A model for allosteric regulation of Na+/K+-transporting ATPase

Measuring enzyme activities in crude homogenates: Na+/K+-ATPase as a case study in optimizing assays

In this review of assays of Na⁺/K⁺-ATPase (NKA), we explore the choices made by researchers assaying the enzyme to investigate its role in physiological regulation. We survey NKA structure and function in the context of how it is typically assayed, and how technical choices influence what can be said about the enzyme. In comparing different methods for extraction and assay of NKA, we identified a series of common pitfalls that compromise the veracity of results. We include experimental work to directly demonstrate how choices in detergents, salts and substrates influence NKA activities measured in crude homogenates. Our review of assay approaches integrates what is known from enzymology, biomedical physiology, cell biology and evolutionary biology, offering a more robust method for assaying the enzyme in meaningful ways, identifying caveats and future directions to explore its structure and function. The goal is to provide the sort of background on the enzyme that should be considered in exploring the function of the enzyme in comparative physiology.

Half-site modification of Lys-480 of the Na+,K+-ATPase alpha-chain with pyridoxal 5'-diphospho-5'-adenosine reduces ATP-dependent phosphorylation stoichiometry from half to a quarter

Pig and dog kidney Na+,K+-ATPase preparations, irrespective of specific activity, showed approximately 0.5 mol of maximum phosphorylation/mol alpha-chain for ATP or acetyl phosphate (AcP) at steady state conditions. Pyridoxal 5'-diphospho-5'-adenosine (AP2PL)-treated pig kidney enzymes containing approximately 0.5 mol of AP2PL probe at Lys-480/mol (Tsuda, T., Kaya, S., Funatsu, H., Hayashi, Y., and Taniguchi, K. (1998) J. Biochem. (Tokyo) 123, 169-174) showed a quarter-site phosphorylation by ATP and half-site phosphorylation from AcP. The addition of 10 microM ATP to the Mg2+-Na+-bound AP2PL enzyme induced rapid quarter-site phosphorylation (47/s), followed by two different AP2PL fluorescence changes, a rapid decrease (29/s) and a slow increase (1.1/s). The addition of 1 mM AcP to the Mg2+-Na+-bound AP2PL enzyme induced a slow half-site phosphorylation (3/s), followed by a monophasic AP2PL fluorescence increase (1.2/s). After treatment of the AP2PL enzyme with fluorescein 5'-isothiocyanate to modify Lys-501 fully, the Mg2+-Na+-dependent phosphorylation capacity from ATP of the resulting AP2PL-fluorescein 5'-isothiocyanate enzyme was reduced to approximately 6% without significant changes in half-site phosphorylation capacity with respect to AcP, dynamic AP2PL fluorescence change by ATP and change by AcP. These data and others support the hypothesis that the functional membrane-bound Na+, K+-ATPase has tetrameric properties.

ATP and acetyl phosphate induces molecular events near the ATP binding site and the membrane domain of Na+,K+-ATPase. The tetrameric nature of the enzyme

The addition of ATP to Mg2+-Na+-bound-probe labeled Na+,K+-ATPase preparations containing approximately 0.5 mol of pyridoxal 5'-diphospho-5'-adenosine (AP2PL) probe at Lys-480 and approximately 0.9 mol of fluorescein 5'-isothiocyanate (FITC) probe at Lys-501 showed a decrease and an increase in the AP2PL fluorescence intensity with neither significant ATP-dependent phosphorylation nor FITC fluorescence change. The rate constants for the fluorescence change increased nearly linearly with increasing ATP concentrations. The substitution of AcP for ATP decreased the FITC fluorescence rather monophasically, 8.5/s, which was followed by the half-site phosphorylation with same amount of components with different rate constant, 7.2 and 4.6/s, followed by a much slower increase in the two components of AP2PL fluorescence, 1.4 and 0.2/s. The addition of Na+ with increasing concentrations of ATP to the K+-bound AP2PL-FITC enzymes induced accelerations in the decrease and an increase in the AP2PL fluorescence intensity with two different increases in the FITC fluorescence intensity, showing that the same concentration of ATP is capable of inducing four different fluorescence changes. The addition of ATP to the Mg2+-Na+-bound enzymes modified with N-[p-(2-benzimidazolyl)phenyl]-maleimide (BIPM) at Cys-964 and retaining full Na+,K+-ATPase activity induced two different increases in BIPM fluorescence intensity. Each rate constant for the BIPM fluorescence change versus concentrations of ATP gave two intersecting straight lines. These data and the stoichiometries of fluorescence probe bindings and ATP- and AcP-dependent phosphorylation provide strong support for the conclusion that the functional membrane-bound Na+,K+-ATPase is a tetramer.

