Inoculum effect of antimicrobial peptides

Significance

Bacterial drug resistance is a crucial threat to global health, and antimicrobials with novel mechanisms of action are urgently needed. Antimicrobial peptides are natural molecules that kill bacteria mostly by perturbing their membranes, and they constitute promising compounds for fighting resistant microbes. Their activity is normally tested under standardized conditions of bacterial density. However, the bacterial load in clinically relevant infections varies by many orders of magnitude. Here, we show that the minimum peptide concentration needed for bacterial growth inhibition can vary by more than 100-fold with an increase in the density of cells in the initial inoculum of the assay (a phenomenon termed the “inoculum effect”). These findings question the utility of the currently used activity screening assays.

Abstract

The activity of many antibiotics depends on the initial density of cells used in bacterial growth inhibition assays. This phenomenon, termed the inoculum effect, can have important consequences for the therapeutic efficacy of the drugs, because bacterial loads vary by several orders of magnitude in clinically relevant infections. Antimicrobial peptides are a promising class of molecules in the fight against drug-resistant bacteria because they act mainly by perturbing the cell membranes rather than by inhibiting intracellular targets. Here, we report a systematic characterization of the inoculum effect for this class of antibacterial compounds. Minimum inhibitory concentration values were measured for 13 peptides (including all-D enantiomers) and peptidomimetics, covering more than seven orders of magnitude in inoculated cell density. In most cases, the inoculum effect was significant for cell densities above the standard inoculum of 5 × 10⁵ cells/mL, while for lower densities the active concentrations remained essentially constant, with values in the micromolar range. In the case of membrane-active peptides, these data can be rationalized by considering a simple model, taking into account peptide–cell association, and hypothesizing that a threshold number of cell-bound peptide molecules is required in order to cause bacterial killing. The observed effect questions the clinical utility of activity and selectivity determinations performed at a fixed, standardized cell density. A routine evaluation of the dependence of the activity of antimicrobial peptides and peptidomimetics on the inoculum should be considered.

The minimum inhibitory concentration (MIC) is one of the most common measures for the efficacy of antimicrobial compounds (1, 2). According to the Clinical and Laboratory Standards Institute (CLSI) and European Committee on Antimicrobial Susceptibility Testing (EUCAST) guidelines, the MIC is the lowest drug concentration that abolishes in vitro bacterial growth during a short period (typically 20 h) when using a standard initial cell density (inoculum) of ∼5 × 10⁵ colony-forming units (CFU)/mL in assays performed in broth (with an acceptable range of 2 × 10⁵ to 8 × 10⁵ CFU/mL for CLSI and 3 × 10⁵ to 7 × 10⁵ CFU/mL for EUCAST) (3–5). The choice of a specific value for the inoculum to be applied is dictated by a need for standardizing the assay in clinical practice (2), albeit bacterial cell densities in clinically relevant infections in vivo range from 1 CFU/mL to 10⁹ CFU/mL (in soft tissue or peritoneal infections) (6–8).

Soon after the introduction of penicillin for civilian use in the 1940s, it was realized that the active concentration of antibiotics might need to be increased significantly when higher bacterial cell densities are inoculated in the assay medium (9, 10), a phenomenon termed the “inoculum effect” (IE) (11). The IE can be caused by different mechanisms (12, 13), including enzymatic degradation of the drug (11, 13), a simple consequence of the number of available drug molecules per cell (14, 15), or inhibition of antibiotics by intracellular material released by dead cells, causing enhanced survival of the remaining bacterial population (16). Traditionally, an IE has been defined as a change in MIC greater than or equal to eightfold when an inoculum 100-fold greater than the CLSI recommendation is used, but recent studies have shown that even subtle differences in inoculum may have a dramatic effect on MIC values (17). The IE is commonly examined by determining the MIC; in this assay, the cell density varies by several orders of magnitude with respect to the initial inoculum, during the many hours in which the bacteria are allowed to grow. However, an IE has been demonstrated also under conditions of constant cell density (12).

High-density bacterial infections, including septic bloodstream and urinary tract infections, endocarditis, and abscesses, are quite prevalent and lack efficacious therapies (18). Although some reports have contested the therapeutic relevance of the IE (19, 20), several studies have demonstrated its clinical significance, showing that the MICs determined in the standardized assay were ineffective in the clinical treatment of high-density infections (12, 21–28). In some cases, a concentration 1,000-fold higher than the MIC is required to cure the infection (22, 23).

While the IE is well characterized for traditional antibiotics, little is known about this phenomenon for other antimicrobial compounds. Antimicrobial peptides (AMPs), sometimes referred to as “host defense peptides,” are produced by all living organisms as a first line of defense against pathogens (29–31). These peptides can have many functions (32), but most of them exert direct bactericidal effects that typically involve perturbation of the membrane integrity of microbial cells (31, 33). The majority of known AMPs are short, amphipathic, and cationic peptides capable of binding selectively to the anionic membranes of bacterial cells (34–37). Most AMPs accumulate on the outer leaflet of cell membranes, thereby perturbing their surface tension (36, 38). When a threshold of membrane-bound molecules is reached, the stress is released by the formation of pores or other membrane defects. This mechanism of action has been termed the “carpet” model (39, 40), and it makes the development of bacterial resistance particularly difficult (30, 41, 42). Therefore, AMPs represent promising lead compounds in the fight against multidrug-resistant bacteria (30, 42, 43), which constitute a dramatically increasing worldwide threat (44), and several peptides are undergoing clinical trials (43).

