Directory UMM :Data Elmu:jurnal:M:Mathematical Biosciences:Vol163.Issue1.Jan2000:
Mathematical Biosciences 163 (2000) 35±58
www.elsevier.com/locate/mbs
Feedback mechanisms between T helper cells and macrophages
in the determination of the immune response
Ruth Lev Bar-Or *
Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science, P.O. Box 26,
76100 Rehovot, Israel
Received 5 February 1999; received in revised form 11 June 1999; accepted 24 August 1999
Abstract
The interactions between macrophages and T helper (Th) cells are a complex interplay of positive and
negative signals. Some of the mathematical models of interactions between T helpers have indeed taken the
in¯uence of macrophages into account. In this work the macrophage is not considered as an extrinsic agent,
that is duly directed by the T cells to be cytotoxic, nor is there consideration of T helper cell populations
that are dominantly regulated by extrinsic properties of antigens per se, or by certain classes of presenting
cells that preferentially select certain classes of lymphocytes or bias their commitment. Rather, a simpli®ed
model of feedback loops between Th cells and macrophages is formulated and analyzed. It is suggested how
the mutual in¯uence between Th and macrophages can determine the cytokine secretion pattern of these
populations. The model provides a feedback scenario to account for experimental ®ndings concerning
reversal in the dominance of a speci®c cytokine pro®le in the course of some infections. A possible scenario
accounting for the dierence between the stability of Th1 and Th2 cytokine pattern is put forward. The
model suggests explanations for the variability in the outcome of the immune response according to different body compartments. A rationale is presented that accounts for paradoxical ®ndings indicating that
Th1 cytokines are sometimes responsible for the downregulation of a Th1 dominated response. Ó 2000
Elsevier Science Inc. All rights reserved.
Keywords: Mathematical model; Th1/Th2; Feedback loops; Macrophages; Cytokines
*
Tel.: +972-8 934 2390; fax: +972-8 934 4122.
E-mail address: ruthy@wisorg.weizmann.ac.il (R. Lev Bar-Or).
0025-5564/00/$ - see front matter Ó 2000 Elsevier Science Inc. All rights reserved.
PII: S 0 0 2 5 - 5 5 6 4 ( 9 9 ) 0 0 0 4 6 - 2
36
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
1. Introduction
Since the discovery that CD4+ T cell subsets secrete dierent patterns of cytokines [1±3] substantial evidence has accumulated showing the importance of the T helper 1 (Th1) and Th2
subsets in the success or failure of immune responses. Th1 cells, which secrete mainly IL-2 and
IFN-c, promote immunity to infections by intracellular bacteria, protozoa and viruses [4,5]. Th2
cells, secreting mainly IL-4, IL-5, IL-6, IL-10 and IL-13 control responses against extracellular
pathogens and are involved in the pathogenesis of allergic reactions [6]. Both Th1 and Th2 cells
appear able to cross-suppress each other via the cytokines they secrete, and this provides an
explanation for the inverse relationship observed between Th1 and Th2-directed responses.
It is important to keep in mind though, that the Th1/Th2 dichotomy is a simpli®ed version of
reality. Additional CD4+ T cell phenotypes have been discussed, such as the Th0 phenotype that
secretes both Th1 and Th2 cytokines, indicating that these two classes do not represent two
absolute and mutually exclusive states [7,8]. Furthermore, the terminology referring to `Th1' or
`Th2' responses is misleading, since many of the Th1/Th2 cytokines are also produced by other
cell types. For example, IFN-c is also secreted by natural killer cells, CD8+ cells, and cd cells; IL10 is also produced by macrophages and mast cells [9±11]. Finally, recent evidence indicates that
CD8+ T cells cannot only secrete Th1 but also Th2-like cytokine patterns [12±16]. In spite of the
simpli®cation imbedded in the Th1/Th2 model, evidence shows that the state of health ± the
ability to ®ght infectious agents eectively, and not to succumb to autoimmune diseases ± often
depends on which pattern (Th1 or Th2) overshadows which, i.e. whether an appropriate or an
inappropriate immune response has been achieved.
In the framework of orchestrating an immune response, the pattern of cytokines produced by
dierent subsets of T lymphocytes, are used as communication signals with many other types of
cells, such as B cells and macrophages [4]. Macrophages are central in host immunity to pathogenic agents. They are the major eector cells that contain and kill intracellular pathogens. Optimal macrophage function is dependent on activation of the cells by a variety of extracellular (as
well as intracellular) stimuli, most prominently T-cell-derived lymphokines. Such cytokine production requires antigen recognition by T cells, a process in which macrophages are also involved
as antigen processing and presenting cells [17].
As discussed in Section 2, the interactions between macrophages and T cells are a fascinating
interplay of positive and negative signals. Some of the mathematical models of Th1/Th2 interactions and their implications in immunity, have indeed taken the in¯uence of macrophages into
account [18±22]. In [19], the authors incorporate the eect of antigen presenting cells on the T
helper system, but they consider the capacity of the antigen presenting cells to drive the activation
of its Th population as independent of the T cell population itself. In [18] the Th population is
stimulated by interaction with antigen, via antigen presenting cells. However, the type of interactions between these cells and the Th population that is mediated by cytokines, is ignored. Interactions via cytokines are modeled in part in [20], where an inhibitory, cytokine mediated eect
of Th2 cells on antigen presenting cells, and an excitatory cytokine mediated eect of antigen
presenting cells on Th1 is considered. In a previous paper, referred to subsequently as LS [22],
agents such as macrophages enter the game (i) as providers of excitation to the Th population via
presentation of antigen; (ii) as recipients of the ensembleÕs outcome. Thus in previous modeling of
Th1 vs. Th2 cytokine patterns, macrophages were given rather a secondary role.
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
37
In this work an attempt is made to take a further step in the understanding of the rich, complex,
bidirectional interactions between macrophages and T cells by formulating a simpli®ed model of
feedback loops between Th cells and macrophages. It is hoped thereby to gain some insights into
factors that determine the success or failure of immune responses by engendering a choice between
a dominant Th1 or a dominant Th2 secretion pattern. An understanding of these factors may
provide a means for therapeutic intervention in situations wherein the immune response is not
ecient or even deleterious to the host.
The macrophage is not considered as an extrinsic agent, that is duly directed by the T cells to be
cytotoxic, nor is there consideration of T helper cell populations that are dominantly regulated by
extrinsic properties of antigens per se, or by certain classes of APC that preferentially select
certain classes of lymphocytes or bias the commitment of uncommitted lymphocytes (reviewed in
[23]). Rather, a key question addressed here is how does feedback between Th cells and macrophages allow these populations the possibility of in¯uencing their own fate.
The following are some phenomena that will be addressed. (i) It is believed that for some infections, dierent eector functions may be appropriate at dierent stages of infection, such as in a
mouse malaria model in which Th1 and Th2 responses may be important early and late in infection, respectively [24,25]. (ii) Sometimes, too much of a Th1 cytokine impairs a strong Th1
response [26,27]. (iii) The Th2 cytokine pattern appears more stable than the Th1 pattern [28±30].
(iv) The in¯uence of the location of the immune response (in dierent tissues and body cavities) on
the type of dominance (Th1 or Th2) of the resulting response. (See for example [31±33].)
2. Biological background
T cells and macrophages use cytokines to communicate with each other and among themselves,
and alter each otherÕs behavior. Table 1 is an attempt to provide a crude summary of how cytokines produced by Th cells aect several functions of macrophages (cytokine secretion and
antigen presentation), and also in¯uence the behavior of the Th population itself, and of how
macrophage-derived cytokines modulate cytokine secretion by Th cells and by macrophages. The
next four paragraphs recount the main sources of information.
Cytokines produced by Th cells upon speci®c antigen recognition, modulate diverse eector
functions of macrophages [31]. First, T helper cells aect the ability of macrophages to secrete
several cytokines. The Th1 cytokine IFN-c (also reported to be produced ± by a lesser extent ± by
macrophages, [34]) enhances the macrophagesÕ secretion of products such as nitric oxide (NO),
which plays an important role in the antimicrobial activities of macrophages [35]. IFN-c also
enhances the secretion of several cytokines, such as TNF-a, which possess antiviral activity [36],
and IL-12, which enhances the cellsÕ cytotoxic activity (reviewed in [5]). IFN-c also inhibits
macrophage secretion of IL-10 [37]. Th1 cytokines TNF-a (also produced by macrophages) and
TNF-b induce the production of several macrophage products such as GM±CSF, which shows
microbicidal activity, and NO (reviewed in [38]). Th product GM±CSF, (also produced by
macrophages) induces TNF-a secretion [38,39].
The Th2 cytokine IL-4 blocks the macrophagesÕ production of several in¯ammatory cytokines,
such as TNF-a, IFN-c, IL-12 and GM±CSF and has inhibitory eects on the release of superoxide
by macrophages (reviewed in [40]). Similar eects are shared by the Th2 cytokine IL-10
38
Cytokine
Produced by (among other
cells)
Enhances production of
Decreases production of
Eect on MHCII
Grouped under (model)
IFN-c
Th; (macrophages)
NO, TNF-a, IL-12
IL-10. Suppresses proliferation of Th2 cells
C1T C1M
TNF
GM±CSF, NO, IFN-c
GM±CSF
IL-12
TNF-a: Th; macrophages.
TNF-b: Th.
Th; macrophages
Macrophages
TNF-a: C1T ; C1M ; TNF-b:
C1T
C1T ; C1M
C1M
IL-18
IL-4
Macrophages
Th
C1M
C2T
IL-10
Th; macrophages
¯
C2T ; C2M
TGF-b
IL-13
PGE2
Th; macrophages
Th
Macrophages
¯
¯
C2T ; C2M
C2T
C2M
TNF-a
IFN-c, TNF-a, GM±CSF
dierentiation of Th1
lymphocytes from progenitors
IFN-c, GM±CSF
Drives precursor Th cells
into Th2 cells
Can upregulate the
dierentiation of naive
cells to Th2 cells
IL-10
IL-4, IL-10. inhibits generation of Th2 cells
IL-10
TNF-a, IL-12, GM±CSF,
superoxides, IFN-c,
PGE2
TNF-a, IL-12, GM±CSF,
NO, IFN-c
TNF-a, IL-12
TNF-a, GM±CSF, NO
TNF-a, IL-12
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
Table 1
Eects of Th and macrophage-derived cytokines
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
39
(also produced by macrophages) which inhibits the secretion of proin¯ammatory cytokines such
as TNF-a, GM±CSF, IL-12, and also inhibits nitric oxide production [1,5,41]. The Th2 cytokine
TGF-b (also produced by macrophages) inhibits the production by macrophages of TNF-a, of
reactive oxygen products, of IL-12, and other proin¯ammatory cytokines (reviewed in [5,42]).
TGF-b is also known to promote IL-10 production by macrophages [43]. The Th2 cytokine IL-13
shows a strong inhibitory activity on in¯ammatory cytokine production, such as TNF-a and
GM±CSF, it decreases the production of nitric oxide in murine macrophages [44], and is a negative regulator of the production of IL-12 [5].
T helper cells not only aect the macrophagesÕ secretion ability of cytokines, but also in¯uence
antigen presentation, by regulating the expression of MHC II molecules±molecules whose binding
to the processed antigen is essential in order for the helper cells to recognize it [45]. IFN-c, TNF,
GM±CSF, IL-4 and IL-13 upregulate MHC II expression ([46] for IFN-c; [47] for TNF-a; [48] for
GMC±CSF; [49] for IL-4; [50] for IL-13). In contrast, IL-10 and TGF-b were shown to inhibit the
expression of class II molecules on macrophages ([51] for IL-10; [52] and [42] for TGF-b).
