A membrane-associated phosphoswitch in Rad controls adrenergic regulation of cardiac calcium channels.

The ability to fight or flee from a threat relies on an acute adrenergic surge that augments cardiac output, which is dependent on increased cardiac contractility and heart rate. This cardiac response depends on ß-adrenergic-initiated reversal of the small RGK G protein Rad-mediated inhibition of voltage-gated calcium channels (CaV) acting through the Cavß subunit. Here, we investigate how Rad couples phosphorylation to augmented Ca2+ influx and increased cardiac contraction. We show that reversal required phosphorylation of Ser272 and Ser300 within Rad's polybasic, hydrophobic C-terminal domain (CTD). Phosphorylation of Ser25 and Ser38 in Rad's N-terminal domain (NTD) alone was ineffective. Phosphorylation of Ser272 and Ser300 or the addition of 4 Asp residues to the CTD reduced Rad's association with the negatively charged, cytoplasmic plasmalemmal surface and with CaVß, even in the absence of CaVα, measured here by FRET. Addition of a posttranslationally prenylated CAAX motif to Rad's C-terminus, which constitutively tethers Rad to the membrane, prevented the physiological and biochemical effects of both phosphorylation and Asp substitution. Thus, dissociation of Rad from the sarcolemma, and consequently from CaVß, is sufficient for sympathetic upregulation of Ca2+ currents.

Rad regulation of CaV1.2 channels controls cardiac fight-or-flight response.

Fight-or-flight responses involve ß-adrenergic-induced increases in heart rate and contractile force. In the present study, we uncover the primary mechanism underlying the heart's innate contractile reserve. We show that four protein kinase A (PKA)-phosphorylated residues in Rad, a calcium channel inhibitor, are crucial for controlling basal calcium current and essential for ß-adrenergic augmentation of calcium influx in cardiomyocytes. Even with intact PKA signaling to other proteins modulating calcium handling, preventing adrenergic activation of calcium channels in Rad-phosphosite-mutant mice (4SA-Rad) has profound physiological effects: reduced heart rate with increased pauses, reduced basal contractility, near-complete attenuation of ß-adrenergic contractile response and diminished exercise capacity. Conversely, expression of mutant calcium-channel ß-subunits that cannot bind 4SA-Rad is sufficient to enhance basal calcium influx and contractility to adrenergically augmented levels of wild-type mice, rescuing the failing heart phenotype of 4SA-Rad mice. Hence, disruption of interactions between Rad and calcium channels constitutes the foundation toward next-generation therapeutics specifically enhancing cardiac contractility.

Structure of the Native Muscle-type Nicotinic Receptor and Inhibition by Snake Venom Toxins.

The nicotinic acetylcholine receptor, a pentameric ligand-gated ion channel, converts the free energy of binding of the neurotransmitter acetylcholine into opening of its central pore. Here we present the first high-resolution structure of the receptor type found in muscle-endplate membrane and in the muscle-derived electric tissues of fish. The native receptor was purified from Torpedo electric tissue and functionally reconstituted in lipids optimal for cryo-electron microscopy. The receptor was stabilized in a closed state by the binding of α-bungarotoxin. The structure reveals the binding of a toxin molecule at each of two subunit interfaces in a manner that would block the binding of acetylcholine. It also reveals a closed gate in the ion-conducting pore, formed by hydrophobic amino acid side chains, located ∼60 Å from the toxin binding sites. The structure provides a framework for understanding gating in ligand-gated channels and how mutations in the acetylcholine receptor cause congenital myasthenic syndromes.

Membrane potential and Ca2+ concentration dependence on pressure and vasoactive agents in arterial smooth muscle: A model.