Considering their characteristic mechanism of action as compared to that of commonly used antibiotics, the existence of a pronounced IE is not obvious in the case of AMPs. Surprisingly, the IE within this class of molecules has been investigated only in a handful of studies (45–50), which are summarized in Table 1. In some of these reports (46, 49), the minimum bactericidal concentrations (MBCs; i.e., the minimum drug concentration killing more than 99.9% of the original bacterial cells) (51), rather than the MICs, were measured. While Jones (46) determined the MBC under normal growth conditions, in our previous report (49) we used a minimal medium that ensured a constant cell density. Different media were used also for the MIC assays: salt-free Luria broth (47), Müller–Hinton broth (MHB) (48), or 3–morpholinopropane–1–sulfonic acid (MOPS)–based rich defined media (RDM) (50). In another study concerning the activity of MSI–94 against Pseudomonas aeruginosa (52), quantitative MIC or MBC determinations were not performed, and hence, it is not included in Table 1. However, the time–kill curves obtained at different cell densities were indicative of a significant IE.

Table 1.

Literature studies of IE for AMPs

Peptide	Bacteria	Experiment	Inocula (CFU/mL)	IE*	Reference
Lactoferricin B	E. coli	MBC	3.5 × 104 − 3.5 × 108	20	46
Gramicidin S	E. coli	MIC	105, 1010	2	47
Gramicidin S	S. aureus	MIC	105, 108	8	47
PGLa	E. coli	MIC	105, 1010	2	47
PGLa	S. aureus	MIC	105, 108	4	47
Pexiganan	E. coli	MIC	5 × 100 − 5 × 108	100	48
DNS-PMAP23	E. coli	MBC	5 × 104 − 5 × 108	7	49
LL-37	E. coli	MIC	5 × 105 − 2 × 107	10	50

^*IE indicates the fold increase in MIC or MBC in the inoculum range investigated.

Hartmann (47) studied only two cell densities (Table 1), while Snoussi (50) investigated inocula spanning less than three orders of magnitude. All other studies (46, 48, 49) found an interesting trend: while the active concentration generally depends on the inoculum density, it becomes constant when testing below a certain cell density.

Considering the role of AMPs in innate immunity and the probable clinical relevance of the IE, as well as the scarcity and heterogeneity of available data, we performed a systematic investigation on 11 peptides and peptidomimetics (Table 2). For all compounds, MIC testing was performed under the same experimental conditions, in order to establish whether the IE is a general property of AMPs and to investigate its possible origin. We measured MIC values for a range covering more than seven orders of magnitude of inoculum cell densities.

Table 2.

Peptides investigated in the present study and their properties

Peptide	Class	Sequence	AA*	Q†	Mechanism	Ref.
Indolicidin	Cathelicidin	ILPWKWPWWPWRR	13	+4	Membrane-active	53, 54
LL-37	Cathelicidin	LLGDFFRKSKEKIGKEFKRIVQRIKDFLRNLVPRTES	37	+8	Membrane-active	55, 56
Melittin	Toxin	GIGAVLKVLTTGLPALISWIKRKRQQ	26	+6	Membrane-active	59, 60
Novicidin	Artificial	KNLRRIIRKGIHIIKKYF	18	+8	Membrane-active	57, 58
P9-4	Artificial	KWRRWIRWL	9	+5	Membrane-active	61
1	Mimetic	Ac-(hR-βNPhe)6	12	+6	Membrane-active	62
2	Mimetic	(K-βNspe-hR-βNspe)3	12	+7	Membrane-active	62
3	Mimetic	Ac-(K-βNPhe)8	16	+8	Membrane-active	62
Bac (1–16)	P-rich	RRIRPRPPRLPRPRPR	16	+9	Intracellular target	74, 75
Bac (1–17)	P-rich	RRIRPRPPRLPRPRPRP	17	+9	Intracellular target	67, 73
Drosocin	P-rich	GKPRPYSPRPTSHPRPIRV	19	+6	Intracellular target	71, 72

βNPhe = N-phenylmethyl-β-alanine; βNspe = N-[(S)-1-phenylethyl]-β-alanine, hR = homoarginine. Drosocin was not glycosylated on its T residue. All sequences are amidated at the C terminus. All peptides have been demonstrated to be bactericidal.

^*No. of amino acids.

^†Electrostatic charge (under physiological pH).