Not only does the type of cytokines produced by activated T cells in the process of antigen
presentation in¯uence the speci®c pattern of macrophage functions, but the eector functions of
the Th cells themselves are modulated in turn by the eects of macrophages. TNF-a enhances the
production of GM±CSF (by both T cells and macrophages), and IFN-c [38]. Macrophage product
IL-12 induces the production of IFN-c, TNF-a and GM±CSF. IL-12 has inhibitory eects on the
generation of Th2 cells (reviewed in [5,53]), and according to novel data on IL-4 and IL-10 secretion [54,55]. GM±CSF induces TNF-a secretion (by T cells and macrophages). IL-18, a new
cytokine found to be produced by macrophages, enhances IFN-c and GM±CSF production by Th
cells, and inhibits the secretion of IL-10 by Th cells, and macrophages [56]. Several macrophage
products are known to downregulate cytotoxic functions of T cells (and also macrophages). IL-10
inhibits the secretion of TNF-a, GM±CSF, and IFN-c by T cells [37]. The macrophage product
prostaglandin E2 (PGE2) inhibits the secretion of TNF-a and IL-12, and downregulates MHC
class II expression [57±59]. Finally, TGF-b inhibits the production of TNF-a and enhances the
production of IL-10.
3. The model
Accumulating research on cytokines paint a picture that seems hopelessly complex. Pleotropism
and redundancy abound. As sketched above, a single cytokine can interact with more than one
type of cell, a single cytokine can have multiple biological activities, a single cell can interact with
more than one cytokine, many cytokines have overlapping activities, and a single cytokine may
induce or inhibit the expression of a gene encoding another cytokine. Moreover, during the last
decade, 5±10 new cytokines have been cloned every year [60]. Today more than 100 cytokines have
been cloned. Hundreds more probably exist.
Instead of attempting to incorporate this myriad of cytokines into the model, or to implement
the detailed biology of individual cytokines, I consider for the sake of simplicity four patterns of
cytokines, denoted as ÔT-Type1Õ, ÔT-Type2Õ, ÔM-Type1Õ and ÔM-Type2Õ. Following the nomenclature recently proposed in [61], patterns of cytokines associated with Th1 and Th2 responses, are
denoted by Type-1 and Type-2, respectively. Grouped under ÔT-Type1Õ are T helper cell-derived
40
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
cytokines such as IFN-c, TNF-a and -b, and GM±CSF. Cytokine pro®le ÔT-Type2Õ lumps together T helper cell-derived cytokines such as IL-4, IL-10, IL-13, and TGF-b. ÔM-Type1Õ and ÔMType2Õ denote cytokines secreted by macrophages, which as seen in Section 1, have extensive
overlap with T helper-derived cytokines. The category ÔM-Type1Õ contains macrophage-derived
in¯ammatory cytokines such as TNF-a, IL-12, GM±CSF, IL-18, NO, and other antimicrobicidal
products. ÔM-Type2Õ bundles macrophage-derived anti-in¯ammatory cytokines such as IL-10,
PGE-2, and TGF-b.
The model envisions a population comprised by nT T helper cells, which may have dierent
antigen speci®cities, and nM macrophages that are active within a speci®c target area, such that
every cell can aect all others. Any given Th cell i i 1; . . . ; nT can secrete certain amounts of TType1 and T-Type2 cytokines, denoted respectively by C1Ti and C2Ti . Any given macrophage
i i 1; . . . ; nM can secrete certain amounts of M-Type1 and M-Type2 cytokines, denoted respectively by C1Mi and C2Mi . The parameters chosen to characterize each of the four cytokine
pattern types are taken to be qualitative averages of the characteristics of the array of cytokines
that constitute each category.
C1T and C2T denote the arithmetic average of secreted cytokine amounts C1Ti and C2Ti over the
whole T cell population. Similarly, C1M and C2M denote the mean secretion levels of Type-1 and
Type-2 cytokines over the macrophage population.
An important point taken into consideration is that, as mentioned in Section 1, it is an oversimpli®cation to say that T helper cells have totally distinct patterns of cytokine secretion. There is
evidence indicating the possibility that each individual T cell is capable of producing the entire
array of cytokines [40]. This picture promoted the idea to leave aside the destiny of the T helper
cells themselves, and to focus on their products (in the form of cytokines). Thus it is not discarded
that some T helper cells secrete both cytokine pro®les simultaneously.
The model is illustrated in Fig. 1. Fig. 1(a) depicts a schematic representation of the interaction mechanisms between T helpers and macrophages, and within each group, that are taken
into account in the model. Fig. 1(b) represents the modeling of the eect that the multiple
signals have on the secretion of each cytokine pro®le C1T , C2T , C1M and C2M . The basic phenomenology that remains after lumping numerous cytokines into four pro®les is (i) cross inhibition
between Type-1 and Type-2 secretion pro®les of macrophages and T helpers, (ii) excitation among
each of both Type-1 and Type-2 subclasses, and (iii) upregulation and down(up)regulation of the
macrophagesÕ presentation ability by Type-1 and Type-2 (Th and macrophage-derived) secretion
pro®les.
The following equations for the responses C1T , C2T are assumed:
ÿ
ÿ
ÿ
ÿ
1
d C2T =dt ÿd2 C2T t g hT2 t :
d C1T =dt ÿd1 C1T t g hT1 t ;
In (1) the coecients d1 , d2 specify characteristic decay times. hT1 t and hT2 t designate the total
input aecting the secretion of C1T and C2T at time t. g is a sigmoidal gain function of the input h,
chosen for the sake of simplicity to be
ÿ
1ÿ
2
g hT 1 tanh hT ÿ h :
2
Eq. (2) re¯ects the assumption that in the neighborhood of some threshold h the cell responses
increase steeply with the input, and saturate at higher inputs [62]. Eqs. (1) and (2) therefore
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
41
Fig. 1. A schematic illustration of the model: (a) Interaction mechanisms between T helpers and macrophages, and
within each group. (b) Eect of multiple signals on the secretion of each cytokine pro®le.
constitute a general framework that embodies the idea of excitation, via saturation and threshold.
The nature of the excitation and its related terms are discussed below.
42
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
The terms that contribute to the inputs hT1 and hT2 are assumed to be
T non-specific
hT1 h1
T presentation
h1
;
T non-specific
hT2 h2
T presentation
h2
:
3
The ®rst term in both sums, hT non-specific , re¯ects the contribution of non-speci®c Th and
macrophageÕs cytokines to the input and is given by
T non-specific
h1
T non-specific
ÿh2
J1 C1T ÿ J2 C2T J1M C1M ÿ J2M C2M :
4
Underlying this choice of expression are the observations presented in Section 1 (and summarized
in Table 1), according to which Th cytokine pro®le C1T and macrophage cytokine pro®le C1M have
± on the average ± a positive eect on C1T secretion (and a negative eect on C2T production). In
contrast, Th cytokine pro®le C2T and macrophage cytokine pro®le C2M have ± on the average ± a
negative eect on C1T secretion (and a positive eect on C2T secretion). The positive coecients J
denote the sensitivity of C1T (or C2T ) secretion to Th-derived cytokines, and J M denote their sensitivity to macrophage-derived cytokines.
The second part of the input term aecting the secretion of cytokine patterns C1T and C2T relies
on speci®c interaction mechanisms between macrophages and Th cells, namely on antigen presentation by the former. This interaction is implemented as follows:
T presentation
b1 Ag ap1 C1T ap2 C2T ap1M C1M ap2M C2M ;
T presentation
b2 Ag ap1 C1T ap2 C2T ap1M C1M ap2M C2M :
h1
h2
5
In Eq. (5), Ag represents the amount of presented antigen and b1 and b2 denote the sensitivity of
C1T and C2T secretion to the antigen. In biological terms, b1 and b2 can quantitate memories of past
antigen exposure. A large b re¯ects a high overall memory of the Th population of the antigen. If,
for instance, b1 > b2, then a given antigen will induce a larger impact on the C1T cytokine secretion
pattern than on the C2T cytokine secretion pattern. In addition to the antigen amount and the
sensitivity to it, the input due to macrophage presentation is also determined by the ability of the
macrophages to exert their presentation functions. The term in brackets represents the presentation ability of the macrophage, a function of positive and negative signals exchanged between
the macrophages and the Th cells, and between the macrophages themselves. The sensitivity
coecients [ap] provide a measure of how these signals aect the antigen presentation ability. As
summarized in Table 1, the cytokines categorized as C1T and C1M , have on the average a positive
eect on the macrophagesÕ presentation ability, through their eect on MHC class II upregulation.
This implies positive ap1 and ap1M . In contrast, it is not clear whether ap2 and ap2M should be
positive or negative: Type-2 Th-derived cytokines IL-4 and IL-13 have positive eects on MHC
class II expression, whereas Type-2 Th and macrophage-derived cytokines IL-10, PGE-2 and
TGF-b are known to downregulate the expression of this molecule. Both possibilities are therefore
implemented and tested.
The dynamics of the macrophagesÕ cytokine secretion patterns, C1M and C2M , are governed by
ÿ
ÿ
ÿ
d C1M =dt ÿd1M C1M t g hM
d C2M =dt ÿd2M C2M t g hM
6
1 t ;
2 t :
As in Eq. (1) g is taken to be a sigmoidal gain function of the input h. The inputs that aect the
M
secretion of C1M and C2M cytokine patterns, denoted by hM
1 and h2 are described by the following
equation:
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
T
T
M
M
M
M
hM
1 K1 C1 ÿ K2 C2 K1 C1 ÿ K2 C2 ;
M
hM
2 ÿh1 :
43
7
In Eq. (5), the dependence of the macrophagesÕ presentation ability on non-speci®c Th and
macrophage-derived cytokines is implemented. Eq. (7) embodies the dependence of the macrophagesÕ secretatory function, on the above cytokines. As seen in Section 1, and reviewed in Table
1, Th cytokines classi®ed under cytokine pro®le C1T and macrophage cytokine pro®le C1M have a
positive eect on C1M secretion (and a negative eect on C2M production). In contrast, Th cytokine
pro®le C2T and macrophage cytokine pro®le C2M have a negative eect on C1M secretion (and a
positive eect on C2M production). The positive coecients K denote the sensitivity of C1M (or C2M )
secretion to Th cytokines while the K M denote the sensitivity to macrophage-derived cytokines.
The sensitivities J, J M (Eq. (4)) and K, K M , can be biologically interpreted as the quantity and or/
quality of receptors for the dierent cytokines. As an example, the major structural component of
the bacterial outer membrane, namely lipopolysaccharide (LPS), is known to induce changes in
responsiveness to cytokines, by mediating cytokine receptor expression in macrophages [63]. In
the terms of the model, this eect is translated as a modi®cation of the K values.
