Domain swapping of a llama VHH domain builds a crystal-wide beta-sheet structure

Among mammals, camelids have a unique immunological system since they produce functional antibodies devoid of light chains and CH1 domains. To bind antigens, whether they are proteins or haptens, camelids use the single domain VH from their heavy chain (VHH). We report here on such a llama VHH domain (VHH-R9) which was raised against a hapten, the RR6 red dye. This VHH possesses the shortest complementarity determining region 3 (CDR3) among all the known VHH sequences and nevertheless binds RR6 efficiently with a K(d) value of 83 nM. However, the crystal structure of VHH-R9 exhibits a striking feature: its CDR3 and its last beta-strand (beta9) do not follow the immunoglobulin VH domain fold, but instead extend out of the VHH molecular boundary and associate with a symmetry-related molecule. The two monomers thus form a domain-swapped dimer which establishes further contacts with symmetry-related molecules and build a crystal-wide beta-sheet structure. The driving force of the dimer formation is probably the strain induced by the short CDR3 together with the cleavage of the first seven residues.     

Comparison of physical chemical properties of llama VHH antibody fragments and mouse monoclonal antibodies

Antigen specific llama VHH antibody fragments were compared to antigen specific mouse monoclonal antibodies with respect to specificity, affinity and stability. The llama VHH antibody fragments and the mouse monoclonal antibodies investigated were shown to be highly specific for the protein antigen hCG or the hapten antigen RR-6. The affinity of the interaction between monovalent llama VHH antibody fragments and their antigen is close to the nanomolar range, similar to the bivalent mouse monoclonal antibodies studied. Llama VHH antibody fragments are similar to mouse monoclonal antibodies with respect to antigen binding in the presence of ammonium thiocyanate and ethanol. The results show that relative to antigen specific mouse monoclonal antibodies, antigen specific llama VHH fragments are extremely temperature stable. Two out of six llama VHHs are able to bind antigen specifically at temperatures as high as 90 degrees C, whereas four out of four mouse monoclonal antibodies are not functional at this temperature. Together with the finding that llama VHH fragments can be produced at high yield in Saccharomyces cerevisiae, these findings indicate that in the near future antigen specific llama VHH fragments can be used in for antibodies unexpected products and processes.     

Refolding of partially thermo-unfolded cinnamomin A-chain mediated by B-chain

The pure cinnamomin A-chain is unstable compared to that in the mixture of A- and B-chain or in intact cinnamomin molecule either being stored at 4 degrees C or being heated. When being heated at 45 degrees C for 20min, the A-chain generates partially unfolded intermediate and loses its tertiary structure as monitored by circular dichroism (CD) and tryptophan fluorescence, thus resulting in the inactivity of its RNA N-glycosidase albeit it retains most of its secondary structures. This partially unfolded intermediate is sensitive to protease, exhibiting property of a molten globule. The changes in conformation and activity are irreversible upon cooling. The partially unfolded intermediate can fully restore its RNA N-glycosidase activity in the presence of cinnamomin B-chain. The phenomenon, that the cinnamomin B-chain mediates the refolding of partially unfolded A-chain, probably plays an important role in the intracellular transport of the cytotoxic protein, i.e., keeping the structural stability of A-chain and refolding partially unfolded A-chain that occasionally appeared in the process of intracellular transport, to avoid the destiny of proteolysis that occurs in most denatured proteins in cell.     

Specific production rate of VHH antibody fragments by Saccharomyces cerevisiae is correlated with growth rate, independent of nutrient limitation

Saccharomyces cerevisiae carrying a multicopy integrated expression vector containing the gene encoding a Llama antibody fragment, has been cultivated in continuous cultures both under carbon and nitrogen limiting conditions with galactose as the sole carbon source. VHH-R2 expression was under control of the inducible GAL7 promoter. Induction however, was independent of the galactose consumption rate and maximal at all growth rates. VHH-R2 was secreted with 70% efficiency at all growth rates and under both limitations. The specific production rate increased linear with increasing growth rate in a growth-associated manner. However, when grown under nitrogen limitation at growth rates above 0.09 h(-1), the extracellular VHH-R2 was less active or part of the VHH-R2 was in an inactive form. From our results we conclude that to obtain a maximal amount of VHH per kilogram biomass per hour, VHH production should be done in carbon limited continuous cultures at high specific growth rates.     

