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Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel
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Abstract |
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 Top Abstract IntroductionMaking Effectors More EffectiveSelecting Effective EffectorsDiscussionAppendix 1References |
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Introduction |
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TopAbstractIntroductionMaking Effectors More EffectiveSelecting Effective EffectorsDiscussionAppendix 1References |
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1) Biosphere: The biosphere has no goals; evolution unfolds without purpose according to the laws of physics and chemistry.
2) Organism: Accepting no. 1, scientists can still postulate goals as useful approximations in suitably restricted circumstances. In particular, it is often helpful to pursue the hypothesis that organisms evolve to maximize "fitness," characterized perhaps by a high level of long-term reproduction.
3) Immune system: The immune system can contribute to the evolutionary goal of maximizing fitness if it deals effectively with pathogens. (It must not be forgotten, however, that elements of the immune system have diverse functions, such as participation in wound healing and other homeostatic processes.) One specific way to focus the fuzzily defined systemic goal of "dealing effectively with pathogens" is for the immune system to exercise appropriate effector choice; i.e., the system must somehow choose which spectrum of effectors are to be deployed to deal with a given attack, such as how much complement, for example, and how much Ab (and of what isotypes), how much IFN, how many B cells, macrophages, T helpers, and T killers. "Striving" toward some form of effector optimization, for a given effector type, is another way to make immune system performance more effective. An example here is optimal switching in B cells from proliferation to Ab secretion (1).
4) Immune cells: Here we reach a novel feature of this paper with the assertion that it is illuminating to assume that in "real time" cells of the immune system have monitorable partial goals that typically overlap and even contradict each other. By real time we mean over the days or weeks during which a typical disease runs it course.
We discuss here the implementation of the two postulated "low
level" goals for immune system performance that are displayed in
Table I
. There are doubtless other such
goals (for example, minimizing energy expenditure, all other
things being equal), but we will concentrate on showing that the goals
in Table I can be achieved in real time, driven by feedbacks from
sensor molecules that continually monitor the state of the organism and
its pathogens.
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We begin with a discussion of effector optimization. A model
illustrates deficiencies in the performance of a rigidly preprogrammed
effector cell. We then show how these deficiencies can be alleviated if
the cells monitor their own performance and feed back this information
to alter effector behavior. In particular, we discuss the
implementation of the two postulated goals for immune system
performance that are displayed in Table I
. Next, we apply our approach
to the problem of effector choice. In particular, we examine how the
initial spatial clustering of different effectors can play an essential
role in the process of selecting more effective effectors.
To make an additional point before proceeding, we note that effector choice might be primarily pre-set by evolution, perhaps as follows. Different sets of dominant epitopes respectively characterize all the pathogens. For each epitope set, a panel of attacking effectors is fully designated in advance. The connection between an epitope set and the response panel would somehow be mediated by cytokines.
This is a stimulus-response and top down view of immune organization. Some top down organization is undoubtedly present, and it is particularly associated with the innate immune system and its various special receptors. Nonetheless, we will argue here that there must also be a strong bottom up feedback-based component of organization. The argument has two parts. 1) We will demonstrate that feedbacks can in principle provide for marked improvement in immune system performance. 2) We will provide evidence that components with the required properties are indeed present in the immune system.
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Making Effectors More Effective |
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TopAbstractIntroductionMaking Effectors More EffectiveSelecting Effective EffectorsDiscussionAppendix 1References |
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). We wish to examine the trade off
between the two conflicting roles of N, directly damaging
the host but also playing an essential role in the destruction of
damaging pathogens. Model A could also provide a first schematic
treatment in situations where N is not a noxious chemical
but rather a cell class that is up-regulated by effectors E
and that plays roles both in pathogen destruction and host damage. For
example, E might represent macrophages and N
inflammatory CD4 T cells (2 , p. 7:44).
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are associated with a positive
feedback, that of the pathogen level on the effector proliferation
rate. There is a certain arbitrariness here in labeling feedbacks, for
perhaps the level of noxious chemical should have been regarded as
providing a feedback on effector destruction. Thus, even this very
simple example gives a good opportunity to pin down a working
definition of "feedback." We suggest the following, where newly
defined terms are italicized.