Arterial smooth muscle (SM) cells respond autonomously to changes in intravascular pressure, adjusting tension to maintain vessel diameter. The values of membrane potential (Vm) and sarcoplasmic Ca(2+) concentration (Ca(in)) within minutes of a change in pressure are the results of two opposing pathways, both of which use Ca(2+) as a signal. This works because the two Ca(2+)-signaling pathways are confined to distinct microdomains in which the Ca(2+) concentrations needed to activate key channels are transiently higher than Ca(in). A mathematical model of an isolated arterial SM cell is presented that incorporates the two types of microdomains. The first type consists of junctions between cisternae of the peripheral sarcoplasmic reticulum (SR), containing ryanodine receptors (RyRs), and the sarcolemma, containing voltage- and Ca(2+)-activated K(+) (BK) channels. These junctional microdomains promote hyperpolarization, reduced Ca(in), and relaxation. The second type is postulated to form around stretch-activated nonspecific cation channels and neighboring Ca(2+)-activated Cl(-) channels, and promotes the opposite (depolarization, increased Ca(in), and contraction). The model includes three additional compartments: the sarcoplasm, the central SR lumen, and the peripheral SR lumen. It incorporates 37 protein components. In addition to pressure, the model accommodates inputs of α- and ß-adrenergic agonists, ATP, 11,12-epoxyeicosatrienoic acid, and nitric oxide (NO). The parameters of the equations were adjusted to obtain a close fit to reported Vm and Ca(in) as functions of pressure, which have been determined in cerebral arteries. The simulations were insensitive to ± 10% changes in most of the parameters. The model also simulated the effects of inhibiting RyR, BK, or voltage-activated Ca(2+) channels on Vm and Ca(in). Deletion of BK ß1 subunits is known to increase arterial-SM tension. In the model, deletion of ß1 raised Ca(in) at all pressures, and these increases were reversed by NO.

Positions of the cytoplasmic end of BK α S0 helix relative to S1-S6 and of ß1 TM1 and TM2 relative to S0-S6.

The large-conductance, voltage- and Ca(2+)-gated K(+) (BK) channel consists of four α subunits, which form a voltage- and Ca(2+)-gated channel, and up to four modulatory ß subunits. The ß1 subunit is expressed in smooth muscle, where it slows BK channel kinetics and shifts the conductance-voltage (G-V) curve to the left at [Ca(2+)] > 2 µM. In addition to the six transmembrane (TM) helices, S1-S6, conserved in all voltage-dependent K(+) channels, BK α has a unique seventh TM helix, S0, which may contribute to the unusual rightward shift in the G-V curve of BK α in the absence of ß1 and to a leftward shift in its presence. Such a role is supported by the close proximity of S0 to S3 and S4 in the voltage-sensing domain. Furthermore, on the extracellular side of the membrane, one of the two TM helices of ß1, TM2, is adjacent to S0. We have now analyzed induced disulfide bond formation between substituted Cys residues on the cytoplasmic side of the membrane. There, in contrast, S0 is closest to the S2-S3 loop, from which position it is displaced on the addition of ß1. The cytoplasmic ends of ß1 TM1 and TM2 are adjacent and are located between the S2-S3 loop of one α subunit and S1 of a neighboring α subunit and are not adjacent to S0; i.e., S0 and TM2 have different trajectories through the membrane. In the absence of ß1, 70% of disulfide bonding of W43C (S0) and L175C (S2-S3) has no effect on V50 for activation, implying that the cytoplasmic end of S0 and the S2-S3 loop move in concert, if at all, during activation. Otherwise, linking them together in one state would obstruct the transition to the other state, which would certainly change V50.

Orientations and proximities of the extracellular ends of transmembrane helices S0 and S4 in open and closed BK potassium channels.

The large-conductance potassium channel (BK) α subunit contains a transmembrane (TM) helix S0 preceding the canonical TM helices S1 through S6. S0 lies between S4 and the TM2 helix of the regulatory ß1 subunit. Pairs of Cys were substituted in the first helical turns in the membrane of BK α S0 and S4 and in ß1 TM2. One such pair, W22C in S0 and W203C in S4, was 95% crosslinked endogenously. Under voltage-clamp conditions in outside-out patches, this crosslink was reduced by DTT and reoxidized by a membrane-impermeant bis-quaternary ammonium derivative of diamide. The rate constants for this reoxidation were not significantly different in the open and closed states of the channel. Thus, these two residues are approximately equally close in the two states. In addition, 90% crosslinking of a second pair, R20C in S0 and W203C in S4, had no effect on the V50 for opening. Taken together, these findings indicate that separation between residues at the extracellular ends of S0 and S4 is not required for voltage-sensor activation. On the contrary, even though W22C and W203C were equally likely to form a disulfide in the activated and deactivated states, relative immobilization by crosslinking of these two residues favored the activated state. Furthermore, the efficiency of recrosslinking of W22C and W203C on the cell surface was greater in the presence of the ß1 subunit than in its absence, consistent with ß1 acting through S0 to stabilize its immobilization relative to α S4.

Positions of ß2 and ß3 subunits in the large-conductance calcium- and voltage-activated BK potassium channel.

