of the acute phase response (equation 14). This reflects an increasing effect of the antigenic stimulation of the baseline immunity on its own development.

The acute phase response was assumed not to be affected by the maternal immunity. This was assumed, because no clear demonstration of such an effect has been seen in chicks and, further, acute phase response is likely to be initiated before pathogens come in contact with maternal antibodies, which to our knowledge are mainly present in the blood. In contrast, the acute phase response was assumed to depend on the baseline immunity, because the acute phase response is defined as consisting of innate immune responses (Stvrtinova et al., 1995). The acute phase response was also assumed to depend on the challenge, because the acute phase response is defined as a response to antigenic stimulation. The magnitude of the acute phase response increases with increasing baseline immunity and increasing challenge load (Jacobsen et al., 2004). It was assumed that the effect of the baseline immunity and challenge on the magnitude of the acute phase response could be captured in the parameters APRa and APRb as follows:


Formula 11([11])

and


Formula 12([12])

These parameter definitions reflect an assumption that the acute phase response is a linear function of the baseline immunity, based on the definition of baseline immunity being the ability to mount an immune response, and the relationship is such that the acute phase response is a function of the challenge given by the initial challenge dose and the proliferation rate of the pathogen. It was assumed that, in addition to the initial challenge dose, the proliferation rate of the pathogen would also have an effect on the acute phase response because of the expected lag between challenge age and age at initiation of the acute phase response.

Entering APRa and APRb into the equation for the acute phase response ("Acute Phase Response" above) and solving APR'(age ageAPR) = 0 for age gives the age at which the acute phase response reaches its peak:


Formula 13([13])

Therefore, it follows that the peak of the acute phase response (APRmax) is:


Formula 14([14])

The antibody response was assumed to be negatively affected by the maternal immunity, because antibody responses have been shown to be inhibited by the presence of maternal antibodies (Siegrist, 2001). It was assumed that any positive effects of maternal antibodies on the antibody response repertoire after fading of the maternal antibodies (Lemke et al., 2000) were not of importance. It was also assumed that the antibody response was affected by the acute phase response, and thereby the baseline immunity, because stimulation by various elements of the innate immunity (response) are necessary for the initiation of the antibody response (Siegrist, 2001). The antibody response was also assumed to be affected by challenge because of the definition of the antibody response as a response to antigenic stimulation. The magnitude of the antibody response increases with an increasing acute phase response and challenge load (Janeway et al., 2005) but decreases with an increasing maternal immunity (Siegrist, 2001). It was assumed that the effects of the acute phase response, challenge, and maternal immunity on the magnitude of the antibody response could be captured in the parameter ABRa as follows:


Formula 15([15])

This parameter definition results in an increasing stimulating effect of the challenge, given by the initial challenge dose and the expected proliferation limit of the pathogen, on the antibody response. It was assumed that not only the initial challenge dose would have an effect on the antibody response but also the expected proliferation limit of the pathogen, because the duration of an antibody response is dependent on the presence of antigens, and a greater proliferation limit is reflective of the necessity for an increased antibody response.

Maternal immunity inhibits antibody response, and the effect is presumably nonlinear. The explanation for this is that at high levels of maternal immunity, the inhibitory effect of a unit increase in maternal immunity on the antibody response is less than at lower levels of maternal immunity. This is based on the assumption that at high levels of maternal immunity, the antibody response is already so strongly inhibited that further inhibition is without effect. Such a nonlinear inhibition of the antibody response by the maternal immunity can be reflected by raising the maternal immunity to the power 0.5.

Entering this into the equation for the antibody response ("Antibody Response" above) and solving ABR'(ageageABR) = 0 for age gives the age at which the antibody response reaches its peak:


Formula 16([16])

Therefore, it follows that the peak of the antibody response is:


Formula 17([17])

Estimation of Model Parameters
To parameterize the model, the model component equations were fitted to published experimental data. Experimental data were mainly found in the poultry research. However, because of the limited availability of data with sufficient measurements, published studies on mammalian species were also used, because temporal patterns of many immunological variables in mammalian species appear to be similar to those in poultry (Sharma, 1991).

