TNF-
neutralization in cytokine-driven diseases: a mathematical model to account for therapeutic success in rheumatoid arthritis but therapeutic failure in systemic inflammatory response syndrome
M. Jit,
B. Henderson1,
M. Stevens2 and
R. M. Seymour
Department of Mathematics and 1 Cellular Microbiology Research Group, Eastman Dental Institute, University College London, London and 2 European Bioinformatics Institute, Wellcome Trust Genome Campus, Hinxton, Cambridge, UK.
Correspondence to: R. M. Seymour, Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK.
E-mail: rms{at}math.ucl.ac.uk
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Abstract
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Objectives. Neutralization of TNF-
with either monoclonal antibodies or soluble receptors, although not curative, has significant clinical benefit in patients with rheumatoid arthritis (RA). In contrast, blockade of TNF-
has little clinical benefit in the majority of patients with systemic inflammatory response syndrome (SIRS) in spite of the identification of TNF-
as a key factor in its pathology. It is not clear why there is such a significant difference in the responses to TNF-
neutralization in these two conditions. Here we use mathematical modelling to investigate this discrepancy.
Methods. Using the known pharmacokinetic and pharmacodynamic properties of TNF-
-blocking biological agents, we constructed a mathematical model of the biological actions of soluble (s)TNFR2, Etanercept and Infliximab.
Results. Our model predicts that all three inhibitors, but especially Etanercept, are effective at controlling TNF-
levels in RA, which we propose is a condition in which TNF-
production and inhibition are in equilibrium. However, when free TNF-
drops to a low level, as can occur in SIRS, which we propose is a non-equilibrium condition, the sequestered TNF-
can act as a slow-release reservoir, thereby sabotaging its effectiveness.
Conclusions. These results may explain the effectiveness of TNF-
blockade in the equilibrium condition RA and the ineffectiveness in the non-equilibrium condition SIRS.
KEY WORDS: Rheumatoid arthritis, SIRS, TNF-
, Enbrel, Remicade, Cytokine networks, Mathematical modelling
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Introduction
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Tumour necrosis factor
(TNF-
) is a key early response cytokine involved in many aspects of innate and acquired immunity [1]. Overproduction of this cytokine is associated with tissue and organismal pathology in conditions such as rheumatoid arthritis (RA) [2] and systemic inflammatory response syndrome (SIRS) [3], a collective term for an uncontrolled inflammatory response to a variety of insults, which can lead to shock, organ dysfunction and ultimately death. By the late 1980s/early 1990s, blockade of TNF-
, using a variety of reagents, was shown to be effective in inhibiting experimental SIRS, such as endotoxin shock [3]. However, a number of clinical trials with TNF-
-blocking reagents in patients with SIRS have failed to demonstrate significant clinical effect [4]. This finding contrasts with the current clinical picture with TNF-
-blocking reagents in RA, for which Infliximab (Remicade®) and Etanercept (Enbrel®) are licensed treatments in the USA and Europe [5, 6].
It is unclear why the blockade of TNF-
should have limited clinical efficacy in one condition driven by this cytokine, yet in another provide significant clinical benefit. It is becoming increasingly clear that cytokine synthesis and the networks of interactions that early response cytokines such as TNF-
can induce are highly dynamic events whose explication requires the use of mathematical models [7]. One explanation for the differences in the efficacy of TNF-
blocking biologicals in these two diseases may relate to the dynamics of the interaction of TNF-
with neutralizing agents. In this report we have utilized the published kinetic parameters for Etanercept, Infliximab and soluble (s)TNFR2 in order to develop a mathematical model of the disease-modulating activity of these reagents in human disease.
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Materials and methods
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The model developed here is based upon earlier work on a two-dimensional model of single cytokine dynamics [7, 8]. The model represents TNF-
dynamics in the receptor compartment, which we define as the inflamed synovial joint within which locally produced TNF-
can bind to cell-surface receptors. We assume that free TNF-
(with receptor compartment concentration L) can bind to cell-surface receptors (TNFR1, of total density Rtot) to form receptorligand complexes (with bound proportion r and unbound proportion 1 r), or to antibodies (with receptor compartment concentration A) to form antibodyantigen complexes (with receptor compartment concentration C). The two reactions are assumed to obey mass-action kinetics with association rates k1 and ka, and dissociation rates k1 and ka. Internalization of bound receptors occurs at rate
. The total receptor density, Rtot, is assumed to remain constant due to compensating receptor cycling and synthesis (see reference 8 for a discussion of this point). Clearance processes from the receptor compartment are assumed to be first-order with rates
1 (for free TNF-
),
a (for free antibody) and
c (for antibodyantigen complexes). Combining these processes gives the following set of four coupled ordinary differential equations:
 | (1) |
The constant
1 represents the rate of production of TNF-
arising from some sustaining external stimulus that maintains the inflammatory response. The constant
a represents the rate at which antibodies are introduced into the receptor compartment. Finally, the constant
measures the strength of a possible stimulated autocrine response, which up-regulates TNF-
production in response to the density of bound receptors. Since such a response is unquantified, we have assumed a linear form for the sake of simplicity. In particular, if
= 0 there is no such response.