Large-conductance voltage- and Ca(2+)-gated K(+) channels are negative-feedback regulators of excitability in many cell types. They are complexes of α subunits and of one of four types of modulatory ß subunits. These have intracellular N- and C-terminal tails and two transmembrane (TM) helices, TM1 and TM2, connected by an ∼100-residue extracellular loop. Based on endogenous disulfide formation between engineered cysteines (Cys), we found that in ß2 and ß3, as in ß1 and ß4, TM1 is closest to αS1 and αS2 and TM2 is closest to αS0. Mouse ß3 (mß3) has seven Cys in its loop, one of which is free, and this Cys readily forms disulfides with Cys substituted in the extracellular flanks of each of αS0-αS6. We identified by elimination mß3-loop Cys152 as the only free Cys. We inferred the disulfide-bonding pattern of the other six Cys. Using directed proteolysis and fragment sizing, we determined this pattern first among the four loop Cys in ß1. These are conserved in ß2-ß4, which have four additional Cys (eight in total), except that mß3 has one fewer. In ß1, disulfides form between Cys at aligned positions 1 and 8 and between Cys at aligned positions 5 and 6. In mß3, the free Cys is at position 7; position 2 lacks a Cys present in all other ß2-ß4; and the disulfide pattern is 1-8, 3-4, and 5-6. Presumably, Cys 2 cross-links to Cys 7 in all other ß2-ß4. Cross-linking of mß3 Cys152 to Cys substituted in the flanks of αS0-S5 attenuated the protection against iberiotoxin (IbTX); cross-linking of Cys152 to K296C in the αS6 flank and close to the pore enhanced protection against IbTX. In no case was N-type inactivation by the N-terminal tail of mß3 perturbed. Although the mß3 loop can move, its position with Cys152 near αK296, in which it blocks IbTX binding, is likely favored.

Characterization of KCNQ1 atrial fibrillation mutations reveals distinct dependence on KCNE1.

The I(Ks) potassium channel, critical to control of heart electrical activity, requires assembly of α (KCNQ1) and ß (KCNE1) subunits. Inherited mutations in either I(Ks) channel subunit are associated with cardiac arrhythmia syndromes. Two mutations (S140G and V141M) that cause familial atrial fibrillation (AF) are located on adjacent residues in the first membrane-spanning domain of KCNQ1, S1. These mutations impair the deactivation process, causing channels to appear constitutively open. Previous studies suggest that both mutant phenotypes require the presence of KCNE1. Here we found that despite the proximity of these two mutations in the primary protein structure, they display different functional dependence in the presence of KCNE1. In the absence of KCNE1, the S140G mutation, but not V141M, confers a pronounced slowing of channel deactivation and a hyperpolarizing shift in voltage-dependent activation. When coexpressed with KCNE1, both mutants deactivate significantly slower than wild-type KCNQ1/KCNE1 channels. The differential dependence on KCNE1 can be correlated with the physical proximity between these positions and KCNE1 as shown by disulfide cross-linking studies: V141C forms disulfide bonds with cysteine-substituted KCNE1 residues, whereas S140C does not. These results further our understanding of the structural relationship between KCNE1 and KCNQ1 subunits in the I(Ks) channel, and provide mechanisms for understanding the effects on channel deactivation underlying these two atrial fibrillation mutations.

Location of modulatory beta subunits in BK potassium channels.

Large-conductance voltage- and calcium-activated potassium (BK) channels contain four pore-forming alpha subunits and four modulatory beta subunits. From the extents of disulfide cross-linking in channels on the cell surface between cysteine (Cys) substituted for residues in the first turns in the membrane of the S0 transmembrane (TM) helix, unique to BK alpha, and of the voltage-sensing domain TM helices S1-S4, we infer that S0 is next to S3 and S4, but not to S1 and S2. Furthermore, of the two beta1 TM helices, TM2 is next to S0, and TM1 is next to TM2. Coexpression of alpha with two substituted Cys's, one in S0 and one in S2, and beta1 also with two substituted Cys's, one in TM1 and one in TM2, resulted in two alphas cross-linked by one beta. Thus, each beta lies between and can interact with the voltage-sensing domains of two adjacent alpha subunits.

Location of the beta 4 transmembrane helices in the BK potassium channel.

