Evidence for bistable bacteria-neutrophil interaction and its clinical implications

Neutropenia, which may develop as a consequence of chemotherapy, increases the risk of bacterial infection. Similarly, increased risk of bacterial infection appears in disorders of phagocytic functions, such as the genetic disorder chronic granulomatous disease. To elucidate the organizing principles behind these distinct immunodeficiency conditions, we investigated the interaction between in vitro bacteria and human neutrophils by experiments and mathematical modeling. The model and the experiments showed that the in vitro bacterial dynamics exhibit bistability for a certain range of neutrophil concentration and function. Thus, there is a critical bacterial concentration above which infection develops, and below which neutrophils defeat the bacteria. Whereas with normal neutrophil concentration and function, an infection may develop when the initial bacterial concentration is very high, under neutropenic conditions or when there is neutrophil dysfunction, the critical bacterial concentration can be lower, within the clinically relevant range. We conclude that critical bacterial concentration has clinically relevant implications. The individual maximum bearable bacterial concentration depended on neutrophil concentration, phagocytic activity, and patient barrier integrity; thus, the resulting maximal bearable bacterial concentration may vary by orders of magnitude between patients. Understanding the interplay between neutrophils and bacteria may enhance the development of new therapeutic approaches to bacterial infections.

Neutropenia is common in cancer patients treated with intensive chemotherapy regimens. When the peripheral neutrophil blood count is below 500 × 10³/ml, there is a dramatic increase in the risk of severe pyogenic infections (1), often resulting in organ damage and death (2). The reasons for this well-documented critical threshold are not fully understood. In addition, conditions associated with neutrophil dysfunction, even with normal neutrophil counts, are known to lead to inability to fight infections (3–5).

To explain these clinical findings, in vitro bactericidal experiments have been conducted. Initially, these in vitro studies suggested that the occurrence of infection depends on the ratio between bacterial concentration (B) and neutrophil concentration (N) (6–8); we refer to this herein as the ratio-dependent model (Figure 1A). Further investigations of Staphylococcus epidermidis–neutrophil interaction in vitro (9, 10), in conjunction with a linear mathematical model, suggested that there exists a single critical neutrophil concentration (CNC), below which neutrophils are completely unable to control bacterial growth, and above which they can control any bacterial concentration (neutrophil-threshold model; Figure 1B). Most recently, mathematical models that take into account nonlinear effects such as saturation in bacterial growth and in neutrophil killing rates were proposed and analyzed (11, 12), resulting in the monostable (Figure 1C) and bistable (Figure 1D) models.

Figure 1

Bacteria versus neutrophils: 4 plausible behaviors. Red regions correspond to experimental B and N concentrations that lead to an increase in the bacterial population (B locally wins); blue regions correspond to concentrations that lead to a decrease in the bacterial population (N locally wins). (A) Ratio-dependent models propose that the initial B/N ratio determines the result (6–8). (B) The neutrophil-threshold model proposes that a single neutrophil threshold exists, below which the bacterial population grows, and above which the bacterial population decreases (9, 10). (C) Monostable models propose that when the bacterial natural growth conditions are mild, the presence of neutrophils leads to a gradual decrease in the bacterial maximum capacity, down to extinction (11). (D) Bistable models propose that when the bacterial natural growth conditions are more favorable, the presence of neutrophils leads to bistable behavior (see Figure 1 in ref. 11). Here, we focused on the experimentally relevant region. The BNC (dashed and solid black curves) separates regions of bacterial growth from regions of bacterial decrease. Only in the bistable case (D) does the BNC have a positive slope, not conserving the B/N ratio.