The model's output is based upon a range of estimates of the key parameters defining the network interactions between TNF-
and the specific ligand-binding inhibitor (Tables 1 and 2). Numerical integration of the equations was performed using the NDSolve routine in Mathematica 4.0 (Wolfram Software).
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Results
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Equilibrium
We assume that the normal state of the system is zero TNF-
production, and that pathology arises from non-zero production maintained by the exogenous production rate
1. In the absence of this production (
1 = 0) and the absence of antibody treatment (
a = 0), the zero state, in which all variables in equations (1) have zero value, is an equilibrium. Furthermore, it can be shown analytically that this state is stable, provided the autocrine response
is not too large; specifically, provided
<
+
1K1, where K1 = (k1 +
)/Rtotk1. Using the parameters identified in Table 1,
has order 104 s1, whereas
1K1 has order 106 s1, so that in effect the zero equilibrium is stable provided
.
On the other hand, if
is large, specifically
>
+
1K1, then the zero equilibrium becomes unstable and there is a non-zero stable equilibrium in which TNF-
production is maintained purely by autocrine action. In what follows, we shall ignore this latter possibility on the grounds that any increase in TNF-
production from the zero state, as occurs in SIRS, could not subsequently return to the zero state, but would inevitably lead to a stable state of chronic TNF-
production. It is because we wish to allow for the possibility of natural recovery from SIRS that we ignore this scenario.
Given that the zero state is a stable equilibrium in the absence of exogenous stimulation, it can be shown analytically that, with non-zero stimulation (
1>0,
a
0), there is unique, non-zero stable equilibrium with the following properties: (i) the equilibrium TNF-
level is an increasing function of both
1 and
; and (ii) the equilibrium TNF-
level is a decreasing function of
a. In other words, increasing the rate of delivery of TNF-
inhibitors always acts to decrease the equilibrium level of TNF-
.
In what follows we first consider the kinetics of TNF-
production in the absence of an autocrine response (
= 0), and then assess the effects of such a response.
Etanercept, Infliximab and sTNFR2 all reduce bioactive TNF-
The model predicts that all three inhibitors reduce the concentration of bioactive TNF-
(i.e. free TNF-
not bound to either inhibitor or cell-surface receptor) to a new, lower equilibrium level. Applying the parameters identified in Tables 1 and 2 to the model, the effect of various concentrations of sTNFR2, Etanercept and Infliximab on the equilibrium concentration of bioactive TNF-
in the receptor compartment is shown in Fig. 1a, c and e. Etanercept has the most dramatic effect, and in the case of the highest rate of production modelled (i.e. delivery at 10 times the rate of background TNF-
production), the TNF-
level was reduced to 98% of its original value. In comparison, Infliximab, at the same level of delivery, achieved only a 29% reduction in bioactive TNF-
and sTFNR2 only a 16% reduction. The proportion of receptors filled by ligand, r, showed similar dynamics to the concentration of free ligand, L (results not shown), indicating that L is a good indicator of the bioactivity of TNF-
. Note that in all three cases equilibrium is reached within 4 h. (Infliximab, with its low association rate constant, takes the longest to reach the new equilibrium.) However, this does not imply that this antibody takes full effect within 4 h of administration. Drug distribution throughout the circulation and ultimately to the synovial joint, which is not modelled here, is a process that takes place on a longer time scale [9]. However, once the drug reaches the synovial joint the simulation shows that it acts on TNF-
to produce a new equilibrium very quickly.

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FIG. 1. The change over 4 h in the receptor compartment concentrations of free (bioactive) TNF- (graphs a, c, e) and free plus inhibitor-bound TNF- (graphs b, d, f) for each inhibitor type, and for three rates of input of inhibitor into the receptor compartment, as predicted by the model (1): no inhibitor ( a = 0; solid curves), the rate of inhibitor supply equals the equilibrium rate of TNF- production ( a = 1eq; long-dashed curves), and the rate of inhibitor supply equals 10 times the equilibrium rate of TNF- production ( a = 10 1eq; short-dashed curves). The background rate of production of TNF- is 1 = 1eq, where 1eq is the inhibitor-free equilibrium rate of TNF- production, chosen so that the equilibrium concentration of free TNF- in the absence of inhibitor is 6 x 1012 M (Table 1). The initial state at time zero is the inhibitor-free equilibrium of the system (1).
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Total TNF-
concentrations are increased by all three TNF-binding proteins
Since TNF-
sequestered by the various proteinaceous inhibitors is not permanently cleared from the system but can be released in some circumstances, we investigated the effect of these inhibitors on the total (free and bound-to-inhibitor) concentration of TNF-
. The model predicts the effects of various rates of delivery of sTNFR2, Etanercept and Infliximab on the concentration of total TNF-
in the receptor compartment (Fig. 1b, d, f). All three inhibitors have a dramatic effect on the total concentration of TNF-
, causing it to rise several times above its equilibrium value. After 4 h, the total concentration of TNF-
was between 3 (sTNFR2) and 20 (Etanercept) times its background equilibrium value when the TNF-
inhibitor was delivered at a rate 10 times that of TNF-
. However, most of the TNF-
was inhibitor-bound and not bioactive.