The parameters of the maternal and baseline immunity equations (mi0, rmi, bi0, kbi, and cbi) were estimated from published experimental data (Table 3Go). When the experimental data on maternal antibodies included more than 1 measurement from 0 to 4 d of age, then the initial maternal immunity, mi0, was assumed to be equal to the measurement that was closest to 0 d of age. This was assumed realistic considering the uptake of maternal antibodies from the yolk during this age interval (Kaleta et al., 1977; Kowalczyk et al., 1985; Shawky et al., 1994). The maternal immunity degradation rate, rmi, could then be estimated by linear regression. Otherwise, mi0 and rmi were simultaneously estimated by nonlinear regression. The parameters of the baseline immunity equation (bi0, kbi, and cbi) were estimated from published experimental data by nonlinear regression.


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Table 3. Parameter values (mi0, rmi, bi0, kbi, and cbi) either estimated from published experimental data or suggested based on estimates from other studies1
 
The model requires the determination of the values of 5 parameters. Estimating the values of all of these parameters from experimental data of a single study was difficult because of the data sparsity. Whenever possible, all the parameter values were estimated from the same study, but when sufficient experimental data were not available, estimates were suggested based on other studies. For example, in most published studies with experimental data on either acute phase or antibody response, no data were available on maternal or baseline immunity, and suggestions for the parameter values therefore had to be made based on other studies.

The published data were standardized into values with restricted intervals (Table 2Go). Standardization of the data was necessary to enable interpretation and comparisons of different immunological variables, which were measured on different scales (e.g., macrophage count and potential nitrite production by macrophages) or by different methods (e.g., ELISA or hemagglutination assay). A linear transformation was used to standardize all values to the interval [0:1]: z = [xmin]/[maxmin], where z = the transformed value; x = the published data point; min = the minimum; and max = the maximum. The minima were set to 0 when this made sense biologically (for example, the titer of maternal antibodies will always decrease to 0 at some point). In some cases, it did not make biological sense to set the minima to 0 (for example, leukocyte or lymphocyte counts), and in those cases, the minima were set to the lowest observed value for the particular immunological measure in published studies. Maxima were set to the greatest observed value for the particular immunological measure in published studies using immature animals. The transformation is linear, and the effect of the choices of minima and maxima is therefore a pure scaling effect, which will not have any effect on the relative outputs of the model (i.e., when comparing individual chicks or group means).

Experimental Design and Evaluation of Immunoresponsiveness
Many factors may affect traits describing immunocompetence and immunoresponsiveness and, hence, the conclusions drawn from experimental studies. These include age at challenge, type of variable measured, and the number and relative timing of measurements. This is of great importance in, for example, comparative studies and genetic evaluations. To explore this, 4 scenarios that represented combinations of challenge age and measurement timing were simulated. In each scenario, the immunoresponsiveness (acute phase, antibody response, or both) to a particular challenge was compared for 3 different levels of baseline immunity. The 3 levels of baseline immunity were illustrative and could, for example, be representative of 3 broiler genotypes in a line comparison experiment, 3 family groups, or simply 3 individual chicks in a genetic evaluation. In the remainder of this paper, the 3 levels of baseline immunity will be assumed to represent different broiler genotypes. The following scenarios and simulated broiler genotypes were compared:

Chal14T7 and Chal14T14: challenge at 14 d of age; measurements at 7 and 14 d postchallenge, respectively.

Chal35T7 and Chal35T14: challenge at 35 d of age; measurements at 7 or 14 d postchallenge, respectively.

LiHr: low bi0 but a high kbi (bi0 = 0.10; kbi = 0.05; and cbi = –0.50).

HiLr: high bi0 but a low kbi (bi0 = 0.50; kbi = 0.01; and cbi = 0.00).

HiHr: high bi0 and a high kbi (bi0 = 0.50; kbi = 0.05; and cbi = –0.50).


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Model Fitting
In Figure 2Go, the fit of the modeled maternal immunity is illustrated along with the standardized published data points (Kaleta, 1972; Islam et al., 2002). In both cases, the model equation fit published data well as measured by the R2. The model fit to maternal immunity published in other studies was also investigated (Kaleta et al., 1977; Cawthraw et al., 1994; Shawky et al., 1994; Smith et al., 1994; Boa-Amponsem et al., 1997; Toro et al., 1997; Jeurissen et al., 2000; Mondal and Naqi, 2001; Sahin et al., 2001), though not illustrated here, and the model equation generally fit this data well (0.62 ≤ R2 ≤ 1.00; mean R2 = 0.91 based on 29 cases).

