The Shapes Of Scatchard Plots For Systems With Two Sets Of Binding Sites PDF

172 0307-4412(95)00122-0 The Shapes of Scatchard Plots for Systems with Two Sets of Binding Sites A K BORDBARt, A A SABOURYt and A A MOOSAVI-MOVAHEDI* *Institute of Biochemistry and Biophysics University of Tehran, Tehran and tDepartment of Chemistry University of Tarbiat-Modares Tehran, Iran Intr...

172 0307-4412(95)00122-0 The Shapes of Scatchard Plots for Systems with Two Sets of Binding Sites A K BORDBARt, A A SABOURYt and A A MOOSAVI-MOVAHEDI* *Institute of Biochemistry and Biophysics University of Tehran, Tehran and tDepartment of Chemistry University of Tarbiat-Modares Tehran, Iran Introduction One of the most familiar and important processes in biochemistry is the reversible combination of small ions or molecules with specific sites on the surface of a protein or other biopolymer. The interaction of ligand with macromolecule of biological systems is one of the most extensively studied phenomena in biochemical research. Such studies are an essential part of the physico-chemical characterization of many biological phenomena ranging from enzyme catalysis and its control, hormone action, membrane transport, and nerve conduction to muscle contraction and other forms of mobility) -3 Protein-surfactant interactions have been extensively studied as the ligand-protein binding affinities. It is important for understanding the stabilization of membrane and food emulsions and foams that the interactions between the protein and surfactant which lead to the formation of such complexes are characterized? -5 Moreover, denaturation of protein with surfactant by determining the strength and number of binding sites and the magnitude of the interaction between multiple sites provide the essential data for the evaluation of the structure of the protein and its relationship with the function of protein. 6-~° Experimentally the measurement of binding is straightforward. However, interpretation of the data requires different models of analysis that depend on various features of the binding process. A number of methods for graphical and computer-assisted analysis of the binding data have been employed. The purpose of this paper is to consider the most common presentation of ligand-acceptor binding data in the biological sciences; the Scatchard Plot." Although, there are many reports on Scatchard plots for systems with one set of binding sites, there are relatively few reports on the shapes of Scatchard plots for systems with two sets of binding sites. ~2-~3 The similarities that can exist between the shapes of Scatchard plots in systems with one set and two sets of binding sites, have caused some misinterpretations of the binding process. 14-~6 This lead us to evaluate the shapes of Scatchard plots for hypothetical systems with two sets of binding sites and different kinds of co-operativity on each set. The Scatehard plot In 1949 the distinguished physical chemist, George Scatchard, published a paper entitled, 'The Attraction of Proteins for Small Molecules and Ions'." He described a graphical method for extracting the parameters of a binding system. This graphical method, ever since called the Scatchard plot, is the most common method used for the presentation of ligand binding data. For a large acceptor molecule which has g binding sites, and in which binding sites are characterized by identical intrinsic association binding constant, K, and independent each other without interacting (that is, occupancy of one site does not affect the probability of binding to any other), from mass action equations, Scatchard showed that: BIOCHEMICAL EDUCATION 24(3) 1996 = g K[L]/(1 + KILl) (1) or o/[L] = K ( g - 0 (2) where f~ is the number of moles of ligand bound per mole of macromolecule, and [L] is the free concentration of ligand. It is obvious that the Scatchard plot, e/[L] versus ~, is linear for systems which have one identical and independent set of sites. Scatchard pointed out in his original paper" that 'curvature may indicate different intrinsic constants or deviations from independent probabilities'. It is now widely recognized that upward-curved Scatchard plots are obtained when there is negative co-operativity in binding (binding sites are identical, but interacting between them lead to binding at one site decreases the affinity of others) and downward-curvedScatchard plots are obtained when there is positive co-operativity in binding (if the affinity of other sites is increased)2 7 For these systems, we use the Hill equation: TM g(K[L]) n = 1 + (K[L]) n (3) where n is called the Hill coefficient, n = 1 for noncooperative systems, n > 1 for co-operative systems (positive co-operativity in binding), and n < 1 for anticooperative systems (negative co-operativity in binding). For two