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Role of Na⁺ and K⁺ in Enzyme Function

Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St. Louis, Missouri

ABSTRACT

I. INTRODUCTION

A. Historical Perspective

B. Halophilic and Halotolerant Adaptations

C. Mechanisms of Salt Homeostasis

II. M+ COORDINATION CHEMISTRY

A. M+ Coordination in Synthetic Molecules

B. Naturally Occurring Small Molecules

C. M+ Coordination in Biological Macromolecules

D. Macromolecular Stability and Solubility

E. M+ Selectivity

III. M+-ACTIVATED ENZYMES

A. Kinetics of M+ Activation

B. Structural Classification

C. K+-Activated Type I Enzymes

D. K+-Activated Type II Enzymes

E. Na+-Activated Type I Enzymes

F. Na+-Activated Type II Enzymes

G. Other Examples of M+ Activation

IV. Na+-ACTIVATED PROTEOLYTIC ENZYMES

A. Coagulation Factors IXa, Xa, and Activated Protein C

B. Thrombin Allostery

C. Na+ Binding and the Evolution of Serine Proteases

V. M+ AS AGENTS OF STABILITY

VI. PROTEIN ENGINEERING AND MOLECULAR MIMICRY OF M+ ACTIVATION

VII. SUMMARY

GRANTS

ACKNOWLEDGMENTS

REFERENCES

	ABSTRACT

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	I. INTRODUCTION

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Regulation of activity through metal ion complexation plays a key role in many enzyme-catalyzed reactions. Molecular mechanisms of metal ion coordination and their effects are an important aspect in the characterization of biological macromolecules. Over one-third of known proteins are metalloproteins (46, 154, 320). Conceptual associations with protein-metal complexes tend to favor divalent metals. Examples of Fe²⁺ involvement in redox cycles, Ca²⁺ in structural stability, or Zn²⁺ as electrophile in an enzyme-catalyzed reaction readily come to mind. Significance of divalent metals in protein structure and function has been reviewed in detail (11, 89, 284). Indeed, many bioinorganic chemistry textbooks are devoted to the description of divalent and polyvalent ions with monovalent cations (M⁺) discussed only in the context of membrane potentials. However, a large body of evidence suggests that group I alkali metals Na⁺ and K⁺play important roles other than nonspecific ionic buffering agents or mediators of solute exchange and transport. Na⁺ is the most abundant metal in human plasma, the backbone of biological fluids, and its occurrence mirrors that found in environmental liquids (Table 1). Molecular evolution has driven incorporation of selective M⁺ binding sites to enhance activity, diversity, and/or stability of many enzymes.

A. Historical Perspective

Earliest evidence for M⁺ activation of enzymes was provided by Boyer et al. (30). Further work led to a now classic paper by Kachmar and Boyer (165) showing the absolute requirement of K⁺ by an enzyme, pyruvate kinase. Earlier descriptions also demonstrated Na⁺-dependent catalytic rate enhancement in -galactosidase (53). After these discoveries, many enzymes were observed to display increased activity in the presence of M⁺ (314). For numerous systems, selectivity for a particular M⁺ is low, and a weak increase in activity is achieved by larger cations (i.e., K⁺, Rb⁺, or NH₄⁺). These effects can be understood in terms of kosmotropic effects on the water structure surrounding the protein. Selective activation by K⁺ occurs in many instances, yet fewer enzymes have been identified to be selective for Na⁺. Dichotomy in the activation profiles likely arises from the unequal distribution of Na⁺ and K⁺ in cells and extracellular fluids (Table 1). Involvement of M⁺ in allosteric regulation is possible through sufficient charge density to drive conformational changes and formation of stable complexes with biological molecules. However, charge density is not adequate to be the causative agent of catalysis as commonly observed with M²⁺. The biological context of the group IA alkali metals (Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺) provides the beginning of our discussion.

Sodium chloride lies at the heart of human biology and the roots of human civilization. Abundance or absence of this simple compound has had profound effects on human health and has provided a casus belli in many important milestones in the history of man (for an excellent historical account, see Ref. 182). Several initial forms of economics were based on salt rather than metal coinage and the words salary and soldier are derived from the Latin sal for salt, as is salus, the Latin word for "health." Industrial advances have largely eliminated salt as a limiting component of human nutrition or resource. In contrast, current farming practices are leading to significant Na⁺ accumulation in soil (94) and have fostered the development of saline-tolerant plants (378). Of the group IA metals, only Na⁺ and K⁺ are essential for human nutrition despite abundance of Rb⁺ and Li⁺ in the earth crust. Curiously, Li⁺ is noted to be an essential nutrient in rodents and goats. Human health is negatively influenced by excess sodium intake that may result in hypertension and other health problems (69, 101, 212). Naturally occurring organisms have adapted to concentrations of Na⁺ far exceeding that of human tolerance.