Imaging bioluminescent indicators shows Ca2+ and ATP permeability thresholds in live cells attacked by complement

A series of permeability thresholds to Ca2+ metabolites and macromolecules, occurring at different times when cells are attacked by complement, has been established by imaging HeLa cells transiently expressing a recombinant cytosolic fusion protein of firefly luciferase and aequorin (luciferase-aequorin) to measure changes in ATP and cytosolic free Ca2+. Nuclear fluorescence of propidium was used as a measure of permeability to small molecules, and luciferase activity imaged to assess lysis. The rise in cytosolic free Ca2+ observed after C9 attack preceded by at least 60 s both the increase in propidium fluorescence, measured in single cells, and the decrease in ATP monitored by luciferase light emission. These effects were dependent on the concentration of C9. At concentrations of C9 up to 4 micrograms/ml no loss of luciferase-aequorin protein was detected at the end of the experiment. Thus the membrane integrity of the cells remained intact, even though the cells were permeable to propidium. These results confirmed our earlier observations that propidium permeability in cells attacked by complement was not a reliable measure of cell death. They also show that it is vital to take account of cellular heterogeneity if the mechanisms by which cells respond to membrane pore former attack are to be correctly interpreted.

Modeling of the three-dimensional structure of the digitalis intercalating matrix in Na+/K(+)-ATPase protodimer

Based on the knowledge that the digitalis receptor site in Na+/K(+)-ATPase is the interface between two interacting alpha-subunits of the protodimer (alpha beta)2, the present review makes an approach towards modeling the three-dimensional structure of the digitalis intercalating matrix by exploiting the information on: the primary structure and predicted membrane topology of the catalytic alpha-subunit; the determinants of the secondary, tertiary and quaternary structure of the membrane-spanning protein domains; the impact of mutational amino acid substitutions on the affinity of digitalis compounds, and the structural characteristics in potent representatives. The designed model proves its validity by allowing quantitative interpretations of the contributions of distinct amino acid side chains to the special bondings of the three structural elements of digitalis compounds.

Location and properties of the digitalis receptor site in Na+/K(+)-ATPase

Since 1985, several research groups have shown that a number of amino acids in the catalytic alpha-subunit of Na+/K(+)-ATPase more or less strongly modulate the affinity of a digitalis compound like ouabain to the enzyme. However, scrutiny of these findings by means of chimeric Na+/K(+)-ATPase constructs and monoclonal antibodies has recently revealed that the modulatory effect of most of these amino acids does not at all result from direct interaction with ouabain, but rather originates from long-range effects on the properties of the digitalis binding matrix. Starting from this knowledge, the present review brings together the various pieces of evidence pointing to the conclusion that the interface between two interacting alpha-subunits in the Na+/K(+)-ATPase protodimer (alpha beta)2 provides the cleft for inhibitory digitalis intercalation.

Oscillations and multiple steady states in active membrane transport models

The dynamic behavior of some non-linear extensions of the six-state alternating access model for active membrane transport is investigated. We use stoichio-metric network analysis to study the stability of steady states. The bifurcation analysis has been done through standard numerical methods. For the usual six-state model we have proved that there is only one steady state, which is globally asymptotically stable. When we added an autocatalytic step we found self-oscillations. For the competition between a monomer cycle and a dimer cycle, with steps of dimer formation, we have also found self-oscillations. We have also studied models involving the formation of a complex with other molecules. The addition of two steps for formation of a complex of the monomer with another molecule does not alter either the number or the stability of steady states of the basic six-state model. The model which combines the formation of a complex with an autocatalytic step shows both self-oscillations and multiple steady states. The results lead us to conclude that oscillations could be produced by active membrane transport systems if the transport cycle contains a sufficiently large number of steps (six in the present case) and is coupled to at least one autocatalytic reaction,. Oscillations are also predicted when the monomer cycle is coupled to a dimer cycle. In fact, the autocatalytic reaction can be seen as a simplification of the model involving competition between monomer and dimer cycles, which seems to be a more realistic description of biological systems. A self-regulation mechanism of the pumps, related to the multiple stationary states, is expected only for a combined effect of autocatalysis and formation of complexes with other molecules. Within the six-state model this model also leads to oscillation.