Large-conductance, voltage- and Ca(2+)-gated potassium (BK) channels control excitability in a number of cell types. BK channels are composed of alpha subunits, which contain the voltage-sensor domains and the Ca(2+)- sensor domains and form the pore, and often one of four types of beta subunits, which modulate the channel in a cell-specific manner. beta 4 is expressed in neurons throughout the brain. Deletion of beta 4 in mice causes temporal lobe epilepsy. Compared with channels composed of alpha alone, channels composed of alpha and beta 4 activate and deactivate more slowly. We inferred the locations of the two beta 4 transmembrane (TM) helices TM1 and TM2 relative to the seven alpha TM helices, S0-S6, from the extent of disulfide bond formation between cysteines substituted in the extracellular flanks of these TM helices. We found that beta 4 TM2 is close to alpha S0 and that beta 4 TM1 is close to both alpha S1 and S2. At least at their extracellular ends, TM1 and TM2 are not close to S3-S6. In six of eight of the most highly crosslinked cysteine pairs, four crosslinks from TM2 to S0 and one each from TM1 to S1 and S2 had small effects on the V(50) and on the rates of activation and deactivation. That disulfide crosslinking caused only small functional perturbations is consistent with the proximity of the extracellular ends of TM2 to S0 and of TM1 to S1 and to S2, in both the open and closed states.

Location of KCNE1 relative to KCNQ1 in the I(KS) potassium channel by disulfide cross-linking of substituted cysteines.

The cardiac-delayed rectifier K(+) current (I(KS)) is carried by a complex of KCNQ1 (Q1) subunits, containing the voltage-sensor domains and the pore, and auxiliary KCNE1 (E1) subunits, required for the characteristic I(KS) voltage dependence and kinetics. To locate the transmembrane helix of E1 (E1-TM) relative to the Q1 TM helices (S1-S6), we mutated, one at a time, the first four residues flanking the extracellular ends of S1-S6 and E1-TM to Cys, coexpressed all combinations of Q1 and E1 Cys-substituted mutants in CHO cells, and determined the extents of spontaneous disulfide-bond formation. Cys-flanking E1-TM readily formed disulfides with Cys-flanking S1 and S6, much less so with the S3-S4 linker, and not at all with S2 or S5. These results imply that the extracellular flank of the E1-TM is located between S1 and S6 on different subunits of Q1. The salient functional effects of selected cross-links were as follows. A disulfide from E1 K41C to S1 I145C strongly slowed deactivation, and one from E1 L42C to S6 V324C eliminated deactivation. Given that E1-TM is between S1 and S6 and that K41C and L42C are likely to point approximately oppositely, these two cross-links are likely to favor similar axial rotations of E1-TM. In the opposite orientation, a disulfide from E1 K41C to S6 V324C slightly slowed activation, and one from E1 L42C to S1 I145C slightly speeded deactivation. Thus, the first E1 orientation strongly favors the open state, while the approximately opposite orientation favors the closed state.

Locations of the beta1 transmembrane helices in the BK potassium channel.

BK channels are composed of alpha-subunits, which form a voltage- and Ca(2+)-gated potassium channel, and of modulatory beta-subunits. The beta1-subunit is expressed in smooth muscle, where it renders the BK channel sensitive to [Ca(2+)](i) in a voltage range near the smooth-muscle resting potential and slows activation and deactivation. BK channel acts thereby as a damped feedback regulator of voltage-dependent Ca(2+) channels and of smooth muscle tone. We explored the contacts between alpha and beta1 by determining the extent of endogenous disulfide bond formation between cysteines substituted just extracellular to the two beta1 transmembrane (TM) helices, TM1 and TM2, and to the seven alpha TM helices, consisting of S1-S6, conserved in all voltage-dependent potassium channels, and the unique S0 helix, which we previously concluded was partly surrounded by S1-S4. We now find that the extracellular ends of beta1 TM2 and alpha S0 are in contact and that beta1 TM1 is close to both S1 and S2. The extracellular ends of TM1 and TM2 are not close to S3-S6. In almost all cases, cross-linking of TM2 to S0 or of TM1 to S1 or S2 shifted the conductance-voltage curves toward more positive potentials, slowed activation, and speeded deactivation, and in general favored the closed state. TM1 and TM2 are in position to contribute, in concert with the extracellular loop and the intracellular N- and C-terminal tails of beta1, to the modulation of BK channel function.

Position and role of the BK channel alpha subunit S0 helix inferred from disulfide crosslinking.