different kinds of binding sets on the same macromolecule using: ~2 = g~ (K,[L]) °' g2(K2[L]) °2 + 1 + (K,[L]) "l 1 + (Kz[L]) "2 (4) The Scatchard plots for these systems may be obtained with one maximum or minimum, or it may even be downward-curved or upward-curved, which may lead to a misunderstanding with one set of binding sites. Discussion For the construction of a Scatchard plot, a hypothetical system with two sets of binding sites have been considered. The number of binding sites and intrinsic binding constant have been taken as 50 and 1000 for first binding set, and 80 and 100 for second binding set, respectively. Different kinds of the system, in relation to the kind of co-operativity in each set have been selected by taking the suitable amount of Hill coefficient for each set. The shape of Scatchard plots for these systems is discussed below: (a) Specific-Negative(SN) and Negative-Negative(NN) Figure la shows the Scatchard plots for systems with specific and negative co-operativity in first and second of binding set, respectively, and Figure lb is the Scatchard plots for systems with negative co-operativity in both its binding sets. The general shape of these plots is like systems with one set of binding sites with negative co-operativity. Moreover, the slope of the first region is reduced with increasing the Hill coefficient, or in other words, with decreasing the extent of negative co-operativity. However, the general similarities between the Scatchard plot of these systems and system with negative co-operativity may be misunderstood in interpretation of binding system. (b) Positive-Negative(PN) Figure 2 shows the Scatchard plot, for systems with two binding sets according to positive and negative co-operativity in the first and second binding set, respectively. These plots show a markedly non-linear curve characterized by a pronounced maximum like system with one set of binding sites containing positive co-operativity between 173 sites. The position of the maximum in the horizontal axis depends to the degree of the co-operativity in the first binding set. By increasing the positive co-operativity in the first binding set the position of this maximum shifts along the abscissa to high values of ~ (high degrees of saturation). However, the amount of bound/free depends on the extent of negative co-operativity in the second binding set, so that by increasing the negative co-operativity (decreasing n) in the second binding set, the amount of the maximum of bound/free shifts to the higher values. There is also a distinct minimum at the lower values of t~for the systems. However, the position of this minimum shifts to lower values of with increasing Hill coefficient in the second binding set and disappeared in the positive-specific system. The value of bound/ free at the minimum point increased by decreasing the positive co-operativity in the first binding set. It is important to note that misunderstanding may arise due to failing to observe lower values of t~ which appear as a distinct minimum in the experiment. This may cause misleading analysis and be interpreted as a system with one set of binding sites having positive co-operativity. (c) Negative-Positive (NP) The Scatchard plot of this system is shown in Figure 3. This plot is concave and has a 'tail' near to saturation. This plot has more concavity than NN, NS and system with one set of binding sites with negative co-operativity. However, the extent of the concavity and the appearance of the tail depends to the difference between the affinity of binding in each set and the amount of positive co-operativity in the second binding set. The general shape of specific-positive system which showing in Figure 3 is like the NP system except that the expo- 6 15 5 a 4 ' 'IZ s 10 2 10 x 1 O 0 0 100 50 150 q 50 100 150 Figure 2 Scatchard plots for systems with positive and negative co-operativity in the first and second binding sets, respectively, where g1=50, ge=80, K~=IOOM -1, Ke=IOOOM -1, (rq) n,=3, n2=0.5, (©) n1=5, n2=0.5, (n) n1=3, n2=0.7, (~7) n1=3, n2=l 70 501 7 60 6 5 40 IO ' 'IZ x "~o 4 ¢-. 3o x ' '12 s 2O 2 10 1 50 100 150 q o ?