A system is composed of interacting components. Components have
basic actions, which describe the essence of the
components’ role in the system. In the system of Fig. 1, for example,
the components are effector cells, pathogens, and noxious chemical. Two
basic actions of all components are proliferation and death (or finite
half life). A basic action of the effectors and of the noxious chemical
is killing pathogens. We define as feedback any influence
that flows from the state of the system to modify basic actions of
system components. Thus relatively high levels of the pathogen
population "feed back" to increase the rate of effector
proliferation.
As a way to model the effects of evolution, we shall examine the
consequences of the assumption that the immune system minimizes the
overall host damage, i.e., damage due directly to pathogens and damage
due indirectly to the immune system itself, as a concomitant of its
action to suppress pathogens. We suppose that individual pathogens and
unit concentrations of noxious chemical cause damage at fixed rates
hP and hN, respectively.
During the course of an immune response, damage rates will vary with
the fluctuating levels of pathogen P and noxious chemical
N. We thus perform an average to obtain a measure of immune
performance 
:
 | (1) |
Let us first ask, how does the secretion rate s of
noxious chemical effect the performance of our simple model immune
system? To answer this question, we fixed all parameters except
s and numerically calculated solutions to the equations of
our model (see Appendix) for several values of s.
The insert to Fig. 2 shows a typical
finding. With all other factors fixed, there is an optimum secretion
rate s that minimizes the average damage . However, the
main graph in Fig. 2 shows that the value of the optimum depends on the
pathogen virulence, as embodied in the pathogen replication rate
r. Upon reflection, such a result was to have been
anticipated. The greater the pathogen threat, the more the host should
be willing to tolerate some self damage in order to destroy pathogens
more rapidly. (An analogous result was demonstrated in Ref. 1,
according to which the optimal strategy for timing the B cell shift to
Ab secretors is different for low and high Ag doses.)
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Efficient immune performance can be obtained if suitable performance measures are monitored and the results used to modify the nature of the immune response. To illustrate this point, we expand model A into model B. In doing so, we consider two possible performance measures. The first of these is a "kill indicator" chemical K that is produced at a rate proportional to the rate NPE at which pathogens are destroyed by the immune system. K has a characteristic half-life. A second performance measure is a "harm indicator" chemical H that monitors the rate of damage (hPP + hNN) done to the host both by the pathogens and by the immune system. Like K, H has finite half-life.
In writing the pathogen kill rate term as proportional to NPE, we reason as follows. It is reasonable and conventional to assume a mass action form PE for the encounter rate between pathogen P and effector E. We then assume that encounters result in pathogen killing with a probability that is proportional to the average concentration of the noxious chemical N. Implicit here is the assumption that the presence of N is essential for killing. In reality, of course, it is the local concentration of N that determines the outcome of a given encounter, but the qualitative results obtained here will not be significantly affected by alterations in details of our simple models.
We now show how monitoring by the immune system of the concentrations
of K and H can lead it to the identification of
the "harmful pathogen killing" that is required for goal I in Table I. The first step is to distinguish the harm HP
done by pathogens from the harm HI done by the
immune system. One way to do this is to estimate
HP by
 | (2) |
, if N is small then
HP is approximately equal to H,
reflecting the fact that in the absence of noxious chemical all the
harm H must be due to pathogen. On the other hand, if
N is large then HP is small according
to Equation 2, and indeed in the presence of large concentrations of
noxious chemical the observed harm will largely be due to the immune
system itself. Given HP, the extent to which
dangerous pathogens are killed, deemed "good" in goal I, can be
measured by HPK. HPK is large if and
only if many pathogens are being killed (K is large), and
they are dangerous (HP is large).