It is important to stress that the array of sensitivities J1 , J2 , K1 , K2 can also be interpreted as a
measure of the number of Th cells. Similarly, J1M , J2M , K1M , and K2M can re¯ect the number of
macrophages. The reason is as follows. Consider nT Th cells, and nM macrophages. According to a
cellular version of Eq. (4), the non-speci®c part of the input aecting the secretion capacity of
cytokine C1Ti of cell i is
j1
hnon-specific
i
nT
nT
nM
nM
X
X
X
X
Mi
M
C1Ti ÿ j2
C2Ti jM
ÿ
j
C
C2Mi ;
1
1
2
i1
i1
i1
8
i1
where we have used j as the cell-level counterpart of J. In Eq. (4), C1T , C2T , C1M , and C2M are de®ned
as arithmetic averages of the cytokines secreted by the nT Th cells and nM macrophages. Thus J1 in
M
M
Eq. (4) equals (j1 nT ), J2 equals (j2 nT ), J1M equals (jM
1 nM ) and J2 equals (j2 nM ). In the same
M
M
manner, K1 in Eq. (7) equals (k1 nT ), K2 equals (k2 nT ), K1 equals (k1 nM ) and K2M equals
(k2M nM ). Thus, a change in the number of Th cells, nT and macrophages, nM will have an eect on
the Ks and Js.
In the model, the question of early events that induce initial dierentiation from a naive cell is
left out. Here, established T helper cells and macrophages already exist, and it is investigated how
this system evolves after an initial event: ÔsomethingÕ induces initial levels of activity among the T
helper and macrophage populations.
As seen before, the groups denoted as C1T and C1M share extensive overlap. TNF and GM±CSF,
for instance, belong to both classes and have similar or complementary functions in the promotion of in¯ammatory and other responses classically categorized and Th1. Similarly, cytokines
classi®ed as C2T and C2M are both associated with functions that are classically categorized as Th2.
The choice of a particular immune response can thus be viewed as between one in which C1T and
C1M secretion pro®les predominate, and one in which C2T and C2M pro®les predominate. Denoting
by `Type-1 pro®le' the sum C1 12 C1T C1M and by `Type-2 pro®le' the sum C2 12 C2T C2M , I
characterize the system by these two variables, and examine its behavior as a function of a number
of dierent parameter sets. The mathematical analysis (i.e., computation of steady states and
examination of the conditions for their stability) was carried out by means of numerical
44
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
simulations in cases for which formal explicit analysis proved too dicult. Examination of sample
sections of the four-dimensional space and time varying plots were used to assert stability.
4. Results
The dependence of the steady-state solution for C1 and C2 on the dierent parameter sets was
examined graphically by time varying plots and by sample sections of the four-dimensional space.
Fig. 2 is a projection of this space that helps us to visualize the dependence of the number of
steady-state solutions on the sensitivity values Js and Ks (Eqs. (4) and (7)). In the case shown in
Fig. 2. A sample section of the four-dimensional space that illustrates the in¯uence of the sensitivities (J1 ; J2 ; J1M ; J2M ;
Eq. (4)) on the steady-state solutions. From numerical simulations, we obtain that for small values of both J1 J1M and
J2 J2M , a unique stable state is possible. Type-1 dominance, i.e., C1 > C2 when J1 J1M > J2 J2M ; Type-2 dominance
when J1 J1M > J2 J2M : (a) Steady-state values of T cell and macrophage-derived cytokines, C1T ; C2T ; C1M and C2M . (b)
Instead of four cytokine pro®les, only two classes, i.e., Type-1 (C1 ) and Type-2 (C2 ) are used to characterize the behavior of the system. (c) For larger sensitivity values, a bistability region exists for which either a Type-1 or a Type-2
dominated response is possible. b1 b2 1; Ag 1; ap's 0:05; here and throughout the following ®gures I take
d's 1; h 0. In (a) J1 J1M K1 K1M 0:4; J2 J2M K2 K2M 0:5. In (b) J1 J1M K1 K1M 0:6; J2
J2M K2 K2M 0:65.
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
45
Fig. 2(a), only one stable steady state is attainable. This is a Type-2 dominated stable steady state
(C1 > C2 ) if the average sensitivities to cytokine pro®les C1T and C1M , are less than the sensitivities
to cytokine pro®les C2T and C2M , i.e. if J1 J1M < J2 J2M . A Type-1 dominated stable steady state
appears, in contrast, when J1 J1M > J2 J2M (not shown). The larger the gap between the sensitivity values, the stronger the dominance of the prevailing type. For larger sensitivity values
however, a bistability region exists for which either a Type-1 or a Type-2 dominated response is
possible, as shown in Fig. 2(b). Here, although J1 J1M < J2 J2M then unlike the previous case, a
Type-1 dominated response is also possible. The initial levels of activation ± or initial conditions ±
induced in the Th population and or/the macrophage population determine the outcome of the
response, selecting between these two possible steady states according to their domains of attraction.
The results presented above stem from the choice of the sigmoidal gain function of the input,
made in Eq. (2). From Eq. (4) it can be seen that for small values of Js that give rise ± all else being
equal ± to small inputs hT1 ; hT2 , the gain function can be approximated by a linear function, allowing only one stable steady state solution. The approximation is no longer valid for the average
of larger values of Js, due to the choice of the non-linear gain function. Larger input values give
rise to three steady-state solutions (two stable and one unstable), provided that the gap between
the cross sensitivities, i.e. J1 J1M and J2 J2M is not too large.
In the following, I show representative cases of biologically interesting behavior of the model,
and therefore sample parameter sets were chosen for presentation. For a more comprehensive
analysis of the systemÕs behavior as a function of its parameter values, see [64].
Note that the results of the model predict long-term coexistence of both Type-1 and Type-2
responses in the same site ± one of them overshadowing the other. Such coexistence has been
observed by [33,65±69]. We note that in the theoretical model formulated in [18], the resulting
picture is of exclusive dominance of either the Th1 or the Th2 secretion pattern. In the present
model, certain parameter values can give rise to a response strongly dominated by one secretion
type. In this case, the dierence between the outcomes of the two models, namely between slight
and no coexistence is immaterial. However, the pictures diverge substantially in the cases of responses characterized by almost equal Type-1 and Type-2 components, obtained in the present
model for certain parameter values. The results of coexistence can be traced to the fact that in the
gain function of the input to T cells and macrophages, i.e., Eq. (2), there is a small constitutive
background excitability. That is, a small constant source of cytokines ± secreted by other cells
active in the environment, such as other tissue cells and natural killers ± is supplied even in the
absence of Th cells and macrophages.
4.1. Auto-reinforcement of response via macrophage±Th cell interactions
Suppose that we have a situation wherein a certain set of conditions led to a Type-1 dominated
response. Let us now ponder ways to bring about a stronger Type-1 response, as depicted in Fig.
3(a). One way is to add (by arti®cial intervention in the lab) sucient amounts of Type-1 cytokines. This adds a constant positive term to the hnon-specific
in Eqs. (4) and (7). However, adding
1
copious amounts of cytokines can have unwelcome harmful eects on the host. Another way to
accomplish the task is shown in Fig. 3(b). Reinforcement is obtained when the sensitivities of the
secretion pro®les of the Th population to macrophage-derived cytokines, i.e., J1M and J2M (Eq. (4))
46
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
Fig. 3. Reinforcement of the response via macrophage±Th cells interactions. (a) A Type-1 dominated response is
obtained. (b) Strengthening the sensitivities of the secretion pro®les of the Th population to macrophage-derived cytokines brings about a stronger Type-1 response. (c) Strengthening the sensitivity of the macrophagesÕ presentation
ability to Type-1 cytokines reinforces the Type-1 response obtained in (a) b1 b2 1; Ag 1; ap's 0:05; J1 K1
K1M 0:5; J2 K2 K2M 0:4; J1M J2M 0:01, in (a); J1M J2M 0:45, in (b); in (c), ap1 10 and remaining
parameter values as in (a).
are increased with respect to their values in Fig. 3(a). The same eect is accomplished if the
sensitivities of the macrophagesÕ secretion pro®les to Th-derived cytokines (i.e., K1 and K2 ) are
increased instead.
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
47
Besides non-speci®c cytokine mediated interactions between macrophages and Th cells, interactions in the context of antigen-presentation (Eq. (5)) can also enhance the predominant response. One way to reinforce a, e.g., Type-1 dominated response via antigen presentation
mechanisms is to increase the sensitivity b1 ± or ÔmemoryÕ ± of the Type-1 secretion pattern with
respect to b2. Another way to accomplish the task is shown in Fig. 3(c). Even if the antigen
amount is constant, reinforcement is obtained by increasing the sensitivity of the macrophagesÕ
presentation ability to Type-1 cytokines secreted by the Th population.
We thus conclude from the above that tightening the macrophages±Th cell feedback mechanisms (via non-speci®c cytokines or via antigen presentation) can reinforce a prevailing response.
4.2. Auto-inhibition of response via macrophage±Th cell interactions
4.2.1. Stability of Type-1 vs. Type-2 dominated responses
In the previous section, we discussed the possibility of reinforcement of the prevailing response
through ± among other ways ± antigen presentation mechanisms. As presented below, stronger
presentation can, under certain conditions, reverse the type of dominance. As exempli®ed in Fig.
(4), in suitable circumstances, antigen presentation can shift equally Type-1 to Type-2 or Type-2
to Type-1.
Considerable experimental evidence seems to point to an asymmetry in switching from one to
the opposite type of response. (Whether this phenomenon takes place on a cellular or a population level is a matter of debate. [30] supports the latter hypothesis.) A number of works report
on the stability of Th2 cytokine pattern ± in contrast to Th1 [28±30].
Motivated by these ®nding, I attempted to envision scenarios in which, for instance, a Type-1 to
Type-2 switch is easier to achieve than a switch in the opposite direction. The switching behavior
shown in Fig. 4(a) and (b) takes place under the condition b2 > b1, i.e., a larger sensitivity of the
C2T cytokine pro®le to the presented antigen than the sensitivity of the C1T cytokine pro®le to the
antigen. Increasing presentation (by taking a larger amount of antigen) can cause a switch from a
Type-1 to a Type-2 dominated state. However, this mechanism does not induce the opposite
switch from a Type-2 to a Type-1 dominated state (not shown). Associating the sensitivities b with
concept of memory to antigen, we can conclude the following. If the system has a Type-2 memory
to a speci®c antigen, but nonetheless has attained a Type-1 response, then it is ÔeasierÕ to switch to
the opposite Type-2 pattern than to reverse an attained Type-2 response. Thus, according to the
above scenario, the asymmetry in switching from one to the opposite type of response can be
encoded in a dierence in sensitivities (or memories) of the Th-cytokine secretion patterns to the
external stimulus.
A qualitatively dierent type of scenario that can account for the switching asymmetry is
discussed next. Increasing the amount of presenting antigen can cause a switch from a Type-1
to a Type-2 dominated state (Fig. 5(a) and (b)), but not a switch in the reverse direction (not
shown), when the macrophagesÕ presentation ability has a larger positive sensitivity to Thderived C1T cytokines than to C2T cytokines, namely when ap1 > ap2 . That this type of asymmetry in the sensitivities [ap] may be biologically plausible was indicated before. It was seen in
Section 1 and in Table 1 that cytokines characterized as C1T have on the average a positive
eect on the macrophagesÕ presentation ability, through their eect of MHC class II upregulation. With respect to C2T cytokines, it is believed that some cytokines comprising this category
48
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
Fig. 4. Stability of Type-1 vs. Type-2 responses. In (a)±(d), increasing the antigen amount can shift a Type-1 to a Type2, or a Type-2 to a Type-1 dominated response. (a) A Type-1 response is attained. (b) Increasing the antigen amount
causes a switch to a Type-2 dominated response. (c) A Type-2 dominated response is attained. (d) Increasing the antigen
amount causes a switch to a Type-1 dominated response. In (a), Ag 0:1; b1 0:2; b2 1; ap's 0:05; J1 J1M
K1 K1M 0:5; J2 J2M K2 K2M 0:45; initial Type-1 conditions. In (b), Ag 10, and remaining parameter values as in (a). In (c), J1 J1M K1 K1M 0:45; J2 J2M K2 K2M 0:5; b1 1; b2 0:2; Ag 0:1. In (d),
Ag 10, and remaining parameter values as in (c).