As discussed above, for most AMPs, the bacterial membrane is the main target. Among the peptides investigated in the present study, the natural AMPs indolicidin (53, 54), LL-37 (55, 56), novicidin (57, 58), the bee toxin melittin (59, 60), the artificial peptide P9-4 (61), and peptidomimetics 1, 2, and 3 (62) all belong to different subclasses of membrane-active antimicrobials that are bactericidal. In principle, upon perturbation of the bacterial membrane, some membrane-active AMPs may penetrate into the cell and interact with intracellular targets (63, 64). For instance, indolicidin and LL-37 bind DNA (as many cationic AMPs do), but the role of this phenomenon in the mechanism of bacterial killing is debated (65–68). It is also worth mentioning that, in addition to their antimicrobial action, some of these peptides (e.g., LL-37) exert other activities, including immunomodulation and endotoxin neutralization (69). Other AMPs enter the cell through transporters, without significantly perturbing its membranes, and act on specific intracellular proteins (70). As examples of such peptides, we included the proline-rich drosocin (in nonglycosylated form) (71, 72) as well as fragments 1 to 16 and 1 to 17 of bactenecin 7 [i.e., Bac (1–16) and Bac (1–17)] (67, 73–75).

Results

Influence of Cell Density on AMP Activity Is a Universal Phenomenon.

The IE was evaluated by determining MIC values for inoculum densities of Escherichia coli American Type Culture Collection (ATCC) 25922 ranging from 5 × 10¹ to 1 × 10⁸ CFU/mL. As illustrated in Fig. 1, a significant increase in MIC values (ranging from a factor of 3 to more than 100-fold) was observed for all compounds when applying inoculum densities above the standard value of 5 × 10⁵ CFU/mL. By contrast, when bacterial cell densities were below this standard value, the cell density dependence of the MIC values was much less marked, and in most cases, a clear plateau for the MIC values was observed in the range between 5 × 10¹ and 5 × 10⁵ CFU/mL. For all peptides and peptidomimetics investigated, these plateau values (MIC_min) were in the micromolar range. These findings are in agreement with the few previously available investigations on the IE for AMPs (46, 48, 49).

Fig. 1.

IE for the MIC values of different AMPs and peptidomimetics against E. coli ATCC 25922 (or S. epidermidis ATCC 12228, where indicated). Each measurement was repeated in triplicate, and all three data points (which often overlap) are reported (in different shades of blue). Error bars indicate the interval between the lowest concentration inhibiting bacterial growth and the highest concentration not causing inhibition. For membrane-active peptides and peptidomimetics, the best fit to Eq. 2 is reported as a red line. When the MIC was higher than the highest concentration tested (i.e., 64 µM), the data point was reported arbitrarily as 96 ± 32 µM, as a crossed square, but it was not included in the fit.

Due to the broad panel of peptides and peptidomimetics investigated, the present data infer a general relevance of the IE for AMPs and of the MIC trend observed here. Indeed, for indolicidin, selected as a representative membrane-active peptide, we observed a similar behavior also with the Gram-positive bacterium Staphylococcus epidermidis ATCC 12228 (Fig. 1). It is worth mentioning that a similar dependence on cell density has been observed also for the lytic activity of an AMP on erythrocytes (49). Overall, these data suggest that a general mechanism, not depending on the specific cell properties, is likely causing the IE of AMPs.

The IE Is Not Caused by Peptide Degradation.

For many traditional antibiotics, the IE is caused by degradation of the drug by bacterial enzymes (13). In the case of AMPs, a common mechanism of bacterial resistance involves the production and release of proteases into the extracellular medium, thereby degrading the peptide (76, 77). To examine whether this phenomenon plays a role also with respect to the IE, enantiomeric peptides (consisting entirely of D-amino acids) not expected to be susceptible to proteases were tested as well. As shown in Fig. 2, the MIC of the P9-4 peptide and of its enantiomer exhibited a similar activity, and both had a significant IE at high cell densities. By contrast, in the case of Bac (1–17), which inhibits protein synthesis by binding to the ribosome, the D enantiomer was much less active, as expected, since its mechanism involves a stereospecific interaction with a protein. Noteworthy, peptidomimetics 1, 2, and 3 belong to a compound class previously demonstrated to be resistant to proteolysis too (78). Based on these data, we can rule out proteolytic degradation as a possible cause of the IE.

Fig. 2.

Comparison of the IE for the MIC values of enantiomeric peptides against E. coli ATCC 25922. Data for the all-L and all-D enantiomers are reported in shades of blue and red, respectively. For the definition of symbols and error bars, please refer to Fig. 1.

The Plateau in MIC Values Does Not Arise from Peptide Sequestration by Culture Medium or Container Walls.

It has been reported that AMPs can be sequestered by medium components, and their activity is consequently partially lost (79). It is conceivable that a minimum AMP concentration is needed to saturate the binding sites in the medium components. If this actually was the case, only peptide concentrations exceeding this value would leave some peptide molecules free to interact with the bacteria, resulting in a detectable activity. Therefore, the minimum MIC value observed at vanishing cell densities might in principle correspond to the threshold needed for the saturation of the medium components.