We have discussed a way for the immune system to determine the level of
harmful pathogen killing required for goal I. The corresponding
information required for goal II, the level of self harm, can be
determined by measuring HI. If the harm is not
done by the pathogens, then presumably it is done by the immune system:
H = HP + HI. We thus
suggest that the harm done by the immune system,
HI, be represented as follows:
 | (3) |
Only if it is utilized properly can even the most accurate
information on the state of a system be used to improve system
performance. To illustrate how performance modification might be
engendered by information concerning goals I and II, we suggest that it
would be to the advantage of our model immune system if the constant
secretion rate of noxious chemical N, s, is replaced by a
fixed contribution s1 plus an additional "goal
oriented" contribution proportional to s2:
 | (4) |
, all the si are constants,
i = 1, 2, 3, 4.
The conflicting goals I and II are incorporated into the second "goal
oriented" term of Equation 4. On the one hand, this term is a
decreasing function of HI, so that harm to self
owing to immune action depresses the intensity of immune response (goal
II). On the other hand, the goal oriented term is an increasing
Michaelean function of KHP, so that the
intensity of response is saturatively increased by evidence that
dangerous pathogens are being killed (goal I) (see Fig. 3).
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, on measures
HP and HI (given in
Equations 2, and 3) of damage respectively due to pathogens and the
immune system. These measures depend on monitoring the chemicals
H and K, which have been discussed above. Fig. 4 depicts the additional feedbacks now
present in the model. (See the Appendix for a detailed
mathematical description.)
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, the system of model B can compensate for the fact that in the
preprogrammed "rigid" model A the optimum secretion rate
s is different for different pathogen growth rates
r. More precisely, one expects that for a range of
r (say 0.1 < r < 5 as in Fig. 2)
there will be better performance (lower ) for a well-chosen adaptive
s than for a situation in which s is fixed at a
value that is optimal only for some fixed r. These
expectations are not only met but exceeded. Even against the attack by
a single type of pathogen only, with fixed r, the adaptive
system performs significantly better. When r = 0.1 for
example, = 36 in model B compared to = 80 in model A
when s is held at its optimal fixed value. In model B, the
secretion rate of noxious chemical is temporarily elevated to eliminate
the pathogen, and the damaging secretion quickly subsides after the
pathogen ceases to be a threat (Fig. 5).
(Note that the eventual disappearance of noxious chemical N
is guaranteed for fixed s, because the effectors
E that secrete N disappear when pathogens are
eliminated.)
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Selecting Effective Effectors |
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TopAbstractIntroductionMaking Effectors More EffectiveSelecting Effective EffectorsDiscussionAppendix 1References |
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One might think that each isotype is selected by a particular cytokine,
say IgE by IL-4, IgA by IL-5, IgG2a by IFN-
, IgG2b by TGF-
. (The
respective cytokines listed favor choice of the corresponding isotopes
(2, 8, 9).) However, two considerations render this
assumption implausible. 1) Many observations demonstrate that in
general, more than one cytokine affects a given isotype and more than
one isotype is affected by a given cytokine (e.g., IL-4 promotes IgG1
as well as IgA; IFN- inhibits IgM and IgG1 and induces IgG3 and
IgG2a). 2) If every isotype is selected by one and only one specific
"messenger boy" cytokine, then the problem of isotype selection
remains unsolved; that is, it is merely shifted to a problem of
cytokine selection.
We believe that cytokines and other chemicals are indeed not mere conduits for relaying decisions already made, but rather that they convey information on the state of the system. Model B illustrates how typically it is a combination of chemical levels that is needed to convey information. For example, if the levels of the harm chemical H and the kill chemical K are both high and also if the level of noxious chemical is low, then it can be concluded that "dangerous pathogens are being killed."
Given that the cytokines convey information, the question arises as to how this information is employed "appropriately" to modify immune response. Here are several principles that we believe apply. 1) The various possible pieces of information are "interpreted" by cells of the immune system in the sense that the cells modulate their spectrum of activities in response to this information. 2) Different cell types, with different functions, interpret the same information differently. 3) The interpretation of the same information by a given cell may vary in time and space because the significance of a given piece of information changes in accord with the shifting background of other pieces of information.