High temperature increases the refolding yield of reduced lysozyme: implication for the productive process for folding

Misfolding poses a serious problem in the biotechnological field in obtaining the active protein from inclusion bodies. Here we show that high temperature increases the refolding yield of reduced lyosyzme by a simple dilution method. The refolding yields at 98 degrees C were three times higher than those at 20 degrees C in the solutions tested, which is related to the fact that the thermally unfolded state of lysozyme is a more productive form for folding than the denaturant-induced fully unfolded state. The thermal-assisted refolding could be used for various reduced and denatured proteins as a result of its simplicity and low cost.     

Unusually slow denaturation and refolding processes of pyrrolidone carboxyl peptidase from a hyperthermophile are highly cooperative: real-time NMR studies

The refolding rate of heat-denatured cysteine-free pyrrolidone carboxyl peptidase (PCP-0SH) from Pyrococcus furiosus has been reported to be unusually slow under some conditions. To elucidate the structural basis of the unusually slow kinetics of the protein, the denaturation and refolding processes of the PCP-0SH were investigated using a real-time 2D (1)H-(15)N HSQC and CD experiments. At 2 M urea denaturation of the PCP-0SH in the acidic region, all of the native peaks in the 2D HSQC spectrum completely disappeared. The conformation of the PCP-0SH just after removal of 6 M GuHCl could be observed as a stable intermediate (D(1) state) in 2D HSQC and CD experiments, which is similar to a molten globule structure. The D(1) state of the PCP-0SH, which is the initial state of refolding, corresponded to the state at 2 M urea and seemed to be the denatured state in equilibrium with the native state under the physiological conditions. The refolding of PCP-0SH from the D(1) state to the native state could be observed to be highly cooperative without any intermediates between them, even if the refolding rate was quite slow. In the higher concentration of denaturants, PCP-0SH showed HSQC and CD spectra characteristic of completely unfolded proteins called the D(2) state. The unusually slow refolding rate was discussed as originating in the conformations in the transition state and/or the retardation of reorganization in an ensemble of nonrandom denatured structures in the D(1) state.     

Single-domain antibody fragments with high conformational stability

A variety of techniques, including high-pressure unfolding monitored by Fourier transform infrared spectroscopy, fluorescence, circular dichroism, and surface plasmon resonance spectroscopy, have been used to investigate the equilibrium folding properties of six single-domain antigen binders derived from camelid heavy-chain antibodies with specificities for lysozymes, beta-lactamases, and a dye (RR6). Various denaturing conditions (guanidinium chloride, urea, temperature, and pressure) provided complementary and independent methods for characterizing the stability and unfolding properties of the antibody fragments. With all binders, complete recovery of the biological activity after renaturation demonstrates that chemical-induced unfolding is fully reversible. Furthermore, denaturation experiments followed by optical spectroscopic methods and affinity measurements indicate that the antibody fragments are unfolded cooperatively in a single transition. Thus, unfolding/refolding equilibrium proceeds via a simple two-state mechanism (N <--> U), where only the native and the denatured states are significantly populated. Thermally-induced denaturation, however, is not completely reversible, and the partial loss of binding capacity might be due, at least in part, to incorrect refolding of the long loops (CDRs), which are responsible for antigen recognition. Most interestingly, all the fragments are rather resistant to heat-induced denaturation (apparent T(m) = 60-80 degrees C), and display high conformational stabilities (DeltaG(H(2)O) = 30-60 kJ mole(-1)). Such high thermodynamic stability has never been reported for any functional conventional antibody fragment, even when engineered antigen binders are considered. Hence, the reduced size, improved solubility, and higher stability of the camelid heavy-chain antibody fragments are of special interest for biotechnological and medical applications.     