B. Halophilic and Halotolerant Adaptations

Life can withstand the extremes of ionic conditions found throughout the planet. NaCl concentrations approach saturation in the Dead Sea, which despite its name supports growth of archaea, bacteria, and fungi, such as Haloarcula marismortui, Dunaliella salina, and Eurotium herbariorium (38, 58, 269). Other bodies of water are known for their high salinity, such as the Sargasso and Red Seas and the Persian Gulf. Salt mines, salt marshes, oil field brines, hydrothermal brines, sodic soils, and drying salt lakes may approach saturation levels of salt (306). The ability to thrive or require salt, halotolerance or halophily, requires a number of energetically expensive cellular adaptations that are typically complemented by photosynthetic metabolism (16, 200). Organisms found in these environs tend to present anionic phospholipid membranes and acidic protein machinery (102, 331, 332). Chelation of cations stabilizes macromolecules in conditions of high ionic strength and provides shielding against the ionic environment (58, 82). Specific ion binding sites and extensive salt bridge networks have also been identified as important structural elements (81, 131). Microorganisms in conditions of high ionic strength may synthesize ectoine, a novel cyclic amino acid, or other small molecules, such as glycerol, sucrose, and glycine betaine, to maintain osmotic balance with the extracellular medium rather than rely on M⁺ exchange (368, 369). Alternatively, osmotic balance is achieved with accumulation of high levels of cytosolic K⁺ and concomitant adaptation of intracellular machinery to allow higher levels of K⁺ (340). Osmotolerance mechanisms have been suggested as putative therapeutic targets to inhibit growth of human pathogens such as Vibrio cholerae and Candida albicans (135, 259). Furthermore, Na⁺ may be employed in extremophilic bacteria as a coupling ion that substitutes for or complements the traditional H⁺ cycle (134). Little is known on how the earliest forms of life defended themselves in high ionic conditions, and the defense mechanisms of nonhalotolerant organisms are beginning to be defined.

C. Mechanisms of Salt Homeostasis

Yeast serves as a useful model to dissect fungal and plant responses to saline environments. Ion transport systems, cation detoxification mechanisms, and signal transduction mechanisms are similar in these organisms (108, 188, 248, 283). Ionic strength and/or osmolarity activates mitogen-activated protein (MAP) kinase signaling via a two-component system and the Sho1 membrane protein (201, 202, 266). Upregulated genes include those for synthesis of glycerol and trehalose for osmoprotection and a shift in metabolism to favor protein synthesis. Transcription factors involved in the yeast response are not clearly defined yet overlap other stress response elements (32, 272, 278, 295). A genomic approach to the yeast reaction to saline stress indicated that up to 7% of the yeast genome is upregulated during stress (265). It is surprising that such a large complement of genes is involved, mostly transiently, in response to high ionic strength or osmolarity. High levels of NaCl affect plants through osmotic effects in addition to intracellular accumulation of Na⁺. Cellular uptake of essential ions such as K⁺ and Ca²⁺ is also inhibited. In turn, imbalanced intracellular M⁺ratios result in substitution of Na⁺ for sites requiring K⁺. In particular, pyruvate synthesis and protein translation are decreased (196). Regulation of ionic balance in humans is mediated by several mechanisms on a system-wide basis that reduces energetic load on individual cells.

Overall control of water flux plays a key role in regulating the concentration of Na⁺ in the human cardiovascular system. Hormone signaling between the hypothalamus, adrenal cortex, heart, and kidney is mediated through vasopressin (antidiuretic hormone), aldosterone, and atrial natriuretic peptide (ANP) to control electrolyte balance. These signals tightly regulate systemic osmotic pressure near a set-point value (29, 68). Vasopressin increases the volume of circulating water by acting on renal collecting ducts via activation of V₂ receptors. Intracellular trafficking of aquaporin channels directs them to cell membranes and increases cell permeability and reabsorption (3, 113, 232). Vasopressin release from the hypothalamus is controlled by osmoreceptors that sense changes in osmolarity of the extracellular fluid (339). Only recently have mechanisms of mechanosensation begun to be unraveled (180, 216). Stretch receptors also control release of ANP in the atrial myocardium, which antagonizes the effects of vasopressin and aldosterone (318). In contrast, aldosterone levels are controlled by the renin-angiotensin system. Aldosterone acts on distal convoluted tubule cells of the kidney through activation of cytoplasmic mineralocorticoid receptors that activate gene expression (103). Of genes expressed, the epithelial Na⁺ channel (ENaC) plays a key role in maintaining the proper level of Na⁺.

