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Are Quasi-Steady-State Approximated Models Suitable for Quantifying Intrinsic Noise Accurately?

Sengupta D, Kar S - PLoS ONE (2015)

Bottom Line: Our results strongly suggest that the performance of a stochastic QSSA model in comparison to SSA performed for a mechanistic model critically relies on the absolute values of the mRNA and protein half-lives involved in the corresponding GRN.For the GRNs considered, the stochastic QSSA quantifies the intrinsic noise at the protein level with greater accuracy and for larger combinations of half-life values of mRNA and protein, whereas in case of mRNA the satisfactory accuracy level can only be reached for limited combinations of absolute values of half-lives.Based on our findings, we conclude that QSSA model can be a good choice for evaluating intrinsic noise for other GRNs as well, provided we make a rational choice based on experimental half-life values available in literature.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry, IIT Bombay, Powai, Mumbai - 400076, India.

ABSTRACT
Large gene regulatory networks (GRN) are often modeled with quasi-steady-state approximation (QSSA) to reduce the huge computational time required for intrinsic noise quantification using Gillespie stochastic simulation algorithm (SSA). However, the question still remains whether the stochastic QSSA model measures the intrinsic noise as accurately as the SSA performed for a detailed mechanistic model or not? To address this issue, we have constructed mechanistic and QSSA models for few frequently observed GRNs exhibiting switching behavior and performed stochastic simulations with them. Our results strongly suggest that the performance of a stochastic QSSA model in comparison to SSA performed for a mechanistic model critically relies on the absolute values of the mRNA and protein half-lives involved in the corresponding GRN. The extent of accuracy level achieved by the stochastic QSSA model calculations will depend on the level of bursting frequency generated due to the absolute value of the half-life of either mRNA or protein or for both the species. For the GRNs considered, the stochastic QSSA quantifies the intrinsic noise at the protein level with greater accuracy and for larger combinations of half-life values of mRNA and protein, whereas in case of mRNA the satisfactory accuracy level can only be reached for limited combinations of absolute values of half-lives. Further, we have clearly demonstrated that the abundance levels of mRNA and protein hardly matter for such comparison between QSSA and mechanistic models. Based on our findings, we conclude that QSSA model can be a good choice for evaluating intrinsic noise for other GRNs as well, provided we make a rational choice based on experimental half-life values available in literature.

No MeSH data available.


Impact of absolute values of τP and τM on CV of X (Total protein) and MP (mRNA) as well as on ZX and  (where Zi = % deviation of the measured intrinsic noise between the QSSA and the mechanistic models for i = X or MP).Plot of CV of X versus τP and τM for (A) KC = 1E-02 (B) KC = 1.0 (C) KC = 100.0. Plot of CV of MP versus τP and τM for (D) KC = 1E-02 (E) KC = 1.0 (F) KC = 100.0. (G) Impact of absolute values of τP and τM on ZX. (H) Impact of absolute values of τP and τM on . τP and τM are the half-lives of P and MP respectively and are given in minutes.
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pone.0136668.g004: Impact of absolute values of τP and τM on CV of X (Total protein) and MP (mRNA) as well as on ZX and (where Zi = % deviation of the measured intrinsic noise between the QSSA and the mechanistic models for i = X or MP).Plot of CV of X versus τP and τM for (A) KC = 1E-02 (B) KC = 1.0 (C) KC = 100.0. Plot of CV of MP versus τP and τM for (D) KC = 1E-02 (E) KC = 1.0 (F) KC = 100.0. (G) Impact of absolute values of τP and τM on ZX. (H) Impact of absolute values of τP and τM on . τP and τM are the half-lives of P and MP respectively and are given in minutes.