The effect of inhibitor clearance rate on TNF-
levels
To investigate what effect different values of the rates of decay of the TNF-
inhibitors have on the system's dynamics, the model was simulated using two extremes of the range of possible values for inhibitor clearance, namely
a = 0 and
a =
c. Reducing the rate of inhibitor clearance to zero had little discernible effect on the qualitative features of the time course (results are almost identical to those shown in Fig. 1; not shown). There was a minor effect on the endpoints of the time course of TNF-
concentration (Table 3), and the value of L was reduced by between 4% (sTNFR2) and 14% (Etanercept).
TNF-
inhibitors act as slow-release reservoirs if endogenous TNF-
production drops below a threshold level
Aderka et al. [10] reported that certain concentrations of soluble TNF-
receptors actually prolong TNF-
bioactivity by reducing its rate of clearance and acting as a slow-release ligand reservoir. The same effect has been observed for certain concentrations of Etanercept [11] and Infliximab [12]. This does not occur in our equilibrium model; although the inhibitor increases total TNF-
concentrations, the level of free TNF-
is always reduced (Fig. 1). However, this equilibrium situation differs from that described by Aderka et al. [10], who added a fixed concentration of TNF-
to serum at the start of the experiment and then measured its bioactivity thereafter. In contrast, we assumed constant endogenous production of TNF-
rather than a one-off exogenous rise.
To model the experimental setup used by Aderka et al. [10], we set
1 = 0 to investigate whether or not TNF-
inhibitors would be able to increase the long-term concentration of bioactive ligand. The initial concentration of free TNF-
was retained at 6.0 x 1012 M. The time course of TNF-
concentration (both free and free plus inhibitor-bound) is shown in Fig. 2. All three inhibitors are seen to act as slow-release reservoirs. They decrease free TNF-
concentrations at first, but once TNF-
levels have been reduced by clearance they release the TNF-
they have sequestered. This is consistent with results of Aderka et al. [10] and Ramanathan [13], who found that sTNFR2 always reduced bioactive TNF-
concentrations initially but showed mixed effects after prolonged exposure. The inhibitor always increased the total concentration of non-receptor-bound TNF-
(free and bound to inhibitor) compared with no inhibitor. In the case of Etanercept (which has the highest association rate and an intermediate clearance rate), the total concentration of non-receptor-bound TNF-
actually increased from its initial level. This is because, when free TNF-
decreases to a low level, Etanercept is able to compete with the pool of free cell-surface receptors to bind the available TNF-
, an effect predicted by Mohler et al. [11].
Figure 3 shows the predicted effect on production of TNF-
after 4 h in response to variation in the initial production rates of TNF-
and its inhibitor (
1 and
a). All inhibitors absorb free TNF-
increasingly effectively over an increasing range of production rates
=
1/
1eq, with the exception of Etanercept, which has its maximum effectiveness at low rates of production, effectiveness declining for higher rates. However, the effectiveness of Etanercept declines significantly only at very high TNF-
production rates.
Effect of autocrine response
Increasing the autocrine response parameter,
, from zero increases the equilibrium level of bioactive TNF-
for any
1<0 and any given rate of inhibitor input
a. Thus, an autocrine response is antagonistic to effective TNF-
blockade.
In the non-equilibrium situation, illustrated in Fig. 2, there is an early decrease in bioactive TNF-
levels in the presence of inhibitor relative to the no-inhibitor situation, but later there is a relative increase. The times of crossover from relative decrease to relative increase are approximately 1 h (sTNFR), 2.5 h (Infliximab) and 3 h (Etanercept). As
increases from zero, the qualitative picture shown in Fig. 2 remains unchanged, but with increasing time to crossover. However, the crossover still occurs in less than 24 h except for very large autocrine responses (
greater than
0.9
), beyond which the crossover time increases very rapidly with
. This is illustrated in Fig. 4.
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Discussion
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Blocking TNF-
with biological reagents such as monoclonal antibodies or soluble forms of TNF-
receptor is clearly effective for some diseases such as RA [6] and inflammatory bowel disease [14], but appears not to be effective for treating others, such as SIRS [15]. To understand this phenomenon, we have constructed a mathematical model of the action of TNF-
inhibitors that sequester TNF-
and prevent it from binding to its cell-surface receptor. The model was used specifically to predict the effect of three anti-TNF-
agents, sTNFR2, Etanercept and Infliximab, which have been used as therapy for RA.
The model developed in this report contains a number of simplifying assumptions.