(IL-4 and IL-13) have positive eects on MHC class II expression, whereas others (IL-10, PGE2 and TGF-b) downregulate the expression of this molecule. Thus, averaging these properties
may result in ap1 > ap2 .
Note that the second scenario proposed to account for the asymmetric reversibility diers
qualitatively from the ®rst in that it does not rely on qualities of the Th-population with respect to
an external stimulus. Rather, it is based on macrophage±Th cells interaction, speci®cally on the
way that the Th population aects the macrophages to present antigen to them.
The issue of asymmetry is a particular aspect of a general phenomena of reversibility of responses. Experimental evidence indicates that for the system to generate a stable secretion pattern
(which may reinforce itself in the process) is not always the best strategy. It is believed that for
some infections, dierent eector functions may be appropriate at dierent stages of infection. An
example is a mouse malaria model in which Th1 and Th2 responses may be important early and
late in infection, respectively [24,25]. Th1±Th2 switches also occur in the course of self-limiting
auto-immune disease. In a study of experimental auto-immune myocarditis (EAM) the authors
demonstrate that Th1 type cytokines are expressed in the in¯ammatory phase of EAM and are
subsequently followed by the expression of Th2 type cytokines in the recovery phase [70]. By
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
49
Fig. 5. Eect of the sensitivity of the macrophagesÕ presentation ability [ap] to cytokines, on the switching asymmetry.
(a) A Type-1 dominated response is attained. (b) A switch is obtained for larger antigen amount. In (a)
b1 b2 1; J1 J1M K1 K1M 0:6; J2 J2M K2 K2M 0:7; ap2 ap2M 0; ap1 ap1M 0:2; Ag 0:01. In
(b) Ag 0:2, remaining parameter values as in (a).
introducing macrophage±Th cell feedback mechanisms, we have thus obtained a possible scenario
that can account for these phenomena.
4.2.2. Lots of Type-1 cytokine, little Type-1 response
According to seemingly paradoxical ®ndings, too much of a Type-1 cytokine, can shut down a
Type-1 dominated response. For example, the proin¯ammatory Th1 cytokine IFN-c is thought to
play a pivotal role in the pathology of EAE, which has been shown to be a Th1 mediated disease.
In [27] it is found that in vivo inhibition of IFN-c enhances EAE, thus concluding that IFN-c
apparently acts in some manner to down-regulate disease. IFN-c is also known to be involved in
combating tuberculosis. However, in [71] it is reported that incubation of human macrophages or
monocytes with this lymphokine often causes increased proliferation of the pathogen.
Apparently, NO has a dual role in in¯ammation as well. On the one hand, NO is cytotoxic, and
can contribute to tissue destruction in in¯ammatory responses. On the other hand, NO produced
by macrophages seems to act as an immune-suppressive agent. In [26] it is reported that when rats
were treated with inhibitors of NO synthase, this resulted in a marked aggravation of clinical signs
50
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
of EAE. Thus they conclude that therapeutic intervention of EAE based on NO modulation
should perhaps be aimed at increasing rather than inhibiting local NO production.
In order to account for these confusing observations, [35] proposes that NO might somehow
inhibit the production of IFN-c, and this in turn inhibits its own synthesis. From the model, I
propose a scenario relying on antigen-presentation mechanisms which, as discussed in the previous section, can induce a reversal in responses. Note that the switch from a Type-1 to a Type-2
dominated response obtained in Fig. 5(a) and (b) is not possible in the cases of smaller Type-1
responses (not shown) for example when the coecients K are taken to be smaller. For in those
cases, small amounts of Type-1 cytokine have less eect on enhancing macrophage presentation.
Thus, in the cases discussed in the previous section, too much of a given cytokine can cause
downregulation of the response dominated by it.
4.3. Compartmentalization of immune responses
According to several studies, it seems that the spatial location of the immune response is a very
important factor in the resulting cytokine balance. Findings of specialized environments in which
dierent spectra of cytokine production occur bring Mossman (®nal discussion in [28]) to suggest
a vaccine strategy in which two dierent immune responses might be induced in the same person
by vaccinating simultaneously in dierent locations. In [72] it is argued that the physical compartmentalization of the immune system may underlie the phenomenon of immunotherapy in
allergy.
In a study aimed to evaluate Th-like cytokine patterns in dierent compartments of the body in
patients with sarcoidosis, it was found that in the lungs, the cells shifted to the Th1 side of the
spectrum, whereas cells in the peripheral blood exhibited intermediate cytokine pro®les [33].
Observations made in [73] point to the conclusion that the production of a speci®c cytokine pro®le
is largely compartmentalized to distinct lymphoid organs. They demonstrate that in mice infected
by T. spiralis, IFN-c producing cells predominate in the spleen, whereas IL-5 producing cells
prevail in the mesenteric lymph nodes. (See also [74].) Similarly, a substantial body of experimental evidence indicates that routes of vaccination (oral, subcutaneous, etc.) can somehow determine the type of dominance (Th1 or Th2) of a resulting response. In leishmania infections, for
instance, a Th1 pattern was noted in CB6F1 mice infected in the footpad while a Th2 pattern
developed in mice infected in the dorsal skin [32].
A variety of mechanisms have been oered to explain why cytokine responses may be compartmentalized. According to one view, subsets of Th cells may display distinct homing characteristics via the expression of disparate homing receptors or adhesion molecules [75]. Another type
of explanation conceives disparate populations of presenting cells that preferentially activate
dierent subpopulations of T cells. This explanation relies on observations according to which
Th1 and Th2 cells seem to dier in their requirement for the costimulatory signals provided by
antigen presenting cells (reviewed in [23]).
The present model suggests alternative explanations for the variability in the outcome of the
immune response throughout the body. In Fig. 6 it was shown that even in the case where the Th
population share the same characteristics, dierent properties characterizing dierent clusters of
macrophages can determine the systemÕs behavior, thus accounting for the variability. Fig. 6(a)
shows that the macrophagesÕ sensitivity to cytokines can in¯uence the type of response.
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
51
Fig. 6. Eect of macrophagesÕ characteristics on the systemÕs behavior. (a) Eect of the sensitivities K1 ; K1M (Eq. (7)) of
macrophagesÕ cytokine secretion to Th and macrophage-derived Type-1 cytokines. (i) Small sensitivities K1 and K1M
result in a Type-2 response. (ii) Mild sensitivities give a Type-1 response. (iii) Larger sensitivities result in a stronger
Type-1 response. (b) Eect of the macrophagesÕ population size. (i) Small numbers, J1M ; J2M ; K1M ; K2M result in a Type-2
dominated response. (ii) Mild number give a Type-1 response. (iii) Larger numbers give a stronger Type-1 dominated
response. In (a), b1 b2 1; Ag 1; ap's 0:05; J 's 0:2; K2 K2 0:2. In (ai) K1 K1M 0:06. In (aii) K1
K1M 0:2. In (aiii) K1 K1M 0:6. In (b) J 's K's 0:6; C1T 0 C2T 0 0:5. In (bi), J1M J2M K1M K2M 0:3. In
(bii) J1M J2M K1M K2M 0:6. In (biii) J1M J2M K1M K2M 1:2.
Signi®cantly, studies seem to indicate that in dierent body locations, macrophages share dierent
sensitivities to cytokines. For example, alveolar macrophages are activated by lower doses of IFNc than peritoneal macrophages [76]. According to another study as little as 5 U/ml IFN-c induces
50% intracellular killing activity in in¯ammatory macrophages, whereas 20 U/ml IFN-c induces
an equivalent amount of intracellular killing in dierentiated tissue cells [77]. These experiments
52
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
are supportive of the view that the macrophagesÕ sensitivity to cytokines might be a cause of the
variability in outcome in dierent body locations. Fig. 6(b) shows that the macrophagesÕ population size can determine the type of the response. Certain conditions leading to a Type-2 dominated state in the case of small macrophage numbers can result in a Type-1 dominated response
in the case of large macrophage amounts, and in a stronger Type-1 response for even larger
amounts. If we take under consideration the fact that the number of macrophage colonies dier in
bone marrow, spleen, blood, lung (Table 2 in [78]) we have found another possible explanation for
the variability in outcomes throughout the body.
Arti®cial intervention directed to the macrophage population can have important eects on the
outcome of the immune response. For example, macrophages from diabetes-resistant donors were
shown to prevent insulitis and diabetes in most non-obese diabetic mice recipients, `however the
mechanism for protection is unclear', it is reported in [79]). I propose that the in¯uence of the set
of macrophage properties stated above can be experimentally tested, and may provide a therapeutic strategy in cases where an arti®cial intervention is needed in order to induce a desirable
cytokine pattern type. Macrophage numbers might be arti®cially varied to render protection.
MacrophagesÕ sensitivity to cytokines can presumably be experimentally changed, for example by
blocking suitable receptors.
Pathogens are known to be able to develop interesting and diverse strategies for survival in
macrophages. In particular, it might be the case that pathogens have adopted such strategies as
tampering with the sensitivity of the macrophages secretion and presentation abilities to dierent
cytokines. For example, M. leprae's constituent LAM (lipoarabinomannan), produced in copious
amounts in infected macrophages, apparently downregulates IFN-c-induced MHC-II expression
and killing functions. (A similar eect is shared by L donovani, [80].) Moreover, defective responses to IFN-c that were observed when macrophages harbored leprosy bacilli for 3±5 days
were not observed in recently infected macrophages [81].
5. Summary
In this study, I argue that previous mathematical models attribute a secondary role to macrophages in the determination of the immune response. An attempt is made to take a further step
in the direction of modeling feedback mechanisms between T helper cells and macrophages.
Motivated by accumulating data on the complex interplay between these populations, I considered
(i) the eect of macrophages on the T helpersÕ cytokine secretion, exerted via non-speci®c cytokine
communication, and via antigen presentation; (ii) the eect of T helpers on the macrophagesÕ
abilities to secrete cytokines, and to present antigens. The model focused on how the feedback
between both populations can determine the balance between a Type-1 and a Type-2 dominated
response, allowing us to put forward new explanations to interesting phenomena (such as reversal,
asymmetry, and compartmentalization of responses), which can be experimentally tested.
The results of the model indicated that in certain conditions, this mutual feedback is responsible
for the reinforcement of an unfolding response (Section 4.1). A tighter connection, e.g., higher
sensitivity of each population to the cytokines produced by the other, or stronger antigen presentation, can reinforce the prevailing response. Yet under other sets of conditions, the same
feedback mechanisms can lead instead to the downregulation of the response, providing a switch
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
53
from the prevailing to the opposite type of domination. In the context of this ®nding, several
points are worth stressing.
(i) Reversals in the dominance of a speci®c cytokine pro®le are indeed observed experimentally.