The acid-induced state of glucose oxidase exists as a compact folded intermediate

A systematic investigation of the acid-induced unfolding of glucose oxidase (beta-D-glucose: oxygen 1-oxidoreductase) (GOD) from Aspergillus niger was made using steady-state tryptophan fluorescence, circular dichroism (CD), and ANS (1-anilino 8-naphthalene sulfonic acid) binding. Intrinsic tryptophan fluorescence studies showed a maximally unfolded state at pH 2.6 and the presence of a non-native intermediate in the vicinity of pH 1.4. Flavin adenine dinucleotide (FAD) fluorescence measurements indicate that the bound cofactors are released at low pH. In the pH range studied, near- and far-UV CD spectra show maximal loss of tertiary as well as secondary structure (40%) at pH 2.6 although glucose oxidase at this pH is relatively less denatured as compared to the conformation in 6M GdnHCl. Interestingly, in the vicinity of pH 1.4, glucose oxidase shows a refolded conformation (A-state) with approximately 90% of native secondary structure and native-like near-UV CD spectral features. ANS fluorescence studies, however, show maximal binding of the dye to the protein at pH 1.4, indicating a "molten-globule"-like conformation with enhanced exposure of hydrophobic surface area. Acrylamide quenching data exhibit reduced accessibility of quencher to tryptophan, suggesting a more compact conformation at low pH. Thermal stability of this state was assessed by ellipticity changes at 222 nm relative to native protein. While native glucose oxidase showed a completely reversible thermal denaturation profile, the state at pH 1.4 showed approximately 50% structural loss and the denatured state appeared to be in a different conformation exhibiting prominent beta-sheet structure (around 85 degrees C) that was not reversible. To summarize; the A-state of GOD exists as a compact folded intermediate with "molten-globule"-like characteristics, viz., native-like secondary structure but with non-native cofactor environment, enhanced hydrophobic surface area and non-cooperative thermal unfolding. That the A-state also possesses significant tertiary structure is an interesting observation made in this study.     

Intermediate studies on refolding of arginine kinase denatured by guanidine hydrochloride.

The refolding course and intermediate of guanidine hydrochloride (GuHCl)-denatured arginine kinase (AK) were studied in terms of enzymatic activity, intrinsic fluorescence, 1-anilino-8-naphthalenesulfonte (ANS) fluorescence, and far-UV circular dichroism (CD). During AK refolding, the fluorescence intensity increased with a significantly blue shift of the emission maximum. The molar ellipticity of CD increased to close to that of native AK, as compared with the fully unfolded AK. In the AK refolding process, 2 refolding intermediates were observed at the concentration ranges of 0.8-1.0 mol/L and 0.3-0.5 mol GuHCl/L. The peak position of the fluorescence emission and the secondary structure of these conformation states remained roughly unchanged. The tryptophan fluorescence intensity increased a little. However, the ANS fluorescence intensity significantly increased, as compared with both the native and the fully unfolded states. The first refolding intermediate at the range of 0.8-1.0 mol GuHCl/L concentration represented a typical "pre-molten globule state structure" with inactivity. The second one, at the range of 0.3-0.5 mol GuHCl/L concentration, shared many structural characteristics of native AK, including its secondary and tertiary structure, and regained its catalytic function, although its activity was lower than that of native AK. The present results suggest that during the refolding of GuHCl-denatured AK there are at least 2 refolding intermediates; as well, the results provide direct evidence for the hierarchical mechanism of protein folding.     

Partially folded state of the disulfide-reduced N-terminal half-molecule of ovotransferrin as a renaturation intermediate

A previous report (Hirose, M., Akuta, T., and Takahashi, N. (1989) J. Biol. Chem. 264, 16867-16872) has shown that for the efficient oxidative refolding of disulfide-reduced ovotransferrin, a preincubation under reduced conditions at a low temperature is essential. To study the renaturation pathway, the disulfide-reduced N-terminal half-molecule of ovotransferrin was analyzed by CD spectrum. The reduced protein was found to take, at low temperatures, a partially folded conformation that can be distinguished from both the native and denatured states. The folded protein was in a metastable state with delta GD value of 2.2-2.8 kcal/mol at 6 degrees C. The conformation was variable depending on temperature conditions; its stability was decreased at a lower temperature (1.0-1.2 kcal/mol at 0 degrees C). Subsequent reoxidation at 6 degrees C by oxidized glutathione led efficiently the reduced protein to the correctly renatured form having the iron-binding capacity, indicating that the partially folded state is the immediate precursor to subsequent oxidative refolding.     

A kinetic study of the folding of staphylococcal nuclease using size-exclusion chromatography.

