Nonlinear least-squares fitting with Gepasi
This document is a complement to the paper Mendes, P. & Kell, D.B. (1998) Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics 14, 869-883.
We want to estimate a number of rate constants of the mechanism of
irreversible inhibition of HIV proteinase (Fig 1). For this
we use data kindly supplied by Drs. Sergei
Gulnik, Leonid Suvorov and John W. Erickson (National Cancer Institute) and already used
for similar purposes in
Kuzmic
(1996) Anal. Biochem. 237, 260-273. Five progress curves were
measured fluorimetrically in the presence of an irreversible inhibitor. The
data were then formatted according to Gepasi's
requirements and the program was set to fit the rate constants k22, k3,
k42, k52 and k6 to the experimental data. In this fit, it was also assumed that
there is a certain degree of uncertainty (+/- 50%) in the value of the initial
concentrations of substrate and enzyme and that the offset (base line) of the
fluorimeter was not exactly zero.
There are a total of 20 adjustable parameters: the 5 rate constants, 5 initial concentrations of enzyme, 5 initial concentrations of substrate and 5 offset values (as there are 5 time course curves). Below are the results of fitting this model to the experimental data using a series of optimisation methods.
You can download the Gepasi simulation file that was used to run these fits. Right click the two icons below and save the files to disk. Then load hivfit.gps into Gepasi 3.20 or above. (note that if you run simulated annealing this will take a very long time even on very fast computers).
 Gepasi file |
 data file |
| Method | Simulated annealing | Levenberg-Marquardt | Hooke and Jeeves | Genetic algorithm | L-BFGS-B | Steepest descent | Random search |
| SSq | 0.0211024 | 0.0213425 | 0.0253683 | 0.226773 | 1.92704 | 4.05282 | 0 |
| Simulations | 3131135 | 4475 | 43715 | 1020255 | 18690 | 1270 | 0 |
*******************************
* Gepasi version 3.20 beta 4 *
* DEC Alpha AXP executable *
* Friday, 17 July 1998, 13:51 *
*******************************
PARAMETER FITTING
method: Simulated annealing
Tolerance = 1e-005
T0 = 1
dT = 0.8
iterations = 630000
simulations = 3131135
time = 309718 s
speed = 10.1096 simulation/s
Sum of squares = 0.0211024
Std. deviation = 0.00377602
|
Parameter Value Std.Deviation -------------------------------------- R2(k2) 201.1 135.7 R3(k) 7.352 0.6785 R4(k2) 1171 1070 R5(k2) 1.314e+004 2.687e+004 R6(k) 3e+004 8.978e+004 [S]i Exper. 1 24.79 0.03285 Exper. 2 23.43 0.03882 Exper. 3 26.79 0.05742 Exper. 4 32.1 2.103 Exper. 5 26.81 1.773 [E]i Exper. 1 0.004389 0.0003404 Exper. 2 0.004537 0.0002353 Exper. 3 0.00547 0.0001906 Exper. 4 0.004175 1.338e-005 Exper. 5 0.003971 9.885e-006 [offset]i Exper. 1 -0.008013 0.0007571 Exper. 2 -0.003911 0.0008744 Exper. 3 -0.008962 0.001338 Exper. 4 -0.016 0.001819 Exper. 5 -0.003789 0.001613 |
[ table ]
*********************************
* Gepasi version 3.20 beta 6 *
* Intel Pentium executable *
* Thursday, 23 July 1998, 01:34 *
*********************************
PARAMETER FITTING
method: Levenberg-Marquardt
Max. Iter. = 100
Tolerance = 1e-005
iterations = 37
simulations = 4475
time = 735.558 s
speed = 6.08382 simulation/s
Sum of squares = 0.0213425
Std. deviation = 0.00379745
|
Parameter Value Std.Deviation -------------------------------------- R2(k2) 180.6 25.7 R3(k) 10.39 1.02 R4(k2) 1072 202.5 R5(k2) 2.825e-016 1.13e-015 R6(k) 2.486e-016 2.585e-015 [S]i Exper. 1 24.76 0.03321 Exper. 2 23.56 0.04232 Exper. 3 27.09 0.06503 Exper. 4 28.17 1.365 Exper. 5 23.51 1.159 [E]i Exper. 1 0.003068 0.0002724 Exper. 2 0.003622 0.0001862 Exper. 3 0.004728 0.0001543 Exper. 4 0.004135 1.119e-005 Exper. 5 0.003994 4.843e-006 [offset]i Exper. 1 -0.007377 0.0007672 Exper. 2 -0.00718 0.0009906 Exper. 3 -0.01605 0.001527 Exper. 4 -0.02281 0.00213 Exper. 5 -0.009926 0.001862 |
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*********************************
* Gepasi version 3.20 beta 6 *
* DEC Alpha AXP executable *
* Thursday, 23 July 1998, 12:49 *
*********************************
method: Hooke and Jeeves
Max. Iter. = 50
Tolerance = 1e-005
Rho = 0.2
iterations = 7
simulations = 43715
time = 5582.92 s
speed = 7.83013 simulation/s
Sum of squares = 0.0253683