Autocatalytic cooperativity and self-regulation of ATPase pumps in membrane active transport

We investigate the effect of autocatalysis on the conformational changes of membrane pumps during active transport driven by ATP. The translocation process is described by means of an alternating access model. The usual kinetic scheme is extended by introducing autocatalytic steps and allowing for dynamic formation of enzyme complexes. The usual features of cooperative models are recovered, i.e., sigmoid shapes of flux versus concentration curves. We show also that two autocatalytic steps lead to a mechanism of inhibition by the substrate as experimentally observed for some ATPase pumps. In addition, when the formation of enzyme complexes is allowed, the model exhibits a multiple stationary states regime, which can be related to a self-regulation mechanism of the active transport in biological systems.

Role of protein conformation changes and transphosphorylations in the function of Na+/K(+)-transporting adenosine triphosphatase: an attempt at an integration into the Na+/K+ pump mechanism

The particular aim of the review on some basic facets of the mechanism of Na+/K(+)-transporting ATPase (Na/K-ATPase) has been to integrate the experimental findings concerning the Na(+)- and K(+)-elicited protein conformation changes and transphosphorylations into the perspective of an allosterically regulated, phosphoryl energy transferring enzyme. This has led the authors to the following summarizing evaluations. 1. The currently dominating hypothesis on a link between protein conformation changes ('E1 in equilibrium with E2') and Na+/K+ transport (the 'Albers-Post scheme') has been constructed from a variety of partial reactions and elementary steps, which, however, do not all unequivocally support the hypothesis. 2. The Na(+)- and K(+)-elicited protein conformation changes are inducible by a variety of other ligands and modulatory factors and therefore cannot be accepted as evidence for their direct participation in effecting cation translocation. 3. There is no evidence that the 'E1 in equilibrium with E2' protein conformation changes are moving Na+ and K+ across the plasma membrane. 4. The allosterically caused ER in equilibrium with ET ('E1 in equilibrium with E2') conformer transitions and the associated cation 'occlusion' in equilibrium with 'de-occlusion' processes regulate the actual catalytic power of an enzyme ensemble. 5. A host of experimental variables determines the proportion of functionally competent ER enzyme conformers and incompetent ET conformers so that any enzyme population, even at the start of a reaction, consists of an unknown mixture of these conformers. These circumstances account for the occurrence of contradictory observations and apparent failures in their comparability. 6. The modelling of the mechanism of the Na/K-ATPase and Na+/K+ pump from the results of reductionistically designed experiments requires the careful consideration of the physiological boundary conditions. 7. Na+ and K+ ligandation of Na/K-ATPase controls the geometry and chemical reactivity of the catalytic centre in the cycle of E1 in equilibrium with E2 state conversions. This is possibly effected by hinge-bending, concerted motions of three adjacent, intracellularly exposed peptide sequences, which shape open and closed forms of the catalytic centre in lock-and-key responses. 8. The Na(+)-dependent enzyme phosphorylation with ATP and the K(+)-dependent hydrolysis of the phosphoenzyme formed are integral steps in the transport mechanism of Na/K-ATPase, but the translocations of Na+ and K+ do not occur via a phosphate-cation symport mechanism.(ABSTRACT TRUNCATED AT 400 WORDS)

Blocking of Na+/K+ transport by the MgPO4 complex analogue Co(NH3)4PO4 leaves the Na+/Na(+)-exchange reaction of the sodium pump unaltered and shifts its high-affinity ATP-binding site to a Na(+)-like form

