Large-ligand adsorption to membranes III. Cooperativity and general ligand shapes

In previous reports (Stankowski, S. (1983) Biochim. Biophys. Acta 735, 341–351 and 352–360) the ordinary Scatchard-type analysis has been shown to yield erroneous results when applied to the binding of large molecules to membranes or cells. Formulae have been given to treat the limiting cases of very thin and of very bulky ligands. These results are now extended to include ligands of any shape and cooperative interactions. As an example, data on the cooperative binding of polymyxin to charged lipid bilayers are reevaluated. Adsorption with concomitant incorporation of the large molecule into the membrane is also considered.     

Cooperative ligand-lattice binding. Approximate Gaussian binding distribution

Nearest-neighbor cooperative binding of a ligand covering n sites and binding with equilibrium constant K and cooperativity factor omega to a large molecule with m binding sites (m much greater than n omega, n/omega) can be approximately described by a Gaussian distribution P(q-qmax), where q is the number of ligands bound and qmax the most probable value of q. The variance of the Gaussian is equal to the derivative dqmax/d ln(L), where L is the free ligand concentration. This variance, sigma 2, is a complicated function of qmax. However, in the limits of very large cooperativity, omega much greater than 1, very large anticooperativity, omega much less than 1, or noncooperativity, omega = 1, simpler expressions for sigma 2 can be given. For qmax = m/(n + 1), where the most probable number of bound ligands equals the number of free binding sites, sigma 2 has a particularly simple form: sigma 2 = 2m omega 1/2/(n + 1)3. The Gaussian and the infinite lattice approximations for the average number of ligands bound are good approximations only if sigma is much smaller than the number of binding sites. The variance may therefore provide an easy check on the validity of the infinite lattice approximation, which is commonly used to analyze experimental binding data.     

NMR structures of apo L. casei dihydrofolate reductase and its complexes with trimethoprim and NADPH: contributions to positive cooperative binding from ligand-induced refolding, conformational changes, and interligand hydrophobic interactions

In order to examine the origins of the large positive cooperativity (ΔG(0)(coop) = -2.9 kcal mol(-1)) of trimethoprim (TMP) binding to a bacterial dihydrofolate reductase (DHFR) in the presence of NADPH, we have determined and compared NMR solution structures of L. casei apo DHFR and its binary and ternary complexes with TMP and NADPH and made complementary thermodynamic measurements. The DHFR structures are generally very similar except for the A-B loop region and part of helix B (residues 15-31) which could not be directly detected for L. casei apo DHFR because of line broadening from exchange between folded and unfolded forms. Thermodynamic and NMR measurements suggested that a significant contribution to the cooperativity comes from refolding of apo DHFR on binding the first ligand (up to -0.95 kcals mol(-1) if 80% of A-B loop requires refolding). Comparisons of Cα-Cα distance differences and domain rotation angles between apo DHFR and its complexes indicated that generally similar conformational changes involving domain movements accompany formation of the binary complexes with either TMP or NADPH and that the binary structures are approaching that of the ternary complex as would be expected for positive cooperativity. These favorable ligand-induced structural changes upon binding the first ligand will also contribute significantly to the cooperative binding. A further substantial contribution to cooperative binding results from the proximity of the bound ligands in the ternary complex: this reduces the solvent accessible area of the ligand and provides a favorable entropic hydrophobic contribution (up to -1.4 kcal mol(-1)).     

Nucleoprotein melting. I. Theory of helix-coil transition of DNA in the presence of proteins with cooperative character of interaction under conditions of reversible binding]

Helix-coil transition of DNA with attached extended ligands able to interact with one another during adsorption on DNA (cooperative or uncooperative binding) has been considered. The general formulae describing dependence of polymer melting curve on concentration of attached ligands have been obtained. It has been shown that cooperativity of interaction with DNA stipulates for two phase profile of the melting curve. The results obtained show that proteins which interact with DNA cooperatively may cause two phase helix-coil transition under conditions of reversible binding.     