In several diseases, this process is thought to be bene®cial to the host, so that mechanisms of autoregulation may be a
www.elsevier.com/locate/mbs
Feedback mechanisms between T helper cells and macrophages
in the determination of the immune response
Ruth Lev Bar-Or *
Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science, P.O. Box 26,
76100 Rehovot, Israel
Received 5 February 1999; received in revised form 11 June 1999; accepted 24 August 1999
Abstract
The interactions between macrophages and T helper (Th) cells are a complex interplay of positive and
negative signals. Some of the mathematical models of interactions between T helpers have indeed taken the
in¯uence of macrophages into account. In this work the macrophage is not considered as an extrinsic agent,
that is duly directed by the T cells to be cytotoxic, nor is there consideration of T helper cell populations
that are dominantly regulated by extrinsic properties of antigens per se, or by certain classes of presenting
cells that preferentially select certain classes of lymphocytes or bias their commitment. Rather, a simpli®ed
model of feedback loops between Th cells and macrophages is formulated and analyzed. It is suggested how
the mutual in¯uence between Th and macrophages can determine the cytokine secretion pattern of these
populations. The model provides a feedback scenario to account for experimental ®ndings concerning
reversal in the dominance of a speci®c cytokine pro®le in the course of some infections. A possible scenario
accounting for the dierence between the stability of Th1 and Th2 cytokine pattern is put forward. The
model suggests explanations for the variability in the outcome of the immune response according to different body compartments. A rationale is presented that accounts for paradoxical ®ndings indicating that
Th1 cytokines are sometimes responsible for the downregulation of a Th1 dominated response. Ó 2000
Elsevier Science Inc. All rights reserved.
Keywords: Mathematical model; Th1/Th2; Feedback loops; Macrophages; Cytokines
*
Tel.: +972-8 934 2390; fax: +972-8 934 4122.
E-mail address: ruthy@wisorg.weizmann.ac.il (R. Lev Bar-Or).
0025-5564/00/$ - see front matter Ó 2000 Elsevier Science Inc. All rights reserved.
PII: S 0 0 2 5 - 5 5 6 4 ( 9 9 ) 0 0 0 4 6 - 2
36
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
1. Introduction
Since the discovery that CD4+ T cell subsets secrete dierent patterns of cytokines [1±3] substantial evidence has accumulated showing the importance of the T helper 1 (Th1) and Th2
subsets in the success or failure of immune responses. Th1 cells, which secrete mainly IL-2 and
IFN-c, promote immunity to infections by intracellular bacteria, protozoa and viruses [4,5]. Th2
cells, secreting mainly IL-4, IL-5, IL-6, IL-10 and IL-13 control responses against extracellular
pathogens and are involved in the pathogenesis of allergic reactions [6]. Both Th1 and Th2 cells
appear able to cross-suppress each other via the cytokines they secrete, and this provides an
explanation for the inverse relationship observed between Th1 and Th2-directed responses.
It is important to keep in mind though, that the Th1/Th2 dichotomy is a simpli®ed version of
reality. Additional CD4+ T cell phenotypes have been discussed, such as the Th0 phenotype that
secretes both Th1 and Th2 cytokines, indicating that these two classes do not represent two
absolute and mutually exclusive states [7,8]. Furthermore, the terminology referring to `Th1' or
`Th2' responses is misleading, since many of the Th1/Th2 cytokines are also produced by other
cell types. For example, IFN-c is also secreted by natural killer cells, CD8+ cells, and cd cells; IL10 is also produced by macrophages and mast cells [9±11]. Finally, recent evidence indicates that
CD8+ T cells cannot only secrete Th1 but also Th2-like cytokine patterns [12±16]. In spite of the
simpli®cation imbedded in the Th1/Th2 model, evidence shows that the state of health ± the
ability to ®ght infectious agents eectively, and not to succumb to autoimmune diseases ± often
depends on which pattern (Th1 or Th2) overshadows which, i.e. whether an appropriate or an
inappropriate immune response has been achieved.
In the framework of orchestrating an immune response, the pattern of cytokines produced by
dierent subsets of T lymphocytes, are used as communication signals with many other types of
cells, such as B cells and macrophages [4]. Macrophages are central in host immunity to pathogenic agents. They are the major eector cells that contain and kill intracellular pathogens. Optimal macrophage function is dependent on activation of the cells by a variety of extracellular (as
well as intracellular) stimuli, most prominently T-cell-derived lymphokines. Such cytokine production requires antigen recognition by T cells, a process in which macrophages are also involved
as antigen processing and presenting cells [17].
As discussed in Section 2, the interactions between macrophages and T cells are a fascinating
interplay of positive and negative signals. Some of the mathematical models of Th1/Th2 interactions and their implications in immunity, have indeed taken the in¯uence of macrophages into
account [18±22]. In [19], the authors incorporate the eect of antigen presenting cells on the T
helper system, but they consider the capacity of the antigen presenting cells to drive the activation
of its Th population as independent of the T cell population itself. In [18] the Th population is
stimulated by interaction with antigen, via antigen presenting cells. However, the type of interactions between these cells and the Th population that is mediated by cytokines, is ignored. Interactions via cytokines are modeled in part in [20], where an inhibitory, cytokine mediated eect
of Th2 cells on antigen presenting cells, and an excitatory cytokine mediated eect of antigen
presenting cells on Th1 is considered. In a previous paper, referred to subsequently as LS [22],
agents such as macrophages enter the game (i) as providers of excitation to the Th population via
presentation of antigen; (ii) as recipients of the ensembleÕs outcome. Thus in previous modeling of
Th1 vs. Th2 cytokine patterns, macrophages were given rather a secondary role.
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
37
In this work an attempt is made to take a further step in the understanding of the rich, complex,
bidirectional interactions between macrophages and T cells by formulating a simpli®ed model of
feedback loops between Th cells and macrophages. It is hoped thereby to gain some insights into
factors that determine the success or failure of immune responses by engendering a choice between
a dominant Th1 or a dominant Th2 secretion pattern. An understanding of these factors may
provide a means for therapeutic intervention in situations wherein the immune response is not
ecient or even deleterious to the host.
The macrophage is not considered as an extrinsic agent, that is duly directed by the T cells to be
cytotoxic, nor is there consideration of T helper cell populations that are dominantly regulated by
extrinsic properties of antigens per se, or by certain classes of APC that preferentially select
certain classes of lymphocytes or bias the commitment of uncommitted lymphocytes (reviewed in
[23]). Rather, a key question addressed here is how does feedback between Th cells and macrophages allow these populations the possibility of in¯uencing their own fate.
The following are some phenomena that will be addressed. (i) It is believed that for some infections, dierent eector functions may be appropriate at dierent stages of infection, such as in a
mouse malaria model in which Th1 and Th2 responses may be important early and late in infection, respectively [24,25]. (ii) Sometimes, too much of a Th1 cytokine impairs a strong Th1
response [26,27]. (iii) The Th2 cytokine pattern appears more stable than the Th1 pattern [28±30].
(iv) The in¯uence of the location of the immune response (in dierent tissues and body cavities) on
the type of dominance (Th1 or Th2) of the resulting response. (See for example [31±33].)
2. Biological background
T cells and macrophages use cytokines to communicate with each other and among themselves,
and alter each otherÕs behavior. Table 1 is an attempt to provide a crude summary of how cytokines produced by Th cells aect several functions of macrophages (cytokine secretion and
antigen presentation), and also in¯uence the behavior of the Th population itself, and of how
macrophage-derived cytokines modulate cytokine secretion by Th cells and by macrophages. The
next four paragraphs recount the main sources of information.
Cytokines produced by Th cells upon speci®c antigen recognition, modulate diverse eector
functions of macrophages [31]. First, T helper cells aect the ability of macrophages to secrete
several cytokines. The Th1 cytokine IFN-c (also reported to be produced ± by a lesser extent ± by
macrophages, [34]) enhances the macrophagesÕ secretion of products such as nitric oxide (NO),
which plays an important role in the antimicrobial activities of macrophages [35]. IFN-c also
enhances the secretion of several cytokines, such as TNF-a, which possess antiviral activity [36],
and IL-12, which enhances the cellsÕ cytotoxic activity (reviewed in [5]). IFN-c also inhibits
macrophage secretion of IL-10 [37]. Th1 cytokines TNF-a (also produced by macrophages) and
TNF-b induce the production of several macrophage products such as GM±CSF, which shows
microbicidal activity, and NO (reviewed in [38]). Th product GM±CSF, (also produced by
macrophages) induces TNF-a secretion [38,39].
The Th2 cytokine IL-4 blocks the macrophagesÕ production of several in¯ammatory cytokines,
such as TNF-a, IFN-c, IL-12 and GM±CSF and has inhibitory eects on the release of superoxide
by macrophages (reviewed in [40]). Similar eects are shared by the Th2 cytokine IL-10
38
Cytokine
Produced by (among other
cells)
Enhances production of
Decreases production of
Eect on MHCII
Grouped under (model)
IFN-c
Th; (macrophages)
NO, TNF-a, IL-12
IL-10. Suppresses proliferation of Th2 cells
C1T C1M
TNF
GM±CSF, NO, IFN-c
GM±CSF
IL-12
TNF-a: Th; macrophages.
TNF-b: Th.
Th; macrophages
Macrophages
TNF-a: C1T ; C1M ; TNF-b:
C1T
C1T ; C1M
C1M
IL-18
IL-4
Macrophages
Th
C1M
C2T
IL-10
Th; macrophages
¯
C2T ; C2M
TGF-b
IL-13
PGE2
Th; macrophages
Th
Macrophages
¯
¯
C2T ; C2M
C2T
C2M
TNF-a
IFN-c, TNF-a, GM±CSF
dierentiation of Th1
lymphocytes from progenitors
IFN-c, GM±CSF
Drives precursor Th cells
into Th2 cells
Can upregulate the
dierentiation of naive
cells to Th2 cells
IL-10
IL-4, IL-10. inhibits generation of Th2 cells
IL-10
TNF-a, IL-12, GM±CSF,
superoxides, IFN-c,
PGE2
TNF-a, IL-12, GM±CSF,
NO, IFN-c
TNF-a, IL-12
TNF-a, GM±CSF, NO
TNF-a, IL-12
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
Table 1
Eects of Th and macrophage-derived cytokines
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
39
(also produced by macrophages) which inhibits the secretion of proin¯ammatory cytokines such
as TNF-a, GM±CSF, IL-12, and also inhibits nitric oxide production [1,5,41]. The Th2 cytokine
TGF-b (also produced by macrophages) inhibits the production by macrophages of TNF-a, of
reactive oxygen products, of IL-12, and other proin¯ammatory cytokines (reviewed in [5,42]).
TGF-b is also known to promote IL-10 production by macrophages [43]. The Th2 cytokine IL-13
shows a strong inhibitory activity on in¯ammatory cytokine production, such as TNF-a and
GM±CSF, it decreases the production of nitric oxide in murine macrophages [44], and is a negative regulator of the production of IL-12 [5].
T helper cells not only aect the macrophagesÕ secretion ability of cytokines, but also in¯uence
antigen presentation, by regulating the expression of MHC II molecules±molecules whose binding
to the processed antigen is essential in order for the helper cells to recognize it [45]. IFN-c, TNF,
GM±CSF, IL-4 and IL-13 upregulate MHC II expression ([46] for IFN-c; [47] for TNF-a; [48] for
GMC±CSF; [49] for IL-4; [50] for IL-13). In contrast, IL-10 and TGF-b were shown to inhibit the
expression of class II molecules on macrophages ([51] for IL-10; [52] and [42] for TGF-b).