To verify the possible role of this propensity for adsorption with respect to the IE, we repeated the MIC determinations in three different dilutions of the MHB medium: 100, 50, and 10%, for the membrane-active peptide LL-37 (Fig. 3). This peptide was selected because it has been previously reported that its activity is inhibited by the cell culture medium (79). LL-37 was found to be more active in the diluted media, possibly as a consequence of reduced peptide sequestration (but also of enhanced bacterial sensitivity caused by the lack of nutrients). In any case, its MIC still depended on cell density, and the presence of a plateau at low bacterial loads was conserved. The level of the plateau changed only by a factor of four when the assay was performed in a 10-fold diluted medium. In addition, we have previously observed the IE of AMPs and a plateau at low cell densities even in a minimal medium containing only buffer, salts, and glucose (49). Therefore, sequestration by medium components can be ruled out as the possible cause of the observed trend.

Fig. 3.

IE of LL-37 against E. coli ATCC 25922 after 20 h at 37 °C in 100, 50, and 10% MHB. Results of three independent measurements are reported in different shades of blue, green, and red, for 100, 50, and 10% broth, respectively. For the definition of symbols and error bars, please refer to Fig. 1.

Considering the amphipathic properties of AMPs, peptide sequestration because of adsorption to the surface of the microtiter plate appeared possible too (80–82). Similarly to peptide sequestration by medium components, a saturation effect in this phenomenon (82) could explain the plateau value for the MIC at lower cell densities. However, to the best of our knowledge, a real-time measurement of peptide adsorption to container walls over several hours has not been reported previously. To reduce peptide adsorption to the plate surfaces, we performed all our experiments in polypropylene rather than polystyrene plates (2, 83). In addition, we tested the effect of peptide adsorption to the microplate walls under the worst possible conditions, that is, in the absence of bacteria and medium, merely using a simple buffer. Adsorption was followed by utilizing the intrinsic fluorescence of tryptophan residues present in some of the AMPs (i.e., indolicidin, melittin, and the all-D enantiomer of P9-4, d(P9-4)). The recording of the emission signal was focused at the center of the well volume, so that any peptide adsorbed on the walls of the well would not be detected. A control experiment with a tryptophan solution ruled out any photobleaching effects under the experimental conditions used (Fig. 4). Three concentrations were tested for each peptide: 2, 4, and 8 μM. For indolicidin, all three values are lower than the MIC_min (∼10 μM). By contrast, for melittin and d(P9-4), MIC_min (∼2 μM) coincides with the lowest concentration tested.

Fig. 4.

Peptide adsorption to the microtiter plate surface as determined by the fluorescence in the center of the well volume. Peptide concentrations of 2, 4, and 8 µM are reported in blue, green, and red, respectively. The dashed lines in the indolicidin plot correspond to a 40 µM tryptophan solution, used as a control for possible photobleaching effects. Top: 20 h; bottom: 60 min.

For all AMPs, significant adsorption was observed during the 20 h used as incubation time in the MIC determinations (Fig. 4). The peptide molecules were adsorbed to the plate walls to different degrees, and the effect was concentration dependent: at 8 µM, the adsorbed fractions were about 20, 30, and 30%, for melittin, d(P9-4), and indolicidin, respectively; these values were much higher at 2 µM (40, 70, and 90%), consistent with a saturation effect. However, adsorption during the first hour of incubation was negligible at all concentrations tested (Fig. 4). Membrane-active AMPs are usually bactericidal rather than bacteriostatic and a bactericidal mechanism has been demonstrated for all the peptides investigated in the present study. In addition, the bacterial killing by membrane-active AMPs is usually very fast, and all peptides investigated in Fig. 4 exert their killing activity in less than 1 h (53, 59, 61). Therefore, peptide adsorption to the microtiter plate appears negligible during the time needed for the peptides to exert their action, and it can be ruled out as the main cause for the plateau in MIC values at vanishing cell densities. Nevertheless, the adsorption to plate material is particularly important to consider when testing very potent AMPs that may display an apparent low activity when applying inappropriate plates for MIC testing (83).

High Cell Densities Do Not Decrease the Intrinsic Bacterial Susceptibility.

To test whether high cell densities cause changes in the bacterial state that lead to a reduced intrinsic susceptibility to the AMPs, we selected indolicidin as a test peptide. Survivors in cultures of the different inocula of E. coli ATCC 25922, incubated overnight with indolicidin at a sub-MIC concentration (1/2 × MIC or 1/4 × MIC), were regrown to mid-log phase (6 × 10⁸ cells/mL) and then diluted to the standard cell density used for MIC assays, that is, 5 × 10⁵ cells/mL (irrespective of the original inoculum of the culture from which they were derived). The MIC was determined again, and it turned out to be the same for all cultures, irrespective of the original inocula (Table 3). In particular, the MIC was 32 to 64 µM when measured at 5 × 10⁷ cells/mL, but it went down to 16 µM when the survivors of these cells were regrown to mid-log phase and diluted to 5 × 10⁵ cells/mL. This value coincides with the MIC measured directly at 5 × 10⁵ cells/mL.

Table 3.