Mentions: This implies that one can have fixed value of KC for different values of τM and τP, which can eventually change the burst size and burst frequencies and impact the overall intrinsic noise significantly. The important question is whether stochastic calculation from QSSA model can capture that feature accurately or not? To address this issue, we keep on changing the absolute values of the half-lives (τM and τP) for mRNA and protein by keeping the ratio KC fixed at 0.01 (Fig 4A and 4D), 1 (Fig 4B and 4E) and 100 (Fig 4C and 4F) (the average number of the total protein (~ 458 molecules) and mRNA (~ 185 molecules) are also kept fixed for all the cases deterministically, parameters are given in S2 Table). The way we varied the absolute values of the half-lives τM and τP (with KC fixed at 0.01, 1, 100) span almost all the possibilities of half-life combinations that can exist in reality for mammalian cells found in recent experiment [30]. The stochastic simulation results obtained for both the models performed equally well to quantify intrinsic noise at the total protein (X) level for all the KC values used in Fig 4A–4C for a certain range of absolute values of τM and τP. For KC = 0.01 (Fig 4A), the intirnsic noise quantified from QSSA model at the protein (X) level starts to differ from mechanistic model when τM = 0.1 min and τP = 10 min. Similarly for KC = 1 (Fig 4B), the deviation starts at τM = 7 min and τP = 7 min and for KC = 100 (Fig 4C), the deviation starts at τM = 10 min and τP = 0.1 min. Interestingly, we found that in Fig 4D–4F for certain combinations of absolute values of τM and τP (at different fixed values of KC), the stochastic QSSA model can also quantify the intrinsic noise at the mRNA (MP) level with reasonable accuracy in comparison to the mechanistic model. In all the cases (Fig 4A–4F), the CVs obtained from stochastic calculation of the QSSA model hardly changes for a fixed value of KC when the absolute values of the τM and τP are changed whereas the CVs calculated from the mechanistic model starts to deviate from QSSA model as soon as the value of either τM or τP or both τM and τP are such that they can significantly change the burst frequency and burst size related to the intrinsic noise of the concerned network. This evidently shows an important fact that even for ratio KC>0.1 the QSSA model can quantify the intrinsic noise (for protein as well as for mRNA) as accurately as the mechanistic model and we can have situations where for ratio KC<0.1 the QSSA model can fail to quantify the intrinsic noise (even at the protein level) as precisely as the mechanistic model. This result is quite different than what has been shown by Shahrezaei and Swain [15] earlier as they did not concentrate on changing the absolute values of τP and τM while performing their analysis.


Are Quasi-Steady-State Approximated Models Suitable for Quantifying Intrinsic Noise Accurately?

Sengupta D, Kar S - PLoS ONE (2015)

Impact of absolute values of τP and τM on CV of X (Total protein) and MP (mRNA) as well as on ZX and  (where Zi = % deviation of the measured intrinsic noise between the QSSA and the mechanistic models for i = X or MP).Plot of CV of X versus τP and τM for (A) KC = 1E-02 (B) KC = 1.0 (C) KC = 100.0. Plot of CV of MP versus τP and τM for (D) KC = 1E-02 (E) KC = 1.0 (F) KC = 100.0. (G) Impact of absolute values of τP and τM on ZX. (H) Impact of absolute values of τP and τM on . τP and τM are the half-lives of P and MP respectively and are given in minutes.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4556639&req=5