The kinetics of the hydrodynamic volume change accompanying the reversible unfolding of staphylococcal nuclease have been observed by size-exclusion chromatography at 4 degrees C and pH 7.0 using the denaturant guanidine hydrochloride. The observed chromatographic profiles have been simulated by a six-component unfolding/refolding mechanism using a consistent set of equilibrium and kinetic parameters. The native protein is an equilibrium mixture of the cis and trans isomers of the peptide bond preceding proline-117. The native conformation containing the cis isomer dominates the equilibrium mixture, is more stable, and unfolds more slowly at its transition midpoint. The denatured protein is an equilibrium mixture of at least four components, the cis/trans isomers of proline-117 and one of the five remaining prolines. The dominant refolding pathway is initiated from the denatured component containing the trans isomer of proline-117. The six-component mechanism is consistent with tryptophan fluorescence kinetic measurements of the wild-type protein and with chromatographic measurements of a mutant P117G protein.     

Insulin amyloid fibrillation at above 100 degrees C: new insights into protein folding under extreme temperatures

To investigate the folding behavior of amyloidogenic proteins under extreme temperatures, the kinetics of fibrillation and accompanying secondary structure transitions of bovine insulin were studied for temperatures ranging up to 140 degrees C. The presence of extreme heat stress had traditionally been associated with irreversible denaturation of protein while the initial steps of such a denaturation process may be common with a fibril formation pathway of amyloidogenic proteins. The present work demonstrates the ability of insulin to form amyloid fibrils at above 100 degrees C. Amyloid formation was gradually replaced by random coil generation after approximately 80 degrees C until no amyloid was detected at 140 degrees C. The morphology of insulin amyloid fibrils underwent sharp changes with increasing the temperature. The dependence of amyloid formation rate on incubation temperature followed non-Arrhenius kinetics, which is explained by temperature-dependent enthalpy change for amyloid formation. The intermediate stage of amyloid formation and random coil generation consisted of a partially folded intermediate common to both pathways. The fully unfolded monomers in random coil conformation showed partial reversibility through this intermediate by reverting back to the amyloid pathway when formed at 140 degrees C and incubated at 100 degrees C. This study highlights the non-Arrhenius kinetics of amyloid fibrillation under extreme temperatures, and elucidates its intermediate stage common with random coil formation.     

The human cytosolic molecular chaperones hsp90, hsp70 (hsc70) and hdj-1 have distinct roles in recognition of a non-native protein and protein refolding.

The properties of molecular chaperones in protein-assisted refolding were examined in vitro using recombinant human cytosolic chaperones hsp90, hsc70, hsp70 and hdj-1, and unfolded beta-galactosidase as the substrate. In the presence of hsp70 (hsc70), hdj-1 and either ATP or ADP, denatured beta-galactosidase refolds and forms enzymatically active tetramers. Interactions between hsp90 and non-native beta-galactosidase neither lead to refolding nor stimulate hsp70- and hdj-1-dependent refolding. However, hsp90 in the absence of nucleotide can maintain the non-native substrate in a 'folding-competent' state which, upon addition of hsp70, hdj-1 and nucleotide, leads to refolding. The refolding activity of hsp70 and hdj-1 is effective across a broad range of temperatures from 22 degrees C to 41 degrees C, yet at extremely low (4 degrees C) or high (>41 degrees C) temperatures refolding activity is reversibly inhibited. These results reveal two distinct features of chaperone activity in which a non-native substrate can be either maintained in a stable folding-competent state or refolded directly to the native state; first, that the refolding activity itself is temperature sensitive and second, that hsp90, hsp70 (hsc70) and hdj-1 each have distinct roles in these processes.     

Refolding of thioredoxin reductase assisted by groEL and PDI

Thioredoxin reductase was unfolded in 2 M guanidine hydrochloride as revealed by fluorescence and CD spectroscopy. Spontaneous refolding of denatured species resulted in low recovery of 10% catalytic activity after 4 h incubation at 25 degrees C. Addition of groEL or protein disulfide isomerase to the renaturation buffer accelerated the rate of recovery of catalytic activity to a level of 35 and 15%, respectively. Fluorescence spectroscopy has been used to investigate the interaction of groEL and protein disulfide isomerase with denatured thioredoxin reductase tagged with a fluorescent probe. The fluorescence emitted by the denatured protein was quenched upon binding to either groEL or protein disulfide isomerase. It is suggested that encapsulation of the protein substrate by the chaperone plays an important role in the process of folding by facilitating the formation of correctly folded species.     