Na⁺ transport by the ENaC is a vital component in the maintenance of ion homeostasis (107). Activity of the ENaC channel must vary greatly in response to dietary Na⁺ intake. Intracellular trafficking of ENaC proteins is a powerful regulatory mechanism and acts similarly to that observed with aquaporin channels. Trafficking yields a dynamic and large range of response. This contrasts with ligand- or voltage-gated channels that open or close rapidly in response to a stimulus (107). Low serum Na⁺ concentration (hyponatremia) is the most common electrolyte disorder and a common medical problem that affects 1–5% of all hospital inpatients (2, 99, 179). Vigorous exercise, like marathon running, can also cause life-threatening hyponatremia (5). Inherited forms of hypertension and hypotension have been ascribed to several genes involved in ENaC trafficking (192). Like many membrane proteins and channels, structural information regarding the ENaC is lacking. For example, the number and stoichiometry of the three subunits that heteromultimerize to form the channel is debated (90, 174, 304). A three-residue tract, Gly/Ser-Xxx-Ser, present within all three subunits is suggested to act as the putative selectivity filter where side chain hydroxyl moieties line the channel pore. Such a configuration would contrast with that observed in K⁺ channels (79, 224, 296). Although progress has been made in the elucidation of the crystal structures of several M⁺ channels and pumps, only a few examples of a potentially diverse class of enzymes have been provided to date. Our best examples of M⁺ coordination come from small-molecule studies that provide a useful framework for understanding M⁺ binding in proteins and other biological macromolecules.

	II. M+ COORDINATION CHEMISTRY

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Sir Humphrey Davy (1807) first isolated sodium by the electrolysis of fused soda (NaOH). Earliest definitions of group IA metals classify them as type A metals and very hard Lewis acids (252). Group IA metals have small ionic radii that bear a strong positive charge with no electron pairs in the valence shell (Table 2). They have low electron affinity and a strong tendency for hydration. Both the strong charge and small ionic radius of group IA metals impart bonding characteristics that are more covalent in nature. However, interaction between M⁺ and ligand is based solely on electrostatics and is not technically a "bond" (251). Importantly, ligand exchange rates (k_ex) of M⁺ are very high and allow rapid association and dissociation kinetics. Charge density of any M⁺ is insufficient to be the causative agent of catalysis as the single positive charge is spread over a large volume. However, M⁺ coordination can play an important role in rate enhancement or allosteric regulation of an enzyme-catalyzed reaction. From the perspective of organic chemistry, M⁺s are typically viewed as counter- or spectator ions to more interesting Lewis bases. The biochemical influence of M⁺ is of more considerable scope.

Small molecule chemistry provides a useful introduction to M⁺ coordination in biological macromolecules. Lehn, Pederson, and Cram (60, 189, 253) synthesized a series of high-affinity M⁺chelators. Their work led to the development of host-guest chemistry in which a ligand (guest) binds a multidentate macromolecule (host) to drive its synthesis. Cyclic polyethers (crown ethers, Fig. 1A) are capable of M⁺ coordination through six O atoms, yet conformational flexibility of these molecules requires a significant entropic penalty for complexation (253). Such chelators must significantly alter conformation for M⁺ binding. Creation of a bicyclic system (cryptand, Fig. 1B) locks the desired conformation and adds dimensionality (189). Rigidification of the system (spherand, Fig. 1C) abrogates the need for conformational change and leads to femtomolar affinity and exceptional selectivity (60). Conceptual simplicity, broad applicability, and utility of these designed molecules led to a most deserved Nobel Prize in 1987 for these authors. Chemical coupling of these compounds yields fluorescent M⁺sensors (136, 208, 302). Even larger macrocyclic compounds, such as calixarenes, have been developed more recently for use in M⁺-selective electrodes (10, 44). Affinity and selectivity of these synthetic compounds exceed that observed in enzymes.

View larger version (15K): [in this window] [in a new window]   FIG. 1. Principles of M+ coordination from small molecules. A: in crown ethers, significant rearrangement is required for cation binding. B: creation of a cryptand adds dimensionality and significantly enhances M+ selectivity. C: rigidification of the system through creation of a spherand provides extreme affinity as the molecule is essentially unchanged upon cation coordination.

View larger version (27K): [in this window] [in a new window]   FIG. 2. Examples of coordination shells in proteins. Four to eight ligands may be involved in complexation of M+ (yellow sphere). Examples shown are from 1DGD, 2DKB, 1B57, 1U7H, and 1T5A. Six ligands in octahedral configuration are most commonly observed. Notably, ideal geometry is rarely observed in M+-protein complexes and may be compensated by a formal charge. Such distortions may be linked with key mechanistic aspects of M+ activation. Variable numbers of O atoms donated from the polypeptide and water molecules permit a wide diversity of cation binding sites found in disparate protein families.