Inactivation of Na+/K(+)-ATPase activity by the MgPO4 complex analogue Co(NH3)4PO4 leads, in everted red blood cell vesicles, to the parallel inactivation of 22Na+/K+ flux and 86Rb/Rb+ exchange, but leaves the 22Na+/Na(+)-exchange activity and the uncoupled ATP-supported 22Na+ transport unaffected. Furthermore, inactivation of purified Na+/K(+)-ATPase by Co(NH3)4PO4 leads to a parallel decrease of the capacity of the [3H]ouabain receptor site, when binding was studied by the Mg2+/Pi-supported pathway (ouabain-enzyme complex II) but the capacity of the ouabain receptor site was unaltered, when the Na+/Mg2+/ATP-supported pathway (ouabain-enzyme complex I) was used. No change in the dissociation constants of either ouabain receptor complex was observed following inactivation of Na+/K(+)-ATPase. When eosin was used as a marker for the high-affinity ATP-binding site of the E1 conformation, formation of stable E'2.Co(NH3)4PO4 complex led to a shift in the high-affinity ATP-binding site towards the sodium form. This led to an increase in the dissociation constant of the enzyme complex with K+, from 1.4 mM with the unmodified enzyme to 280 mM with the Co(NH3)4PO4-inactivated enzyme. It was concluded, that the effects of Co(NH3)4PO4 on the partial activities of the sodium pump are difficult to reconcile with an alpha, beta-protomeric enzyme working according the Albers-Post scheme. The data are consistent with an alpha 2, beta 2 diprotomeric enzyme of interacting catalytic subunits working with a modified version of the Albers-Post model.

Identification of monoclonal antibody binding domains of Na+,K(+)-ATPase by immunoelectron microscopy

Treatment of purified preparations of porcine Na+,K(+)-ATPase with phospholipase A2, MgCl2 and NaVO3 leads to the formation of two-dimensional crystals exclusively in a dimeric configuration. Two-dimensional computer-averaged projections of the electron microscopy images of the crystalline enzyme with bound Fab fragments of monoclonal antibody M10-P5-C11 were accomplished using image enhancement software and showed that the antibody fragments caused only a modest increase in the unit cell size, while reducing the extent of asymmetry of the two promoters in each unit cell. The digital imaging also showed that the antibody's epitope on the alpha subunit resides on the 'lobe' or 'hook' region of the intracellular portion of the enzyme. Since functional studies indicate that M10-P5-C11 binds near or between the ATP binding site and the phosphorylation site, this visualized 'lobe' region of alpha may comprise the catalytic site. In addition, the binding of another inhibitory antibody, 9-A5, has been found to prevent crystal formation and the presence of the carbohydrate sugars on the enzyme's beta subunit shown to be required for crystal formation.

The prostate plasma membrane as an androgen receptor

The pivotal role of the cell nucleus in androgenic control of target organs, such as the prostate, has become increasingly suspect. Equally qualified receptor activities have been found in the cytosol, endoplasmic reticulum, and plasma membrane. It is presently difficult to explain how a sex steroid can manage proliferation, metabolism, biosynthesis and secretion, all through chromatin-directed signals. In my search for a more satisfactory mediator of androgen action, I discovered that the sodium-potassium-dependent ATPase of the prostate plasma membrane binds androgen, and is activated by the hormone's presence to serve as a metabolic pacemaker. This paper is my terminal status report on one aspect of this hypothesis; namely, the nature and site of androgen binding, with clues as to the mode of action. SDS-PAGE indicates that androgen can be bound to the beta-subunit of prostatic Na,K-ATPase. Selective enrichment of the enzyme by reversible coupling to either concanavalin A or a DHT-affinity column support this conclusion. Several studies show the dynamic effect of androgen binding: increased ouabain binding; enhancement of this binding by facilitated phosphorylation; spectroscopic evidence of conformational shifts, possibly consequences of these suggested activities for regulation, especially of metabolism, are examined.

Metabolic dynamics in the human red cell. Part II--Interactions with the environment

The maintenance of human red cell volume under multitude of trying physiological conditions is a self regulated dynamic process. Theoretical and experimental studies on red cell osmotic states have been primarily focussed on three different interdependent areas: the permeative properties of the red cell membrane, the kinetic studies of transmembrane fluxes of various ionic and nonionic chemical constituents of the red cell and plasma, and the ideal and non-ideal thermodynamic formulation of the osmotic states. The primary objective of this work is to provide a general model that converges the above mentioned components of the red cell and its environment under one umbrella. Such a model facilitates the simultaneous interpretation and prediction of quantitative changes in the red cell volume, pH, Donnan ratios, osmotic effects, plasma volume, transmembrane fluxes, and permeable and impermeable solute concentration.