Not only does the type of cytokines produced by activated T cells in the process of antigen
presentation in¯uence the speci®c pattern of macrophage functions, but the eector functions of
the Th cells themselves are modulated in turn by the eects of macrophages. TNF-a enhances the
production of GM±CSF (by both T cells and macrophages), and IFN-c [38]. Macrophage product
IL-12 induces the production of IFN-c, TNF-a and GM±CSF. IL-12 has inhibitory eects on the
generation of Th2 cells (reviewed in [5,53]), and according to novel data on IL-4 and IL-10 secretion [54,55]. GM±CSF induces TNF-a secretion (by T cells and macrophages). IL-18, a new
cytokine found to be produced by macrophages, enhances IFN-c and GM±CSF production by Th
cells, and inhibits the secretion of IL-10 by Th cells, and macrophages [56]. Several macrophage
products are known to downregulate cytotoxic functions of T cells (and also macrophages). IL-10
inhibits the secretion of TNF-a, GM±CSF, and IFN-c by T cells [37]. The macrophage product
prostaglandin E2 (PGE2) inhibits the secretion of TNF-a and IL-12, and downregulates MHC
class II expression [57±59]. Finally, TGF-b inhibits the production of TNF-a and enhances the
production of IL-10.
3. The model
Accumulating research on cytokines paint a picture that seems hopelessly complex. Pleotropism
and redundancy abound. As sketched above, a single cytokine can interact with more than one
type of cell, a single cytokine can have multiple biological activities, a single cell can interact with
more than one cytokine, many cytokines have overlapping activities, and a single cytokine may
induce or inhibit the expression of a gene encoding another cytokine. Moreover, during the last
decade, 5±10 new cytokines have been cloned every year [60]. Today more than 100 cytokines have
been cloned. Hundreds more probably exist.
Instead of attempting to incorporate this myriad of cytokines into the model, or to implement
the detailed biology of individual cytokines, I consider for the sake of simplicity four patterns of
cytokines, denoted as ÔT-Type1Õ, ÔT-Type2Õ, ÔM-Type1Õ and ÔM-Type2Õ. Following the nomenclature recently proposed in [61], patterns of cytokines associated with Th1 and Th2 responses, are
denoted by Type-1 and Type-2, respectively. Grouped under ÔT-Type1Õ are T helper cell-derived
40
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
cytokines such as IFN-c, TNF-a and -b, and GM±CSF. Cytokine pro®le ÔT-Type2Õ lumps together T helper cell-derived cytokines such as IL-4, IL-10, IL-13, and TGF-b. ÔM-Type1Õ and ÔMType2Õ denote cytokines secreted by macrophages, which as seen in Section 1, have extensive
overlap with T helper-derived cytokines. The category ÔM-Type1Õ contains macrophage-derived
in¯ammatory cytokines such as TNF-a, IL-12, GM±CSF, IL-18, NO, and other antimicrobicidal
products. ÔM-Type2Õ bundles macrophage-derived anti-in¯ammatory cytokines such as IL-10,
PGE-2, and TGF-b.
The model envisions a population comprised by nT T helper cells, which may have dierent
antigen speci®cities, and nM macrophages that are active within a speci®c target area, such that
every cell can aect all others. Any given Th cell i i 1; . . . ; nT can secrete certain amounts of TType1 and T-Type2 cytokines, denoted respectively by C1Ti and C2Ti . Any given macrophage
i i 1; . . . ; nM can secrete certain amounts of M-Type1 and M-Type2 cytokines, denoted respectively by C1Mi and C2Mi . The parameters chosen to characterize each of the four cytokine
pattern types are taken to be qualitative averages of the characteristics of the array of cytokines
that constitute each category.
C1T and C2T denote the arithmetic average of secreted cytokine amounts C1Ti and C2Ti over the
whole T cell population. Similarly, C1M and C2M denote the mean secretion levels of Type-1 and
Type-2 cytokines over the macrophage population.
An important point taken into consideration is that, as mentioned in Section 1, it is an oversimpli®cation to say that T helper cells have totally distinct patterns of cytokine secretion. There is
evidence indicating the possibility that each individual T cell is capable of producing the entire
array of cytokines [40]. This picture promoted the idea to leave aside the destiny of the T helper
cells themselves, and to focus on their products (in the form of cytokines). Thus it is not discarded
that some T helper cells secrete both cytokine pro®les simultaneously.
The model is illustrated in Fig. 1. Fig. 1(a) depicts a schematic representation of the interaction mechanisms between T helpers and macrophages, and within each group, that are taken
into account in the model. Fig. 1(b) represents the modeling of the eect that the multiple
signals have on the secretion of each cytokine pro®le C1T , C2T , C1M and C2M . The basic phenomenology that remains after lumping numerous cytokines into four pro®les is (i) cross inhibition
between Type-1 and Type-2 secretion pro®les of macrophages and T helpers, (ii) excitation among
each of both Type-1 and Type-2 subclasses, and (iii) upregulation and down(up)regulation of the
macrophagesÕ presentation ability by Type-1 and Type-2 (Th and macrophage-derived) secretion
pro®les.
The following equations for the responses C1T , C2T are assumed:
ÿ
ÿ
ÿ
ÿ
1
d C2T =dt ÿd2 C2T t g hT2 t :
d C1T =dt ÿd1 C1T t g hT1 t ;
In (1) the coecients d1 , d2 specify characteristic decay times. hT1 t and hT2 t designate the total
input aecting the secretion of C1T and C2T at time t. g is a sigmoidal gain function of the input h,
chosen for the sake of simplicity to be
ÿ
1ÿ
2
g hT 1 tanh hT ÿ h :
2
Eq. (2) re¯ects the assumption that in the neighborhood of some threshold h the cell responses
increase steeply with the input, and saturate at higher inputs [62]. Eqs. (1) and (2) therefore
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
41
Fig. 1. A schematic illustration of the model: (a) Interaction mechanisms between T helpers and macrophages, and
within each group. (b) Eect of multiple signals on the secretion of each cytokine pro®le.
constitute a general framework that embodies the idea of excitation, via saturation and threshold.
The nature of the excitation and its related terms are discussed below.
42
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
The terms that contribute to the inputs hT1 and hT2 are assumed to be
T non-specific
hT1 h1
T presentation
h1
;
T non-specific
hT2 h2
T presentation
h2
:
3
The ®rst term in both sums, hT non-specific , re¯ects the contribution of non-speci®c Th and
macrophageÕs cytokines to the input and is given by
T non-specific
h1
T non-specific
ÿh2
J1 C1T ÿ J2 C2T J1M C1M ÿ J2M C2M :
4
Underlying this choice of expression are the observations presented in Section 1 (and summarized
in Table 1), according to which Th cytokine pro®le C1T and macrophage cytokine pro®le C1M have
± on the average ± a positive eect on C1T secretion (and a negative eect on C2T production). In
contrast, Th cytokine pro®le C2T and macrophage cytokine pro®le C2M have ± on the average ± a
negative eect on C1T secretion (and a positive eect on C2T secretion). The positive coecients J
denote the sensitivity of C1T (or C2T ) secretion to Th-derived cytokines, and J M denote their sensitivity to macrophage-derived cytokines.
The second part of the input term aecting the secretion of cytokine patterns C1T and C2T relies
on speci®c interaction mechanisms between macrophages and Th cells, namely on antigen presentation by the former. This interaction is implemented as follows:
T presentation
b1 Ag ap1 C1T ap2 C2T ap1M C1M ap2M C2M ;
T presentation
b2 Ag ap1 C1T ap2 C2T ap1M C1M ap2M C2M :
h1
h2
5
In Eq. (5), Ag represents the amount of presented antigen and b1 and b2 denote the sensitivity of
C1T and C2T secretion to the antigen. In biological terms, b1 and b2 can quantitate memories of past
antigen exposure. A large b re¯ects a high overall memory of the Th population of the antigen. If,
for instance, b1 > b2, then a given antigen will induce a larger impact on the C1T cytokine secretion
pattern than on the C2T cytokine secretion pattern. In addition to the antigen amount and the
sensitivity to it, the input due to macrophage presentation is also determined by the ability of the
macrophages to exert their presentation functions. The term in brackets represents the presentation ability of the macrophage, a function of positive and negative signals exchanged between
the macrophages and the Th cells, and between the macrophages themselves. The sensitivity
coecients [ap] provide a measure of how these signals aect the antigen presentation ability. As
summarized in Table 1, the cytokines categorized as C1T and C1M , have on the average a positive
eect on the macrophagesÕ presentation ability, through their eect on MHC class II upregulation.
This implies positive ap1 and ap1M . In contrast, it is not clear whether ap2 and ap2M should be
positive or negative: Type-2 Th-derived cytokines IL-4 and IL-13 have positive eects on MHC
class II expression, whereas Type-2 Th and macrophage-derived cytokines IL-10, PGE-2 and
TGF-b are known to downregulate the expression of this molecule. Both possibilities are therefore
implemented and tested.
The dynamics of the macrophagesÕ cytokine secretion patterns, C1M and C2M , are governed by
ÿ
ÿ
ÿ
d C1M =dt ÿd1M C1M t g hM
d C2M =dt ÿd2M C2M t g hM
6
1 t ;
2 t :
As in Eq. (1) g is taken to be a sigmoidal gain function of the input h. The inputs that aect the
M
secretion of C1M and C2M cytokine patterns, denoted by hM
1 and h2 are described by the following
equation:
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
T
T
M
M
M
M
hM
1 K1 C1 ÿ K2 C2 K1 C1 ÿ K2 C2 ;
M
hM
2 ÿh1 :
43
7
In Eq. (5), the dependence of the macrophagesÕ presentation ability on non-speci®c Th and
macrophage-derived cytokines is implemented. Eq. (7) embodies the dependence of the macrophagesÕ secretatory function, on the above cytokines. As seen in Section 1, and reviewed in Table
1, Th cytokines classi®ed under cytokine pro®le C1T and macrophage cytokine pro®le C1M have a
positive eect on C1M secretion (and a negative eect on C2M production). In contrast, Th cytokine
pro®le C2T and macrophage cytokine pro®le C2M have a negative eect on C1M secretion (and a
positive eect on C2M production). The positive coecients K denote the sensitivity of C1M (or C2M )
secretion to Th cytokines while the K M denote the sensitivity to macrophage-derived cytokines.
The sensitivities J, J M (Eq. (4)) and K, K M , can be biologically interpreted as the quantity and or/
quality of receptors for the dierent cytokines. As an example, the major structural component of
the bacterial outer membrane, namely lipopolysaccharide (LPS), is known to induce changes in
responsiveness to cytokines, by mediating cytokine receptor expression in macrophages [63]. In
the terms of the model, this eect is translated as a modi®cation of the K values.