- Figure I Scatchard plotsfor systems with two setsof binding sites where g1=50, g2=80, K1=IOO M -~, K2=IOOO M -~. (a) Specific-Negative: (D) n1=1, n2=0.5, (A) n1=1, n2=0.8, (~7) nl=n2=1. (b) Negative-Negative: ([2) nl=n2=0.5, (/x) nl =0.5, n2=0.8, (~7) n, =0.5, N2=1 BIOCHEMICAL EDUCATION 24(3) 1996 Figure 3 Scatchard plots for systems with two sets of binding sites where gl=50, g2=80, K1=IOO M -1, K2=IOOOM 1, ([]) Specific-Positive (ni = 1, n2 = 5), (A) Negative-Positive (n1=0.8, n2=5) 174 4 20 15 ,4£ 2 fO x 1 0I 150 Figure 4 Scatchard plots for systems with positive co-operativity in both binding sets. Where g~ =50, g2 =80, K,=IOOM -~, K2=IOOOM-~, ([3) n,=n2=5, (A) n,=5, n2=3 nentiality and slope of the first region is reduced with respect to the NP system. (d) Positive-Positive (PP) Figure 4 shows the Scatchard plot for this system. It has a distinct maximum like a system with one binding set and positive co-operativity between sites. However, it has a tail at the end region that has an indistinct maximum. The difference between the Scatchard plot of this system and the positive-negative system, which was discussed in the preceding paragraph is at the end region, which is smooth and exponential for positive-negative system and concave for positive-positive system. Examples of misinterpretation For binding of ionic surfactants to water soluble proteins, there are two kinds of interaction, electrostatic and hydrophobic, and the binding data should therefore be interpreted in the terms of two sets of binding sites. Scatchard plots have sometimes been interpreted in papers in terms of one set of binding sites. Figure 5a is a typical example of one of these misinterpretations and shows the Scatchard plots for binding of sodium n-dodecyl sulphate (SDS) to bovine catalase at pH 3.2 and 4.3.19 Due to the similarities between Figure 5 and the negative co-operative curve containing the system with one set of binding sites, the authors misunderstood this system with negative co-operativity in the binding and took the extrapolated value of ~ obtained by extrapolation of the first part of the Scatchard plot as the number of cationic binding sites. However, the general shape of this plot is like that in Figures la, lb and 3, in which the extrapolated value of none of them is equal to 50 (the number of binding sites in the first binding set), so this extrapolation method for determining the number of binding sites in the first binding set is not correct. Figure 6 is another example of misinterpretation of the Scatchard plot and shows the plot for the interaction of SDS with bovine catalase at pH 6.430 The authors have interpreted this as a system with one set of binding sites and positive co-operativity. The general shape of this plot is like that shown in the first part of Figures 2 and 4. However, due to the absence of end points in the experiment, the end part of the curve could not be plotted and the system was wrongly taken as a system with one set of binding sites. BIOCHEMICAL EDUCATION 24(3) 1996 10 0 100 300 500 700 Figure 5 Scatchard plots for sodium n-dodecylsulphate (SDS) binding to bovine catalase at 25°C: o, pH 3.2; e, pH 4.3 (Redrawn from reference 19) x Figure 6 Scatchard plot for sodium n-dodecylsulphate (SDS) binding to bovine catalase pH 6.4, 25°C (Redrawn from ref 20) Conclusion The general shape of the Scatchard plot for some of the systems discussed are very similar to each other and the analysis of the binding data in terms of Scatchard plots may be misunderstood. However, knowledge of the form of Scatchard plots as discussed in this paper can provide a better understanding of binding systems, and these shapes may be taken as reference shapes for predicting the kind of co-operativity in each binding set. Problem The binding data for the interaction of SDS with bovine hemoglobin at pH 6.4 and 25°C were obtained by the technique of 175 Table 1 Problem: binding data for the interaction o f SDS with hemoglobin [L], x 105 M [L]j x 105 M 4.453 9.118 11.913 16.559 18.751 25.978 29.002 48.725 58.927 70.591 0.145 0.196 0.22 0.251 0.289 0.439 1.309 4.416 6.310 8.128 Solution The average number of bound ligand per each protein molecule, 0, is equal to o = ( [ L ] t - [Llf)/[P] (5) 0 from eqn (5) is divided by [L]f, to obtain values of 0/[L]f at any 0, and hence it is possible to plot the Scatchard curve. Figure 7 shows the Scatchard plot for this system, it is like the Scatchard plot for system with positive co-operativity in both binding sets (Fig 4). The binding parameter in eqn (4) has been obtained by fitting the binding data in this equation by using any non-linear fitting computer program. These parameters have been listed in Table 2 and the values of Hill coefficients shows the positive co-operativity in both binding sets. Acknowledgment Financial assistance from the Research Council of the University of Tehran is gratefully acknowledged. 25 References 15 x ' 'IZ Io o 2'oo Figure 7 Scatchard plots for sodium n-dodecylsulphate (SDS) on binding to bovine hemoglobin pH 6.4, 25°C Table 2 Values obtained (see Fig 6) from fitting of binding data to eqn 4for sodium n-dodecylsulphate (SDS) p H 6.4, 25°C gl kl nl g2 k2 n2 90 426211.6 3.32 650 417 1.47 equilibrium dialysis, are listed in Table 1, where [L], and [L]f are total and free concentrations of SDS. The total concentration of protein, [P] was 3.077 x 10 -6 M. Plot and interpret the Scatchard curve. 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