Shift to the Na+ form of Na+/K+-transporting ATPase due to modification of the low-affinity ATP-binding site by Co(NH3)4ATP

1. Inactivation of purified Na+/K+-transporting ATPase by the MgATP complex analogue Co(NH3)4ATP, which binds to the low-affinity ATP-binding site, results in the concomitant inhibition of the K+-activated p-nitrophenylphosphatase, which is considered to be a partial reaction catalyzed by the enzyme in the E2 conformational state. 2. Complete inactivation of Na+/K+-transporting ATPase by Co(NH3)4ATP does not alter the ADP/ATP exchange reaction which is considered to be part of the catalytic activity in the E1 conformation. 3. The enzyme binds eosin at the high-affinity ATP-binding site as measured by the change in eosin fluorescence. Eosin binding to the Co(NH3)4ATP-inactivated enzyme is, in contrast to the untreated enzyme, not stimulated by Na1. Inactivation by Co(NH3)4ATP increased the half-maximal opposing effect of K+ on eosin binding from 1.1 mM in the control to 43.2 mM in the almost completely inactive enzyme. No eosin fluorescence changes were observed when the Co(NH3)4ATP-inactivated enzyme was treated subsequently with CrATP. This MgATP complex analogue forms a stable complex at the high-affinity ATP-binding site. CrATP thus abolishes eosin binding. 4. It is concluded, that Co(NH3)4ATP interacts with Na+/K+-transporting ATPase in the E2 conformation and arrests it there. This affects eosin binding to the high-affinity ATP-binding site, since the K+ sensitivity is lost. A possible interpretation of these differing effects of Co(NH3)4ATP on partial reactions of Na+/K+-transporting ATPase is that the sodium pump works as an (alpha,beta)2 diprotomer. It is likely that the arrest of one alpha,beta promoter in the E2 conformational state by occupancy of the low-affinity ATP-binding site with Co(NH3)4ATP induces the Na+ form (E1 form) in the corresponding alpha,beta promoter, as is indicated by the unaffected ADP/ATP exchange and the response of the eosin fluorescence on Na+ and K+.

Digital image analysis of two-dimensional Na,K-ATPase crystals: dissimilarity between pump units

Two-dimensional crystals of purified Na,K-ATPase were induced by treatment with phospholipase-A2 and vanadate. The negatively stained crystals were imaged by electron microscopy and analysed by digital image processing. Two-dimensional averaged projections of the crystals were calculated by the technique of correlation analysis, utilizing SPIDER (System for Processing of Image Data in Electron microscopy and Related fields) image processing software. The calculated dimensions of the unit cell were found to be 13.3 X 4.59 nm with included angle of 98 degrees, comparable to those reported by others. However, the two protomers of the unit cell were found always to be dissimilar in shape and in orientation. All protomers of one side of the dimer ribbon had a triangular outline, and all protomers of the opposing side had a comma shape. This dissimilarity could be explained by two orientations of identical protomers: one orientation for one side of the dimer ribbon, and another orientation for the protomers of the opposing side of the ribbon. An alternative explanation is that the protomers of one side of the dimer ribbon are actually in a conformation different from that of the protomers of the opposing of the ribbon.

Determination of monoclonal antibody-induced alterations in Na+/K+-ATPase conformations using fluorescein-labeled enzyme