In Figure 3Go, the fit of the modeled baseline immunity is illustrated, along with the standardized published data points (Islam et al., 2002; Okamura et al., 2004). In general, the model equation fit the data well as measured by the R2. The model fit to measures of baseline immunity published in other studies was also investigated (Burton and Harrison, 1969; Anderson and Stephens, 1970; Cawthraw et al., 1994; Dusbábek et al., 1994; Toro et al., 1997; Jeurissen et al., 2000; Qureshi et al., 2000; Bar-Shira et al., 2003), although not illustrated here, and the model equation generally fit this data well (0.32 ≤ R2 ≤ 1.00; mean R2 = 0.87 based on 47 cases).

In Figure 4Go, the fit of the modeled acute phase response is illustrated along with the standardized published data points (Jarosinski et al., 2002; Okamura et al., 2004). The model generally fit the data well as measured by the R2. The model fit to acute phase responses published in other studies was also investigated (Qureshi et al., 2000; Kaiser et al., 2003; Glass et al., 2003, 2005; Withanage et al., 2005), although not illustrated here. The goodness of fit to the data from these studies varied considerably, because it attempted to describe the kinetics of a large range of immunological variables by a single equation, and these variables do not all show the modeled pattern consistently (0.001 ≤ R2 ≤ 0.98; mean R2 = 0.69 based on 37 cases). However, the model generally fit the published data on acute phase proteins and fever well.

In Figure 5Go, the fit of the modeled antibody response is illustrated along with the standardized published data points (Ubosi et al., 1985; Parmentier et al., 1998). Again, the model fit the data well as measured by the R2. The model fit to antibody responses published in other studies was also investigated (Kreukniet and van der Zijpp, 1990; Leitner et al., 1990; Cook et al., 1992; Smith et al., 1994), although not illustrated here. The goodness of fit to the data from these studies varied but was good in many cases (0.31 ≤ R2 ≤ 0.98; mean R2 = 0.77 based on 58 cases). The lower fit was mainly observed for studies in which total antibodies or IgG was measured rather than IgM.

Model Output: Experimental Design and Evaluation of Immunoresponsiveness
The immunoresponsiveness of the 3 broiler genotypes is illustrated in Figure 6Go. The scenarios Chal14T7 and Chal14T14 are illustrated in Figure 6Go, panels A and C, and the scenarios Chal35T7 and Chal35T14 are illustrated in Figure 6Go, panels B and D.


Figure 6
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Figure 6. Immunocompetence reflected by the acute phase and antibody response in 3 hypothetical broiler genotypes: LiHr (—), HiLr (---), and HiHr (–·–·). The figures are as follows: panels A and C: Chal14T7 and Chal14T14: challenge at 14 d and measuring of the acute phase (A) and antibody response (C) at 7 or 14 d postchallenge, respectively (indicated by the dotted vertical lines); panels B and D: Chal35T7 and Chal35T14: challenge at 35 d and measuring of the acute phase (B) and antibody response (D) at 7 or 14 d postchallenge, respectively.

 
In scenario Chal14T7, HiHr is the most immunoresponsive genotype, LiHr is the least immunoresponsive genotype, and HiLr is intermediate when the evaluation is based on the acute phase response (Figure 6Go, panel A), whereas when the evaluation is based on the antibody response, HiHr is the most immunoresponsive genotype along with HiLr, and LiHr is the least immunoresponsive genotype (Figure 6Go, panel C). When the evaluation is based on the acute phase response in scenario Chal35T7, HiHr is the most immunoresponsive genotype, HiLr is the least immunoresponsive genotype, and LiHr is intermediate (Figure 6Go, panel B), whereas when the evaluation is based on the antibody response, LiHr is the most immunoresponsive genotype, and HiHr is the least immunoresponsive genotype along with HiLr (Figure 6Go, panel D). This illustrates the potential influence of the type of immunoresponsiveness measured. Note that for the acute phase response, the ranking of the 2 less immunoresponsive genotypes is changed with age of challenge.