- Repeated exposure to antibodies or other agents can cause the body to produce its own neutralizing antibodies and therefore decrease therapeutic potential over time. In the case of infusions of chimeric antibodies, this reaction is called the human anti-chimeric antibody (HACA) response. The HACA response has been observed following repeated Infliximab treatment. However, when Infliximab is combined with methotrexate, the incidence of the HACA response is reduced to levels that are extremely low, and in many cases undetectable [16, 17]. Since Infliximab must be prescribed together with methotrexate in the UK [18] and the USA [19], the HACA response is not likely to be significant and is not modelled. For Etanercept, an antibody response was only detected sporadically in a small number of patients, and has not been correlated with a specific clinical response [20].
- The rate of inhibitor delivery,
a, is dependent on the difference in inhibitor concentration between the serum and the receptor compartment. This in turn depends on the pharmacokinetics of the drug from the point it is delivered to the body. More precisely,
a should be modelled realistically as a function of time and/or inhibitor concentration. However, it was chosen not to fully model the pharmacokinetics of the inhibitor in the various compartments of the body. Instead, the model focuses on the dynamic interactions between receptor, ligand and inhibitor over relatively short time periods. We have assumed, therefore, that drug delivery is in steady state, and hence that
a is a zero-order rate constant.
- A further complication is that monocytes themselves can shed TNFR2 in response to ligand binding [21], which can contribute to the level of inhibitor. However, as discussed below, the concentration of natural sTNFR2 in synovial fluid is two orders of magnitude lower than that of the exogenously administered anti-TNF-
reagent, so this should have a negligible effect. The inadequacy of naturally produced sTNFR2 to bind TNF-
in the rheumatoid synovial joint supports the thesis of Feldmann et al., that RA represents a state of imbalance between pro- and anti-inflammatory cytokines, with the balance heavily shifted towards the proinflammatory side [22].
Our results show that the use of TNF-
inhibitors causes the accumulation of a large pool of non-bioactive TNF-
bound to inhibitor. This pool is only slowly cleared from the receptor compartment. However, in the presence of a continuous, exogenous supply of TNF-
, the inhibitor-bound TNF-
remains sequestered until clearance and is not available for cell-receptor binding. This is due to the low dissociation rate between ligand and inhibitor. Hence, these drugs do not appear to act as a slow-release reservoir that can increase the bioactive concentration of TNF-
over time (Fig. 1). Our results concur with studies by Brennan et al. [23], who found that approximately half the TNF-
found in the RA synovial joint is not bioactive due to sequestering by naturally produced sTNFR2. This is despite the fact that sTNFR2 is generated in extremely low levels compared with the level of drug during a normal dosing regimen of Infliximab or Etanercept.
One surprising result of the model is that Infliximab poorly inhibited TNF-
levels, largely due to its lower affinity for TNF-
compared with Etanercept (Fig. 1). This conflicts with the excellent results Infliximab has shown when used in clinical trials. One explanation for this discrepancy could be that TNF-
levels in the rheumatoid joint exhibit large interpatient variations [24, 25]. This may be related to the stage of the disease or may be caused by genetic variations within patients, as even healthy individuals show large variations in TNF-
production [26]. Infliximab may be more efficacious for patients with low to moderate levels of TNF-
. Evidence for this comes from the reported responses to anti-TNF-
drugs, which also show considerable heterogeneity. In multicentre trials with Infliximab [27], about half of the patients failed to respond according to the American College of Rheumatology criterion for 20% or better improvement. On the other hand, about a third showed an excellent response according to the more stringent criterion of 50% or better improvement.
Another possibility is that Infliximab may be able to inhibit TNF-
activity in other ways besides preventing cellreceptor binding. For example, Infliximab is able to bind strongly to transmembrane TNF-
, a mechanism that results in the destruction of the TNF-
-producing cell and thus ultimately a decrease in inflammation [28, 29]. The results of our mathematical simulation suggest that this effect may be responsible for a greater proportion of the therapeutic efficacy of Infliximab than previously suspected. Although Etanercept is also able to bind to transmembrane TNF-
, the resulting complex is much less stable. As a result, Scallon et al. [30] found that, at saturating concentrations, Infliximab bound four times as much transmembrane TNF-
as Etanercept.
The challenge now is to develop DMARDs that can permanently restore non-pathological equilibrium to the cytokine network in the synovium. Our model suggests why Infliximab and Etanercept cannot bring about a lasting effect when therapy is terminated. Following TNF-
suppression, there are three possible outcomes depending on the mechanism driving TNF-
production in the synovial joint.
- If TNF-
is being driven by an exogenous source of stimulation, such as factors secreted by T lymphocytes or fibroblasts, then anti-TNF-
inhibitors can only reduce the equilibrium level of TNF-
if they are continuously delivered to the receptor compartment. However, if treatment is ever terminated, the TNF-
concentration will return to its original level.