It is important to stress that the array of sensitivities J1 , J2 , K1 , K2 can also be interpreted as a
measure of the number of Th cells. Similarly, J1M , J2M , K1M , and K2M can re¯ect the number of
macrophages. The reason is as follows. Consider nT Th cells, and nM macrophages. According to a
cellular version of Eq. (4), the non-speci®c part of the input aecting the secretion capacity of
cytokine C1Ti of cell i is
j1
hnon-specific
i
nT
nT
nM
nM
X
X
X
X
Mi
M
C1Ti ÿ j2
C2Ti jM
ÿ
j
C
C2Mi ;
1
1
2
i1
i1
i1
8
i1
where we have used j as the cell-level counterpart of J. In Eq. (4), C1T , C2T , C1M , and C2M are de®ned
as arithmetic averages of the cytokines secreted by the nT Th cells and nM macrophages. Thus J1 in
M
M
Eq. (4) equals (j1 nT ), J2 equals (j2 nT ), J1M equals (jM
1 nM ) and J2 equals (j2 nM ). In the same
M
M
manner, K1 in Eq. (7) equals (k1 nT ), K2 equals (k2 nT ), K1 equals (k1 nM ) and K2M equals
(k2M nM ). Thus, a change in the number of Th cells, nT and macrophages, nM will have an eect on
the Ks and Js.
In the model, the question of early events that induce initial dierentiation from a naive cell is
left out. Here, established T helper cells and macrophages already exist, and it is investigated how
this system evolves after an initial event: ÔsomethingÕ induces initial levels of activity among the T
helper and macrophage populations.
As seen before, the groups denoted as C1T and C1M share extensive overlap. TNF and GM±CSF,
for instance, belong to both classes and have similar or complementary functions in the promotion of in¯ammatory and other responses classically categorized and Th1. Similarly, cytokines
classi®ed as C2T and C2M are both associated with functions that are classically categorized as Th2.
The choice of a particular immune response can thus be viewed as between one in which C1T and
C1M secretion pro®les predominate, and one in which C2T and C2M pro®les predominate. Denoting
by `Type-1 pro®le' the sum C1 12 C1T C1M and by `Type-2 pro®le' the sum C2 12 C2T C2M , I
characterize the system by these two variables, and examine its behavior as a function of a number
of dierent parameter sets. The mathematical analysis (i.e., computation of steady states and
examination of the conditions for their stability) was carried out by means of numerical
44
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
simulations in cases for which formal explicit analysis proved too dicult. Examination of sample
sections of the four-dimensional space and time varying plots were used to assert stability.
4. Results
The dependence of the steady-state solution for C1 and C2 on the dierent parameter sets was
examined graphically by time varying plots and by sample sections of the four-dimensional space.
Fig. 2 is a projection of this space that helps us to visualize the dependence of the number of
steady-state solutions on the sensitivity values Js and Ks (Eqs. (4) and (7)). In the case shown in
Fig. 2. A sample section of the four-dimensional space that illustrates the in¯uence of the sensitivities (J1 ; J2 ; J1M ; J2M ;
Eq. (4)) on the steady-state solutions. From numerical simulations, we obtain that for small values of both J1 J1M and
J2 J2M , a unique stable state is possible. Type-1 dominance, i.e., C1 > C2 when J1 J1M > J2 J2M ; Type-2 dominance
when J1 J1M > J2 J2M : (a) Steady-state values of T cell and macrophage-derived cytokines, C1T ; C2T ; C1M and C2M . (b)
Instead of four cytokine pro®les, only two classes, i.e., Type-1 (C1 ) and Type-2 (C2 ) are used to characterize the behavior of the system. (c) For larger sensitivity values, a bistability region exists for which either a Type-1 or a Type-2
dominated response is possible. b1 b2 1; Ag 1; ap's 0:05; here and throughout the following ®gures I take
d's 1; h 0. In (a) J1 J1M K1 K1M 0:4; J2 J2M K2 K2M 0:5. In (b) J1 J1M K1 K1M 0:6; J2
J2M K2 K2M 0:65.
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
45
Fig. 2(a), only one stable steady state is attainable. This is a Type-2 dominated stable steady state
(C1 > C2 ) if the average sensitivities to cytokine pro®les C1T and C1M , are less than the sensitivities
to cytokine pro®les C2T and C2M , i.e. if J1 J1M < J2 J2M . A Type-1 dominated stable steady state
appears, in contrast, when J1 J1M > J2 J2M (not shown). The larger the gap between the sensitivity values, the stronger the dominance of the prevailing type. For larger sensitivity values
however, a bistability region exists for which either a Type-1 or a Type-2 dominated response is
possible, as shown in Fig. 2(b). Here, although J1 J1M < J2 J2M then unlike the previous case, a
Type-1 dominated response is also possible. The initial levels of activation ± or initial conditions ±
induced in the Th population and or/the macrophage population determine the outcome of the
response, selecting between these two possible steady states according to their domains of attraction.
The results presented above stem from the choice of the sigmoidal gain function of the input,
made in Eq. (2). From Eq. (4) it can be seen that for small values of Js that give rise ± all else being
equal ± to small inputs hT1 ; hT2 , the gain function can be approximated by a linear function, allowing only one stable steady state solution. The approximation is no longer valid for the average
of larger values of Js, due to the choice of the non-linear gain function. Larger input values give
rise to three steady-state solutions (two stable and one unstable), provided that the gap between
the cross sensitivities, i.e. J1 J1M and J2 J2M is not too large.
In the following, I show representative cases of biologically interesting behavior of the model,
and therefore sample parameter sets were chosen for presentation. For a more comprehensive
analysis of the systemÕs behavior as a function of its parameter values, see [64].
Note that the results of the model predict long-term coexistence of both Type-1 and Type-2
responses in the same site ± one of them overshadowing the other. Such coexistence has been
observed by [33,65±69]. We note that in the theoretical model formulated in [18], the resulting
picture is of exclusive dominance of either the Th1 or the Th2 secretion pattern. In the present
model, certain parameter values can give rise to a response strongly dominated by one secretion
type. In this case, the dierence between the outcomes of the two models, namely between slight
and no coexistence is immaterial. However, the pictures diverge substantially in the cases of responses characterized by almost equal Type-1 and Type-2 components, obtained in the present
model for certain parameter values. The results of coexistence can be traced to the fact that in the
gain function of the input to T cells and macrophages, i.e., Eq. (2), there is a small constitutive
background excitability. That is, a small constant source of cytokines ± secreted by other cells
active in the environment, such as other tissue cells and natural killers ± is supplied even in the
absence of Th cells and macrophages.
4.1. Auto-reinforcement of response via macrophage±Th cell interactions
Suppose that we have a situation wherein a certain set of conditions led to a Type-1 dominated
response. Let us now ponder ways to bring about a stronger Type-1 response, as depicted in Fig.
3(a). One way is to add (by arti®cial intervention in the lab) sucient amounts of Type-1 cytokines. This adds a constant positive term to the hnon-specific
in Eqs. (4) and (7). However, adding
1
copious amounts of cytokines can have unwelcome harmful eects on the host. Another way to
accomplish the task is shown in Fig. 3(b). Reinforcement is obtained when the sensitivities of the
secretion pro®les of the Th population to macrophage-derived cytokines, i.e., J1M and J2M (Eq. (4))
46
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
Fig. 3. Reinforcement of the response via macrophage±Th cells interactions. (a) A Type-1 dominated response is
obtained. (b) Strengthening the sensitivities of the secretion pro®les of the Th population to macrophage-derived cytokines brings about a stronger Type-1 response. (c) Strengthening the sensitivity of the macrophagesÕ presentation
ability to Type-1 cytokines reinforces the Type-1 response obtained in (a) b1 b2 1; Ag 1; ap's 0:05; J1 K1
K1M 0:5; J2 K2 K2M 0:4; J1M J2M 0:01, in (a); J1M J2M 0:45, in (b); in (c), ap1 10 and remaining
parameter values as in (a).
are increased with respect to their values in Fig. 3(a). The same eect is accomplished if the
sensitivities of the macrophagesÕ secretion pro®les to Th-derived cytokines (i.e., K1 and K2 ) are
increased instead.
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
47
Besides non-speci®c cytokine mediated interactions between macrophages and Th cells, interactions in the context of antigen-presentation (Eq. (5)) can also enhance the predominant response. One way to reinforce a, e.g., Type-1 dominated response via antigen presentation
mechanisms is to increase the sensitivity b1 ± or ÔmemoryÕ ± of the Type-1 secretion pattern with
respect to b2. Another way to accomplish the task is shown in Fig. 3(c). Even if the antigen
amount is constant, reinforcement is obtained by increasing the sensitivity of the macrophagesÕ
presentation ability to Type-1 cytokines secreted by the Th population.
We thus conclude from the above that tightening the macrophages±Th cell feedback mechanisms (via non-speci®c cytokines or via antigen presentation) can reinforce a prevailing response.
4.2. Auto-inhibition of response via macrophage±Th cell interactions
4.2.1. Stability of Type-1 vs. Type-2 dominated responses
In the previous section, we discussed the possibility of reinforcement of the prevailing response
through ± among other ways ± antigen presentation mechanisms. As presented below, stronger
presentation can, under certain conditions, reverse the type of dominance. As exempli®ed in Fig.
(4), in suitable circumstances, antigen presentation can shift equally Type-1 to Type-2 or Type-2
to Type-1.
Considerable experimental evidence seems to point to an asymmetry in switching from one to
the opposite type of response. (Whether this phenomenon takes place on a cellular or a population level is a matter of debate. [30] supports the latter hypothesis.) A number of works report
on the stability of Th2 cytokine pattern ± in contrast to Th1 [28±30].
Motivated by these ®nding, I attempted to envision scenarios in which, for instance, a Type-1 to
Type-2 switch is easier to achieve than a switch in the opposite direction. The switching behavior
shown in Fig. 4(a) and (b) takes place under the condition b2 > b1, i.e., a larger sensitivity of the
C2T cytokine pro®le to the presented antigen than the sensitivity of the C1T cytokine pro®le to the
antigen. Increasing presentation (by taking a larger amount of antigen) can cause a switch from a
Type-1 to a Type-2 dominated state. However, this mechanism does not induce the opposite
switch from a Type-2 to a Type-1 dominated state (not shown). Associating the sensitivities b with
concept of memory to antigen, we can conclude the following. If the system has a Type-2 memory
to a speci®c antigen, but nonetheless has attained a Type-1 response, then it is ÔeasierÕ to switch to
the opposite Type-2 pattern than to reverse an attained Type-2 response. Thus, according to the
above scenario, the asymmetry in switching from one to the opposite type of response can be
encoded in a dierence in sensitivities (or memories) of the Th-cytokine secretion patterns to the
external stimulus.
A qualitatively dierent type of scenario that can account for the switching asymmetry is
discussed next. Increasing the amount of presenting antigen can cause a switch from a Type-1
to a Type-2 dominated state (Fig. 5(a) and (b)), but not a switch in the reverse direction (not
shown), when the macrophagesÕ presentation ability has a larger positive sensitivity to Thderived C1T cytokines than to C2T cytokines, namely when ap1 > ap2 . That this type of asymmetry in the sensitivities [ap] may be biologically plausible was indicated before. It was seen in
Section 1 and in Table 1 that cytokines characterized as C1T have on the average a positive
eect on the macrophagesÕ presentation ability, through their eect of MHC class II upregulation. With respect to C2T cytokines, it is believed that some cytokines comprising this category
48
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
Fig. 4. Stability of Type-1 vs. Type-2 responses. In (a)±(d), increasing the antigen amount can shift a Type-1 to a Type2, or a Type-2 to a Type-1 dominated response. (a) A Type-1 response is attained. (b) Increasing the antigen amount
causes a switch to a Type-2 dominated response. (c) A Type-2 dominated response is attained. (d) Increasing the antigen
amount causes a switch to a Type-1 dominated response. In (a), Ag 0:1; b1 0:2; b2 1; ap's 0:05; J1 J1M
K1 K1M 0:5; J2 J2M K2 K2M 0:45; initial Type-1 conditions. In (b), Ag 10, and remaining parameter values as in (a). In (c), J1 J1M K1 K1M 0:45; J2 J2M K2 K2M 0:5; b1 1; b2 0:2; Ag 0:1. In (d),
Ag 10, and remaining parameter values as in (c).