Cooperative effects during the binding of large ligands with DNA. Non-contact interaction between adsorbed ligands

Equations are derived to describe the cooperative binding of large ligands to DNA. A mathematical approach is developed which enables one to give a simple probabilistic interpretation of binding equations and to solve them in the general case when long-range interactions are allowed between bound ligands. These interactions can be mediated by conformation changes induced in the DNA in the course of binding process and transformed over some distances beyond the DNA region immediately covered by a bound ligand molecule (allosteric effect of DNA). Interactions between ligand molecules can be formally described in terms of model potential characterizing pairwise interactions between bound ligands. A procedure is developed which allows one to determined the form of such potential from experimentally measured binding isotherms. It is based on a comparison of experimental binding isotherms with the appropriate curves calculated for the case of non-interacting ligands.     

Kinetic mechanism of rat polymerase beta-dsDNA interactions. Fluorescence stopped-flow analysis of the cooperative ligand binding to a two-site one-dimensional lattice

Kinetics of cooperative binding of rat polymerase beta to a double-stranded DNA has been studied using the fluorescence stopped-flow techniques. The data have been analyzed by an approach developed to examine complete kinetics of cooperative large ligand binding to a one-dimensional lattice. The method is based on using the smallest possible system that preserves key ingredients of cooperative binding; i.e., at saturation, the lattice can accept only two ligand molecules. It allows the identification of collective amplitudes as well as amplitudes describing particular normal modes of the reaction. The mechanism of the intrinsic binding of pol beta to the dsDNA is different from the analogous mechanism for the ssDNA. The difference originates from different enzyme orientations in the corresponding complexes. Intrinsic binding to the dsDNA includes only two sequential steps: a very fast bimolecular association followed by an energetically favorable conformational transition of the complex. The transition following the bimolecular step does not facilitate the engagement of the enzyme in cooperative interactions. Its role seems to be reinforcing the affinity of the bimolecular step. Salt and magnesium cations affect both the bimolecular step and the conformational transition. As a result, the bimolecular step is less sensitive to the increased salt concentration, allowing the enzyme to preserve its initial dsDNA affinity. The changing character of cooperative interactions between bound enzyme molecules as a function of NaCl concentration and MgCl(2) concentration does not affect the binding mechanism. The engagement in cooperative interactions is approximately 3-4 orders of magnitude slower than the conformational transition of the DNA-bound polymerase. The importance of the obtained results for the pol beta activities is discussed.     

Cooperation effects in binding of large ligands to DNA. II. Contact interactions between adsorbed ligands

Cooperative effects arising upon binding of biologically active ligands to DNA are considered. Equations are derived which enable one to describe the binding of two different ligands to DNA. We also consider the case when ligand can form two type of DNA complexes. The cooperative binding of the ligand in the vicinity of saturation level of binding can be described with a good accuracy by equation derived for the non-cooperative adsorption of the same ligand with some effective binding constant Keff. It is shown that cooperative effects arising upon binding of proteins and other ligands to DNA can be divided into two groups depending on the symmetry of interactions between the bound ligand molecules. In particular, if such interactions favor the formation of dimeric ligand species on the DNA, Keff approximately a1/2, where a is the ligand-ligand interaction constant. If cooperative interactions favor the formation of aggregates of unrestricted size, then Keff approximately aL+Y, where L is the size of the binding site for the ligand on DNA.     

Ligand binding to proteins: the binding landscape model.

Models of ligand binding are often based on four assumptions: (1) steric fit: that binding is determined mainly by shape complementarity; (2) native binding: that ligands mainly bind to native states; (3) locality: that ligands perturb protein structures mainly at the binding site; and (4) continuity: that small changes in ligand or protein structure lead to small changes in binding affinity. Using a generalization of the 2D HP lattice model, we study ligand binding and explore these assumptions. We first validate the model by showing that it reproduces typical binding behaviors. We observe ligand-induced denaturation, ANS and heme-like binding, and "lock-and-key" and "induced-fit" specific binding behaviors characterized by Michaelis-Menten or more cooperative types of binding isotherms. We then explore cases where the model predicts violations of the standard assumptions. For example, very different binding modes can result from two ligands of identical shape. Ligands can sometimes bind highly denatured states more tightly than native states and yet have Michaelis-Menten isotherms. Even low-population binding to denatured states can cause changes in global stability, hydrogen-exchange rates, and thermal B-factors, contrary to expectations, but in agreement with experiments. We conclude that ligand binding, similar to protein folding, may be better described in terms of energy landscapes than in terms of simpler mass-action models.     

Cooperativity of binding of anilinonaphthalenesulfonate to serum albumin induced by a second ligand.