Generally, monostability refers to a system with a single stable steady state, whereas bistability refers to a system that has 2 stable states for some range of parameter values. Here, N serves as a controlling parameter, and the 2 possible pronounced (stable) states are bacterial population capacity and no-bacteria or extinction state. In the bistable regime, both states are stable and are separated by an additional intermediate unstable steady state. B values above this unstable state grow to the population capacity concentration, whereas concentrations below it decay to the extinction state. In the bistable case in particular, for N above some threshold, the ability of neutrophils to overcome bacterial infection depends on the initial B (Figure 1D). It was shown previously that the neutrophil bactericidal experiments of Li et al. using S. epidermidis (10) are consistent with such bistable behavior (11).

These behaviors may be represented mathematically by ordinary differential equations governing the rate of change in B, where N is held fixed. The rate of change in B may be divided into the natural growth function of B (which depends on B and on the control experimental conditions) and to the bacteria-neutrophil interaction term. The interaction term depends on B, N, and neutrophil function in the given experimental condition. These 4 behaviors may be realized by considering different classes of natural growth terms and interaction terms (see ref. 12 and Methods). Such models were extended to explore the bistable bacteria-neutrophil dynamics under the influence of chemotherapy and G-CSF intervention by allowing N to vary (see refs. 12, 13, and Methods).

Here, we designed and performed an experiment to examine whether in vitro Staphylococcus aureus bacteria growth under attack from human neutrophils exhibits bistability. Our most important finding was a strong indication of bistability in all data examined, independent of the explicit forms of the mathematical models. We further used these data to parameterize the bistable bacteria-neutrophil equation via a specific previously proposed model (12), and the parameterized equation indeed fit the in vitro data. The parameterized model was then used to study the bacterial dynamics under neutropenic conditions. Under mild prolonged neutropenic conditions, the bacterial threshold for infection (i.e., maximum bearable bacterial influx) was found to be sensitive to the observed variability in the bactericidal activity (BA) of the neutrophils.

The S. aureus–human neutrophil interaction is bistable. We performed a series of bactericidal experiments in which S. aureus bacteria were incubated for 60 minutes in 24-well plates in suspensions containing 10% autologous sera and fixed N values. After 60 minutes, the neutrophils were lysed to stop the interaction, and the bacteria were assayed by colony culturing (see Methods). The ranges of experimental B and N values were chosen to detect the bistable regime. This series of experiments was repeated independently 4 times, each time using neutrophils and sera from a different healthy volunteer; each of the 4 experiments contained around 20 data points. Our experimental findings are summarized in Table 1.

Table 1

Bactericidal experiment

Next, we examined which of the 4 plausible behaviors shown in Figure 1 was consistent with our data. In all cases, there was a critical bacteria-neutrophil curve (BNC) that separated regions of bacterial growth from regions of reduction. On this curve, B is fixed: bacterial growth is exactly balanced by neutrophil elimination. In the ratio-dependent behavior, the BNC is a straight line through the origin, along which the B/N ratio is constant (Figure 1A). In the neutrophil-threshold behavior, the BNC is a vertical line (cutting the B axis at the CNC described in refs. 9, 10; Figure 1B). In the monostable case, the BNC is a decreasing function of N (Figure 1C). In the bistable case, for the relevant range of B, the BNC is an increasing function of N: bacterial load increases if the initial B exceeds the BNC, but decreases if initial B falls below the BNC (Figure 1D).

Here, we estimated the experimental BNC and established that its properties were in best agreement with the bistable behavior. Note that the bistable case is the only one of the plausible behaviors in which this curve has a positive slope and a nonconstant B/N ratio. For the ratio-dependent case, the B/N ratio along the curve is constant; for monostable and neutrophil-threshold behaviors, the curve has negative and vertical slopes, respectively.

By using the sign test (see Methods), we demonstrated that the experimentally derived BNC had a positive slope (Figure 2). This strongly indicated that the neutrophil-threshold and monostable behaviors are inconsistent with the data. Additionally, the B/N ratio along the experimentally derived curve was not constant (see Methods and Figure 3). Hence, the ratio-dependent behavior is inconsistent with our data and with the data of Li et al. (10). Therefore, we concluded that of the 4 plausible bacteria-neutrophil behaviors, only the bistable behavior is consistent with our data using S. aureus in suspension and with the previously reported data using S. epidermidis in gel (10).