High stability to irreversible inactivation at elevated temperatures of enzymes covalently modified by hydrophilic reagents: alpha-Chymotrypsin

Based on the idea that proteins can be stabilized by a decrease in the thermodynamically unfavorable contact of the hydrophobic surface clusters with water, alpha-chymotrypsin (CT) was acylated with carboxylic acid anhydrides or re-ductively alkylated with aliphatic aldehydes. Modification of CT with hydrophilic reagents leads to 100-1000-fold increase in stability against the irreversible thermoinactivation. The correlation holds: the greater the hydrophilization increment brought about by the modification, the higher is the protein thermostability. After some limiting value, however, a further increase in hydrophilicity does not change thermostability.It follows from the dependence of the thermoinactivation rate constants on temperature that for hydrophilized CT there is the conformational transition at 55-65 degrees C into an unfolded state in which inactivation is much slower than that of the low-temperature conformation. The thermodynamic analysis and fluorescent spectral data confirm that the slow inactivation of hydrophilized CT at high temperatures proceeds via a chemical mechanism rather than Incorrect refolding operative for both the native and low-temperature form of the modified enzyme. Hence, the hydrophilization stabilizes the unfolded high-temperature conformation by eliminating the incorrect refolding. (c) 1992 John Wiley & Sons, Inc.     

Unassisted refolding of urea unfolded rhodanese

In vitro refolding after urea unfolding of the enzyme rhodanese (thiosulfate:cyanide sulfurtransferase, EC 2.8.1.1) normally requires the assistance of detergents or chaperonin proteins. No efficient, unassisted, reversible unfolding/folding transition has been demonstrated to date. The detergents or the chaperonin proteins have been proposed to stabilize folding intermediates that kinetically limit folding by aggregating. Based on this hypothesis, we have investigated a number of experimental conditions and have developed a protocol for refolding, without assistants, that gives evidence of a reversible unfolding transition and leads to greater than 80% recovery of native enzyme. In addition to low protein concentration (10 micrograms/ml), low temperatures are required to maximize refolding. Otherwise optimal conditions give less than 10% refolding at 37 degrees C, whereas at 10 degrees C the recovery approaches 80%. The unfolding/refolding phases of the transition curves are most similar in the region of the transition, and refolding yields are significantly reduced when unfolded rhodanese is diluted to low urea concentrations, rather than to concentrations near the transition region. This is consistent with the formation of "sticky" intermediates that can remain soluble close to the transition region. Apparently, nonnative structures, e.g. aggregates, can form rapidly at low denaturant concentrations, and their subsequent conversion to the native structure is slow.     

Thermodynamic characterization of an equilibrium folding intermediate of staphylococcal nuclease.

High-sensitivity differential scanning calorimetry and CD spectroscopy have been used to probe the structural stability and measure the folding/unfolding thermodynamics of a Pro117-->Gly variant of staphylococcal nuclease. It is shown that at neutral pH the thermal denaturation of this protein is well accounted for by a 2-state mechanism and that the thermally denatured state is a fully hydrated unfolded polypeptide. At pH 3.5, thermal denaturation results in a compact denatured state in which most, if not all, of the helical structure is missing and the beta subdomain apparently remains largely intact. At pH 3.0, no thermal transition is observed and the molecule exists in the compact denatured state within the 0-100 degrees C temperature interval. At high salt concentration and pH 3.5, the thermal unfolding transition exhibits 2 cooperative peaks in the heat capacity function, the first one corresponding to the transition from the native to the intermediate state and the second one to the transition from the intermediate to the unfolded state. As is the case with other proteins, the enthalpy of the intermediate is higher than that of the unfolded state at low temperatures, indicating that, under those conditions, its stabilization must be of an entropic origin. The folding intermediate has been modeled by structural thermodynamic calculations. Structure-based thermodynamic calculations also predict that the most probable intermediate is one in which the beta subdomain is essentially intact and the rest of the molecule unfolded, in agreement with the experimental data. The structural features of the equilibrium intermediate are similar to those of a kinetic intermediate previously characterized by hydrogen exchange and NMR spectroscopy.     