- A second possibility is that TNF-
inhibitors can actually affect the rate at which TNF-
is being produced (autocrine response). This may happen if TNF-
induces its own production. For example, Ulfgren et al. [31] found that Infliximab therapy reduces TNF-
synthesis in the synovium of RA patients. In this auto-induction scenario, the production rate of TNF-
is an increasing function of bound cell-receptor density, r. Even so, our simulations predict that anti-TNF-
drugs are not able to suppress TNF-
permanently when there is a constant background rate of production.
- Inhibition of TNF-
may actually up-regulate cell production of TNF-
. This is because TNF-
causes an increase in levels of TNF-
inhibitors produced by monocytes and macrophages, such as IL-10 [32] and PGE2 [33, 34]. Hence, artificial suppression of TNF-
also results in the suppression of natural TNF-
inhibitors. If this is the case, then there is a natural negative feedback mechanism that will always seek to return TNF-
to its equilibrium level. Of course, the assumption is that there is also a non-pathological equilibrium where TNF-
is produced at a much lower level. In order to reach it, the network would have to leave the zone of attraction of the pathological equilibrium and enter the zone of attraction of the non-pathological equilibrium. However, this pathological zone could be quite large since RA is able to perpetuate itself over a wide range of cytokine concentrations.
Anti-TNF-
therapy has also been attempted for a group of disorders involving excessive inflammatory response: SIRS. A local inflammatory response towards a focus of infection or injury results in the release of a cascade of cytokines and other mediators (such as eicosanoids, adhesion factors and complement components) in order to bring the insult under control. However, if this does not occur rapidly enough, some of these mediators may escape into the circulation and trigger a systemic response [35]. Often this response persists long after the initial trigger itself has cleared. Superficially, the cytokine networks involved in RA and SIRS appear almost identical. TNF-
is well established as a key mediator in SIRS, just as it is in RA [reviewed in 15, 36]. As in RA, a sequential cascade has been suggested, with TNF-
and IL-1 at its apex [37]. In spite of this, anti-TNF-
therapy for SIRS has been clearly unsuccessful. A recent survey of clinical studies using this therapy [15] found that a number of studies reported positive improvements in mortality, but the benefits were relatively minor (none in excess of 4% decrease in mortality). On the other hand, other studies actually reported deleterious effects, including two that showed increases in mortality in excess of 10%. Indeed, no therapy aimed at a single inflammatory mediator in SIRS has been safe and effective [reviewed in 38, 39].
Several reasons have been suggested for the failure of TNF-
inhibitors and anti-inflammatory therapy in general to improve mortality in SIRS. TNF-
plays a role in mobilizing host defence against infection [40], so that suppressing it in cases of infection may block both its harmful and protective effects [41]. It has also been suggested that focused intervention is unable to suppress proinflammatory responses sufficiently because, in fact, there are several mediators of inflammation with overlapping and compensatory functions [37, 42]. Zanetti et al. [43] found that anti-TNF-
antibodies decreased IL-1 and IL-6 levels as well as mortality in lipopolysaccharide (LPS)-challenged mice. However, in mice with Gram-negative bacterial peritonitis, anti-TNF-
antibodies neither decreased proinflammatory cytokine levels nor afforded any protection from lethality. This may provide a better model of sepsis in humans than an intravenous LPS or bacterial challenge because the infection develops in the abdomen and spreads gradually to become a systemic infection. These experimental results suggest that the cytokine cascade in sepsis does not have a sole cytokine (TNF-
) at its apex.
Nevertheless, there may be a more mechanistic reason for the failure of anti-TNF therapy in SIRS, related to the way anti-TNF-
works to sequester TNF-
. This, we suggest, is because SIRS is fundamentally a non-equilibrium condition, in contrast to RA, which, as discussed above, is assumed to be a (pathological) equilibrium condition. Both proinflammatory and anti-inflammatory cytokines are up-regulated during SIRS [44]. Bone [45] has suggested that it may be too simple to characterize sepsis as runaway proinflammatory cytokine production. Instead, he sees two distinct phases in the systemic response to insult. The first is SIRS, involving a proinflammatory cytokine response. However, SIRS triggers an anti-inflammatory response in an attempt by the body to restore a non-pathological equilibrium. This he terms the compensatory anti-inflammatory response syndrome (CARS), which may be inadequate, may overcompensate or may successfully restore homeostasis. A further complication is that SIRS actually involves multiple sites of inflammation, which may be out of phase with each other in terms of the kind of response they are undergoing [35]. This analysis argues for SIRS as a non-equilibrium condition; in fact, as a large, and potentially dangerous, transient perturbation away from the healthy equilibrium, characterized by rapidly varying cytokine levels.
Viewed in this light, the dynamics of TNF-
concentration levels in the presence of an inhibitor in our model could help to explain the mixed results of anti-TNF-
therapy in sepsis. When TNF-
levels decrease during the CARS stage, the inhibitors may actually sabotage the body's own attempt to restore homeostasis (equilibrium). This happens when inhibitor-bound TNF-
is released at the very point that the immune system is attempting to suppress excessive TNF-
levels. In fact, as Fig. 2 shows, even if the immune system succeeds in switching off TNF-
production altogether (
1 = 0), slow release from the reservoir stored by the drug inhibitor can still ensure that TNF-
remains at a potentially dangerously high level. On the other hand, a local, well-measured and timed intervention could moderate both the peaks and troughs of TNF-
levels, preventing both runaway TNF-
production and overcompensation by CARS. This could account for the mixed results during clinical trials of TNF-
inhibitors, with some reports of improvement (albeit small ones) in mortality rates and others reporting an adverse effect.
