0README enzyme-kinetics-nonlinear |-- 0-Old directory: old files |-- 0README obvious |-- Plots directory | |-- ldh.simpfit.out.sgi ldh.data, structured for ldhplot.all.s | |-- ldhplot.all.s R commands to generate "fancy" plots | |-- ldhplot.lac-6250.ps "fancy" plot | |-- ldhplot.pri.A-6246.ps "fancy" plot | |-- ldhplot.pri.B-6244.ps "fancy" plot | `-- ldhplot.sec-6248.ps "fancy" plot |-- ldh.data kinetic data for lactate dehyrodgenase |-- tutorial.txt long discussion ldh mechanism + fit [OLD! OLD!] `-- short.txt same but short with cut/paste R commands LACTATE DEHYDROGENASE RATE DATA AND MECHANISM The file "ldh.data" has 26 steady-state initial-rate data measured for the enzyme lactate dehydrogenase (LDH) with the cofactor NADH, the substrate pyruvate, and the product (as inhibitor) lactate. The model for the LDH reaction is a compulsory-order mechanism, with binary LDH-NADH and LDH-NAD complexes and ternary substrate complexes, LDH-NADH-pyruvate and LDH-NAD-lactate. There are also ternary abortive complexes, LDH-NADH-lactate and LDH-NAD-pyruvate, formed from reduced cofactor and reduced substrate and oxidized cofactor and oxidized substrate, respectively. These are not on the reaction path and when present inhibit the reaction. The LDH reaction is described by the mechanism: LDH + NADH <--> LDH-NADH LDH-NADH + pyruvate <--> LDH-NADH-pyruvate (LDH-NADH-pyruvate == LDH-NAD-lactate) LDH-NAD-lactate <--> LDH-NAD + lactate LDH-NAD <--> LDH + NAD LDH-NADH + lactate <--> LDH-NADH-lactate LDH-NAD + pyruvate <--> LDH-NAD-pyruvate which gives the rate equation: v0 = Vmax / (1 + C1 * p + KmA/a + KmB/b * (1 + C1 * p) * (1 + C2 * p) + KmAB/(a * b) * (1 + C1 * p) + C3 * b) eq. 1 where: v0 is the initial rate of reaction. a, b, and p are the concentrations of NADH, pyruvate, and lactate, respectively. Vmax, KmA, KmB, and KmAB have the usual meaning as kinetic constants for a two-substrate reaction. C1 = KmQ/KmPQ is the kinetic constant that describes inhibition by the first product. C2 = 1/KiP is the equilibrium constant that describes formation of the first abortive complex, LDH-NADH-lactate. C3 is the kinetic constant that describes formation of the LDH-NAD-pyruvate abortive complex. C3 can be shown to be unimportant for these data, and so can be fixed at a very small value or eliminated from the rate The model is nonlinear, with, neglecting C3, six variable parameters. The data overspecify the parameters by a factor of 4, perhaps less than what would be optimal. NONLINEAR FIT -- GRADIENT METHOD NOTE! The file "short.txt" should be read and the code in it used for fitting and testing of the fit. The R commands and surrounding text are extracted from the file "tutorial.txt". NOTE! The file "tutorial.txt" has not been adapted to run under R (although this would not be hard to do}. The commands in "tutorial.txt" remain somewhat S-specific and SGI-specific. Nevertheless, "tutorial.txt", as its name implies, is a decent tutorial in fitting enzyme-kinetic data. The R-language function "nls" fits a nonlinear model. Commands given in the file "short.txt" apply this function to the LDH data (file "ldh.data"). The principal commands of the fit are: ldh.df<-read.table("ldh.data",header=T) parameters.ldh<-list(Vmax=1e+00,KmA=1e-03,KmB=1e-02,KmAB=1e-03, C1=1e-03,C2=1e-06) ldh.out1<-nls(v0 ~ Vmax/(1 + C1*p + KmA/a + (KmB/b)*(1 + C1*p)*(1 + C2*p) + (KmAB/(a*b))*(1 + C1*p)), ldh.df, start=parameters.ldh, trace=TRUE) summary(ldh.out1) vcov(ldh.out1) QUALITY OF THE NONLINEAR FIT Various test are applied for assessing the quality of the fit (see the files "short.txt" or "tutorial.txt" for R (or S) language commands): 1. Are the residuals (deviations between measured and calculated values = v0 - v0calc) normally distributed? 1a. Are the residuals uncorrelated? 2. Is each parameter significant in influencing the fit? What is the confidence level for each of the parameters being different from 0? 3. Is the std. error of the fit reasonable from an experimental view? 4. Are the same parameter estimates (the same fit) obtained with different starting values of the parameters? If not, then the fit is suspect. 5. What is the effect of leaving parameters out of the fit? 6. What is the effect of introducing the C3 parameter into the fit? GRAPHICS DISPLAYS The R language has strong graphics. Applied here: 1. pair-wise plots; 2. standard enzyme-kinetic reciprocal plots; 3. plots of the distributions of the variables; 4. perspective and contour plots. The standard enzyme-kinetic reciprocal plots, in somewhat snazzy form, are produced also by the following commands: source("Plots/ldhplot.all.s") ldh.simpfit.out.sgi<-dget("Plots/ldh.simpfit.out.sgi") ldhplot(ldh.simpfit.out.sgi$data, ldh.simpfit.out.sgi$coef) [X11 device displays are produced] The command "ldhplot" and those it calls are loaded from the file "ldhplot.all.s". The kinetic data and parameter values are in the file "ldh.simpfit.out.sgi" loaded as the same-name dataframe. The graphical output is in the PostScript files of the directory "Plots". Details are given in the header of the function "ldhplot". LINEAR FITS The R-language routines for linear fitting and analysis can be applied by removing the model factors (and data) with product ("p"). These fits are chiefly of pedagogical interest only. John Rupley rupley@u.arizona.edu -or- jar@rupley.com 30 Calle Belleza, Tucson AZ 85716 - (520) 325-4533; fax - (520) 325-4991 Dept. Biochemistry & Molecular Biophysics, Univ. Arizona, Tucson AZ 85721