Many naturally occurring small molecules are well defined for their ability to bind M⁺ with high selectivity and affinity (270). Ionophoric antibiotics are produced by several gram-positive bacterial species such as Streptomyces, Streptoverticillium, Nocardiopsis, Nocardia, and Actinomadura (20). M⁺ binding by these compounds involves a conformational change that allows the complex to transport across a membrane through facilitated diffusion. Valinomycin from Streptomyces fulvissimus is a 12-membered macrocyclic peptide that prefers larger cations (Rb⁺ and K⁺). The macrocycle is composed of three repeats of alternating L- and D-amino acids (L-Val-D-Hiv-D-Val-L-Lac, where Hiv is -hydroxyisovaleric acid and Lac is lactic acid). Crystal structures of valinomycin in the free and bound state provide an elegant example of M⁺ complexation. In the free state all six NH groups are intramolecularly H-bonded, four to amide C=O groups with two to C=O from ester moieties (263). Upon complexation with a M⁺, the cyclical chain forms a bracelet-like conformation around the ion, and six ester carbonyl groups coordinate the ion in octahedral configuration (Fig. 3). Further stabilization of the complex is achieved through H-bonding between carbonyl O and amide H moieties (230). A Na⁺-selective cyclic decapeptide, antamanide, has been described from the poisonous Amanita mushroom (350). Interestingly, this ionophore counteracts the effects of other toxic compounds produced by the organism. Noncyclical ionophoric compounds have also been described. Monensin and narasin are polyketides that form stable complexes with Na⁺ through conformational changes upon ion complexation (Fig. 4). (47). Monensin, like other antibacterial M⁺ ionophores, has been used for many years in the dairy industry for selective reduction of bacterial fauna (40). Most naturally occurring synthetic ionophores prefer K⁺ including nonactin (169), monactin (260), dinactin (260), salinomycin (282), and nigericin (195). Several antifungal agents interact with sterols in the cell membrane (ergosterol in fungi, cholesterol in humans) forming ion channels that disrupt cellular concentration gradients such as amphotericin B (25), nystatin (92), and pimaricin (9). Of known small molecule ion permeation channels, gramicidins are the best characterized.

View larger version (39K): [in this window] [in a new window]   FIG. 3. Valinomycin bound to K+. An inner sphere of interactions (dashed gray lines) provides near-perfect octahedral coordination of the cation (yellow sphere). Further stability arises from a second shell of intramolecular H-bonds (dashed green lines). In turn, the surface of the complex is hydrophobic and permits facilitated diffusion through a phospholipid bilayer.

View larger version (19K): [in this window] [in a new window]   FIG. 4. Monensin selectively binds Na+, causing a significant change in the conformation. Complexation drives the hydrophilic moieties of the molecule to the core of the complex, leaving a surface of hydrophobic residues. Facilitated diffusion of the molecule through gram-positive bacterial membranes leads to destruction of ionic gradients and the antibiotic effect of the compound.

View larger version (21K): [in this window] [in a new window]   FIG. 5. Pore architecture from K+ complexes. A: ion permeation in gramicidin A (1GMK) is mediated through a dimer of antiparallel single-stranded 6.3-helix, a structure permitted by the presence of alternating L- and D-amino acids. Carbonyl groups lining the pore orient parallel to the motion of the ion, and low selectivity results. Fewer carbonyl groups line the pore of the nonselective NaK channel from B. cereus (2AHZ) (B) than the KcsA K+ channel from S. lividans (1K4C) (C) and explain the reduced M+ selectivity.

C. M⁺ Coordination in Biological Macromolecules

Nucleic acids commonly bind M⁺ and M²⁺ to mediate structure, stability, and protein-nucleic acid interactions. Physiological cations bind both the major and minor groove of DNA double helices as demonstrated through experimental (67, 152) and theoretical approaches (50). In particular, Na⁺ and other M⁺ preferentially bind the minor groove of adenine-rich sequences in A-form of DNA. Ions are thought to bind at similar positions to water molecules yet with considerably longer residence times in the spine of hydration that runs along the groove (126). M²⁺ are thought to bind both the minor and major grooves of DNA also with a preference for the A-form of DNA. Notably, the effect of M⁺ binding to DNA structure has met with debate (51). Irrespective of whether M⁺ play a role in the A- to B-DNA transition, more definite roles are noted for other nucleic acids. Mg²⁺ and M⁺ are well known to be essential for the folding and stability of large RNA molecules. For example, rRNA of the large ribosomal subunit from Haloarcula marismortui binds 116 Mg²⁺ and 88 M⁺. Similar to DNA, M⁺ bind to nucleotide bases in the major groove sides of G-U wobble pairs. The extent to which M⁺ bind rRNA is suggestive of a vital role for these ions prior to emergence of proteins.