This underscores the fact that SIRS involves interactions between several cytokines, both pro- and anti-inflammatory [46, 47]. It is not well characterized by a model of a single cytokine (TNF-
) in isolation from other factors, which is implicitly the basis of most anti-TNF-
therapies. When such a model is explicitly represented in mathematical terms, as we have done here, the limitations of this approach become more obvious. To draw an accurate picture of what is happening during SIRS, and to predict the form, timing and duration of therapy that would be helpful, account will need to be taken of interactions between several cytokines [45]. This is beyond the scope of the theory developed so far (but see reference 8 for a model involving both pro- and anti-inflammatory cytokines).
In summary, we propose that RA is a chronic disease that can be mathematically represented as a dynamical system in a pathological equilibrium, whereas SIRS is an exaggerated, transient and fundamentally non-equilibrium response to a specific insult. In RA, anti-TNF-
therapy succeeds in reducing TNF-
levels to a new, lower equilibrium, resulting in improvement of symptoms, though not permanent cure. In SIRS, by contrast, anti-TNF-
therapy is highly likely to sabotage the body's own restorative systems by acting as a slow-release reservoir that can maintain inappropriately high levels of TNF-
.
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Acknowledgments
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This work was supported by a grant jointly funded by the BBSRC/EPSRC and by UCL graduate school.
The authors have declared no conflicts of interest.
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References
|
---|
- Wallach D, Varfolomeev EE, Malinin NL, Goltsev YV, Kovalenko AV, Boldin MP. Tumor necrosis factor receptor and Fas signaling mechanisms. Annu Rev Immunol 1999;17:33167.[CrossRef][ISI][Medline]
- Dayer JM. The saga of the discovery of IL-1 and TNF and their specific inhibitors in the pathogenesis and treatment of rheumatoid arthritis. Joint Bone Spine 2002;69:12332.[CrossRef][ISI][Medline]
- Bone RC. Toward a theory regarding the pathogenesis of the systemic inflammatory response syndrome: what we do and do not know about cytokine regulation. Crit Care Med 1996;24:16372.[ISI][Medline]
- Kox WJ, Volk T, Kox SN, Volk HDI. Immunomodulatory therapies in sepsis. Intensive Care Med 2000;26(Suppl. 1):S1248.[CrossRef][Medline]
- Feldmann M, Maini RN. Anti-TNF-
therapy of rheumatoid arthritis: what have we learned? Annu Rev Immunol 2001;19:16396.[CrossRef][ISI][Medline]
- Feldmann M, Maini RN. Discovery of TNF-
as a therapeutic target in rheumatoid arthritis: preclinical and clinical studies. Joint Bone Spine 2002;69:128.[CrossRef][ISI][Medline]
- Henderson B, Seymour R, Wilson M. The cytokine network in infectious diseases. J Immunol Immunopharmacol 1998;18:714.
- Seymour RM, Henderson B. Pro-inflammatoryanti-inflammatory cytokine dynamics mediated by cytokinereceptor dynamics in monocytes. IMA J Math Appl Med Biol 2001;18:15992.[CrossRef][Medline]
- Simkin PA, Wu MP, Foster DM. Articular pharmacokinetics of protein-bound antirheumatic agents. Clin Pharmacokinet 1993;25:34250.[ISI][Medline]
- Aderka D, Engelmann H, Maor Y, Brakebusch C, Wallach D. Stabilization of the bioactivity of tumor necrosis factor by its soluble receptors. J Exp Med 1992;175:3239.[Abstract/Free Full Text]
- Mohler KM, Torrance DS, Smith CA et al. Soluble tumor necrosis factor (TNF) receptors are effective therapeutic agents in lethal endotoxemia and function simultaneously as both TNF carriers and TNF antagonists. J Immunol 1993;151:154861.[Abstract/Free Full Text]
- Wagner C, Mace K, DeWoody K et al. Infliximab treatment benefits correlate with pharmacodynamic parameters in Crohn's disease patients. Digestion 1998;59(Suppl. 3):1245.