Figure 2

Sign diagrams. At each initial experimental data point [B(0),N], we indicate whether the final bacterial population in each of the 2 duplicates after 60 minutes has a larger or smaller value than the initial one (+ or O, respectively). As each initial data point corresponds to 2 experiments (duplicates; see Methods), 2 symbols are plotted for each point. Points with 2 different signs appear near the BNC, where small experimental deviations between the duplicates may lead to opposite outcomes. (A) A slanted line (here in log scale) divided the symbols better than a vertical line (n = 78). (B) S. epidermidis data (n = 34), adopted from ref. 10. (C and D) Addition of the BNC (black curve), determined from the fitted mathematical model of Equation 3 and Table 2 (the dashed BNC curve of Figure 1D in a logarithmic plot). The entire data set (n = 86) is presented in C, and the single subject P1 (n = 22) in D, with the extent of increase/decrease (i.e., magnitude of Y = log[B(60 minutes),N/B(0)]) shown by color. As expected, near the BNC, the rates were close to 0 (greenish symbols).

Figure 3

PBK diagram. PBK is plotted as a function of N, with lines connecting data points having the same experimental B. The points at which these PBK lines crossed the N axis were designated N*[B(0)]. The B/N ratios at the N*[B(0)] points approximated the B/N ratios on the BNC; thus, (B(0),N*[B(0)]) belongs to the experimentally extracted BNC. (A) Growth rate lines for S. aureus with experimental B of 10⁴, 10⁶, and 10⁷ CFU/ml for the collective data set (n = 86). Data represent mean ± SD. Note that for experimental B of 10⁴ CFU/ml, the intersection occurred at N* ≈ 10⁵, in contrast to N* ≈ 2 × 10⁶ for 10⁷ CFU/ml; that is, the B/N ratio changed by at least 1 order of magnitude along the estimated BNC. (B) Growth rate lines for the S. epidermidis data (n = 34) adopted from ref. 10 with the indicated experimental B values. For experimental B of 2 × 10³ CFU/ml, the intersection occurred at N* ≈ 2 × 10⁵, in contrast to N* ≈ 2 × 10⁶ for 1.6 × 10⁸ CFU/ml; that is, the B/N ratio changed by at least 3 orders of magnitude along the BNC.

The above findings were qualitative and independent of the explicit mathematical form of the relevant models. We next used the data to parameterize a specific bistable model of the bacteria-neutrophil interaction (11). Table 2 presents the parameter fit for the S. aureus data for each of the 4 subjects, in which neutrophil functionality is measured with the autologous sera of each subject; for the pooled data set; and for the S. epidermidis data extracted graphically from the study of Li et al. (10). A large clinical study is needed to establish the optimal functional form of a bistable model and the typical average and variability of the model’s parameters (see Discussion). Nonetheless, there was good correspondence between the parameterized model and the fitted data sets (see Methods). Hence, we concluded that the parameterized model is adequate for describing the available data sets.

Table 2

Personal and pooled parameter estimates for the model in Equation 3

For each of these data sets, we also determined the predicted N_c, the point at which the fitted BNC intersects the B = 0 axis. Below this CNC, a small initial B would grow exponentially, whereas above it, a small initial B would be cleared. Whereas our in vitro experiments were conducted at B values of 10⁴ CFU/ml and above, this prediction provides insights regarding the dynamics at much lower B. In particular, when N is very close to the predicted N_c, the small blood B of septicemic patients (which may reach 10²–10³ CFU/ml; refs. 14–17) may be above the BNC, and thus develop to an acute infection. In our sample of 4 healthy individuals, the average N_c for the 4 subjects was 557 × 10³ neutrophils/ml, with a coefficient of variation of 18.5%. Notably, the standard classification for grade IV/severe neutropenia is an absolute neutrophil count (ANC) less than 500 × 10³ neutrophils/ml (2).