Scenario Chal14T14 leads to the same conclusion as Chal14T7 concerning the acute phase response (Figure 6Go, panel A). However, for the antibody response (Figure 6Go, panel C), the ranking of genotypes changes: LiHr now appears to be the most immunoresponsive genotype, whereas HiHr and HiLr are both less immunoresponsive. Again, this illustrates the potential influence of the type of immunoresponsiveness measured, and moreover, it illustrates how the effect of the type of immunoresponsiveness measured interacts with measurement timing. Scenario Chal35T14 also leads to the same conclusion as Chal35T7 concerning the acute phase response (Figure 6Go, panel B), but for the antibody response (Figure 6Go, panel D), HiLr is the most immunoresponsive genotype, and HiHr is the least immunoresponsive genotype.

To summarize, the potential influence of measurement timing on the evaluation of immunoresponsiveness is illustrated by the differences in the genotype ranking concerning the acute phase response (Figure 6Go, panel C) between scenario Chal14T7 and Chal14T14 and concerning the antibody response (Figure 6Go, panel D) between scenario Chal35T7 and Chal35T14. The potential influence of age at challenge on the evaluation of immunoresponsiveness is illustrated in the difference in the genotype ranking concerning the acute phase response (Figure 6Go, panels A and B) and the antibody response (Figure 6Go, panels C and D) between scenario Chal14T7 and Chal35T7 and between scenario Chal14T14 and Chal35T14.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Based on current available knowledge on the immune system, we have developed a model that describes the development of immunocompetence and the kinetics of immunoresponsiveness in the face of an extracellular bacterial challenge in the young chick. In addition, we have demonstrated that the individual components of this model fit published experimental data well in most cases. A lack of fit of the equation for, for example, acute phase response for some immunological variables was moreover to be expected. The acute phase response is an immune system component that covers a wide range of variables and it is, therefore, not realistic to expect that one very simple equation could adequately describe all scenarios. Simplicity as well as transparency must, however, have a trade-off with accuracy, and, for the ultimate goal of this model, small deviations from the modeled pattern are not expected to have a large effect on the global results and the inferences drawn from the model. The fact that the acute phase and antibody response components fit published experimental data well even when parameter input values were based on other published studies is promising for the validity of the model. Although the model did not fit published experimental data equally well in all cases, the choice of equations, therefore, seems appropriate. Unfortunately, it was not possible to evaluate the interrelations between the individual model components because of the sparsity of studies with sufficient experimental data. For the same reason, the predictive ability of the model cannot, as yet, be fully validated. Fitting of the modeled acute phase and antibody response to experimental data was in most cases based on parameter estimates obtained from separate studies, and these generally did indicate a good predictive ability of the model.

In some cases, deviations between model predictions and experimental data were observed. The SE on the experimental data, which in some cases are considerable (Burton and Harrison, 1969; Leitner et al., 1992; Jeurissen et al., 2000), were not taken into account, and this may explain the observed deviations. Moreover, some data were based on experiments with other pathogens than extracellular bacterial, because sufficient data with extracellular bacterial pathogens were not available. An effect of such pathogens interacting differently with the immune system cannot be excluded as a possible explanation for deviations in these data. Globally, however, effects of type of pathogen are mainly expected to be observed in the type of variables activated (e.g., in the baseline immunity and acute phase response) as well as in scaling (e.g., in the antibody response). Hence, such data are still considered informative for the global patterns of development of immunocompetence and the immunoresponsiveness kinetics. Further, moderate changes in immunological variables may not have an effect of actual biological significance on immunocompetence or immunoresponsiveness (Keil et al., 2001). Therefore, given the currently available experimental data, it is concluded that the predictive abilities of the individual model components are adequate. Potentially, the model may also be used as a generator of hypotheses on global immunological relationships to be tested experimentally.

To fully validate the model, a comprehensive study with experimental data is needed. Such data should include measurements of maternal antibodies and baseline immunity as well as of acute phase and antibody response. Model parameterization should then ideally be done with independent data (e.g., 2 halves of the data set arising from the study). Experimental data from different studies, in which different populations of chickens have been used, is less suitable for validation, because the model parameters are unlikely to be universal, given the variation observed in immunological variables among different chicken genotypes and flocks (Kaleta and Siegmann, 1978; Jarosinski et al., 2002; Kaiser et al., 2003). For the ultimate goal of this model (i.e., to evaluate challenge and measurement strategies for selection purposes), universal parameters are not an absolute requirement, because selection is done within genotypes. The evaluation of challenge and measurement strategies should, therefore, also be done within genotypes. To allow for such an evaluation, a preliminary study could be done in which maternal antibodies and baseline immunity are measured in healthy chicks from a given genotype, to parameterize the model, and, subsequently, different challenge and measurement strategies could be investigated and evaluated.