In considering these principles we confine ourselves here to an illustration of point 3. We show how exactly the same information at different points in space can act to help select more effective effectors. As a possible concrete manifestation of what we have in mind, consider a lymph node with a pair of spatially separated clusters of B cells (selected perhaps from oligoclonal foci (3)), each cluster secreting an Ab of the same specificity but one cluster producing IgG1 and the other IgA. Suppose that invading bacteria are highly susceptible to elimination via opsonization, so that IgG1 will be the more effective Ab. How might the IgG1 producers be preferentially amplified compared to the IgA producers?
To investigate this question, we employ model C (See Fig. 6). Considered in this model are two
effector types, A and G, secretors respectively
of IgA and IgG1, each of which can in principle lead to the destruction
of a pathogen P. Information is incorporated in the kill
indicator chemical K, which is produced by cells
m (of fixed concentration in this model) at a rate
proportional to the rate of pathogen destruction. The contribution of
G (the IgG1 secretor) to pathogen destruction is assumed to
be much greater than that of A; i.e., G is the
"more effective effector." In this model, spatial effects are
represented in the simplest possible way, by assuming that cells and
chemicals occupy a pair of intercommunicating compartments, in each of
which the concentration is uniform but between which concentrations
generally differ. Cells and chemicals switch compartments randomly;
i.e., there is diffusion between compartments.
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How can we quantitate the extent to which the more effective cell type
is selected? A simple approach is to calculate a figure of merit
M that is simply the average over time of the difference
between the total G population level in both compartments
(G1 + G2) and the corresponding
A population level (A1 +
A2). But if a certain dose of K, say,
merely doubles the average population levels of both G and
A, then M will be doubled. In such circumstances,
one would hesitate to say that higher concentrations of K
more strongly induce selection of the more appropriate effector. It is
thus sensible to "control for cell numbers," i.e. to define a
figure of merit M that measures the differences in
G and A population relative to their average
population size:
=
 | (5) |
The solid curve in Fig. 7 shows a
marked dependence of M on a key parameter,
n, the half saturation coefficient in the expression for the
variation of the effector reproduction rate (for both G and
A) as a function of the concentration of the kill indicator
chemical K. It is seen that there is an optimal value for
n, for which M is maximized. The reason for
the optimum can readily be discerned. When n is small,
typical values of K saturate the effector reproduction rate,
so that the information incorporated in K barely influences
G and A. When n is large, both
G and A proliferate slowly (at a rate
proportional to K/n). Under such circumstances, diffusive
exchanges are the dominant mechanism for altering population levels.
Here too there is little effect of the information contained in
spatially varying K production, for diffusion tends to
efface significant differences in the concentrations of the
information-bearing chemicals.
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, which shows a low value of the figure of merit
M of Equation 5, when dK has
the value dK = 20 days-1
estimated from the time it would take a small molecule in water to
diffuse a distance of the order of magnitude of the size of a human
lymph node. Only when the diffusivity is 10 times slower, is there a
significant value of M and hence a significant
enhancement of the more appropriate effector. Because free diffusion of K tends to impair its usefulness as a signal chemical, it could be that diffusivity of the K molecule is markedly slowed by binding to some buffer. An alternative possibility, which we now consider, is that chemotaxis plays a prominent role in the process. To this end, let us now assume that the kill indicator chemical K acts as a chemoattractant for the cells mi that secrete K in compartment i. We have seen how secretion of K provides positive feedback that increases the effectiveness of the immune response in the spatial locations where that response is relatively "successful" (compartment 1). Chemotaxis will guide K secretors from compartment 2 to compartment 1, thereby decreasing K secretion in compartment 2 as well as increasing it in compartment 1.
To illustrate these considerations, we construct model D by modifying
the equation for K so that secretion in a given compartment
is proportional to the number of K secretors in that
compartment, m1 or m2.
(We denote these cells by mi because it is
likely that they are macrophages.) In addition, we add an equation for
m1 that takes into account both chance migration
and chemotaxis. This equation is a discrete version of the standard
chemotaxis equation (4). m2 is
determined by the simplifying assumption that total macrophage numbers,
m1 + m2, can be regarded as
constant (see Appendix) and Fig. 6B).