The chemotherapy-induced severe neutropenia scenario. To better illustrate the possible clinical implications of the variability in the model parameters, we considered the following common clinical situation. The neutrophil levels of a patient drop for a period of time and then recover. While this neutropenic cycle occurs, the patient is exposed to a constant bacterial influx. Such a scenario often arises after chemotherapy, as the neutrophil counts are temporarily reduced due to bone marrow damage, and bacterial influx may be increased due to degradation of the integrity of the patient’s barriers. We examine whether the variability in neutrophil function (i.e., in the model parameters shown in Table 2) may be critical in such clinical scenarios.

To examine such issues, we incorporated our experimental data set into the bacteria-neutrophil equation of our previously proposed in vivo mathematical model (see Methods and ref. 12). This model was designed specifically to study scenarios of infection when the neutrophil supply is limited, as in neutropenia. We used it here to isolate the influence of neutrophil functionality and barrier integrity from all other factors. First, we chose the parameters governing blood N of a hypothetical patient that undergoes chemotherapy and receives G-CSF support (see refs. 12, 13, and Methods). The chosen parameters provided a neutropenic time profile [N(t)] of a patient with prolonged severe neutropenia. Without G-CSF support, the patient’s N would be below the critical threshold of 500 × 10³ neutrophils/ml for 10 days, whereas with 10 daily G-CSF injections, N would be mostly above the threshold of severe neutropenia, yet would remain neutropenic (i.e., N less than 1,000 × 10³ neutrophils/ml) for about 7 days (Figure 4A). Note that for this hypothetical patient, standard daily shots suffice to abrogate the severe neutropenia, and he belongs to the lower G₁ class previously reported (13), with acute marrow capacity of 0.15.

Figure 4

Evolution of infection in hypothetical patients during a 21-day cycle of chemotherapy-induced neutropenia. (A) Hypothetical N with no G-CSF support (untreated) and with 10 daily injections (treated). Thresholds for neutropenia (1,000 × 10³ neutrophils/ml) and severe neutropenia (500 × 10³ neutrophils/ml) are shown by dashed and solid red lines, respectively. (B–D) Bacterial dynamics for 3 hypothetical patients with increasing bacterial influx (s). Hypothetical patients P1-treated and P4-treated received G-CSF support and thus had mild neutropenia. Their neutrophil functionality parameters are taken to be those of volunteers P1 and P4, respectively (see Table 2). Hypothetical patient P1-untreated did not receive G-CSF support and thus had severe neutropenia. His neutrophil functionality parameters are taken to be those of volunteer P1. (B) P1-treated could bear the 300-CFU/ml/h load, whereas for P4-treated and P1-untreated, this small s led to the development of acute infection. (C) With a more than 350-fold increase in s, P1-treated still succeeded in overcoming the infection. (D) With s increased 400-fold, all hypothetical patients developed an infection, regardless of G-CSF support.

We then examined the resulting bacterial growth for 3 hypothetical patients. The first hypothetical patient received G-CSF support, and his neutrophils’ functionality parameters were set to be the same as those of volunteer P1; therefore, we refer to this patient hereafter as P1-treated (Figure 4A). P1-treated overcame both small and quite large bacterial influx contaminations; in fact, a 400-fold increase of the small bacterial influx was needed to cause this patient to get an acute infection (Figure 4, B–D). The second hypothetical patient, P4-treated, had neutrophil functionality parameters set to those of volunteer P4. P4-treated also received G-CSF support and had a neutropenic profile identical to that of P1-treated, so his N was mostly above 500 × 10³ neutrophils/ml. Given their similarities, the change in response caused by different neutrophil functionality was dramatic: P4-treated could not overcome even the smallest bacterial influx (Figure 4B). Finally, the third hypothetical patient, P1-untreated, had the high neutrophil BA plus the autologous serum of volunteer P1 in the absence of G-CSF support. For P1-untreated, neutrophil counts were below the threshold value for almost 10 days (Figure 4A), as expected, which indicated that the hypothetical patient could not overcome even the smallest bacterial influx.

