Co-operativity in biological machines

McClare has recently discussed the properties of machines which operate too fast for there to be appreciable thermalization between components. We argue that co-operative behaviour is likely in those machines and that if there is co-operativity, the machine cannot be treated as the superposition of a large number of “molecular energy machines”. This point may be relevant to models of muscle contraction.     

Cooperativity in monomeric enzymes with single ligand-binding sites

Cooperativity is widespread in biology. It empowers a variety of regulatory mechanisms and impacts both the kinetic and thermodynamic properties of macromolecular systems. Traditionally, cooperativity is viewed as requiring the participation of multiple, spatially distinct binding sites that communicate via ligand-induced structural rearrangements; however, cooperativity requires neither multiple ligand binding events nor multimeric assemblies. An underappreciated manifestation of cooperativity has been observed in the non-Michaelis–Menten kinetic response of certain monomeric enzymes that possess only a single ligand-binding site. In this review, we present an overview of kinetic cooperativity in monomeric enzymes. We discuss the primary mechanisms postulated to give rise to monomeric cooperativity and highlight modern experimental methods that could offer new insights into the nature of this phenomenon. We conclude with an updated list of single subunit enzymes that are suspected of displaying cooperativity, and a discussion of the biological significance of this unique kinetic response.     

Co-operativity in seminal ribonuclease function. Kinetic studies.

Maltose-maleimide was synthesized as a potential affinity label for the facilitative hexose carrier with selectivity for exofacial sulphydryl groups. This reagent, although probably a mixture of isomers, did not significantly penetrate the plasma membrane of human erythrocytes at concentrations below 5 mM at 37 degrees C. When allowed to react to completion, it irreversibly inhibited the uptake of 3-O-methylglucose, with a half-maximal response at about 1.5-2.0 mM-reagent. The rate of transport inactivation was a saturable function of the maltose-maleimide concentration. Studies of reaction kinetics and effects of known transport inhibitors demonstrated that irreversible reaction occurred on the exofacial outward-facing carrier, although not at a site involved in substrate binding. Reaction of intact erythrocytes with [14C]maltose-maleimide resulted in labelling of a broad band 4.5 protein of Mr (average) 45,000-66,000 in electrophoretic gels. This protein was very likely the hexose carrier, since its labelling was inhibited by cytochalasin B. Exofacial band 4.5 labelling was stoichiometric with respect to transport inhibition, yielding an estimated 300,000 carriers/cell. These results suggest that the exofacial sulphydryl which reacts with maltose-maleimide is distinct from the substrate binding site on the hexose carrier, but that it confers substantial labelling selectivity to impermeant maleimides. Additionally, the high efficiency of carrier labelling obtained with maltose-maleimide is useful in quantifying numbers of carriers in whole cells.     

Functional changes of rat brain mitochondrial enzymes induced by monomeric cholesterol

• 1.1. The binding of [¹⁴C]cholesterol into rat brain mitochondrial membranes follows an exponential path described by the general formula y = a.e^bx. [¹⁴C]cholesterol glucoside binding has a sigmoidal character where the “best-fit” curve of this type of binding is the one described by the Hill equation with Hill coefficient h = 2.06. These findings suggest a positive cooperativity in the binding of both compounds into rat brain mitochondrial membranes.
• 2.2. The specific activity of the outer mitochondrial membrane enzyme monoamine oxidase was linearly decreased at different concentration of cholesterol or its glucoside.
• 3.3. The specific activity of the inner mitochondrial membrane enzyme succinate-cytochrome c reductase was linearly decreased, while that of Rotenone-sensitive NADH-cytochrome c reductase was exponentially increased, at different concentrations of cholesterol.
• 4.4. These results are discussed in terms of specific interactions of cholesterol with constituent mitochondrial membrane lipids and their implications for deviations from normal neuronal function.

     

Novel monomeric luciferase enzymes as tools to study plant gene regulation in vivo

Taking advantage of a specially constructed vector, luciferase LuxA and LuxB subunits were connected in frame to different amino acid linkers to reproduce a series of monomeric luciferase enzymes. A comparison of their activities in E. coli cells demonstrated that the length of the linkers positively affected activity. One luciferase fusion gene was expressed in plant cells, and we showed that this gene activity could be monitored directly without destructive sampling.     