When a ligand X is multiply bound to energetically identical, noninteracting sites of a protein, cooperative binding of this ligand can be induced by the presence of a second ligand Y. This effect should appear whenever multiple interactions exist between the bound X and Y ligands, and vanish when the concentration of Y is made sufficiently large to ensure Y saturation at all concentrations of X. These predictions have been verified for the binding of 8-anilino-1-naphthalenesulfonate to serum albumin, when Y, the effector ion, is 3,5-dihydroxybenzoate. In the presence of 2mM dihydroxybenzoate, the Hill coefficient for anilinonaphthalenesulfonate binding rose steadily from 1 to 1.5 as the number of molecules of ligand bound increased from 1 to 3.3 per albumin molecule. The theory of interactions between isolated ligands, applied in the previous paper (D. A. Kolb and G. Weber (1975), Biochemistry, preceding paper in this issue), is extended to cases of multiple interactions, and applied here to show that the experimental results are tolerably well reproduced for a model in which four anilinonaphthalensulfonate molecules are homogeneously coupled to four molecules of dihydroxybenzoate by free energies of 3.0 and 3.5 thermal units.     

Thermodynamic model of cooperativity in a dimeric protein: unique and independent parameters formulation.

A model of the cooperative interaction of ligand binding to a dimeric protein is presented based upon the unique and independent parameters (UIP) thermodynamic formulation (Gutheil and McKenna, Biophys. Chem. 45 (1992) 171-179). The analysis is developed from an initial model which includes coupled conformational and ligand binding equilibria. This completely general model is then restricted to focus on conformationally mediated cooperative interactions between the ligands and the expressions for the apparent ligand binding constant and the apparent ligand-ligand interaction constant are derived. The conditions under which there is no cooperative interaction between the ligands are found as roots to a polynomial equation. Consideration of the distribution of species among the various conformational states in this general model leads to a set of inequalities which can be represented as a two dimensional plot of boundaries. By superimposing a contour plot of the value of the apparent ligand-ligand interaction constant over the plot of boundaries a complete graphical representation of this system is achieved similar to a phase diagram. It is found that the parameter space homologous to Koshland-Nemethy-Filmer type of model is most consistent with both positive and negative cooperativity in this model. The maximal amount of positive and negative cooperativity are found to be simple functions of Kc, the equilibrium constant associated with the change of a subunit and ligand from the unligated to ligated conformation. It is shown that under certain limiting conditions the apparent allosteric interaction between ligands is equal to the conformational interaction between subunits. The methods presented are generally applicable to the theoretical analysis of thermodynamic interactions in complex systems.     

Protein-ligand interactions: interaction of nitrosamines with nicotinic acetylcholine receptor

Fluorimetry and spectrophotometry have been used to study the binding of dimethyl, dipropyl, dibutyl and diphenylnitrosamine to nicotinic acetylcholine receptor isolated, and purified, from Torpedo fuscomaculata. Scatchard analysis indicates that all four ligands are true agonists of the receptor exhibiting positive cooperative binding with the existence of more than one class of binding site. The number of binding sites for the nitrosamines approximates 2. Diphenylnitrosamine binds to the receptor more tightly at low concentrations (Kd1 = 1.3 microM) than the aliphatic nitrosamine (Kd1 = 8-12 microM). Yet at high concentrations all nitrosamines behaved with similar Kd values (27-38 microM).     

A model for cooperative ligand binding at complementary sites of DNA

The process of cooperative binding of ligands to DNA has been classified into different modes. An additional mode of cooperative interaction amongst ligands binding at sites on complementary strands has been emphasised. A statistical mechanical method has been applied to obtain an analytical expression for the fraction of nucleotide sites bound. Theoretical Scatchard plots have been drawn and analysed.     

Competitive cooperative bindings of a small ligand to a linear homopolymer. I. Extension of the ising model to the case of two competitive interactions.