We cite just one salient result from model D, which shows how
chemotaxis can significantly reinforce the selection of the more
effective cell type A. When the diffusion coefficient has the "too
large" value dk = 20 day-1
of Fig. 7, addition of chemotaxis increases the figure of merit
M from 0.03 to 0.16. (See Appendix for
parameter values in this simulation.) This occurs because the
chemotactic migration from compartment 2 to compartment 1 provides both
additional positive feedback to the successful effectors G
in compartment 1 and also negative feedback to the unsuccessful
effectors A in compartment 2.
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Discussion |
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TopAbstractIntroductionMaking Effectors More EffectiveSelecting Effective EffectorsDiscussionAppendix 1References |
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A major hypothesis is the assumption that the initial response is comprised of a variety of effectors (9), not a single preselected "best" effector. Recent support for this hypothesis is exemplified by findings in humans that an array of cytokines are secreted in response to bacterial invasion by colon epithelial cells (10) and hepatocytes (11). As to Ab isotypes, the subject of our model for effector choice, it was found in Ref. 12 that after a week LPS stimulation of splenic B cells leads to detectable amounts of IgA, the four IgG1 isotypes, and IgM. The levels of IgM were two orders of magnitude higher than the levels of IgG1, IgG2b, and IgG3, and three orders of magnitude higher than levels of IgA and IgG2a. IgE was undetectable. By contrast, when B cells were cultured with a Th2 clone, then as much as 2% of the response was IgE. IgM still dominated the response, but IgG1 levels also were very large. The other isotypes were present in the range of 0.1–1%.
These results concerning isotypes illustrate the principle that, although the initial response is broad, it is not random but rather is biased in certain directions. One would indeed expect that different effector responses would be favored in different areas of the body and in reply to different "danger" receptors. This reflects evolutionary experience that under certain predetermined conditions "the chances are" that invading pathogens should be combatted in a certain way.
But "chances" are not certainty. Unusual pathogens will arise for which standard responses are not appropriate. Here is where the broad spectrum response comes in. Because a variety of possible responses are present, each can be tested "in the field." By monitoring progress towards its "goals," the immune system can provide feedbacks to select those effectors that more appropriately deal with a given pathogen attack.
Our simple models have illustrated the role of feedback as provided by two principal information-bearing chemicals, the damage indicator H and the kill indicator K. Although our models treated only one chemical of each type, we expect that in reality there would be a family of H’s and a family of K’s. Moreover, for simplicity, in our models H and K directly modulated functional aspects of the immune response; in reality, the modulation is expected to occur indirectly, e.g., through the agency of cytokines.
We emphasize the difference between a "kill" indicator and a "danger" indicator. The latter is exemplified by the LPS receptor on macrophages. Indeed, danger lurks if this common bacterial molecule is found to be abundant. But a kill indicator for bacteria must indicate not that bacteria are present but that they are being destroyed. A bacterial danger indicator will be an essential exterior molecule characteristic of bacteria. By contrast, a kill indicator will be an intracellular molecule that plays a key role in bacterial function but not in host function. When and only when bacteria are killed is there an opportunity for these characteristic intracellular molecules to influence the ongoing immune response.
One set of candidates for bacterial kill indicators are the N-formyl peptides that are common in lysates of bacteria but not of eukaryotic cells. These peptides certainly promote inflammation, for they are potent chemoattractants for leukocytes (13). Another set of intracellular bacterial molecules that serve as powerful immune mediators are the palindromic DNA sequences that act as adjuvants in DNA vaccination (14, 15, 16). Lipoarabinomannan and/or capsular polysaccharides of Gram-negative bacteria constitute additional possibilities, for they ligate the CD1 receptor and have a role in Ag presentation even though they are normally buried in the bacterial wall (17).