Susceptibility of E. coli ATCC 25922 survivors to pretreatment at sub-MIC concentrations of indolicidin at different cell densities

Cell density (cells/mL)	5 × 103	5 × 105	5 × 107
MIC (µM)	16; 16	16; 16	32; 64
MIC of survivors*
After 1/2 × MIC pretreatment (µM)	16; 32	16; 16	16; 16
After 1/4 × MIC pretreatment (µM)	16; 16	16; 32	16; 32

^*MIC determined at 5 × 10⁵ cells/mL after pretreatment at sub-MIC concentrations (at different cell densities as indicated in the column heading). Results of duplicate, independent experiments are reported.

We also followed the growth rate of bacteria, treated with indolicidin at 1/2 × MIC, through measurements of optical density (OD) (λ = 590 nm) (Fig. 5). Cell cultures at different inocula, not treated with AMPs, grow at the same initial rate but reach a measurable change in OD at different times, while at the MIC, no growth was observed. An indolicidin concentration equal to half of the MIC did not cause any variation in the initial rate of OD variation but produced only a shift in the time at which a significant OD was reached. This finding is consistent with a bactericidal activity, and it indicates that sub-MIC concentrations kill a fraction of the cells (48, 50). The remaining ones grow at a similar rate as the initial population, which indicates that they do not differ markedly from the other cells.

Fig. 5.

Bacterial growth curves for different inocula of E. coli ATCC 25922 (5 × 10¹, 5 × 10², 5 × 10³, 5 × 10⁴, 5 × 10⁵, 5 × 10⁶, 5 × 10⁷, and 1 × 10⁸ CFU/mL, shown in violet, purple, blue, light blue, green, orange, red, and dark red, respectively), untreated (Left), or in the presence of 1/2 × MIC of indolicidin (Right). A representative growth curve (5 × 10⁵ CFU/mL), in the presence of an indolicidin concentration corresponding to the MIC, is also reported as a black dashed line (Right). The OD of the bacterial culture was measured at 590 nm during incubation at 37 °C. Results are the mean of duplicate samples from a single experiment, representative of two different experiments.

Overall, these findings indicate that phenotypic differences resulting in lower susceptibility to indolicidin are not induced by high cell densities. It is worth mentioning that a previous study demonstrated that the efficacy of AMPs is comparable for persister cells and dividing bacteria (84), unlike what is typically seen for traditional antibiotics.

A Simple Model, Based on Association of Peptides with Bacteria, Describes the Observed Behavior.

Recently, we predicted the trend in activity (measured as MIC) versus inoculum density observed here, for an analog of the membrane-active peptide PMAP23, DNS-PMAP23 (49, 85). In that case, by performing quantitative studies of AMP interaction with bacterial cells, we showed that a threshold number of peptides ($T_B$) must bind to a bacterial cell in order to cause its death (85). Secondly, we experimentally characterized peptide–cell association, showing that this process could be described to a reasonable approximation by a simple partition equilibrium, defined by an apparent partition constant $K_{app.}$ (with units of cells/mL), corresponding to the cell density at which half of the peptide molecules are cell–bound (Materials and Methods) (49, 85).

The IE observed here can be explained by assuming that these two properties are generally valid for membrane-active AMPs. At cell densities significantly higher than $K_{app.}$, all peptide molecules in the sample are associated to bacteria. In this case, the IE is simply due to the fact that more cells need more peptide molecules in order to reach the threshold $T_B$ that is required for killing. By contrast, in the low cell density regime (i.e., $\left[Bacteria\right]\ll K_{app.}$), most of the peptides remain free in solution. In this interval, the partition equilibrium can be approximated by a linear behavior ($f_B\cong \left[Bacteria\right]/K_{app.}$), and therefore, the fraction of cell-bound peptide molecules decreases proportionally to $\left[Bacteria\right]$. As a consequence, these two effects (less cells to kill, and a lower fraction of cell-bound peptide) cancel each other, and the total peptide concentration needed in the sample to kill the bacteria remains essentially constant (45).

As described in Materials and Methods (Eq. 2), the model predicts a linear cell density dependence of the MIC, with a nonzero intercept ($MI{C}_{min.}$). This behavior, in a logarithmic cell density scale, corresponds to the trend observed in our experiments, with a plateau reaching $MI{C}_{min.}$ at inocula significantly lower than $K_{app.}$

The MIC data, determined in the present study on a large panel of membrane-active peptides and peptidomimetics, were analyzed with the model indicated above (solid curves in Figs. 1 and 3), which describes all the data sets within experimental errors. The parameters obtained from this analysis are reported in Table 4.

Table 4.