Because we have no information about the real responses to chemotherapy of healthy volunteers P1 and P4, we examined a case in which P1-treated and P4-treated have identical changes in N in response to chemotherapy and G-CSF support. We further assumed that the neutrophil functionality of each volunteer was unchanged by the chemotherapy. The mathematical model allowed us to examine such hypothetical medical scenarios and isolate the influences of specific factors. The simulations demonstrated that interpatient variability in neutrophil functionality with autologous sera alone led to vast differences in the response to different levels of bacterial influx. Even with G-CSF support, P4-treated could not overcome a bacterial influx of 300 CFU/ml/h (Figure 4B); importantly, as described above, some septicemic patients demonstrate blood B of 10²–10³ CFU/ml (14–17). Conversely, P1-treated overcame a 350-fold increase of this influx (Figure 4C). Put differently, for a given neutropenic profile, the patient’s neutrophil functionality determined the critical bacterial influx above which severe infections developed. It was previously shown that in general, this critical bacterial influx depends sensitively on N, neutrophil functionality, and bacterial growth rates (12). Here, we demonstrated that with the recorded interpatient variability, this critical value changed by at least 2 orders of magnitude. We concluded that this phenomenon is dramatic and is expected to be clinically observable.

The above results applied to neutropenic patients with neutrophil counts close to the medical threshold value of 500 × 10³ neutrophils/ml (Figure 4A). Simulations of the same model with noncritical neutropenic profiles do not exhibit such parameter sensitivity (12). Indeed, when the neutrophil nadir counts were far above (270% increase) or far below (28% decrease) the threshold value, all patients eventually recovered or rapidly developed acute infections, respectively.

Here, the bistable model was shown to provide an organizing structure relating neutropenia-associated conditions, neutrophil dysfunctions, and bacterial influx. It fully explained the current knowledge of in vitro bacteria-neutrophil dynamics and was corroborated by our experimental data. Using a mathematical model, we examined the clinical implications of these findings on infection development in neutropenic patients and in patients with malfunctioning neutrophils. We propose that all major clinical observations regarding the development of infections in neutropenic patients are consistent with our model.

First, the severity and duration of the neutropenic nadir are known to be correlated with increased risk of infection (1, 18). The existence of the BNC indicates that the severity and duration of the nadir directly influence the likelihood of developing a severe infection, thus explaining the observed correlation.

Second, at some ranges of nadir levels and nadir durations, the risk of infection greatly increases (1, 18). For these near-critical ranges, there was strong interpatient variability in infection development. Our model provided a mechanism for handling such variability: the interpatient variability in neutrophil function led to variability in the individual critical N_c and thus to strong variability in infection development among patients with similar neutropenic profiles.

Third, sterility and isolation are known to reduce the risk of infection in some neutropenic patients (19, 20). In our in vivo model, the barriers’ integrity and the sterility conditions influenced one combined parameter: bacterial influx. Occasional contamination appears as a local sudden change in B. The existence of the BNC may explain the sensitivity of neutropenic patients to occasional contamination, hence the need for isolation. Aseptic conditions help to keep the bacterial load below this critical curve. Occasional large bacterial contamination may push the bacterial load above the BNC and lead to a severe infection. The shift of this curve to higher N values when bacterial influx is incorporated (12) explains the importance of sterile conditions for neutropenic patients. This shift means that the same occasional contamination that may be kept under control under sterile conditions would lead to severe infection when the body fights a constant bacterial influx from a nonsterile environment. It also explains the increased risk of infection in chemotherapy-induced neutropenia compared with other neutropenic conditions; indeed, mucosal barrier injury is a known side effect of radiotherapy and chemotherapy treatments (21). Finally, our model showed that in the case of severe neutropenia (N < N_c), even a small bacterial influx (e.g., from the intestines) may cause infection; thus, in this case, isolation cannot prevent the development of infections (22).