Isolation of antigen specific llama VHH antibody fragments and their high level secretion by Saccharomyces cerevisiae

Recently the existence of 'heavy chain' immunoglobulins in Camelidae has been described. However, as yet there is no data on the binding of this type of antibody to haptens. In addition, it was not a priori predictable whether the binding domains (VHH) of these antibodies could be produced and secreted by the lower eukaryotic micro-organism Saccharomyces cerevisiae. In the present study these questions are addressed. Heavy chain immunoglobulins directed against two hapten molecules, the azo-dyes RR6 and RR120 as well as the (proteinaceous) human pregnancy hormone, have been raised in Lama glama. We were able to select specific VHH fragments for all three antigens by direct screening of Escherichia coli or yeast libraries, even without prior enrichment via bio-panning. This is the first example of the isolation of llama anti-hapten VHH domains. Surprisingly, the affinities of the llama VHHs for the RR6 hapten obtained in this way are in the low nM range. Furthermore, some of the antigen specific VHHs were secreted by S. cerevisiae at levels over 100 mg l-1 in shake flask cultures. These two findings extend the possible application areas for the llama VHH fragments significantly.     

Assembly and dissociation of human leukocyte antigen (HLA)-A2 studied by real-time fluorescence resonance energy transfer

Class I major histocompatibility complex (MHC) heterodimer, composed of human leukocyte antigen (HLA)-A2 heavy chain and human beta(2)-microglobulin (beta(2)m), was produced by denaturation and gel filtration of the recombinant water-soluble HLA-A2/beta(2)m/peptide ternary complex in 8 M urea Tris-HCl buffer, followed by refolding of the separated chains without peptide. Peptide affinity and kinetics of the ternary complex formation and dissociation were investigated in real time by monitoring the fluorescence resonance energy transfer (FRET) from intrinsic HLA-A2 heavy-chain tryptophans to a dansyl fluorophore conjugated to the bound peptide. Peptide binding to the heterodimer was a second order process with rate constants linearly dependent upon temperature in Arrhenius coordinates over 0-20 degrees C. The binding rate constant of pRT6C-dansyl [ILKEPC(dansyl)HGV] at 37 degrees C evaluated by extrapolation of the Arrhenius plot was (2.0 +/- 0.5) x 10(6) M(-1) s(-1). Association of the heavy chain with beta(2)m was a first order process, apparently controlled by a conformational transition in the heavy chain. One of these conformations bound to beta(2)m to form the heavy chain/beta(2)m heterodimer whereas the second conformer oligomerized. Peptide dissociation from the ternary complex was a first-order reaction over the temperature range 20-37 degrees C, suggesting that the ternary complex also exists in two conformations. Taken together, the present data suggest that association of beta(2)m changes the HLA-A2 heavy-chain conformation thereby promoting peptide binding. Peptide dissociation from the ternary complex induces dissociation of the heavy-chain/beta(2)m heterodimer thereby causing oligomerization of the heavy chain. The lability of the HLA-A2/beta(2)m heterodimer and the strong tendency of the "free" heavy chain to oligomerize may provide an efficient mechanism for control of antigen presentation under physiological conditions by reducing the direct loading of HLA with exogenous peptide at the cell surface.     

Pressure treatment of tailspike aggregates rapidly produces on-pathway folding intermediates

Protein folding and aggregation are in direct competition in living systems, yet measuring the two pathways simultaneously has rarely been accomplished. In order to identify the mechanism of high-pressure dissociation of aggregates, we compared the simultaneous on- and off-pathway behavior following dilution of freshly denatured P22 tailspike protein. Tailspike assembly at 100 microg/mL was monitored at four temperatures using a combination of size-exclusion chromatography and native polyacrylamide gel electrophoresis (PAGE) and folding and aggregation rates and yields were determined. As temperature increased, the yield of native trimeric tailspike decreased from 26.1 +/- 1.3 microg/mL at 20 degrees C to 0 microg/mL at 37 degrees C. Pressure treatment dissociated 60% of the trapped aggregates created at 37 degrees C and yielded 19.8 +/- 1.1 microg/mL of native trimer following depressurization and incubation at 20 degrees C. The rate of refolding of "freshly denatured" tailspike was compared to that following pressure treatment. The trimer formation rate increased by a factor of roughly five, and the aggregate rate decreased by a factor of three, following pressure treatment. Circular dichroism and high-pressure intrinsic tryptophan fluorescence measurements support the model that a structured intermediate is formed in a rapid manner under high pressure from a pressure-sensitive aggregate population.