- Ramanathan M. A physiochemical modelling approach for estimating the stability of soluble receptor-bound tumour necrosis factor-alpha. Cytokine 1997;9:1926.[CrossRef][ISI][Medline]
- Ganesan S, Travis SP, Ahmad T, Jazrawi R. Therapeutic inhibitors of tumor necrosis factor in Crohn's disease. Curr Opin Investig Drugs 2002;3:13016.[Medline]
- Reinhart K, Karzai W. Anti-tumor necrosis factor therapy in sepsis: update on clinical trials and lessons learned. Crit Care Med 2001;29:S1215.[CrossRef][ISI][Medline]
- Maini RN, Breedveld FC, Kalden JR et al. Therapeutic efficacy of multiple intravenous infusions of anti-tumor necrosis factor alpha monoclonal antibody combined with low-dose weekly methotrexate in rheumatoid arthritis. Arthritis Rheum 1998;41:155263.[ISI][Medline]
- Kavanaugh A, St Clair EW, McCune J, Braakman T, Lipsky P. Chimeric anti-tumor necrosis factor-
monoclonal antibody treatment of patients with rheumatoid arthritis receiving methotrexate therapy. J Rheumatol 2000;27:84150.[ISI][Medline]
- British Medical Association and the Royal Pharmaceutical Society of Great Britain. British National Formulary, 43th edn. London: British Medical Association and the Royal Pharmaceutical Society of Great Britain, 2002:491.
- Markham A, Lamb HM. Infliximab: a review of its use in the management of rheumatoid arthritis. Drugs 2000;59:134559.
- Moreland LW, Schiff MH, Baumgartner SW et al. Etanercept therapy in rheumatoid arthritis. A randomized, controlled trial. Ann Intern Med 1999;130:47886.[Abstract/Free Full Text]
- Lantz M, Malik S, Slevin ML, Olsson, I. Infusion of tumor necrosis factor (TNF) causes an increase in circulating TNF-binding protein in humans. Cytokine 1990;2:4026.[Medline]
- Feldmann M, Brennan FM, Maini RN. Role of cytokines in rheumatoid arthritis. Annu Rev Immunol 1996;14:397440.[CrossRef][ISI][Medline]
- Brennan FM, Gibbons DL, Cope AP, Katsikis P, Maini RN, Feldmann M. TNF inhibitors are produced spontaneously by rheumatoid and osteoarthritic synovial joint cell cultures: evidence of feedback control of TNF action. Scand J Immunol 1995;42:15865.[ISI][Medline]
- Saxne T, Pallidino MA Jr, Heinegård D, Talal N, Wollheim FA. Detection of tumor necrosis factor
but not tumor necrosis factor ß in rheumatoid arthritis synovial fluid and serum. Arthritis Rheum 1988;31:10415.[ISI][Medline]
- Lettesjö H, Nordström E, Stroö H et al. Synovial fluid cytokines in patients with rheumatoid arthritis or other arthritic lesions. Scand J Immunol 1998;48:28692.[CrossRef][ISI][Medline]
- Yaqoob P, Newsholme EA, Calder PC. Comparison of cytokine production in cultures of whole human blood and purified mononuclear cells. Cytokine 1999;11:6005.[CrossRef][ISI][Medline]
- Lipsky PE, van der Heijde DMFM, St Clair EW et al. Infliximab and methotrexate in the treatment of rheumatoid arthritis. Anti-tumor necrosis factor trial in rheumatoid arthritis with concomitant therapy study group. New Engl J Med 2000;343:1594602.[Abstract/Free Full Text]
- Scallon BJ, Moore MA, Trinh H, Knight DM, Ghrayeb J. Chimeric anti-TNF-
monoclonal antibody cA2 binds recombinant transmembrane TNF-
and activates immune effector functions. Cytokine 1995;7:2519.[CrossRef][ISI][Medline]
- Feldmann M, Elliot MJ, Woody JN, Maini RN. Anti-tumor necrosis factor-
therapy of rheumatoid arthritis. Adv Immunol 1997;64:283350.[ISI][Medline]
- Scallon B, Cai A, Solowski N et al. Binding and functional comparisons of two types of tumor necrosis factor antagonists. J Pharmacol Exp Ther 2002;301:41826.[Abstract/Free Full Text]
- Ulfgren AK, Andersson U, Engstrom M, Klareskog L, Maini RN, Taylor PC. Systemic anti-tumor necrosis factor alpha therapy in rheumatoid arthritis down-regulates synovial tumor necrosis factor alpha synthesis. Arthritis Rheum 2000;43:23916.[CrossRef][ISI][Medline]
- Katsikis P, Chu CQ, Brennan FM, Maini RN, Feldmann M. Immunoregulatory role of interleukin 10 (IL-10) in rheumatoid arthritis. J Exp Med 1994;179:151720.[Abstract/Free Full Text]
- Bachwich PR, Chensue SW, Larrick JW, Kunkel SL. Tumor necrosis factor stimulates interleukin-1 and prostaglandin E2 production in resting macrophages. Biochem Biophys Res Commun 1986;136:94101.[ISI][Medline]
- Kunkel SL, Spengler M, May MA, Spengler R, Larrick J, Remick D. Prostaglandin E2 regulates macrophage-driven tumor necrosis factor gene expression. J Biol Chem 1988;263:53804.[Abstract/Free Full Text]
- Bone RC. The pathogenesis of sepsis. Ann Intern Med 1991;115:45769.[ISI][Medline]
- Zhang M, Tracey KJ. Tumor necrosis factor. In: Thompson A, ed. The cytokine handbook, 3rd edn. San Diego: Academic Press, 1998, p. 51748.