Fourth, the bistable behavior may explain specific puzzling clinical scenarios, such as the following 2 cases. The first patient, an immunocompromised neonate (1 month old), also suffers from severe congenital neutropenia (SCN), with ANC less than 200 × 10³ neutrophils/ml. Supportive therapy with G-CSF significantly improved neutrophil count and function (23). Together with antibiotic therapy, the treatment controlled life-threatening infections. The second patient, an adult with acute lymphoblastic leukemia who received chemotherapy, developed a high fever with severe neutropenia (ANC of 380 × 10³ cell/ml). He received specific antibiotics and G-CSF. Despite the recovery of neutrophil counts, the patient died. As shown in Figure 4, our model demonstrated that the disparity in these scenarios may be explained both by the degradation of the adult’s barriers by chemotherapy and by the possible relatively weak functionality of the adult’s neutrophils, caused by either normal interpatient variability or the effect of chemotherapy on neutrophil function.

In addition to neutrophil count and functionality, other factors affect the efficiency of bacterial clearance in cases of septicemia or bacterial growth in the blood: these include bacterial clearance in liver and spleen, blood monocyte concentration, and blood opsonin concentration. Nevertheless, neutrophil BA is known to be essential and amenable to medical intervention. Indeed, the common medical practice for avoiding microbial spreading in neutropenic conditions is early restitution of neutrophil levels by G-CSF treatment as well as administration of antibiotics, as described above. Clinical observations indicate that G-CSF increases both neutrophil counts and neutrophil function (23–25); however, other studies found variability in the effect of G-CSF on in vitro neutrophil BA (26). Finally, with respect to the neutrophil functionality of the volunteers studied here, we measured the functionality of their neutrophils with their autologous sera, which was extracted at the time the blood sample was taken. In future studies, the effect of sera on neutrophil functionality may be explored.

Clinical insights regarding CGD patients. Chronic granulomatous disease (CGD) is an immunodeficiency syndrome caused by defects in NADPH oxidase, the enzyme that generates ROS in phagocytizing leukocytes. The lack of ROS generation is caused by mutations in any one of the genes encoding structural components of NADPH oxidase. CGD patients have an impairment in NADPH oxidase processing, which leads to life-threatening infections and consequently to granuloma formation in different tissues. This granuloma formation is now considered to be a hyperinflammatory reaction to various stimulants in CGD patients, causing granulomatous lesions that eventually result in organ dysfunction (27).

The diagnosis of CGD was established by neutrophil functional and genetic studies (3, 28). In the standard functionality test, S. aureus at a final B of 4.4 × 10⁶ CFU/ml is incubated with 4.4 × 10⁶ neutrophils/ml for 60 minutes, after which the neutrophils are lysed and B is assayed. Since most CGD patients lack or have very low ROS production, their BA (calculated as –log[B(t)/B(0)]) is low, at less than 0.5. Equivalently, these patients have a percentage of bacteria killed (PBK; calculated as [1 – B(t)/B(0)] × 100; e.g., ref. 7) that is smaller than normal, at 68%.

Recently, a 5-year-old patient suffering from repeated infections was tested (28). His BA of 0.62 was not considered compatible with CGD. Inspired by the bistability findings, the test was repeated with a larger initial B of 2 × 10⁷ CFU/ml. The BA of the patient decreased to 0.05, whereas the BA of the control decreased to 0.16. Given that on the BNC, both measures of neutrophil functionality (BA and PBK) vanished (Figure 3), the higher initial B was closer to the BNC for the patient and further below it for the healthy control; that is, the patient’s BNC was lower than that of the control. This difference may explain the patient’s repeated infections. We suspect that the low BA of most CGD patients indicates that their BNCs are considerably lower than normal in both autologous and homologous sera.