The fluorescein 5'-isothiocyanate (FITC)-labeled lamb kidney Na+/K+-ATPase has been used to investigate enzyme function and ligand-induced conformational changes. In these studies, we have determined the effects of two monoclonal antibodies, which inhibit Na+/K+-ATPase activity, on the conformational changes undergone by the FITC-labeled enzyme. Monitoring fluorescence intensity changes of FITC-labeled enzyme shows that antibody M10-P5-C11, which inhibits E1 approximately P intermediate formation (Ball, W.J. (1986) Biochemistry 25, 7155-7162), has little effect on the E1 in equilibrium E2 transitions induced by Na+, K+, Mg2+ Pi or Mg2+. ouabain. The M10-P5-C11 epitope, which appears to reside near the ATP-binding site, does not significantly participate in these ligand interactions. In contrast, we find that antibody 9-A5 (Schenk, D.B., Hubert, J.J. and Leffert, H.L. (1984) J. Biol. Chem. 259, 14941-14951) inhibits both the Na+/K+-ATPase and p-nitrophenylphosphatase activity. Its binding produces a 'Na+-like' enhancement in FITC fluorescence, reduces the ability of K+ to induce the E1 in equilibrium E2 transition and converts E2.K+ to an E1 conformation. Mg2+ binding to the enzyme alters both the conformation of this epitope region and its coupling of ligand interactions. In the presence of Mg2+, 9-A5 binding stabilizes an E1.Mg2+ conformation such that K+-, Pi- and ouabain-induced E1----E2 or E1----E2-Pi transitions are inhibited. Oubain and Pi added together overcome this stabilization. These studies indicate that the 9-A5 epitope participates in the E1 in equilibrium E2 conformational transitions, links Na+-K+ interactions and ouabain extracellular binding site effects to both the phosphorylation site and the FITC-binding region. Antibody-binding studies and direct demonstration of 9-A5 inhibition of enzyme phosphorylation by [32P]Pi confirm the results obtained from the fluorescence studies. Antibody 9-A5 has also proven useful in demonstrating the independence of Mg2+ ATP and Mg2+Pi regulation of ouabain binding. In addition, [3H]ouabain and antibody-binding studies demonstrate that FITC-labeling alters the enzyme's responses to Mg2+ as well as ATP regulation.

Phosphatase activity of Na+/K+-ATPase. Enzyme conformations from ligands interactions and Rb occlusion experiments

The present work compares the effects of several ligands (phosphatase substrates, MgCl2, RbCl and inorganic phosphate) and temperature on the phosphatase activity and the E2(Rb) occluded conformation of Na+/K+-ATPase. Cooling from 37 degrees C to 20 degrees C and 0 degrees C (hydrolysis experiments) or from 20 degrees C to 0 degrees C (occlusion experiments) had the following consequences: (i) dramatically reduced the Vmax for p-nitrophenyl phosphate and acetyl phosphate hydrolysis but it produced little or no changes in the Km for the substrates; (ii) led to a 5-fold drop in the Km for the inorganic phosphate-induced di-occlusion of E2(Rb); (iii) reduced the K0.5 and curve sigmoidicity of the Rb-stimulated hydrolysis of p-nitrophenyl phosphate and acetyl phosphate and the Rb-promoted E2(Rb) formation. At 20 degrees C, in the presence of 1 mM RbCl and no Mg2+, acetyl phosphate did not affect E2(Rb); with 3 mM MgCl2, acetyl phosphate stimulated a release of Rb from E2(Rb) both in the presence and absence of RbCl in the incubation mixture. As a function of acetyl phosphate concentration the Km for iRb release was indistinguishable from the Km found for stimulation of hydrolysis and enzyme phosphorylation under identical experimental conditions; in addition, the extrapolated di-occluded fraction corresponding to maximal hydrolysis was not different from 100%. These results indicate that although E2(K) might be an intermediary in the phosphatase reaction, the most abundant enzyme conformation during phosphatase turnover is E2 which has no K+ occluded in it. The ligand interactions associated to phosphatase activity do not support an equivalence of this reaction with the dephosphorylation step in the Na+ + K+-dependent ATP hydrolysis; on the other hand, there are similarities with the reversible binding of inorganic phosphate in the presence of Mg2+ and K+ ions.

Vascular tissue (Na,K)ATPase activity and aging in the F344 rat

Vascular tissue (heart, thoracic aorta and tail artery) was removed from Fischer 344 rats, 12, 18 and 27 months of age. The intact tissue was then used to determine total, ouabain-sensitive and ouabain-insensitive 86Rubidium (86Rb) uptakes, to provide a reflection of (Na,K)ATPase activity. These studies indicate no change in total, ouabain-sensitive nor ouabain-insensitive 86Rb uptakes into cardiac tissue isolated from these rats. However, tail artery total and ouabain-sensitive 86Rb uptake decreased with age (a 61% decrease in ouabain-sensitive 86Rb uptake in 12 vs. 27-month-old rats) without significant changes in the ouabain-insensitive 86Rb uptake. This pattern was repeated in aortic tissue with a 56% decrease in ouabain-sensitive 86Rb uptake in 12 vs. 27-month-old rats. The results of these studies support an age-related decline in (Na,K)ATPase activity in aortic and tail artery tissue without a significant change in cardiac (Na,K)ATPase activity between 12, 18 and 27-month-old Fischer 344 rats.