(IL-4 and IL-13) have positive eects on MHC class II expression, whereas others (IL-10, PGE2 and TGF-b) downregulate the expression of this molecule. Thus, averaging these properties
may result in ap1 > ap2 .
Note that the second scenario proposed to account for the asymmetric reversibility diers
qualitatively from the ®rst in that it does not rely on qualities of the Th-population with respect to
an external stimulus. Rather, it is based on macrophage±Th cells interaction, speci®cally on the
way that the Th population aects the macrophages to present antigen to them.
The issue of asymmetry is a particular aspect of a general phenomena of reversibility of responses. Experimental evidence indicates that for the system to generate a stable secretion pattern
(which may reinforce itself in the process) is not always the best strategy. It is believed that for
some infections, dierent eector functions may be appropriate at dierent stages of infection. An
example is a mouse malaria model in which Th1 and Th2 responses may be important early and
late in infection, respectively [24,25]. Th1±Th2 switches also occur in the course of self-limiting
auto-immune disease. In a study of experimental auto-immune myocarditis (EAM) the authors
demonstrate that Th1 type cytokines are expressed in the in¯ammatory phase of EAM and are
subsequently followed by the expression of Th2 type cytokines in the recovery phase [70]. By
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
49
Fig. 5. Eect of the sensitivity of the macrophagesÕ presentation ability [ap] to cytokines, on the switching asymmetry.
(a) A Type-1 dominated response is attained. (b) A switch is obtained for larger antigen amount. In (a)
b1 b2 1; J1 J1M K1 K1M 0:6; J2 J2M K2 K2M 0:7; ap2 ap2M 0; ap1 ap1M 0:2; Ag 0:01. In
(b) Ag 0:2, remaining parameter values as in (a).
introducing macrophage±Th cell feedback mechanisms, we have thus obtained a possible scenario
that can account for these phenomena.
4.2.2. Lots of Type-1 cytokine, little Type-1 response
According to seemingly paradoxical ®ndings, too much of a Type-1 cytokine, can shut down a
Type-1 dominated response. For example, the proin¯ammatory Th1 cytokine IFN-c is thought to
play a pivotal role in the pathology of EAE, which has been shown to be a Th1 mediated disease.
In [27] it is found that in vivo inhibition of IFN-c enhances EAE, thus concluding that IFN-c
apparently acts in some manner to down-regulate disease. IFN-c is also known to be involved in
combating tuberculosis. However, in [71] it is reported that incubation of human macrophages or
monocytes with this lymphokine often causes increased proliferation of the pathogen.
Apparently, NO has a dual role in in¯ammation as well. On the one hand, NO is cytotoxic, and
can contribute to tissue destruction in in¯ammatory responses. On the other hand, NO produced
by macrophages seems to act as an immune-suppressive agent. In [26] it is reported that when rats
were treated with inhibitors of NO synthase, this resulted in a marked aggravation of clinical signs
50
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
of EAE. Thus they conclude that therapeutic intervention of EAE based on NO modulation
should perhaps be aimed at increasing rather than inhibiting local NO production.
In order to account for these confusing observations, [35] proposes that NO might somehow
inhibit the production of IFN-c, and this in turn inhibits its own synthesis. From the model, I
propose a scenario relying on antigen-presentation mechanisms which, as discussed in the previous section, can induce a reversal in responses. Note that the switch from a Type-1 to a Type-2
dominated response obtained in Fig. 5(a) and (b) is not possible in the cases of smaller Type-1
responses (not shown) for example when the coecients K are taken to be smaller. For in those
cases, small amounts of Type-1 cytokine have less eect on enhancing macrophage presentation.
Thus, in the cases discussed in the previous section, too much of a given cytokine can cause
downregulation of the response dominated by it.
4.3. Compartmentalization of immune responses
According to several studies, it seems that the spatial location of the immune response is a very
important factor in the resulting cytokine balance. Findings of specialized environments in which
dierent spectra of cytokine production occur bring Mossman (®nal discussion in [28]) to suggest
a vaccine strategy in which two dierent immune responses might be induced in the same person
by vaccinating simultaneously in dierent locations. In [72] it is argued that the physical compartmentalization of the immune system may underlie the phenomenon of immunotherapy in
allergy.
In a study aimed to evaluate Th-like cytokine patterns in dierent compartments of the body in
patients with sarcoidosis, it was found that in the lungs, the cells shifted to the Th1 side of the
spectrum, whereas cells in the peripheral blood exhibited intermediate cytokine pro®les [33].
Observations made in [73] point to the conclusion that the production of a speci®c cytokine pro®le
is largely compartmentalized to distinct lymphoid organs. They demonstrate that in mice infected
by T. spiralis, IFN-c producing cells predominate in the spleen, whereas IL-5 producing cells
prevail in the mesenteric lymph nodes. (See also [74].) Similarly, a substantial body of experimental evidence indicates that routes of vaccination (oral, subcutaneous, etc.) can somehow determine the type of dominance (Th1 or Th2) of a resulting response. In leishmania infections, for
instance, a Th1 pattern was noted in CB6F1 mice infected in the footpad while a Th2 pattern
developed in mice infected in the dorsal skin [32].
A variety of mechanisms have been oered to explain why cytokine responses may be compartmentalized. According to one view, subsets of Th cells may display distinct homing characteristics via the expression of disparate homing receptors or adhesion molecules [75]. Another type
of explanation conceives disparate populations of presenting cells that preferentially activate
dierent subpopulations of T cells. This explanation relies on observations according to which
Th1 and Th2 cells seem to dier in their requirement for the costimulatory signals provided by
antigen presenting cells (reviewed in [23]).
The present model suggests alternative explanations for the variability in the outcome of the
immune response throughout the body. In Fig. 6 it was shown that even in the case where the Th
population share the same characteristics, dierent properties characterizing dierent clusters of
macrophages can determine the systemÕs behavior, thus accounting for the variability. Fig. 6(a)
shows that the macrophagesÕ sensitivity to cytokines can in¯uence the type of response.
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
51
Fig. 6. Eect of macrophagesÕ characteristics on the systemÕs behavior. (a) Eect of the sensitivities K1 ; K1M (Eq. (7)) of
macrophagesÕ cytokine secretion to Th and macrophage-derived Type-1 cytokines. (i) Small sensitivities K1 and K1M
result in a Type-2 response. (ii) Mild sensitivities give a Type-1 response. (iii) Larger sensitivities result in a stronger
Type-1 response. (b) Eect of the macrophagesÕ population size. (i) Small numbers, J1M ; J2M ; K1M ; K2M result in a Type-2
dominated response. (ii) Mild number give a Type-1 response. (iii) Larger numbers give a stronger Type-1 dominated
response. In (a), b1 b2 1; Ag 1; ap's 0:05; J 's 0:2; K2 K2 0:2. In (ai) K1 K1M 0:06. In (aii) K1
K1M 0:2. In (aiii) K1 K1M 0:6. In (b) J 's K's 0:6; C1T 0 C2T 0 0:5. In (bi), J1M J2M K1M K2M 0:3. In
(bii) J1M J2M K1M K2M 0:6. In (biii) J1M J2M K1M K2M 1:2.
Signi®cantly, studies seem to indicate that in dierent body locations, macrophages share dierent
sensitivities to cytokines. For example, alveolar macrophages are activated by lower doses of IFNc than peritoneal macrophages [76]. According to another study as little as 5 U/ml IFN-c induces
50% intracellular killing activity in in¯ammatory macrophages, whereas 20 U/ml IFN-c induces
an equivalent amount of intracellular killing in dierentiated tissue cells [77]. These experiments
52
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
are supportive of the view that the macrophagesÕ sensitivity to cytokines might be a cause of the
variability in outcome in dierent body locations. Fig. 6(b) shows that the macrophagesÕ population size can determine the type of the response. Certain conditions leading to a Type-2 dominated state in the case of small macrophage numbers can result in a Type-1 dominated response
in the case of large macrophage amounts, and in a stronger Type-1 response for even larger
amounts. If we take under consideration the fact that the number of macrophage colonies dier in
bone marrow, spleen, blood, lung (Table 2 in [78]) we have found another possible explanation for
the variability in outcomes throughout the body.
Arti®cial intervention directed to the macrophage population can have important eects on the
outcome of the immune response. For example, macrophages from diabetes-resistant donors were
shown to prevent insulitis and diabetes in most non-obese diabetic mice recipients, `however the
mechanism for protection is unclear', it is reported in [79]). I propose that the in¯uence of the set
of macrophage properties stated above can be experimentally tested, and may provide a therapeutic strategy in cases where an arti®cial intervention is needed in order to induce a desirable
cytokine pattern type. Macrophage numbers might be arti®cially varied to render protection.
MacrophagesÕ sensitivity to cytokines can presumably be experimentally changed, for example by
blocking suitable receptors.
Pathogens are known to be able to develop interesting and diverse strategies for survival in
macrophages. In particular, it might be the case that pathogens have adopted such strategies as
tampering with the sensitivity of the macrophages secretion and presentation abilities to dierent
cytokines. For example, M. leprae's constituent LAM (lipoarabinomannan), produced in copious
amounts in infected macrophages, apparently downregulates IFN-c-induced MHC-II expression
and killing functions. (A similar eect is shared by L donovani, [80].) Moreover, defective responses to IFN-c that were observed when macrophages harbored leprosy bacilli for 3±5 days
were not observed in recently infected macrophages [81].
5. Summary
In this study, I argue that previous mathematical models attribute a secondary role to macrophages in the determination of the immune response. An attempt is made to take a further step
in the direction of modeling feedback mechanisms between T helper cells and macrophages.
Motivated by accumulating data on the complex interplay between these populations, I considered
(i) the eect of macrophages on the T helpersÕ cytokine secretion, exerted via non-speci®c cytokine
communication, and via antigen presentation; (ii) the eect of T helpers on the macrophagesÕ
abilities to secrete cytokines, and to present antigens. The model focused on how the feedback
between both populations can determine the balance between a Type-1 and a Type-2 dominated
response, allowing us to put forward new explanations to interesting phenomena (such as reversal,
asymmetry, and compartmentalization of responses), which can be experimentally tested.
The results of the model indicated that in certain conditions, this mutual feedback is responsible
for the reinforcement of an unfolding response (Section 4.1). A tighter connection, e.g., higher
sensitivity of each population to the cytokines produced by the other, or stronger antigen presentation, can reinforce the prevailing response. Yet under other sets of conditions, the same
feedback mechanisms can lead instead to the downregulation of the response, providing a switch
R. Lev Bar-Or / Mathematical Biosciences 163 (2000) 35±58
53
from the prevailing to the opposite type of domination. In the context of this ®nding, several
points are worth stressing.
(i) Reversals in the dominance of a speci®c cytokine pro®le are indeed observed experimentally.
In several diseases, this process is thought to be bene®cial to the host, so that mechanisms of autoregulation may be a