Coordination of M⁺ in a folded polypeptide occurs often through carbonyl O atoms donated from peptide bonds. In the above examples of synthetic M⁺ ionophores, ion binding is mediated by ligand O atoms from ketones, esters, or ethers. In fewer instances of M⁺ binding, sites employ a negatively charged unidentate carboxyl or phosphoryl group. In contrast, M²⁺ sites often utilize one or more full negatively charged groups to balance the higher charge density of these ions. Peptide bonds possess a useful configuration for allosteric regulation through M⁺ complexation. These bonds are planar and extremely stable due to resonance. In turn, increased dipole moment of the carbonyl O atom provides a stronger electrostatic interaction with the ion. Moreover, recruitment of additional regions of the protein is mediated via H-bonding through the amide H (Fig. 6). Signaling through local peptide bonds can occur upon M⁺ coordination leading to long-range effects on catalytic properties. Notably, polypeptide segments can communicate through a bound M⁺ and its liganding carbonyl O atoms. Conformations not accessible to the polypeptide in aqueous solution alone are stabilized. M⁺ sites occur in regions of the polypeptide that do not form secondary structure and frequently between surface-exposed loops (128). Importantly, M⁺ complexation is largely achieved by residues separated in the linear sequence of the protein. M²⁺ binding in many proteins occurs often through recognizable sequence and structural motifs. For example, EF-hand motifs and zinc fingers are well known for their ability to selectively complex Ca²⁺ and Zn²⁺, respectively (22, 207). Lack of sequence similarity in known M⁺ binding sites renders bioinformatic analysis impossible in the absence of structural information. However, structural similarities link the selectivity filter of the K⁺ channel with the M⁺ binding environment of disparate enzyme families (see sect. IIC).

View larger version (9K): [in this window] [in a new window]   FIG. 6. Allosteric communication mediated through peptide bonds. A: in the typical arrangement found in secondary structures, peptide bonds are aligned in parallel. B: in contrast, a M+ binding site allows for antiparallel connections between peptide bonds in regions devoid of secondary structure. H-bonding may be linked to complexation with M+ through the amide H and provides an efficient mechanism for allosteric signaling. C: geometry of water coordination is significantly different from the octahedral configuration typically observed with M+-protein complexes and highlights the mechanistic diversity facilitated by M+ binding.

View larger version (9K): [in this window] [in a new window]   FIG. 7. Stabilization of protein conformational states through M+ binding. Cation binding may alter the population of protein states leading to improved enzymatic properties. Stabilization of the M+ binding site may propagate to the active conformation of catalytic machinery, substrate, or cofactor binding sites. Moreover, the cation may provide stability in conditions of high salinity and/or temperature.

View larger version (13K): [in this window] [in a new window]   FIG. 8. Coordination of M+ can influence the pKa value of ligand atoms. Ligand exchange rates of all group IA M+s are very high and allow for dynamic interplay with atoms in the coordination shell. A: as the distance between ligand atom 1 and M+increases, so does the pKa value. Hence, the plane defined by ligand atoms 2, 3, 5, and 6 plays a key role in octahedral coordination of M+. B: such vertical motion is readily apparent in the K+ channel, where four carbonyl O atoms are held at fixed distances to one another.

Observed differences in valence parameters of M⁺ lead to a host of macroscopic features based on hydration properties of these ions. Group IA alkali metals bear a single positive charge with differing ionic radius (Table 2). Subtle differences in ionic radii correspond with significant alteration of ionic volume, hence charge density, and downstream effects upon bonding parameters. Hydration shells of M⁺ are dissimilar, and this extends to secondary and tertiary shells of the ion. Li⁺ and Na⁺ are small enough to bind three or four water molecules with reasonable affinity and result in a larger apparent size in aqueous solution. K⁺ favors four or five water molecules coordinated with weaker strength (54–56, 75, 150). Biological exploitation of this subtle difference is exemplified in the structure of K⁺ channels whose selectivity is based on the ability to strip water molecules from the hydration shell of the ion (8, 79). In turn, K⁺ channels rather than Na⁺ channels form the basis for numerous ionic balance-based transport systems. Universally, intracellular concentrations of K⁺ are considerably higher relative to the extracellular environment. Overall, Na⁺ balance in all organisms including humans is largely driven through transport of water molecules rather than regulated movement of Na⁺ and stems from electronic differences of M⁺. A parallel concept is thought to explain why Ca²⁺ and not Mg²⁺ acts as an intracellular messenger. Ligand exchange rates of Ca²⁺ are 10,000-fold higher than those of Mg²⁺, allowing rapid and efficient complexation (286). Hydration shells of M⁺ exert dispersive effects on neighboring water molecules through electrostatic interactions and coordination geometry.