The theoretical study of the cooperative binding of a small ligand to a linear homopolymer is extended to systems in which two different complexes can form. The binding isotherms are derived under the assumption that the cooperative interactions exist only between molecules belonging to the same type of binding mode and are limited to nearest neighbors (Ising model). The binding to a single-stranded chain is first considered and two extreme cases are studied: (1) the two complexes can form independently from each other (model of independent classes of binding sites); (2) only one class of binding site exists, each possessing two different states of complexation (three-state model). Binding to a double-helical chain is also considered. Three simple types of competition between the different modes of binding are distinguished. The corresponding models are defined as: (1) the model of independent classes of binding sites; (2) the model of monoexclusive interactions between the different kinds of complexes (the symmetric and asymmetric cases are both considered); (3) the model of biexclusive interactions. The comparative study of the different cases shows that the binding isotherms are very similar at large polymer-to-ligand concentration ratios, while they can be very different at low polymer-to-ligand ratios. This can be used to obtain information on the mechanism of dye binding to nucleic acids by equilibrium studies as shown in a subsequent paper.     

Molecular recognition of poly(A) by small ligands: an alternative method of analysis reveals nanomolar, cooperative and shape-selective binding

A few drug-like molecules have recently been found to bind poly(A) and induce a stable secondary structure (T_m ≈ 60°C), even though this RNA homopolymer is single-stranded in the absence of a ligand. Here, we report results from experiments specifically designed to explore the association of small molecules with poly(A). We demonstrate that coralyne, the first small molecule discovered to bind poly(dA), binds with unexpectedly high affinity (K_a >10⁷ M⁻¹), and that the crescent shape of coralyne appears necessary for poly(A) binding. We also show that the binding of similar ligands to poly(A) can be highly cooperative. For one particular ligand, at least six ligand molecules are required to stabilize the poly(A) self-structure at room temperature. This highly cooperative binding produces very sharp transitions between unstructured and structured poly(A) as a function of ligand concentration. Given the fact that junctions between Watson–Crick and A·A duplexes are tolerated, we propose that poly(A) sequence elements and appropriate ligands could be used to reversibly drive transitions in DNA and RNA-based molecular structures by simply diluting/concentrating a sample about the poly(A)-ligand ‘critical concentration’. The ligands described here may also find biological or medicinal applications, owing to the 3′-polyadenylation of mRNA in living cells.     

Catalytic and regulatory site composition of yeast AMP deaminase by comparative binding and rate studies. Resolution of the cooperative mechanism

Yeast AMP deaminase is allosterically activated by ATP and MgATP and inhibited by GTP and PO4. The tetrameric enzyme binds 2 mol each of ATP, GTP, and PO4/subunit with Kd values of 8.4 +/- 4.0, 4.1 +/- 0.6, and 169 +/- 12 microM, respectively. At 0.7 M KCl, ATP binds to the enzyme, but no longer activates. Titration with coformycin 5'-monophosphate, a slow, tight-binding inhibitor, indicates a single catalytic site/subunit. ATP and GTP bind at regulatory sites distinct from the catalytic site and their binding is mutually exclusive. Inorganic phosphate competes poorly with ATP for the ATP sites (Kd = 20.1 +/- 4.1 mM). However, near-saturating ATP reduces the moles of phosphate bound per subunit to 1 PO4, which binds with a Kd = 275 +/- 22 microM. In the presence of ATP, PO4 cannot effectively compete with ATP for the nucleotide triphosphate sites. The PO4 which binds in the presence of ATP is competitive with AMP at the catalytic site since the Kd equals the kinetic inhibition constant for PO4. Initial reaction rate curves are a cooperative function of AMP concentration and activation by ATP is also cooperative. However, no cooperativity is observed in the binding of any of the regulator ligands and ATP binding and kinetic activation by ATP is independent of substrate analog concentration. Cooperativity in initial rate curves results, therefore, from altered rate constants for product formation from each (enzyme.substrate)n species and not from cooperative substrate binding. The traditional cooperative binding models of allosteric regulation do not apply to yeast AMP deaminase, which regulates catalytic activity by kinetic control of product formation. The data are used to estimate the rates of AMP hydrolysis under reported metabolite concentrations in yeast.     

Internal recognition through PDZ domain plasticity in the Par-6-Pals1 complex

PDZ protein interaction domains are typically selective for C-terminal ligands, but non-C-terminal, 'internal' ligands have also been identified. The PDZ domain from the cell polarity protein Par-6 binds C-terminal ligands and an internal sequence from the protein Pals1/Stardust. The structure of the Pals1-Par-6 PDZ complex reveals that the PDZ ligand-binding site is deformed to allow for internal binding. Whereas binding of the Rho GTPase Cdc42 to a CRIB domain adjacent to the Par-6 PDZ regulates binding of C-terminal ligands, the conformational change that occurs upon binding of Pals1 renders its binding independent of Cdc42. These results suggest a mechanism by which the requirement for a C terminus can be readily bypassed by PDZ ligands and reveal a complex set of cooperative and competitive interactions in Par-6 that are likely to be important for cell polarity regulation.     

