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Parameter estimation in systems biology models using spline approximation.

Zhan C, Yeung LF - BMC Syst Biol (2011)

Bottom Line: Moreover, the cores of our algorithms are LP and NLP based, which are flexible and consequently additional constraints can be embedded/removed easily.Eight system biology models are used for testing the proposed approaches.The proposed approaches have general application to identify unknown parameter values of a wide range of systems biology models.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Electronic Engineering, City University of Hong Kong, PR China. zchoujun2@student.cityu.edu.hk

ABSTRACT

Background: Mathematical models for revealing the dynamics and interactions properties of biological systems play an important role in computational systems biology. The inference of model parameter values from time-course data can be considered as a "reverse engineering" process and is still one of the most challenging tasks. Many parameter estimation methods have been developed but none of these methods is effective for all cases and can overwhelm all other approaches. Instead, various methods have their advantages and disadvantages. It is worth to develop parameter estimation methods which are robust against noise, efficient in computation and flexible enough to meet different constraints.

Results: Two parameter estimation methods of combining spline theory with Linear Programming (LP) and Nonlinear Programming (NLP) are developed. These methods remove the need for ODE solvers during the identification process. Our analysis shows that the augmented cost function surfaces used in the two proposed methods are smoother; which can ease the optima searching process and hence enhance the robustness and speed of the search algorithm. Moreover, the cores of our algorithms are LP and NLP based, which are flexible and consequently additional constraints can be embedded/removed easily. Eight system biology models are used for testing the proposed approaches. Our results confirm that the proposed methods are both efficient and robust.

Conclusions: The proposed approaches have general application to identify unknown parameter values of a wide range of systems biology models.

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Related in: MedlinePlus

The dynamic profiles of two trials. Solid lines represent the "true" time-series data without noise, dots represent the measured time-series data with added artificial noise, and diamonds represent the estimated time-series data produced by the model: (a) noise free condition (b) 10% random noise condition.
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Figure 2: The dynamic profiles of two trials. Solid lines represent the "true" time-series data without noise, dots represent the measured time-series data with added artificial noise, and diamonds represent the estimated time-series data produced by the model: (a) noise free condition (b) 10% random noise condition.

Mentions: Here, P3 was solved by the Stochastic Raking Evolution Strategy (SRES) algorithm [35]. The searching region of the parameters was [0, 50θ ]. SRES uses stochastic ranking as the constraint handling technique, which adjusts the balance between the objective and penalty functions automatically during the evolutionary search. The observation data include 4 sets of time course, which consists of 40 sample points. For trials with noise free data, the algorithm converged in 8 ~ 9 hours after 250,000 ~ 300,000 iterations. The estimated parameter values, as shown in Table 3 are almost identical to the nominal parameter values. However, for k23, k25 and J15, the estimated values are far from the nominal values, but the RSE measure is almost zero, which possibly implies that the system is insensitive with the changes of k23, k25 and J15. This phenomenon reveals that the G1/S transition model either has some parameters that are insensitive to the chosen observation, or they are non-identifiable parameters [36,37]. It is worth mentioning that the this large computational effort is the consequence of the very tight convergence criteria, an almost equal good result can be reached within 200,000 generations in about 6.5 hours with the RSE measure J is smaller than 1%. Figure 2(a) shows the "true" time-series data without noise and computed dynamic time-series data from one identified model. When 10% random noises are added, the convergence time increased and the relative estimation errors between estimated parameters and nominal parameters increased with the increase of noise. However, the time-series produced by the estimated model is very similar to the original data, namely the RSE J is still small. This phenomenon may imply that there is no need to estimated every parameters accurately to achieve a model with equivalent dynamical properties with a good degree of accuracy. As the simulation time is long, performing thousands of simulations as the first method in order to evaluate the mean and variance of estimated parameters is impractical. Thus, due to the lack of space, results of just a few selected trial are shown in Table 3 (more trial results can be found in additional file 1).