Parameters derived from fitting of the IE curves^*

Peptide	$MI{C}_{min.}$(µM)	$K_{app.}$(106 cells/mL)	$T_B$ (106 molecules/cell)	${\chi }_r^2$	Degrees of freedom	P value
Indolicidin	13 ± 1	40 ± 10	200	0.4	22	>0.99
Indolicidin (S. epidermidis)	1.9 ± 0.2	40 ± 10	30	1.0	25	>0.40
LL-37	3.2 ± 0.3	5 ± 1	400	0.6	22	>0.90
Melittin	1.3 ± 0.2	1.7 ± 0.3	500	1.0	22	>0.40
Novicidin	0.76 ± 0.06	31 ± 7	10	0.3	25	>0.99
P9-4	1.6 ± 0.1	3.9 ± 0.6	200	1.6	25	>0.02
1	0.78 ± 0.06	70 ± 20	7	0.6	25	>0.90
2	1.2 ± 0.1	7 ± 2	100	1.2	25	>0.20
3	1.3 ± 0.1	2.0 ± 0.3	400	1.7	25	>0.01

^*All parameters refer to MIC values measured for E. coli (except where explicitly indicated otherwise), in MH medium. For parameter definitions, see the main test. ${\chi }_r^2$ is the reduced χ² reported as a measure of the goodness of fit, the degrees of freedom of the fit indicate the number of data points minus the number of fitting parameters, and the P value indicates the probability of obtaining a reduced χ² value higher than the one that was observed, assuming that the model is correct. According to these P values, and using a 1% probability threshold, no significant discrepancies between the data and the model are present; with a 5% probability threshold, only the curves for peptide P9-4 and peptidomimetic 3 deviate significantly from the data.

$MI{C}_{min.}$ provides a measure of the plateau value of the MIC at vanishing cell densities. All values were in the 1 to 10 µM range, showing that micromolar AMP concentrations are necessary for antimicrobial activity, even when the bacterial load is extremely low.

The apparent partition constant provides a measure of the cell density above which the MIC starts to increase with bacterial counts (more specifically, based on Eq. 2, $K_{app.}$ is the cell density for which the MIC is twice the $MI{C}_{min.}$). The $K_{app.}$ values were within the range of 10⁶ to 10⁸ cells/mL. These values are consistent with the few available values of $K_{app.}$ measured directly in experiments of AMP binding to E. coli cells. For DNS-PMAP23, the measured $K_{app.}$ value was 1.8 × 10⁸ cells/mL (49). Starr (86) reported apparent binding constants for the artificial AMP ARVA interacting with E. coli in the range of 5 × 10⁶ to 5 × 10⁷ cells/mL (depending on peptide concentration).

From the $MI{C}_{min.}$ and $K_{app.}$ values, according to the model (Materials and Methods), an estimate for the threshold of bound peptide molecules per cell needed for bacterial killing can be obtained (i.e., $T_B$; Table 4), which determines the strength of the IE since it defines the slope of the curve (Eqs. 2 and 3). These values ranged from 7 to 500 million molecules per cell, confirming our previous conclusion that a huge accumulation of peptide on each cell is required to achieve an antibacterial effect (45, 49, 63, 85).

Discussion

Our data indicate that the IE is a universal property of the activity of AMPs. In addition, we observed that below a certain peptide-dependent threshold of cell density, the MIC becomes constant. This trend is consistent with the very few previous observations available in the literature, and it seems to be a general characteristic of AMPs. Since AMPs are important players of the innate immunity, characterizing their IE contributes to our understanding of infection dynamics (87) and host–microbiota interactions.

We ruled out cell density–dependent phenotypic effects, proteolytic degradation, and experimental artifacts, such as peptide adsorption to container walls or sequestration by medium components as possible causes for the observed behavior. Our simple model could satisfactorily describe the trend observed for the cell density dependence of MIC values for membrane-active peptides. This model is based on two assumptions: 1) a threshold of cell-bound peptide molecules is needed for bacterial killing, and 2) peptide association to bacteria is approximately described by a partition equilibrium. Although simplifying, these assumptions are supported by previous experimental evidence.

A partition equilibrium is an obvious oversimplification for peptide interaction with an out-of-equilibrium system such as a live bacterial cell, and bacterial membranes can hardly be considered as homogeneous phases. However, previous studies, where we directly measured peptide–cell binding, rather surprisingly showed that the association curves deviate only slightly from those predicted by an ideal partition equilibrium or from those measured for model membranes (49, 63, 85). For instance, the curves obtained for peptide concentrations differing by an order of magnitude (1 and 10 µM) showed cell concentrations corresponding to 50% peptide binding that varied only by a factor of 2 (i.e., ∼1 × 10⁸ and 2 × 10⁸ cells/mL, respectively) (49), approximating the peptide concentration independence expected for an ideal behavior. In addition, curves obtained for binding to E. coli cells or to liposomes were essentially superimposable when expressed as a function of lipid concentration (85).

In our model, the threshold of bound molecules needed for killing is assumed to be the same for all cells in the bacterial population, while differences in susceptibility might be present between individual bacteria. However, unlike traditional antibiotics, AMPs have a very narrow concentration range of intermediate efficacy, that is, the window between concentrations that have no effect and concentrations that result in complete killing (31, 49).