Spectroscopic and equilibrium studies of ligand and organic substrate binding to indolamine 2,3-dioxygenase

The binding of a number of ligands to the heme protein indolamine 2,3-dioxygenase has been examined with UV-visible absorption and with natural and magnetic circular dichroism spectroscopy. Relatively large ligands (e.g., norharman) which do not readily form complexes with myoglobin and horseradish peroxidase (HRP) can bind to the dioxygenase. Except for only a few cases (e.g., 4-phenylimidazole) for the ferric dioxygenase, a direct competition for the enzyme rarely occurs between the substrate L-tryptophan (Trp) and the ligands examined. L-Trp and small heme ligands (CN-,N3-,F-) markedly enhance the affinity of each other for the ferric enzyme in a reciprocal manner, exhibiting positive cooperativity. For the ferrous enzyme, L-Trp exerts negative cooperativity with some ligands such as imidazoles, alkyl isocyanides, and CO binding to the enzyme. This likely reflects the proximity of the Trp binding site to the heme iron. Other indolamine substrates also exert similar but smaller cooperative effects on the binding of azide or ethyl isocyanide. The pH dependence of the ligand affinity of the dioxygenase is similar to that of myoglobin rather than that of HRP. These results suggest that indolamine 2,3-dioxygenase has the active-site heme pocket whose environmental structure is similar to, but whose size is considerably larger than, that of myoglobin, a typical O2-binding heme protein. Although the L-Trp affinity of the ferric cyanide and ferrous CO enzyme varies only slightly between pH 5.5 and 9.5, the unligated ferric and ferrous enzymes have considerably higher affinity for L-Trp at alkaline pH than at acidic pH. L-Trp binding to the ferrous dioxygenase is affected by an ionizable residue with a pKa value of 7.3.     

Equilibrium binding of derivatives of the carcinogen, benzo(a)pyrene, to DNA. Thermodynamic analysis

The physical binding of polycyclic aromatic hydrocarbon derivatives which are ultimate carcinogens to DNA may play a role in the formation of covalent DNA adducts by these compounds or in the detoxification of the compounds via DNA-catalyzed hydrolysis. Previous studies of DNA-binding interactions of derivatives of benzo(a)pyrene (BP) have been confined to low r values (r - ligands bound/base pair). We have now applied the Scatchard formalism (as modified to include neighbor exclusion) to the spectrophotometric determination of the binding of two derivatives of BP, trans - 9,10 - dihydroxydihydro - BP and 7r,8t - dihydroxy-9t,10t-oxy-7,8, 9,10-tetrahydro-BP, to double-stranded DNA at reasonably high r values. Exclusion parameters, binding constants, and thermodynamic parameters are all within the ranges found for other intercalants. Although these ligands are uncharged, the binding exhibits significant ionic strength dependence which can be rationalized (partially) by polyelectrolyte theory. Using the measured ionic strength dependence, a thermodynamic association constant, independent of ionic interactions, can be calculated which is very close to the calculated thermodynamic association constants for ethidium and proflavine.     

Ligand binding modulates the mechanical stability of dihydrofolate reductase

We use single-molecule force spectroscopy to demonstrate that the mechanical stability of the enzyme dihydrofolate reductase (DHFR) is modulated by ligand binding. In the absence of bound ligands, DHFR extends at very low forces, averaging 27 pN, without any characteristic mechanical fingerprint. By contrast, in the presence of micromolar concentrations of the ligands methotrexate, nicotinamide adenine dihydrogen phosphate, or dihydrofolate, much higher forces are required (82 +/- 18 pN, 98 +/- 15 pN, and 83 +/- 16 pN, respectively) and a characteristic fingerprint is observed in the force-extension curves. The increased mechanical stability triggered by these ligands is not additive. Our results explain the large reduction in the degradation rate of DHFR, in the presence of its ligands. Our observations support the view that the rate-limiting step in protein degradation by adenosine triphosphate-dependent proteases is the mechanical unfolding of the target protein.