Parameter estimation in systems biology models using spline approximation.

Zhan C, Yeung LF - BMC Syst Biol (2011)

The dynamic profiles of two trials. Solid lines represent the "true" time-series data without noise, dots represent the measured time-series data with added artificial noise, and diamonds represent the estimated time-series data produced by the model: (a) noise free condition (b) 10% random noise condition.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3750107&req=5

Figure 2: The dynamic profiles of two trials. Solid lines represent the "true" time-series data without noise, dots represent the measured time-series data with added artificial noise, and diamonds represent the estimated time-series data produced by the model: (a) noise free condition (b) 10% random noise condition.
Mentions: Here, P3 was solved by the Stochastic Raking Evolution Strategy (SRES) algorithm [35]. The searching region of the parameters was [0, 50θ ]. SRES uses stochastic ranking as the constraint handling technique, which adjusts the balance between the objective and penalty functions automatically during the evolutionary search. The observation data include 4 sets of time course, which consists of 40 sample points. For trials with noise free data, the algorithm converged in 8 ~ 9 hours after 250,000 ~ 300,000 iterations. The estimated parameter values, as shown in Table 3 are almost identical to the nominal parameter values. However, for k23, k25 and J15, the estimated values are far from the nominal values, but the RSE measure is almost zero, which possibly implies that the system is insensitive with the changes of k23, k25 and J15. This phenomenon reveals that the G1/S transition model either has some parameters that are insensitive to the chosen observation, or they are non-identifiable parameters [36,37]. It is worth mentioning that the this large computational effort is the consequence of the very tight convergence criteria, an almost equal good result can be reached within 200,000 generations in about 6.5 hours with the RSE measure J is smaller than 1%. Figure 2(a) shows the "true" time-series data without noise and computed dynamic time-series data from one identified model. When 10% random noises are added, the convergence time increased and the relative estimation errors between estimated parameters and nominal parameters increased with the increase of noise. However, the time-series produced by the estimated model is very similar to the original data, namely the RSE J is still small. This phenomenon may imply that there is no need to estimated every parameters accurately to achieve a model with equivalent dynamical properties with a good degree of accuracy. As the simulation time is long, performing thousands of simulations as the first method in order to evaluate the mean and variance of estimated parameters is impractical. Thus, due to the lack of space, results of just a few selected trial are shown in Table 3 (more trial results can be found in additional file 1).

Bottom Line: Moreover, the cores of our algorithms are LP and NLP based, which are flexible and consequently additional constraints can be embedded/removed easily.Eight system biology models are used for testing the proposed approaches.The proposed approaches have general application to identify unknown parameter values of a wide range of systems biology models.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Electronic Engineering, City University of Hong Kong, PR China. zchoujun2@student.cityu.edu.hk

ABSTRACT

Background: Mathematical models for revealing the dynamics and interactions properties of biological systems play an important role in computational systems biology. The inference of model parameter values from time-course data can be considered as a "reverse engineering" process and is still one of the most challenging tasks. Many parameter estimation methods have been developed but none of these methods is effective for all cases and can overwhelm all other approaches. Instead, various methods have their advantages and disadvantages. It is worth to develop parameter estimation methods which are robust against noise, efficient in computation and flexible enough to meet different constraints.

Results: Two parameter estimation methods of combining spline theory with Linear Programming (LP) and Nonlinear Programming (NLP) are developed. These methods remove the need for ODE solvers during the identification process. Our analysis shows that the augmented cost function surfaces used in the two proposed methods are smoother; which can ease the optima searching process and hence enhance the robustness and speed of the search algorithm. Moreover, the cores of our algorithms are LP and NLP based, which are flexible and consequently additional constraints can be embedded/removed easily. Eight system biology models are used for testing the proposed approaches. Our results confirm that the proposed methods are both efficient and robust.

Conclusions: The proposed approaches have general application to identify unknown parameter values of a wide range of systems biology models.

Show MeSH
Related in: MedlinePlus