Further support for the model is provided by the parameters determined by fitting the IE data: apparent partition constants and threshold values for bound AMP molecules needed for bacterial killing are in agreement with values previously determined by direct experimental measurements (45, 63, 85, 86, 88, 89). In particular, the data reported here, and previous reports, concur to indicate that the threshold of bound AMP molecules needed for bacterial killing is within the range of 10⁶ to 10⁸ molecules/cell (45). However, simple calculations indicate that these numbers correspond to a complete coverage of all the bacterial membranes or even exceed this limit (49, 63, 85). Therefore, binding to cellular components other than the bacterial membranes is likely. In studies by Jepson (48), Snoussi (50), and Wu (90), it was shown that lysed cells are capable of sequestering a large number of peptide molecules. We have recently measured the association of an AMP to lysed cells, which proved to bind the peptide 10 times stronger than live bacteria (63). Finally, microscopy experiments (68) provided a mechanistic explanation for these observations: once the membranes are permeabilized, AMPs can enter the cell, and hence, molecules in the intracellular compartment (e.g., DNA) become accessible for binding. These effects could contribute to the IE by reducing the free peptide concentration available for bacterial killing (48, 50, 90), and therefore lead to an overestimation of the $T_B$ value. Collective tolerance induced by antibiotic inhibition or sequestration by dead cells is a common response in bacteria (16). However, these phenomena can come into play only after bacterial membranes are permeabilized, which still requires a threshold of bound peptides per cell to be reached (90).

It is interesting to note that considerations extremely similar to those presented here, regarding a drug-target binding equilibrium and a threshold number of bound drug molecules per cell to cause killing or growth inhibition, have been demonstrated to be valid also for the IE of traditional antibiotics (e.g., oxacillin, ciprofloxacin, or gentamicin), including ionophores such as vancomycin (14, 15, 87). In addition, a plateau for the MIC values for inocula lower than 10⁵ to 10⁶ CFU/mL has been observed also for traditional antibiotics, irrespective of their mode of action (14, 91, 92), and this limiting value has by some authors been termed the single-cell MIC (91, 92). Therefore, the relevance of the conclusions reached in this study may extend beyond the class of membrane-active AMPs. Indeed, we have observed a similar trend for peptidomimetics perturbing the bacterial membrane and for AMPs inhibiting intracellular targets.

Alternative explanations for the observed trends are of course still possible and cannot be ruled out. However, our model appears to be sufficient for explaining the IE. Furthermore, the specific mechanism might be marginally relevant as compared to the consequences of the effect for the appropriate selection of leads to undergo preclinical testing and for the future clinical application.

Our findings question the suitability of the standard protocol for determining the MIC at a single-cell density. The use of a range of cell densities provides a much broader characterization of the efficacy of a peptide (or antibiotic). For instance, our data showed that the activity of different peptides is affected by the cell density to a variable degree. Therefore, a comparison of the activities of various AMPs and analogs should take the IE into account.

The standard inoculum used in MIC assays (i.e., 5 × 10⁵ CFU/mL) is close to the range of K_app. values. Since this parameter determines the cell density for which the IE becomes relevant, small errors in the inoculum might affect the MIC values significantly (and to a different extent for different peptides) (17). For traditional antibiotics, it has been suggested that determining the MIC at a lower cell density, where the IE is negligible for all the molecules being characterized, might provide a more robust measurement (91). Based on the data in Table 4, this condition would correspond roughly to 5 × 10⁴ CFU/mL for AMPs.

We have previously shown that cell density affects also the lytic activity of AMPs against erythrocytes (49), and also in that case, a plateau in the active concentration was observed at vanishing cell densities. This finding supports the hypothesis that the mechanism causing the IE is rather general and not dependent on the specific cell type, in agreement with the simple model presented here. In addition, it indicates that a complete characterization of the selectivity of AMPs should consider activity and toxicity at different cell concentrations. The selectivity does not have a single value, but depends on the density of microbial and host cells (34, 45, 49).

Finally, our data indicate that, even at vanishing cell densities, the active concentrations of AMPs do not decrease below the micromolar range. Such concentrations are reached physiologically in the granules of leukocytes (32), on the skin of frogs (93), and in the hemolymph of infected insects (94). Incidentally, the plateau value in the active concentration at low cell densities provides also an explanation for the observation that in some infected insects, the production of AMPs is not dependent on the bacterial load, and is maintained for a long time after the infection (95). Where the physiological concentrations of AMPs are lower than micromolar, other functions, particularly immunomodulation, might be more important than direct bacterial killing (32). However, in most cases, animal hosts elicit a suite of AMPs acting additively and often even synergistically (31, 96). Hence, while the concentration of each individual AMP might be below the activity threshold, bacterial killing could still take place with the mixture.

Materials and Methods

Peptides.

Melittin was purchased from Sigma-Aldrich, while all other peptides were synthesized on a CEM Liberty™ microwave peptide synthesizer by using microwave-assisted Fmoc-based solid-phase peptide synthesis on a Rink Amide resin by using previously reported conditions (97). Peptidomimetics based on the α-peptide/β-peptoid chimeric backbone were prepared by solid-phase synthesis as previously described (98).

Antimicrobial Assays.