The position and role of the unique N-terminal transmembrane (TM) helix, S0, in large-conductance, voltage- and calcium-activated potassium (BK) channels are undetermined. From the extents of intra-subunit, endogenous disulfide bond formation between cysteines substituted for the residues just outside the membrane domain, we infer that the extracellular flank of S0 is surrounded on three sides by the extracellular flanks of TM helices S1 and S2 and the four-residue extracellular loop between S3 and S4. Eight different double cysteine-substituted alphas, each with one cysteine in the S0 flank and one in the S3-S4 loop, were at least 90% disulfide cross-linked. Two of these alphas formed channels in which 90% cross-linking had no effect on the V(50) or on the activation and deactivation rate constants. This implies that the extracellular ends of S0, S3, and S4 are close in the resting state and move in concert during voltage sensor activation. The association of S0 with the gating charge bearing S3 and S4 could contribute to the considerably larger electrostatic energy required to activate the BK channel compared with typical voltage-gated potassium channels with six TM helices.

Determination of the critical concentration of neutrophils required to block bacterial growth in tissues.

We showed previously that the competition between bacterial killing by neutrophils and bacterial growth in stirred serum-containing suspensions could be modeled as the competition between a first-order reaction (bacterial growth) and a second-order reaction (bacterial killing by neutrophils). The model provided a useful parameter, the critical neutrophil concentration (CNC), below which bacterial concentration increased and above which it decreased, independent of the initial bacterial concentration. We report here that this model applies to neutrophil killing of bacteria in three-dimensional fibrin matrices and in rabbit dermis. We measured killing of 10(3)-10(8) colony forming units/ml Staphylococcus epidermidis by 10(5)-10(8) human neutrophils/ml in fibrin gels. The CNC was approximately 4 x 10(6) neutrophils/ml gel in the presence of normal serum and approximately 1.6 x 10(7) neutrophils/ml gel in the presence of C5-deficient serum. Application of our model to published data of others on killing of approximately 5 x 10(7) to 2 x 10(8) E. coli/ml rabbit dermis yielded CNCs from approximately 4 x 10(6) to approximately 8 x 10(6) neutrophils/ml dermis. Thus, in disparate tissues and tissuelike environments, our model fits the kinetics of bacterial killing and gives similar lower limits (CNCs) to the neutrophil concentration required to control bacterial growth.

Transfer in SDS of biotinylated proteins from acrylamide gels to an avidin-coated membrane filter.

Avidin was covalently linked to aldehyde-derivatized polyethersulfone membrane filters. These filters were used in Western blot analysis of proteins reacted with biotinylation reagents and electrophoresed in sodium dodecyl sulfate (SDS) on polyacrylamide gels. Electrophoretic transfer from the gels to these filters was in 0.1% SDS, in which the covalently bound avidin retained its biotin-binding capacity. We compared Western blots on avidin-coated membrane filters of biotinylated and nonbiotinylated forms of mouse immunoglobulin G (IgG), mouse IgG heavy chain, muscle-type acetylcholine receptor alpha subunit, and fused alpha and beta subunits of receptor. Biotinylated proteins were captured with high specificity compared to their nonbiotinylated counterparts and sensitively detected on the avidin-coated membranes.

A touching picture of nicotinic binding.

The snail acetylcholine binding protein (AChBP) is homologous to the extracellular domains of the nicotinic ACh receptors. In this issue of Neuron, Celie et al. show how the crystal structures of AChBP in complexes with carbamylcholine and nicotine reveal the basis for agonist recognition by ACh receptors.

Structural effects of quinacrine binding in the open channel of the acetylcholine receptor.

Noncompetitive inhibitors of the nicotinic acetylcholine (ACh) receptors suppress cation flux directly by binding in and blocking the open channel or indirectly by stabilizing closed states of the receptor. The lidocaine derivative QX-314 and the acridine derivative quinacrine act directly as open channel blockers, but can act indirectly as well. The binding site for quinacrine in the open channel of mouse-muscle ACh receptor was mapped in cysteine-substituted mutants of the alpha subunit expressed with wild-type beta, gamma, and delta subunits. In the open state, substituted cysteines in the inner half of the second membrane-spanning segment (M2), but not in the outer half, were protected by quinacrine from reaction with 2-aminoethyl methanethiosulfonate. In addition, an alkylating derivative, quinacrine mustard, affinity labeled a subset of the substituted cysteines in M2, but only in the open state. These results, mapped onto a model of the open channel surrounded by five alpha-helical M2s, imply that quinacrine binds midway down M2 in the same site previously mapped for QX-314. A cysteine substituted for a residue in the outer third of alphaM1, which reacted with 2-aminoethyl methanethiosulfonate only in the presence of ACh, reacted faster in the additional presence of quinacrine or QX-314. It is proposed that channel opening involves both the opening of the resting gate at the inner end of M2 and the removal of an obstruction formed by the outer end of M1 that retards diffusion of blockers into the closed channel. Blocker binding in the open channel causes a further change in structure.