pone.0136668.g004: Impact of absolute values of τP and τM on CV of X (Total protein) and MP (mRNA) as well as on ZX and (where Zi = % deviation of the measured intrinsic noise between the QSSA and the mechanistic models for i = X or MP).Plot of CV of X versus τP and τM for (A) KC = 1E-02 (B) KC = 1.0 (C) KC = 100.0. Plot of CV of MP versus τP and τM for (D) KC = 1E-02 (E) KC = 1.0 (F) KC = 100.0. (G) Impact of absolute values of τP and τM on ZX. (H) Impact of absolute values of τP and τM on . τP and τM are the half-lives of P and MP respectively and are given in minutes.
Mentions: This implies that one can have fixed value of KC for different values of τM and τP, which can eventually change the burst size and burst frequencies and impact the overall intrinsic noise significantly. The important question is whether stochastic calculation from QSSA model can capture that feature accurately or not? To address this issue, we keep on changing the absolute values of the half-lives (τM and τP) for mRNA and protein by keeping the ratio KC fixed at 0.01 (Fig 4A and 4D), 1 (Fig 4B and 4E) and 100 (Fig 4C and 4F) (the average number of the total protein (~ 458 molecules) and mRNA (~ 185 molecules) are also kept fixed for all the cases deterministically, parameters are given in S2 Table). The way we varied the absolute values of the half-lives τM and τP (with KC fixed at 0.01, 1, 100) span almost all the possibilities of half-life combinations that can exist in reality for mammalian cells found in recent experiment [30]. The stochastic simulation results obtained for both the models performed equally well to quantify intrinsic noise at the total protein (X) level for all the KC values used in Fig 4A–4C for a certain range of absolute values of τM and τP. For KC = 0.01 (Fig 4A), the intirnsic noise quantified from QSSA model at the protein (X) level starts to differ from mechanistic model when τM = 0.1 min and τP = 10 min. Similarly for KC = 1 (Fig 4B), the deviation starts at τM = 7 min and τP = 7 min and for KC = 100 (Fig 4C), the deviation starts at τM = 10 min and τP = 0.1 min. Interestingly, we found that in Fig 4D–4F for certain combinations of absolute values of τM and τP (at different fixed values of KC), the stochastic QSSA model can also quantify the intrinsic noise at the mRNA (MP) level with reasonable accuracy in comparison to the mechanistic model. In all the cases (Fig 4A–4F), the CVs obtained from stochastic calculation of the QSSA model hardly changes for a fixed value of KC when the absolute values of the τM and τP are changed whereas the CVs calculated from the mechanistic model starts to deviate from QSSA model as soon as the value of either τM or τP or both τM and τP are such that they can significantly change the burst frequency and burst size related to the intrinsic noise of the concerned network. This evidently shows an important fact that even for ratio KC>0.1 the QSSA model can quantify the intrinsic noise (for protein as well as for mRNA) as accurately as the mechanistic model and we can have situations where for ratio KC<0.1 the QSSA model can fail to quantify the intrinsic noise (even at the protein level) as precisely as the mechanistic model. This result is quite different than what has been shown by Shahrezaei and Swain [15] earlier as they did not concentrate on changing the absolute values of τP and τM while performing their analysis.

Bottom Line: Our results strongly suggest that the performance of a stochastic QSSA model in comparison to SSA performed for a mechanistic model critically relies on the absolute values of the mRNA and protein half-lives involved in the corresponding GRN.For the GRNs considered, the stochastic QSSA quantifies the intrinsic noise at the protein level with greater accuracy and for larger combinations of half-life values of mRNA and protein, whereas in case of mRNA the satisfactory accuracy level can only be reached for limited combinations of absolute values of half-lives.Based on our findings, we conclude that QSSA model can be a good choice for evaluating intrinsic noise for other GRNs as well, provided we make a rational choice based on experimental half-life values available in literature.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry, IIT Bombay, Powai, Mumbai - 400076, India.

ABSTRACT
Large gene regulatory networks (GRN) are often modeled with quasi-steady-state approximation (QSSA) to reduce the huge computational time required for intrinsic noise quantification using Gillespie stochastic simulation algorithm (SSA). However, the question still remains whether the stochastic QSSA model measures the intrinsic noise as accurately as the SSA performed for a detailed mechanistic model or not? To address this issue, we have constructed mechanistic and QSSA models for few frequently observed GRNs exhibiting switching behavior and performed stochastic simulations with them. Our results strongly suggest that the performance of a stochastic QSSA model in comparison to SSA performed for a mechanistic model critically relies on the absolute values of the mRNA and protein half-lives involved in the corresponding GRN. The extent of accuracy level achieved by the stochastic QSSA model calculations will depend on the level of bursting frequency generated due to the absolute value of the half-life of either mRNA or protein or for both the species. For the GRNs considered, the stochastic QSSA quantifies the intrinsic noise at the protein level with greater accuracy and for larger combinations of half-life values of mRNA and protein, whereas in case of mRNA the satisfactory accuracy level can only be reached for limited combinations of absolute values of half-lives. Further, we have clearly demonstrated that the abundance levels of mRNA and protein hardly matter for such comparison between QSSA and mechanistic models. Based on our findings, we conclude that QSSA model can be a good choice for evaluating intrinsic noise for other GRNs as well, provided we make a rational choice based on experimental half-life values available in literature.

No MeSH data available.