Std. deviation = 0.00414014
|
Parameter Value Std.Deviation -------------------------------------- R2(k2) 189.9 67.98 R3(k) 9.67 1.135 R4(k2) 1267 619.8 R5(k2) 0.02804 0.06485 R6(k) 0.1902 0.1601 [S]i Exper. 1 24.99 0.03525 Exper. 2 23.69 0.04752 Exper. 3 26.95 0.07542 Exper. 4 22.48 1.333 Exper. 5 23.09 1.339 [E]i Exper. 1 0.003325 0.0003604 Exper. 2 0.003792 0.0002465 Exper. 3 0.004834 0.0001983 Exper. 4 0.00417 1.867e-005 Exper. 5 0.003988 7.287e-006 [offset]i Exper. 1 -0.01341 0.0008168 Exper. 2 -0.01111 0.001113 Exper. 3 -0.01413 0.001791 Exper. 4 -0.009199 0.002254 Exper. 5 -0.007293 0.002287 |
[ table ]
*******************************
* Gepasi version 3.20 beta 5 *
* Intel Pentium executable *
* Friday, 17 July 1998, 23:48 *
*******************************
method: Genetic algorithm
Generations = 2000
Population = 100
iterations = 2000
simulations = 1020255
time = 191835 s
speed = 5.31839 simulation/s
Sum of squares = 0.226773
Std. deviation = 0.0123784
|
Parameter Value Std.Deviation -------------------------------------- R2(k2) 129.9 7.24 R3(k) 3.96 1.724 R4(k2) 3170 1.682 R5(k2) 0.3891 9.75 R6(k) 0.0489 8.576 [S]i Exper. 1 23.06 0.04581 Exper. 2 21.98 0.04772 Exper. 3 25.45 0.06283 Exper. 4 26.38 0.9725 Exper. 5 29.22 0.7152 [E]i Exper. 1 0.006 0.5938 Exper. 2 0.005707 0.5507 Exper. 3 0.006 0.6605 Exper. 4 0.002466 0.8067 Exper. 5 0.002 0.5409 [offset]i Exper. 1 0.04071 0.05373 Exper. 2 0.02846 0.06145 Exper. 3 0.0287 0.09759 Exper. 4 0.02346 0.0851 Exper. 5 0.006241 0.0727 |
[ table ]
*******************************
* Gepasi version 3.20 beta 3 *
* Intel Pentium executable *
* Monday, 13 July 1998, 12:41 *
*******************************
method: L-BFGS-B
Corrections = 15
factr = 1
pgtol = 1e-006
iterations = 19
simulations = 18690
time = 3124.71 s
speed = 5.98135 simulation/s
Sum of squares = 1.92704
Std. deviation = 0.036084
|
Parameter Value Std.Deviation -------------------------------------- R2(k2) 300 6.629e+004 R3(k) 9.822 3074 R4(k2) 500 7.459e+004 R5(k2) 0.0667 2.957e+005 R6(k) 0.06671 1.263e+005 [S]i Exper. 1 24.64 0.5066 Exper. 2 24.28 0.8325 Exper. 3 24.14 1.466 Exper. 4 24.41 799.3 Exper. 5 24 1716 [E]i Exper. 1 0.003081 1801 Exper. 2 0.00398 681.9 Exper. 3 0.00542 352.4 Exper. 4 0.004071 0.9871 Exper. 5 0.00352 240 [offset]i Exper. 1 0.0002952 1.49e+006 Exper. 2 0.0003496 2.165e+006 Exper. 3 0.0005894 1.514e+006 Exper. 4 0.000394 5.207e+006 Exper. 5 0.001096 5.801e+005 |
[ table ]
*******************************
* Gepasi version 3.20 beta 3 *
* Intel Pentium executable *
* Monday, 13 July 1998, 14:06 *
*******************************
method: Steepest descent
Max. Iter. = 100
Tolerance = 1e-006
iterations = 7
simulations = 1270
time = 195.031 s
speed = 6.51179 simulation/s
Sum of squares = 4.05282
Std. deviation = 0.0523296
|
Parameter Value Std.Deviation -------------------------------------- R2(k2) 300 2.534e+005 R3(k) 10 1.61e+004 R4(k2) 500 2.886e+005 R5(k2) 0.09999 7.13e+005 R6(k) 0.1 7.522e+005 [S]i Exper. 1 25 0.8954 Exper. 2 25 4.135 Exper. 3 25 3.657 Exper. 4 25 1.339e+005 Exper. 5 25 1.483e+005 [E]i Exper. 1 0.002784 7375 Exper. 2 0.002984 1783 Exper. 3 0.004724 965.9 Exper. 4 0.002766 5.271e+004 Exper. 5 0.002 8.739e+004 [offset]i Exper. 1 0.09995 22.34 Exper. 2 0.09998 48.35 Exper. 3 0.09999 76.24 Exper. 4 0.09998 343 Exper. 5 0.09997 334.1 |
[ table ]
********************************
* Gepasi version 3.11 alpha 6 *
* Intel Pentium executable *
* Monday, 23 March 1998, 19:04 *
********************************
method: Random search
Iterations = 200000
iterations = 200000
simulations = 1000155
time = 90455.3 s
speed = 11.0569 simulation/s
Sum of squares = 5.57454
Std. deviation = 0.0610638
|
Parameter Value Gradient ------------------------------------ R2(k2) 1.998e+004 2.583 R3(k) 1262 -2.559 R4(k2) 147.9 0.08511 R5(k2) 6.195e-007 -0.01825 R6(k) 1.169e-015 -0.0003862 [S]i Exper. 0 26.57 2.992 Exper. 1 33.94 -10.09 Exper. 2 37.01 9.133 Exper. 3 29.04 -2.333 Exper. 4 23.91 -1.054 [E]i Exper. 0 0.002456 1.149 Exper. 1 0.002022 -22.11 Exper. 2 0.003949 19.33 Exper. 3 0.003567 -8.238 Exper. 4 0.003557 -3.672 |
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This document is Copyright © 1998, 1999, 2004 Pedro Mendes, All rights reserved.