A photochemical approach to the lipid accessibility of engineered cysteinyl residues.

Ordinary electrophilic reagents react too slowly in a nonpolar environment to be useful for the determination of the accessibility to lipid of continuous stretches of residues mutated to cysteine. By contrast, photoactivated 5-iodonaphthyl-1-azide (INA) reacted readily with 2-mercaptoethanol and dodecanethiol in nonpolar solvents and in liposomes. Continuous stretches of residues in the amphipathic N-terminal helix and first transmembrane helix of the bacterial potassium channel KcsA were replaced with cysteine, and the mutants were expressed in Escherichia coli and isolated in inner membranes. These membranes were dissolved in detergent and reconstituted into asolectin liposomes incorporating INA. The extent of light-induced reaction of INA with each cysteine was assayed by subsequent reaction with the gel-shifting, SH-specific methoxy-polyethylene glycol-2-pyridine disulfide. The pattern of apparent second-order rate constants for the photoreactions of eight substituted cysteines in the N-terminal helix conformed to other measures of lipid exposure. The pattern of the rate constants for the photoreactions of 15 cysteines in the first transmembrane helix had peaks every third residue, which partly conformed to other measures of lipid exposure.

Reactions of cysteines substituted in the amphipathic N-terminal tail of a bacterial potassium channel with hydrophilic and hydrophobic maleimides.

Single cysteine-substitution mutants of KcsA, a K(+) channel from Streptomyces lividans, were expressed in Escherichia coli, and inner membranes were isolated. The rate constants for the reactions of these cysteines with three maleimides of increasing hydrophobicity, 4-(N-maleimido)phenyltrimethylammonium, N-phenylmaleimide, and N-(1-pyrenyl)maleimide, were determined by back titration of the remaining cysteines with methoxypolyethylene glycol-2-pyridine disulfide (M(r) 3,000) and quantitation of the fraction of gel-shifted KcsA as a function of reaction time. The patterns of the rate constants for the reactions of all three reagents with eight consecutive cysteines in the partially lipid-immersed amphipathic N-terminal tail helix were the same, with cysteines on the hydrophilic side of the helix reacting faster than Cys on the hydrophobic side. The results are consistent with the tail helix lying with its long axis in the lipid-water interface and with the orientation of the helix fluctuating around this axis. The patterns of the rate constants for the three reagents were similar to the pattern of the probabilities that the substituted cysteines were exposed to water, based on the sum of the free energies of transfer from water to octanol of all of the residues exposed to lipid in each orientation of the helix.

A critical concentration of neutrophils is required for effective bacterial killing in suspension.

We have examined the effect of neutrophil concentration on killing of a clinical isolate of Staphylococcus epidermidis. Human neutrophils at concentrations varying from 10(5) to 10(7) per ml were mixed in suspension with S. epidermidis at concentrations varying from 10(3) to 10(8) colony-forming units/ml, and the concentration of viable bacteria was assayed after various times at 37 degrees C. The rate of bacterial killing depended on the concentration of neutrophils and not on the ratio of neutrophils to bacteria. Below a critical concentration of neutrophils, bacteria growth was greater than neutrophil killing of bacteria even when the ratio of neutrophils to bacteria was 100:1. We fitted the time course of bacterial concentration and its dependence on neutrophil concentration with an exponential function, the exponent of which is (-kp + g)t, where k is the second-order rate constant for bacterial killing, p is the neutrophil concentration, g is the first-order rate constant for bacterial growth, and t is time. We found that k approximately 2 x 10(-8) ml per neutrophil per min, and g approximately 8 x 10(-3)/min. Only when p is greater than g/k, which we call the critical neutrophil concentration, does the bacterial concentration fall. Under optimal assay conditions, the critical neutrophil concentration was 3-4 x 10(5) per ml, a value very close to that (< or =5 x 10(5) per ml) known to predispose humans to bacterial and fungal infections.