We have listed some "candidates" for the kill indicator chemical K whose existence we postulated on theoretical grounds. What of the harm indicator chemical? We expect that it will be a subtle matter to search for a harm indicator H because our models lead us to expect that H will either up- or down-regulate the immune response depending on whether the harm is produced by pathogens or by the host’s immune response. Just as a kill indicator K is expected to be an intracellular molecule peculiar to pathogens, so H should be an intracellular molecule peculiar to the host. A suitable fragment of human DNA would fill the bill. Lider et al. (18) report that when inflammatory cells employ heparanase to cleave the extracellular matrix, the cleavage produces a trisulfated disaccharide fragment that down-regulates inflammation; this fragment appears to act as a harm indicator. Given the strong immunogenic nature of heat shock protein (hsp) (19), a characteristic fragment of human hsp would seem to be another prime candidate for a harm indicator molecule. By contrast, a fragment found only in bacterial hsp would make an excellent kill indicator molecule K. The complexity that might be involved with the action of hsp is consonant with findings that hsp autoimmunity can both amplify and restrain inflammation in normal individuals and can also cause disease (20).
There is recent evidence that fragments of dsRNA or dsDNA, whether viral or the result of tissue injury, can up-regulate the immune response in a sequence-independent fashion (21). These fragments seem candidates for both H and K molecules.
Adoption of the point of view advocated here brings a different perspective to certain matters. Consider, for example, the macrophage. Although this cell has manifold activities and secretes many different cytokines, it seems often to be regarded as a "Rambo" doer and follower and not a leader. But feedback operates on the principle that the proof of the pudding is in the eating, and the macrophage does lots of eating (actually and metaphorically). When it ingests cellular debris, a macrophage "knows" that damage has been done to tissue. When it destroys an opsonized Escherichia coli, a macrophage is "aware" that the opsonization has led to destruction of an extracellular pathogen. Macrophages must become activated before they can destroy intracellular pathogens, and here too macrophages are "cognizant" of the state of affairs. Even if the primary destruction is carried out by cytotoxic T cells, the macrophage "knows," for it ingests apoptotic bodies via special receptors (22). Macrophages are aware of their inanimate surroundings too; for example, their adhesion receptors communicate information concerning the state of the extracellular matrix.
There is compelling evidence for the "knowledge" that we attribute to the macrophage, for the various "known" events all characteristically modify macrophage physiology. It could be that these modifications are without influence, but this seems unlikely on a priori grounds and not in accord with considerable evidence. We suggest that macrophages communicate to other cells much of their knowledge concerning the state of the organism and its pathogens, and that this disseminated knowledge serves as a basis for feedbacks for improving immune performance. Communication is expected to be via cytokine secretion, with the various varieties of knowledge inducing the secretion of various combinations of cytokines. In particular, engagement of different macrophage receptors should induce the secretion of different cytokine combinations.
The LPS receptor has usually been used to induce macrophage cytokine
secretion because of the abundant response engendered. Only recently
does it appear that systematic investigations are beginning to be made
of the modulation of cytokine secretion by other macrophage receptors.
Thus IL-12 secretion induced by LPS is inhibited by binding to the
Fc, complement, or scavenger receptors of macrophages (23, 24). Ligation of Fc receptors also upregulates IL-10, which
inhibits IL-12 production.
We interpret such findings that the ligation of different macrophage receptors produces different cytokine secretion patterns as evidence that the macrophage indeed has a profound influence on shaping an appropriate immune response. This influence is exerted not only by signalling potential danger (by the LPS receptor) and then by working to initiate response, but also by providing information that helps the immune system hone its initial response. Recall that it was combinations of the harm indicator H and the noxious chemical N that allowed estimation of how much tissue damage should be attributed to pathogens and how much to the immune system. Thus our theoretical investigations suggest in particular the importance of examining how macrophages and other key cells respond to combinations of receptor ligations.
We have demonstrated that there are a number of specific chemicals that can serve as the physiological substrate for the feedbacks whose existence we have shown would improve the immune response. These chemicals might be termed "natural adjuvants." A possible practical implication of the point of view advocated here is exploitation of better understanding of natural adjuvants in the design of artificial adjuvants. For example, according to our views, a desired effector response can be amplified provided that a suitably-timed combination of signals conveys the message "dangerous pathogens are being destroyed."