Over a century ago, Hofmeister noted the ability of various ions to induce the precipitation of proteins in solution (181). Ionic effects on protein structure have been widely ascribed to their effect on water. Smaller, more strongly hydrated ions are kosmotropic (water structuring) (Li⁺, Na⁺), whereas larger ions are chaotropic (water disrupting) (K⁺, Rb⁺, Cs⁺) (27, 39, 97, 150). The Hofmeister series bears an important relationship with protein solubility. Chaotropic agents are well known for their ability to cause protein precipitation and formed the backbone of protein chemistry before development of more refined chromatographic techniques. At low concentrations of a given salt, solubility of a macromolecule increases slightly in a process termed salting-in. At high concentrations of salt, the protein solubility drops sharply, termed salting-out, and this phenomenon forms the basis of many protein purification strategies. Debye-Hückel theory can explain certain aspects of this phenomenon by applying continuum electrostatics to simplify ions in solution. The positively or negatively charged ion is represented as a point charge in a solvent of constant dielectric constant. The theory dictates that proteins are surrounded by salt counterions that screen charged groups and results in lower electrostatic free energy of the molecule and increased activity of the solvent, which in turn leads to increasing solubility. However, as the concentration of ions is increased, their solvating power decreases, protein solubility decreases, and precipitation results. For solutions of greater ionic strength, the Pitzer equation should be used (264). Although the Pitzer equation is accurate, many empirical values need to be determined for application. Specific ion interaction theory has been proposed more recently as a simplified, yet accurate, alternative (117). All of the above models for ions in solution suggest ionic influences act over fairly large distances with uniform distribution. Many lines of evidence suggest this simplification may be problematic (26, 55). Inhibition of activity by M⁺ at high concentrations has been documented for many enzymes and can be attributed to the chaotropic effect of larger ions. Destabilization of the enzyme structure would then lead to reduced catalytic activity via nonspecific mechanisms. Monovalent anions are more commonly noted for their inhibitory effect on enzyme-catalyzed reactions (374). However, in a large number of systems to be dealt with next, the role of M⁺ is highly specific and mediated by binding to the enzyme and or enzyme-substrate complex. In such instances, nonspecific ionic strength effects become of marginal significance, and mass-law binding becomes of the essence.

E. M⁺ Selectivity

Several M⁺-activated enzymes have been crystallized free or in the presence of Na⁺, K⁺, or other M⁺, and the resulting information has broadened our understanding of M⁺ selectivity. In the case of tryptophan synthase, changes between the Na⁺-bound and K⁺-bound structures are significant (281) but are not matched by differences in the kinetics of activation (357). In pyruvate kinase, replacement of K⁺ with Na⁺ results in no structural changes (185), although the enzyme is practically inactive without K⁺ (30). In thrombin, however, changes in coordination between Na⁺ and K⁺ propagate to the oxyanion hole and explain the differences in the kinetics of activation (247, 262). In the case of dialkylglycine dehydrogenase (324, 325) and Hsc70 (93, 352), replacement of the essential K⁺ with Na⁺ drastically changes the geometry of coordination and perturbs residues that control binding of pyridoxal phosphate (PLP) or ATP. These enzymes have evolved K⁺ selectivity by imposing geometric constraints on the coordination shell that cannot be obeyed by the smaller ionic radius of Na⁺. The linkage with enzyme activation is ensured by the functional connection of these constraints with the optimal orientation of catalytic residues. Rigidity of the coordination shell guarantees selectivity by increasing the entropic cost of any reorganization meant to accommodate a M⁺ of different size. Interestingly, an analogous strategy has been exploited successfully in the synthesis of selective chelators (60, 217).

One striking feature of K⁺ channels is the GYG signature sequence (residues 77–79) whose backbone O atoms shape part of the selectivity filter that gates access to a pore that transverses the phospholipid membrane. Four carbonyl O atoms define a plane that dictates the size of the pore. B-factors of these O atoms indicate that RMS fluctuations of 0.75–1 Å occur and agree with molecular dynamics simulations (17, 36). In turn, the O atoms are in a fluidlike state, and the size of the channel acts simultaneously to provide fast conduction rates. Indeed, size of the pore allows for near-equal transmission of Rb⁺. Naturally occurring nonspecific channels have been identified where the selectivity filter is absent. For example, the NaK channel from Bacillus cereus has reduced selectivity similar to cyclic nucleotide-gated channels and possesses a GDG sequence rather than the typical GYG. In turn, carbonyl O atoms adopt a different conformation, yielding a nonspecific binding site (297). Remarkably, conformation of the GYG sequence relative to the bound K⁺ in the channel is similar to the GYG sequence (residues 325–327) near the K⁺ binding site of pyruvate dehydrogenase kinase (167), the GFG sequence (residues 337–339) near the K⁺ binding site of branched-chain -ketoacid dehydrogenase kinase (197), and the KYG sequence (residues 224–226) near the Na⁺ binding site of thrombin (247) (Fig. 9). Furthermore, mutation of Tyr in this sequence has very similar functional consequences in the K⁺ channel (228) and thrombin (121). This unexpected connection is testimony to the basic similarity of M⁺ recognition mechanisms that evolution has bestowed on proteins of widely different function.

View larger version (30K): [in this window] [in a new window]   FIG. 9. Overlay of the signature sequence GYG (residues 77–79) in the selectivity filter of the KcsA K+ channel (CPK, K+ yellow spheres, 1BL8) with the GYG sequence (residues 325–327) of pyruvate dehydrogenase kinase (magenta, K+ magenta sphere, 1Y8P), the GFG sequence (residues 337–339) of branched-chain -ketoacid dehydrogenase kinase (green, K+ green sphere, 1GJV) and the KYG sequence (residues 224–226) of thrombin (wheat, K+ wheat sphere, 2A0Q). K+ sits in equivalent positions relative to the sequence in all cases. [Modified from Di Cera (70).]