In practice, utilization of the model not only requires parameterization but also requires decisions on which immunoresponsiveness variable(s) it is desired to measure. Whereas measuring the maternal immunity and the antibody response is straightforward, defining which components of baseline immunity and the acute phase response to measure is not. With the model described in this study, suggestions are not made on which variables to measure. Among others, this will depend on the indicative value of such variables for health (the ultimate goal of selection for improved immunocompetence, immunoresponsiveness, or both). The expression of the components in index values does, however, ensure that the model can be used regardless of which variable(s) are eventually measured. The baseline immunity may be parameterized based on a single variable, as in this study, or it may be parameterized based on a combination of variables of importance. The same is also true for the acute phase response.

Few existing mathematical models deal with the immune system in a broad scope (Wodarz and Nowak, 1999). Most have been designed to understand and explore specific molecular and cellular processes of the immune system development or response or interactions among specific immune system components. For example, T-cell and macrophage interactions, T- and B-cell interactions, B-cell networks, and dynamics of primary and secondary antibody responses have been modeled. Others have been tailored to specific diseases, such as human immunodeficiency virus or hepatitis virus (Kaufman et al., 1985; Chowdhury and Stauffer, 1990; Smirnova, 1991; Chowdhury, 1993; Morel, 1998; Wodarz and Nowak, 1999; Kleinstein and Seiden, 2000; Perelson, 2002).

The model in this study is therefore unique in its scope, covering nonspecific immunity along with maternal immunity and humoral immunity. In the evaluation of immunocompetence or immunoresponsiveness, all these parts of the immune system may be of importance, and the relatively broad scope is, therefore, an important part of the strength and usefulness of this model. Additionally, to our knowledge, the model in this study is the first to describe the development of immunocompetence and kinetics of immunoresponsiveness in young chicks, emphasizing the potential importance of the model. Moreover, the model in this study is relatively simple both in terms of the description of biological processes and the number of parameters that require estimation. This simplicity makes it easier to parameterize and easier to use for the purpose of the evaluation of challenge and measurement strategies compared with existing models, which require a relatively large number of parameters (Faro et al., 1997).

To evaluate the immunoresponsiveness of 3 simulated broiler genotypes, 4 scenarios were compared by varying the experimental design concerning challenge age and measurement timing. The comparison illustrated that the ranking of broiler genotypes with different immunocompetence development is expected to be different depending on which type of immunoresponsiveness is measured, measurement timing, and age at challenge. The reranking of the broiler genotypes between the 2 challenge ages for the acute phase and antibody response is caused by different rates of development of the baseline immunity among genotypes. Different development patterns of the maternal immunity also result in reranking of the antibody response and, to some extent, reranking of the acute phase response. For the evaluation of challenge and measurement strategies for selection purposes, the risk of reranking is of major importance, and the development of both maternal and baseline immunity must therefore be taken into account when evaluating these strategies. In practice, the challenge and measurement strategy in which the largest differences among genotypes, groups, or individuals are expected to be observed should be chosen. Hence, the risk of reranking is of importance whether it is desired to evaluate the actual ranking of genotypes or simply to illustrate the presence of differences among genotypes. With the risk of reranking because of the development of maternal and baseline immunity, choosing the best challenge and measurement strategy becomes difficult. The model presented in this study provides a tool to predict immunoresponsiveness, taking this development into account and thereby aiding in choosing the best challenge and measurement strategy.

An influence of the type of immunoresponsiveness measured on genotype, group, or individual ranking has also been found in many published studies on experimental data (Bacon et al., 1972; Lillehoj and Li, 2004; Withanage et al., 2005), but its importance is rarely fully recognized. For example, it has been found that there is genetic independence among selection for antibody response, cell-mediated immune response, and phagocytic activity (Pinard-van der Laan and Monvoisin, 2000). Thus, the ranking conclusions reached may depend on the trait measured.