- Blackwell TS, Christman JW. Sepsis and cytokines: current status. Br J Anaesth 1996;77:1107.[Abstract/Free Full Text]
- Natanson C, Hoffman WD, Suffredini AF, Eichacker PQ, Danner RL. Selected treatment strategies for septic shock based on proposed mechanisms of pathogenesis. Ann Intern Med 1994;120:77183.[Abstract/Free Full Text]
- Zeni F, Freeman B, Natanson C. Anti-inflammatory therapies to treat sepsis and septic shock: a reassessment. Crit Care Med 1997;25:1095100.[CrossRef][ISI][Medline]
- Echtenacher B, Falk W, Mannel DN, Krammer PH. Requirement of endogenous tumor necrosis factor/cachectin for recovery from experimental peritonitis. J Immunol 1990;145:37626.[Abstract/Free Full Text]
- Quezado ZMN, Banks SM, Natanson C. New strategies for combatting sepsis: the magic bullets missed the mark but the search continues. Trends Biotechnol 1995;13:5663.[CrossRef][ISI][Medline]
- Suffredini AF, Reda D, Banks SM, Tropea M, Agosti JM, Miller R. Effects of recombinant dimeric TNF receptor on human inflammatory responses following intravenous endotoxin administration. J Immunol 1995;155:503845.[Abstract]
- Zanetti G, Heumann D, Gérain J et al. Cytokine production after intravenous or peritoneal gram-negative bacterial challenge in mice. J Immunol 1992;148:18907.[Abstract/Free Full Text]
- Gogos CA, Drosou E, Bassaris HP, Skoutelis A. Pro-versus anti-inflammatory cytokine profile in patients with severe sepsis: a marker for prognosis and future therapeutic options. J Infect Dis 2000;181:17680.[CrossRef][ISI][Medline]
- Bone, RC. Sir Isaac Newton, sepsis, SIRS, and CARS. Crit Care Med 1996;24:11258.[CrossRef][ISI][Medline]
- Dinarello CA. Proinflammatory and anti-inflammatory cytokines as mediators in the pathogenesis of septic shock. Chest 1997;112(Suppl. 6):321S9S.
- Seely AJE, Christou, NV. Multiple organ dysfunction syndrome: exploring the paradigm of complex nonlinear systems. Crit Care Med 2000;28:2193200.[ISI][Medline]
- Grell M, Wajant H, Zimmermann G, Scheurich P. The type 1 receptor (CD120a) is the high-affinity receptor for soluble tumor necrosis factor. Proc Natl Acad Sci USA 1998;95:5705.[Abstract/Free Full Text]
- Imamura K, Spriggs D, Kufe D. Expression of tumor necrosis factor receptors on human monocytes and internalization of receptor bound ligand. J Immunol 1987;139:298992.[Abstract/Free Full Text]
- Mosselmans R, Hepburn A, Dumont JE, Fiers W, Galand P. Endocytic pathway of recombinant murine tumor necrosis factor in L-929 cells. J Immunol 1988;141:3096100.[Abstract/Free Full Text]
- Smith DM, Lackides GA, Epstein LB. Coordinated induction of autocrine tumor necrosis factor and interleukin 1 in normal human monocytes and the implications for monocyte-mediated cytotoxicity. Cancer Res 1990;50:314653.[Abstract]
- Simkin PA. Synovial perfusion and synovial fluid solutes. Ann Rheum Dis 1995;54:4248.[ISI][Medline]
- Pennica D, Lam VT, Weber RF et al. Biochemical characterization of the extracellular domain of the 75-kilodalton tumor necrosis factor receptor. Biochemistry 1993;32:31318.[ISI][Medline]
- Moosmayer D, Wajant H, Gerlach E, Schmidt M, Brocks B, Pfizenmaier K. Characterization of different soluble TNF receptor (TNFR80) derivatives: positive influence of the intracellular domain on receptor/ligand interaction and TNF neutralization capacity. J Interferon Cytokine Res 1996;16:4717.[ISI][Medline]
- Northrup SH, Erickson HP. Kinetics of proteinprotein association explained by Brownian dynamics computer simulation. Proc Natl Acad Sci USA 1992;89:333842.[Abstract/Free Full Text]
- Foote J, Eisen HN. Kinetic and affinity limits on antibodies produced during immune responses. Proc Natl Acad Sci USA 1995;92:12546.[Free Full Text]
- Jarvis B, Faulds D. Etanercept: a review of its use in rheumatoid arthritis. Drugs 1999;57:94566.[ISI][Medline]
- Plotz PH, Kimberly RP, Guyer RL, Segal DM. Stable model immune complexes produced by bivalent affinity labelling haptens: in-vivo survival. Mol Immunol 1979;16:7219.[CrossRef][ISI][Medline]
Submitted 2 June 2004;
revised version accepted 22 October 2004.