View larger version (68K): [in this window] [in a new window]   FIG. 10. Na+ coordination in the LeuTAa from Aquifex aeolicus (2A65) (CPK, C in cyan) involves no water in the rigid coordination shell. In this transporter, two Na+ are transferred with Leu with antiport of Cl–, and varying ratios of cations and anions to substrate are known. The amino acid (CPK, C in yellow) has direct contacts that complete the coordination shell of one of the two bound Na+ (yellow sphere).

	III. M+-ACTIVATED ENZYMES

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View larger version (16K): [in this window] [in a new window]   FIG. 11. Enzyme activity in the presence of LiCl (gray), NaCl (white), KCl (black), or RbCl (hatched) for Hsc70 (237) and thrombin (267). Values refer to s = kcat/Km of ATP hydrolysis for Hsc70 in the presence of 150 mM salt, relative to CsCl, or the hydrolysis of H-D-Phe-Pro-Arg-p-nitroanilide by thrombin in the presence of 200 mM salt, relative to choline chloride. The preference for K+ (Hsc70) or Na+ (thrombin) is evident from the plot.

In the study of enzyme activation by M⁺, attention is often focused on the effect of M⁺ on the velocity of substrate hydrolysis. The activating effect is readily observed as an increase in the velocity as a function of [M⁺]. Specificity is detected in this assay by comparing the velocity among different M⁺ at the same concentration. Below we show that quantitative information about the energetics and mechanism of M⁺ can be obtained by measurements of the independent Michaelis-Menten parameters k_cat and s = k_cat/K_m. In general, these parameters can be defined respectively as the velocity of product formation per unit enzyme under saturating conditions of substrate (k_cat) and the velocity of product formation per unit enzyme and substrate when the substrate concentration tends to zero (s). It should be noted that K_m, the concentration of substrate giving half of the maximal velocity of substrate hydrolysis, is not an independent parameter because it requires knowledge of the value of k_cat. The values of s and k_cat, on the other hand, are independent of each other because they define, respectively, the initial slope and asymptotic value of the velocity curve, expressed in units of enzyme concentration.

We will derive the independent parameters defined above for a basic scheme of M⁺ activation (see scheme 1). We will assume that the enzyme E contains a single site for substrate and M⁺. The scheme also applies to the case where the enzyme has multiple active sites that do not interact, but would not apply to oligomeric enzymes that bind substrate or M⁺ at multiple interacting sites. Even in its simple form, scheme 1 finds application in a number of relevant systems and captures the basic features of M⁺ activation. Scheme 1 was introduced by Botts and Morales in a different context to analyze the action of a modifier on substrate hydrolysis (28). The enzyme is assumed to exist in two forms, one free (E) and the other bound to M⁺ (EM), with different values of kinetic rate constants for binding (k_1,0, k_1,1), dissociation (k_-1,0, k_-1,1), and hydrolysis (k_2,0, k_2,1) of substrate S into product P. K_A = k_A/k_-A and K_A = k_A/k_-A are the association constants for M⁺ binding to E and ES, respectively. Detailed balance imposes a constraint among the rate constants in scheme 1, i.e., k_1,0K_Ak_-1,1 = k_-1,0K_Ak_1,1. The exact analytical solution for the velocity of product formation at steady state can be found in a number of different ways. We will use the Hill diagram method (143), because of its elegance and direct connection with the kinetic features of the scheme. Scheme 1 contains four species, of which only three are independent because of mass conservation. Hence, each directional diagram must contain the product of three rate constants. The sum of the trajectories toward each species defines the contribution of that species at steady state. The velocity of product formation is then

(1)

where e_tot is the total concentration of active enzyme and _EX is the sum of the trajectories toward species EX. Coefficients in Equation 1 are listed in Table 3 and are polynomial expansions in the variable [M⁺] = x, with each term mapping into a trajectory in scheme 1. The velocity of product formation for scheme 1 is quadratic in [S], although the enzyme contains only a single site for S. Likewise, polynomial expressions in x are quadratic, although the enzyme contains one binding site for M⁺. This consequence arises from the difference in which terms are calculated for equilibrium and steady-state systems (28, 74, 143). Under the influence of M⁺, an enzyme containing a single substrate binding site can display cooperativity in substrate binding, and this possibility should be kept in mind when analyzing experimental data. Glucokinase is a relevant example of cooperativity in monomeric enzymes because it isomerizes slowly between two forms, E and EM in scheme 1, that differ in affinity and catalytic competence toward substrate (166).