The MIC values against the Gram-negative bacterium E. coli ATCC 25922 and the Gram-positive S. epidermidis ATCC 12228 were evaluated by using the standard broth microdilution assay (2) in cation-adjusted MHB (Becton Dickinson, 212322), as outlined by CLSI (3, 4), using 96-well polypropylene microtiter plates (Thermo Scientific Nunc, 267245). E. coli and S. epidermidis were grown in MHB at 37 °C to a mid-log phase (6 × 10⁸ and 2 × 10⁸ cells/mL, for E. coli and S. epidermidis, respectively). Aliquots of 50 µL of bacterial suspension at different cell densities were added to 50 µL MHB containing serial twofold dilutions of the peptides (from 64 to 0.5 µM) previously prepared in the microplate. After incubation for 20 h at 37 °C, the MIC was determined. The MIC value was considered to be in the interval between the highest concentration not causing inhibition and the lowest concentration inhibiting bacterial growth. MHB diluted 1:2 and 1:10 in water was also used to determine the MIC of a selected peptide using the same procedure (99, 100). Each measurement was performed in triplicate.

Susceptibility of survivors was first evaluated by measuring MICs using different bacterial inocula (5 × 10³, 5 × 10⁵, and 5 × 10⁷ CFU/mL), after overnight incubation. Survivors in different inocula, subjected to treatment with peptide concentrations of 1/2 × MIC or 1/4 × MIC, were isolated and then grown to mid-log phase. Afterward, irrespective of the original inoculum of the culture from which they were derived, samples were diluted to the same cell concentration (5 × 10⁵ CFU/mL). Then, the MICs were determined again as previously described.

Experiments to evaluate bacterial growth were performed by measuring the OD at 590 nm in a microplate reader (Infinite M 200; Tecan AG) over 20 h at 37 °C. Untreated bacterial cells were used as the control.

Peptide Adsorption to the Microtiter Plate Surface.

Adsorption tests were carried out by using the same 96-well polypropylene microtiter plates (Thermo Scientific Nunc, 267245) employed for MIC experiments. Fluorescence data were collected using a Tecan Infinite 200PRO plate reader (Tecan AG). Briefly, 300 µL of Buffer A (phosphate buffer 10 mM and NaCl 140 mM) containing a twofold dilution (from 8 to 2 µM) of peptide or tryptophan (used as a control) was added to different wells. The fluorescence signal coming from the center of the well was recorded every 10 min for a total time of 1,200 min, using λ_ex = 280 nm and λ_em = 360 nm.

Model for the IE.

Based on our previous studies of peptide–bacteria interaction (45, 49, 63, 85), we assume the following:

• 1)a threshold number of peptides ($T_B$) must be bound to a bacterial cell in order to cause its death (78) and
• 2)peptide association to bacterial cells can be approximately described by a simple partition equation (49, 85):

$$f_B=\frac{\left[Bacteria\right]/K_{app.}}{1+\left[Bacteria\right]/K_{app.}},$$ [1]

where $K_{app.}$ is an apparent partition constant corresponding to the cell density at which half of the peptide molecules are cell bound (Fig. 6).

Fig. 6.

Model predictions for peptide-cell binding and the IE. The fraction of cell-bound peptide molecules (f_b, Left) and MIC relative to the plateau value at low cell densities (Right) are both shown as a function of the inoculum cell density relative to the apparent partition constant. The blue and orange zones correspond to inocula in which the peptides are predominantly free in solution or predominantly bound to cells, respectively.

As a consequence of these assumptions, the dependence of the active concentration (i.e., the MIC or the MBC, which essentially coincide in the case of a bactericidal mechanism) on cell density can be predicted (see ref. 49 for a demonstration):

$$MIC=\left(1+\left[Bacteria\right]/K_{app.}\right)MI{C}_{min.},$$ [2]

with

$$MI{C}_{min.}=K_{app.}\frac{{10}^3}{N_A}{T}_B.$$ [3]

Here, $N_A$ is Avogadro’s constant, $MIC$ and $MI{C}_{min.}$ are expressed in moles/L, $K_{app.}$ and the bacterial cell density ([Bacteria]) are reported in cells/mL, and $T_B$ is expressed in molecules per cell. This linear equation, with a nonzero intercept ($MI{C}_{min.}$) in a logarithmic cell density scale, corresponds to the trend reported in Fig. 6 with a plateau reaching $MI{C}_{min.}$ at inocula significantly lower than $K_{app.}$

When fitting the data to Eq. 2, the results of each repeated experiment were reported explicitly, with an uncertainty corresponding to the interval going from the highest concentration not inhibiting bacterial growth to the minimum concentration inhibiting the growth (e.g., if a peptide concentration of 8 μM inhibited the growth and 4 μM did not, we reported a MIC value of 6 ± 2 μM). Since MIC experiments are performed with a twofold dilution spacing in the concentration, they have an intrinsic uncertainty of a factor of two (101, 102). Goodness of fit was assessed by calculating the reduced χ² parameter (103) and the associated P value, that is, the probability of obtaining a value larger than the reduced χ² that was actually observed (assuming that the model is correct and considering the degrees of freedom of the fit, i.e., the number of data points minus the number of fit parameters). Values lower than 5% and 1% for this probability are conventionally considered to indicate a “significant” and “highly significant” discrepancy, respectively, between model and data (103).

Data Availability

All study data are included in the main text.