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QP |!HMea IFILE @ ISSELCODE ? @  .,Tv{ߛBA@>BA\\  Notes  \\Script for independent 2-site injection heat model (model 33) vo=1.401e-3; tc=0.001; dv=7e-6; lo=x_1/k1; up=x_1; fxf=x_2*((n1*k1*lo/(1+k1*lo))+(n2*k2*lo/(1+k2*lo)))+lo-x_1; for(;abs(fxf)>1e-6*x_1;) { xf=(lo+up)/2; fxf=x_2*((n1*k1*xf/(1+k1*xf))+(n2*k2*xf/(1+k2*xf)))+xf-x_1; fup=x_2*((n1*k1*up/(1+k1*up))+(n2*k2*up/(1+k2*up)))+up-x_1; if(fxf*fup>0) {up=xf;} else {lo=xf;}; }; s1=n1*k1*xf/(1+k1*xf); s2=n2*k2*xf/(1+k2*xf); q1=h1*s1; q2=h2*s2; q=1e6*vo*x_2*(q1+q2); lo=x_3/k1; up=x_3; fxf=x_4*((n1*k1*lo/(1+k1*lo))+(n2*k2*lo/(1+k2*lo)))+lo-x_3; for(;abs(fxf)>1e-6*x_3;) { xf=(lo+up)/2; fxf=x_4*((n1*k1*xf/(1+k1*xf))+(n2*k2*xf/(1+k2*xf)))+xf-x_3; fup=x_4*((n1*k1*up/(1+k1*up))+(n2*k2*up/(1+k2*up)))+up-x_3; if(fxf*fup>0) {up=xf;} else {lo=xf;}; }; s1=n1*k1*xf/(1+k1*xf); s2=n2*k2*xf/(1+k2*xf); q1=h1*s1; q2=h2*s2; qp=1e6*vo*x_4*(q1+q2); y=q-qp+(dv/vo)*(q+qp)/2; @ *9?Tv{ߛBA%iBAss  Notes1  \\Script for independent 2-site cumulative heat model vo=1.401e-3; tc=0.001; dv=7e-6; lo=x_1/k1; up=lo; fxf=x_2*((n1*k1*up/(1+k1*up))+(n2*k2*up/(1+k2*up)))+up-x_1; for(;fxf<0;) {up=up+0.01*x_1-lo); fxf=x_2*((n1*k1*up/(1+k1*up))+(n2*k2*up/(1+k2*up)))+up-x_1;}; }; fxf=x_2*((n1*k1*lo/(1+k1*lo))+(n2*k2*lo/(1+k2*lo)))+lo-x_1; for(;abs(fxf)>1e-6*x_1;) { xf=(lo+up)/2; fxf=x_2*((n1*k1*xf/(1+k1*xf))+(n2*k2*xf/(1+k2*xf)))+xf-x_1; fup=x_2*((n1*k1*up/(1+k1*up))+(n2*k2*up/(1+k2*up)))+up-x_1; if(fxf*fup>0) {up=xf;} else {lo=xf;}; }; s1=n1*k1*xf/(1+k1*xf); s2=n2*k2*xf/(1+k2*xf); q1=h1*s1; q2=h2*s2; v=vo+x_3*dv; y=1e6*v*x_2*(q1+q2); @ 6Tv{ߛBA@>BA8 8  Notes2 B Modeling cumulative heats for an independent 2-site system The total heat (Q) evolved at any point in the experiment is given by: Q = SUM[(deltaH(i)*alpha(i)] where SUM indicates the summation over all bound species, deltaH(i) is the reaction enthalpy (cal/mol) for species i, and alpha(i) is the fraction of species i in the ligand-bound state. In this case, there are two sites, so we there will be two terms in the summation. The first step is to develop expressions for alpha(i) in terms of the binding constants and free ligand concentration. Because the sites behave independently, we can view the system as consisting of two single-site systems. The difficult part is to estimate the free ligand concentration. Although it is possible to find an exact solution for this case, we will use a bisection strategy. The general procedure includes these steps: Define a function (fxf) that will equal zero for the correct value of free ligand, xf. fxf will be equal to the calculated bound ligand concentration plus the estimated free ligand concentration minus the known total ligand concentration. Find values of xf for which the function assumes positive and negative values. We call these values up and lo, respectively. Clearly, the root of the equation (ie, the value of fx for which fxf is zero) must lie somewhere between lo and up. So, we set xf equal to the average of lo and up and recalculate fxf. If fxf is positive (i.e, the product of fxf and fup is positive), then this new value of xf becomes the new upper limit (up). If fxf is negative (i.e., fxf*fup is negative), then the new xf becomes the new lower limit (lo). Once again, we take the average of up and lo as the new value of xf (i.e., we "bisect" up and lo)and recalculate fxf. We repeat this procedure until the value of fxf is sufficiently close to zero, say 1e6 times smaller than our total ligand concentration. Use the script that we developed for the Mg vs EDTA titration as a template. Once we have an estimate of xf, we can calculate the alpha(i) values and calculate Q. Because our observed heats have units of energy and our enthalpy is expressed in calories/mol, we need to include the sample volume and total macromolecule concentration on the right-hand side of the equation for Q (to cancel out the "per mol"). We also have to multiply by 1e6 to convert from calories to microcalories. If your function doesn't generate values, be sure you have - specified "y-script" in the fitting function window. - ended each statement in the script with a semicolon. - included all necessary parentheses. @ ResultsLog  [3/24/2006 08:38 "/Graph3" (2453818)] Data: Data2_F Model: twositeinjectheat Weighting: y No weighting Chi^2/DoF R^2 ---------------------------------------- 1.41946 0.98826 ---------------------------------------- Parameter Value Error ---------------------------------------- n1 1 0 k1 13133878.511 4788733.56996 h1 -2790.2687 85.61208 n2 1 0 k2 324971.76968 114875.45924 h2 1468.4318 101.78637 ---------------------------------------- [3/24/2006 08:46 "/Graph3" (2453818)] Data: Data2_E Model: twositetotalheat Weighting: y No weighting Chi^2/DoF R^2 ---------------------------------------- 44.73276 0.98484 ---------------------------------------- Parameter Value Error ---------------------------------------- n1 1 0 k1 54306356.57185 46364149.61642 h1 -2818.94685 112.95076 n2 1 0 k2 1147483.73892 968070.5237 h2 1464.38707 120.19107 ---------------------------------------- [3/24/2006 09:42 "/Graph3" (2453818)] Data: Data2_E Model: twositetotalheat Weighting: y No weighting Chi^2/DoF R^2 ---------------------------------------- 40.10018 0.98641 ---------------------------------------- Parameter Value Error ---------------------------------------- n1 1 0 k1 13489750.18992 7980659.10237 h1 -2727.14289 64.77564 n2 1 0 k2 54021.76182 24725.82419 h2 1853.85211 171.02879 ----------------------------------------   6 v{ߛBA6iBA  two-site_project_2_2006                %  (