An effect of measurement timing on genotype, group, or individual ranking is also observed in several published studies on experimental data, although the importance of this effect is rarely recognized. For example, Boa-Amponsem et al. (1999) compared 2 White Leghorn chicken lines that had been selected for high antibody (HA) or low antibody response (LA) 5 d after a challenge with SRBC from 41 to 51 d of age. The lines were compared based on antibody response to a primary challenge with SRBC at 14 and 28 d of age. It was found that even though the HA line showed a greater antibody response 3 and 6 d after a primary challenge, the LA line showed an equally high antibody response after both a secondary and tertiary challenge. It was proposed that this was due to different genetic control of primary immune responses and immunological memory. However, reranking in the development of baseline immunity or differences in the decline of maternal immunity may also provide an explanation, because selection was based on a measurement at a single time point. When the objective of the studies is not directly related to the kinetics of the immunocompetence or immunoresponsiveness, immunological variables are often measured at only 1 or perhaps 2 points in time. Ranking has been observed to change depending on measurement timing for maternal antibodies (Lemaire et al., 2000), lymphocyte development (Bar-Shira et al., 2003), the acute phase protein {alpha}1-acid glycoprotein (Takahashi et al., 1998), several cytokine responses (Kaiser et al., 2003), and antibody responses (Kreukniet and van der Zijpp, 1990; Koenen et al., 2002; Cheema et al., 2003). Each measurement is only a snapshot of reality, and as was illustrated in this study, conclusions on ranking based on only a single measurement cannot necessarily be reliably extrapolated if there is reranking of, or even differences in, immunocompetence development. The model in this study can take into account differences in immunocompetence development, and therefore, it can assist in choosing the best timing of measurement(s) in the challenge and measurement strategy.

An influence of challenge age on genotype, group, or individual ranking is also observed in several published studies on experimental data. In the study of Boa-Amponsem et al. (1999), the differences in the primary antibody response between the HA and LA line were larger when the age of challenge was 28 d of age than when it was 14 d of age. This may be explained by differences in the development of maternal or baseline immunity and therefore illustrates the importance of challenge age for selection purposes. For example, there is reranking in macrophage function and antibody response (Koenen et al., 2002; Cheema et al., 2003), presumably due to development of the immune system. Whether the importance of this influence is recognized is unclear, because the challenge age is often not explicit or justified in publications. Sometimes the challenge age is based on the ages at which pathogen prevalence is assumed to be greatest in field data. At other times, the challenge age is chosen to avoid major effects of maternal immunity or to coincide with the "window of susceptibility," in which maternal immunity is fading and the chick’s own immune system is still relatively undeveloped. However, this still defines a wide period (e.g., from 2 wk of age up to 6 wk of age). The model in this study can take into account differences in immunocompetence development and predict the expected age at which maternal immunity has faded, and therefore, it can assist in choosing the best challenge age in the challenge and measurement strategy.

In conclusion, this model describes the development of immunocompetence in young chicks along with the kinetics of their immunoresponsiveness, and individual equations fit published data adequately. The model illustrated that experimental design (type of immunoresponsiveness measured, measurement timing, and challenge age) can have an important effect on the ranking of genotypes, groups, or individuals and on the reliability of extrapolations based on this ranking. It is concluded that this model is a potential useful tool in the evaluation of challenge and measurement strategies for selection purposes, such as enhanced immunocompetence or immunoresponsiveness. Moreover, it may be used as a generator of hypotheses on global immunological relationships to be tested experimentally.


    ACKNOWLEDGMENTS
 
We thank the authors who most kindly provided us with data on immunological measurements from their own published studies. Our thanks go to Ronnie Friedman, Orhan Sahin, and S. P. Mondal. We are also grateful to European Animal Disease Genomics Network of Excellence for funding B. Ask to visit the Roslin Institute and to the Biotechnology and Biological Sciences Research Council for funding the contributions made by S. C. Bishop and E. J. Glass.

Received for publication November 23, 2006. Accepted for publication March 8, 2007.


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B. Ask, E. H. van der Waaij, and S. C. Bishop
Modeling Variability in Immunocompetence and Immunoresponsiveness
Poult. Sci., September 1, 2008; 87(9): 1748 - 1759.
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