Clinical perspective. Of the 998 patients referred for immune evaluation at the Laboratory for Leukocyte Function in Meir General Hospital due to repeated infections, the etiology of the immunodeficiency could be established in only 35% of the cases (29). We propose that some of the patients’ undefined disorders are related to a combination of several mild impairments, each one by itself lying within the lower end of the normal population distribution. Designing a protocol for testing immunodeficiency may help in identifying such patients.

Potentially new diagnostic uses. The bistability paradigm suggests that the standard tests for immune evaluation could be optimized by using assays with multiple B and N values. The following protocol may be considered: (a) take a single blood sample; (b) use the multiconcentration bacteria-neutrophil assay (see Methods) using both autologous and homologous sera; (c) find the experimental BNC of the patient for each serum (see Methods); (d) estimate the individual parameters of a bistable model for each serum (see Methods); and (e) compare the individual autologous BNC and the individual parameters with those of the homologous, a control, and a corresponding control population.

We expect that the proposed protocol would be useful to 2 groups of patients. First, for patients with repeated infections associated with deficiencies in neutrophil functionality, we expect that the autologous BNC will be lower than the control’s BNC and that some of the model parameters may be abnormal. Such an assessment may help to determine the proper therapy, for example, by providing a quantitative prediction for the needed G-CSF and antibiotic support. Moreover, comparison of the fitted parameters with the various controls may possibly help to diagnose the deficiency.

Second, for patients needing to undergo chemotherapy treatments that bear significant neutropenic risk, the individually parameterized model and the resulting BNC may help in an a priori assessment of a patient’s critical zone. We propose that such an assessment may help to identify those individuals at high risk of infection due to their intrinsic immune vulnerability. Moreover, such an assessment may help to determine the needed support therapy, including the isolation protocol (accounting for both patient neutrophil count and BNC). Finally, we propose that by repeating the above-described 5-step protocol at several time points after chemotherapy (see ref. 30), separately fitting at step (e) the parameters at each time point, one may examine whether a significant change in neutrophil function has occurred.

Implementation of these ideas in the clinic requires additional empirical studies. To begin with, a large population of healthy subjects should be assayed, and different common experimental settings should be explored; for example, different laboratories use different percentages of autologous serum (9) and different types of bacteria. Then, mathematical forms of bistable models that provide the best fit to the gathered data should be selected — the previously developed model (11) used herein presents only one of many other options (see ref. 12). These experimental and theoretical explorations will generate estimated population parameters and provide their between-subject variability. With these estimations at hand, we envision the suggested protocol will provide a diagnostic tool based on a standard objective measure. We hope that the emerging principle — that the combined effect of mild impairments may lead to significant clinical consequences — can contribute to the current practice for treating patients that suffer from repeated infections or undergo chemotherapy treatments.

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The authors thank Yakar Kannai and Elchanan Mossel for helpful discussions and Dirk Roos and John Higgins for comments on this manuscript. This work was partially supported by the Israel Science Foundation (grant 273/07) and the Minerva Foundation. V. Rom-Kedar is the Estrin Family Chair of Computer Science and Applied Mathematics at Weizmann Institute of Science.

Address correspondence to: Vered Rom-Kedar, Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel. Phone: 972.8934.3170; Fax: 972.8934.4122; E-mail: Vered.Rom-Kedar@weizmann.ac.il.

Conflict of interest: Eliezer Shochat is an employee of Hoffmann-La Roche.

Reference information: J Clin Invest. 2012;122(8):3002–3011. doi:10.1172/JCI59832.

Roy Malka’s present address is: Center for Systems Biology and Department of Pathology, Massachusetts General Hospital, and Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, USA.

See the related article at How many neutrophils are enough (redux, redux)?.

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