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Appendix 1 |
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TopAbstractIntroductionMaking Effectors More EffectiveSelecting Effective EffectorsDiscussionAppendix 1References |
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 | (A2) |
 | (A3) |
 | (A4) |
): a = 0.02, gN =
hN = hP = 1, gE =
0.1, Emax = 100, µP =
0.1, T = 50. At t = 0: P = 10, N = 0,
E = 1.
Model B
Equations A1–4 and 2–4, together with
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| (A5) |
 | (A6) |
) as in Fig. 2. Also r = 0.1,
s1 = 0.01, s2 = 0.05,
s3 = s4 = 1, gK =
cH = gH = 1, cK = 5,
kP = 1. At t = 0: K = H =
0.
 | (A7) |
 | (A8) |
 | (A9) |
 | (A10) |
): r = 5, a = 10, b = 1,
q = 2.5, n = 150, gA = gG =
0.8. gK = 0.5, cK = 20,
dP = 5, dA = dG =
0.1, m1 = m2 = 1. At
t = 0: P1 = P2 = 10,
G1 = A2 = 1, G2 =
A1 = K1 = K2 =
0.
Model D
Model C, but instead of m1 =
m2 = 1
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| (A11) |
 | (A12) |
= 0.1, mtotal =
2.2, dM = 1. At t = 0:
m1 = m2 = 1.1. Other parameters
as in model C. |
Acknowledgments |
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Footnotes |
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2 Address correspondence and reprint requests to Dr. Lee A. Segel, Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel. E-mail address:
Received for publication February 18, 1999. Accepted for publication May 25, 1999.
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References |
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TopAbstractIntroductionMaking Effectors More EffectiveSelecting Effective EffectorsDiscussionAppendix 1References |
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. Proc. Natl. Acad. Sci. USA 93:2879.
is formed from the extracellular matrix by the enzyme heparanase. Proc. Natl. Acad. Sci. USA 92:5037. type I. J. Exp. Med. 188:217.This article has been cited by other articles:
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  M. Cohn What roles do regulatory T cells play in the control of the adaptive immune response? Int. Immunol., September 1, 2008; 20(9): 1107 - 1118. [Abstract] [Full Text] [PDF]
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 I. R Cohen and D. Harel Explaining a complex living system: dynamics, multi-scaling and emergence J R Soc Interface, April 22, 2007; 4(13): 175 - 182. [Abstract] [Full Text] [PDF]
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 K. D Matson Are there differences in immune function between continental and insular birds? Proc R Soc B, September 22, 2006; 273(1599): 2267 - 2274. [Abstract] [Full Text] [PDF]
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 L. Mendes, T. Piersma, D. Hasselquist, K. D. Matson, and R. E. Ricklefs Variation in the innate and acquired arms of the immune system among five shorebird species J. Exp. Biol., January 15, 2006; 209(2): 284 - 291. [Abstract] [Full Text] [PDF]
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J. A. M. Borghans and R. J. De Boer Memorizing innate instructions requires a sufficiently specific adaptive immune system Int. Immunol., May 1, 2002; 14(5): 525 - 532. [Abstract] [Full Text] [PDF]
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 B. R. Levin and R. Antia Why We Don't Get Sick: The Within-Host Population Dynamics of Bacterial Infections Science, May 11, 2001; 292(5519): 1112 - 1115. [Abstract] [Full Text]
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 J. E. Wigginton and D. Kirschner A Model to Predict Cell-Mediated Immune Regulatory Mechanisms During Human Infection with Mycobacterium tuberculosis J. Immunol., February 1, 2001; 166(3): 1951 - 1967. [Abstract] [Full Text] [PDF]
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 S. D. W. Frost, M.-J. Dumaurier, S. Wain-Hobson, and A. J. L. Brown Genetic drift and within-host metapopulation dynamics of HIV-1 infection PNAS, June 5, 2001; 98(12): 6975 - 6980. [Abstract] [Full Text] [PDF]
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