Multifunctionality of lipoamide dehydrogenase: activities of chemically trapped monomeric and dimeric enzymes

Lipoamide dehydrogenase from pig heart exists in monomer-dimer equilibrium. The effect of the state of subunit aggregation on the multifunctionality of lipoamide dehydrogenase was investigated by the use of chemically trapped monomeric and dimeric enzymes. Reductive carboxymethylation with 2-mercaptoethanol-iodoacetate yields the stable monomeric enzyme which has been isolated for structural and kinetic studies. The chemically induced monomerization is accompanied by conformational changes resulting in an increased mobility of flavin-adenine dinucleotide. The chemically trapped monomer shows an enhanced diaphorase activity, a reduced electron transferase activity, and a complete loss in dehydrogenase as well as transhydrogenase activities. The enhanced diaphorase activity is associated with increased catalytic efficiencies and the reversal of an inhibitory NADH effect at high concentrations. Treatment of lipoamide dehydrogenase with dimethyl suberimidate gives amidinated samples containing crosslinked dimer. The crosslinked enzyme exhibits a higher dehydrogenase catalytic efficiency than the noncrosslinked enzyme with different kinetic mechanisms without significantly affecting the kinetic parameters of diaphorase reaction. Although the dimeric structure is intimately associated with the dehydrogenase activity, it does not preclude the diaphorase activity. An altered flavin-adenine dinucleotide environment accompanying monomerization is likely responsible for the enhanced diaphorase activity.     

Co-operativity in seminal ribonuclease function: binding studies.

Binding of nucleotides to bovine seminal RNAase was studied by differential spectrophotometry and equilibrium dialysis. Cytidine 3'-phosphate, the reaction product of the hydrolytic, rate-limiting step of the reaction, was found to be capable, in contrast to related nucleotides, of discriminating between the two structurally identical active sites of the enzyme. Negative co-operativity, with a 'half-of-sites' reactivity, was found at lower concentrations of ligand, whereas at higher concentrations positive co-operativity was detected. These findings exclude that the non-hyperbolic kinetics previously reported for the hydrolytic step of the reaction are due to hysteretic effect. A model of mixed-type co-operativity is proposed for interpreting the binding data.     

Co-operativity and enzymatic activity in polymer-activated enzymes. A one-dimensional piggy-back binding model and its application to the DNA-dependent ATPase of DNA gyrase

The binding of a ligand to a one-dimensional lattice in the presence of a second ("rider") ligand, which binds only to the first ligand (piggy-back binding), is studied. A model derived from this study is used to analyze the effects of co-operativity on the reaction rates of enzymes activated by polymeric cofactors that provide multiple binding sites for the enzyme. It is found that in the presence of strong co-operativity, the steady-state reaction rates of polymer-activated enzymes can be very different from the Michaelis-Menten paradigm. By adjusting the co-operativity parameters and the binding constants of the ligands, the model can generate apparent auto-catalytic enhancement by substrates at low substrate concentrations and apparent substrate inhibition at high substrate concentrations. The model is shown to be able to explain the differences in the rates of ATP hydrolysis by DNA gyrase in the presence of long versus short DNA molecules and in the presence of long DNA molecules at different gyrase to DNA ratios.     

From monomeric to homodimeric endonucleases and back: engineering novel specificity of LAGLIDADG enzymes

Monomeric homing endonucleases of the LAGLIDADG family recognize DNA in a bipartite manner, reflecting the underlying structural assembly of two protein domains (A and B) related by pseudo 2-fold symmetry. This architecture allows for changes in DNA specificity via the distinct combination of these half-site domains. The key to engineering such hybrid proteins lies in the LAGLIDADG two-helix bundle that forms both the domain interface and the endonuclease active site. In this study, we utilize domain A of the monomeric I-DmoI to demonstrate the feasibility of generating functional homodimeric endonucleases that recognize palindromic DNA sequences derived from the original, non-palindromic target. Wild-type I-DmoI domain A is capable of forming a homodimer (H-DmoA) that binds tightly to, but does not cleave efficiently, its anticipated DNA target. Partial restoration of DNA cleavage ability was obtained by re-engineering the LAGLIDADG dimerization interface (H-DmoC). Upon fusing two copies of H-DmoC via a short peptide linker, a novel, site-specific DNA endonuclease was created (H-DmoC2). Like I-DmoI, H-DmoC2 is thermostable and cleaves the new target DNA to generate the predicted 4 nt 3'-OH overhangs but, unlike I-DmoI, H-DmoC2 retains stringent cleavage specificity when substituting Mn2+ for Mg2+ as co-factor. This novel endonuclease allows speculation regarding specificity of monomeric LAGLIDADG proteins, while it supports the evolutionary genesis of these proteins by a gene duplication event.     