(2)

(3)

Three independent parameters k_2,0, k_2,1, and K_A can be resolved from measurements of k_cat as a function of x. On the other hand, measurements of s as a function of x only resolve two parameters because of the form of Equation 3. These parameters are s₀= k_2,0k_1,0/(k_-1,0+ k_2,0) and s₁= k_2,1k_1,1/(k_-1,1+ k_2,1) obtained as the values of s in the absence or presence of saturating concentrations of M⁺. Resolution of K_A, measuring the affinity of M⁺ for the free enzyme, is complicated by the expansion term (x) that contains the additional independent parameters

and k_1,1/k_1,0. When (x) makes a small contribution to the value of s, K_A can be estimated from the value of x at the midpoint transition of s from s₀ to s₁. This appears to be the case under many circumstances (see Fig. 28).

View larger version (9K): [in this window] [in a new window]   FIG. 28. Na+ dependence of the kinetic constants s = kcat/Km (left) and kcat (right) for the hydrolysis of H-D-Phe-Pro-Arg-p-nitroanilide by thrombin. Experimental conditions are as follows: 50 mM Tris, 0.1% PEG, pH 8.0 at 25°C. The [Na+] was changed by keeping the ionic strength constant at 400 mM with choline chloride. The data illustrate the signatures of type II activation with both s and kcat showing a marked Na+ dependence and changing from low, finite values to significantly higher values. Curves were drawn with the equations listed in Table 4 for type II* activation, with best-fit parameter values as follows: (data at left) s0= 2.3 ± 0.1 µM–1 · s–1, s1= 99 ± 3 µM–1 · s–1, KA= 38 ± 1 M–1; (data at right) k2,0= 4.7 ± 0.2 s–1, k2,1= 78 ± 2 s–1, KA' = 45 ± 2 M–1. Also shown is the contribution of the expansion term in Eq. 6 (red line, left) calculated from the reported values of kinetic rate constants (177). This term contributes at most a 3% correction at low [Na+].

(4)

with

(5)

(6)

Interestingly, the expression for k_cat is not affected by the drastic change in the form of v, and even s changes only slightly. It should be pointed out that the condition = 1 was identified by Botts and Morales to ensure Michaelis-Menten kinetics (28). However, the above equations show that such condition is only sufficient, but not necessary, for Michaelis-Menten kinetics. Even when the enzyme obeys Michaelis-Menten kinetics, the value of K_A is difficult to resolve because of the form of Equation 6. Measurements of this important parameter must be carried out by means of other techniques, such as enzyme titration through circular dichroism or fluorescence spectroscopy. Alternatively, the value of and k_1,1/k_1,0 must be resolved from independent measurements of substrate hydrolysis as done for thrombin (177).

Kinetic signatures of relevant types of activation based on a recent classification of M⁺-activated enzymes (70) may differ significantly, and k_cat becomes of diagnostic value (Fig. 12). The mechanism of M⁺ activation can be established unequivocally from crystal structures as cofactor-like (type I) or allosteric (type II). In the former case, substrate anchoring to the enzyme active site of the enzyme is mediated by M⁺, often acting in tandem with a divalent cation like Mg²⁺. In such a mechanism, M⁺ coordination is absolutely required for catalysis or substrate recognition. In the latter, M⁺ binding enhances enzyme activity through conformational transitions triggered upon binding to a site where the cation makes no direct contact with substrate. In this case, the M⁺ is not expected to be absolutely required for either binding or catalysis. M⁺ activation, whether type I or type II, is determined by two events. First, M⁺ binds to the enzyme to convert E to EM and, second, the binding triggers changes in EM that produce higher catalytic activity. There are two important implications in this process. First, structural determinants responsible for M⁺ binding need not be the same as those responsible for transduction of this event into enhanced catalytic activity. Second, the extent of activation s₁/s₀ is energetically independent from the affinity of M⁺ binding. M⁺ activation is not possible in the absence of M⁺ binding (K_A= 0 and K_A = 0). However, absence of M⁺ activation can also be caused by absence of transduction when M⁺ binding is present but does not change the values of the kinetic rate constants.

View larger version (8K): [in this window] [in a new window]   FIG. 12. M+ dependence of kcat is diagnostic for various cases of M+ activation based on scheme 1. In type II activation, the value of kcat changes from a finite low value to a higher value. The midpoint of the transition defines KA, the binding constant for M+ binding to ES. In type Ia activation, M+ is required for S binding and the value of kcat is independent of [M+]. In type Ib activation, M+ is required for S hydrolysis, and the value of kcat changes like in type II activation, but goes to zero when [M+] = 0.

Scheme 1 applies in a reduced form when the M⁺ acts as a cofactor in type I enzymes. Two subgroups of type I enzymes can then be distinguished. Type Ia enzymes cannot bind substrate in the absence of M⁺ (ES does not exist in scheme 1), whereas type Ib enzymes cannot mediate catalysis in the absence of M⁺ (k_2,0 = 0 in scheme 1) yet allow substrate binding. In type Ia activation, scheme 1 is linear and contains only E, EM, and EMS. The enzyme always obeys Michaelis-Menten kinetics, regar