Kinetic co-operativity of monomeric mnemonical enzymes. The significance of the kinetic Hill coefficient

The expression of the kinetic Hill coefficient for a two-substrate, two-product mnemonical enzyme has been derived. Its relation with the gamma coefficient, that is the slope of the reciprocal plots for 1/[A]----O, has been established. The variation of this Hill coefficient, as a function of the second substrate and product concentrations, has been studied theoretically. Whereas the gamma coefficient does not vary as a function of the substrate and first product concentrations, the kinetic Hill coefficient does. If the enzyme is positively co-operative, the Hill coefficient increases upon increasing the second substrate concentration and decreases if the first product concentration is increased. The converse is expected to occur if the enzyme displays a negative co-operativity. The last product may either reverse a positive co-operativity into a negative one or, alternatively, strengthen an already negative co-operativity. The co-operativity generated by the mnemonical model has been compared to the kinetic behaviour of a random model. These two models have been shown to be discriminated on the basis of the departure they show with respect to the Michaelis-Menten behaviour. These theoretical considerations have been applied to previously published data, obtained with wheat germ hexokinase LI. This monomeric enzyme has a negative co-operativity with respect to the preferred substrate, glucose. The Hill coefficient decreases with MgATP concentration, increases with MgADP concentration and decreases with glucose-6-phosphate concentration. This is exactly what is to be expected on the basis of the above theory of kinetic co-operativity.     

Computer Simulation of Assembly and Co-operativity of Hexameric AAA ATPases

AAA ATPases form a functionally diverse superfamily of proteins. Most members form homo-hexameric ring complexes, are catalytically active only in the fully assembled state, and show co-operativity among the six subunits. The mutual dependence among the subunits is clearly evidenced by the fact that incorporation of mutated, inactive subunits can decrease the activity of the remaining wild type subunits. For the first time, we develop here models to describe this form of allostery, evaluate them in a simulation study, and test them on experimental data. We show that it is important to consider the assembly reactions in the kinetic model, and to define a formal inhibition scheme. We simulate three inhibition scenarios explicitly, and demonstrate that they result in differing outcomes. Finally, we deduce fitting formulas, and test them on real and simulated data. A non-competitive inhibition formula fitted experimental and simulated data best. To our knowledge, our study is the first one that derives and tests formal allosteric schemes to explain the inhibitory effects of mutant subunits on oligomeric enzymes.     

Co-operativity in protein-protein association. The structure and stability of the actin filament

Co-operative association, in which a protein subunit is held simultaneously by two bonds, is enormously more favorable than association forming either bond alone. A theoretical framework for calculating the effect of co-operativity is developed here, which should have a broad application to protein-protein and protein-DNA associations. The theory is applied in detail to actin. Fragmentation of an actin filament is extremely unfavorable: the association constant for annealing-fragmentation is estimated here to be at least 10(13) M-1. In contrast to these very strong bonds within the filament, subunits are loosely attached at the end, with an association constant of 2 x 10(5) M-1. The eight orders of magnitude difference between annealing-fragmentation and end association can be attributed to the co-operative formation of one additional protein-protein bond in the annealing reaction. This observation, and a quantitative analysis of the co-operativity, lead to an important conclusion: the longitudinal bond, which connects subunits in the long-pitch helix, must be substantially stronger than the diagonal bond, which connect subunits between these helices. This conclusion contradicts some recent models based on Fourier construction, in which the longitudinal bond is weak or absent. Prominent longitudinal bonds also require a rigidity of the actin filament that must be reconciled with previous reports of torsional flexibility. A hinge within the actin subunit is suggested, separating it into two flexibly attached domains. In one possible model the two domains are oriented radially: the inner domains are connected by longitudinal and diagonal bonds to form a relatively rigid helical backbone, and the outer domains are attached to this backbone by flexible hinges, permitting them to move through angles of 10 degrees to 20 degrees or more. Flexibility of the outer, myosin-binding domain should be functionally important, permitting attachment of myosin cross-bridges over a range of angles.