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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.


Plot of CV of total protein (X) versus mRNA (MP) abundance following approach 1 and approach 2 by keeping deterministic mean of X = 457.9 molecules for all the cases.(A) KC = 1E-02, τP = 700 min (approach 1), (B) KC = 1E-01, τP = 70 min (approach 1), (C) KC = 1.0, τP = 7 min (approach 1), (D) KC = 100.0, τP = 7.0E-02 min (approach 1). In all the cases we kept τM = 7 min. (E) KC = 1E-02, τP = 10 min, τM = 1E-01 min (approach 2). (F) KC = 100.0, τP = 7 min, τM = 700 min (approach 2).
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pone.0136668.g006: Plot of CV of total protein (X) versus mRNA (MP) abundance following approach 1 and approach 2 by keeping deterministic mean of X = 457.9 molecules for all the cases.(A) KC = 1E-02, τP = 700 min (approach 1), (B) KC = 1E-01, τP = 70 min (approach 1), (C) KC = 1.0, τP = 7 min (approach 1), (D) KC = 100.0, τP = 7.0E-02 min (approach 1). In all the cases we kept τM = 7 min. (E) KC = 1E-02, τP = 10 min, τM = 1E-01 min (approach 2). (F) KC = 100.0, τP = 7 min, τM = 700 min (approach 2).

Mentions: Following approach 1, we fixed the values of KC and kept the total protein level fixed at ~ 458 molecules in all the cases for the Fig 6A–6D (parameter values are given in the S5 Table). From Fig 6A it is evident that the CV calculated for the total protein level are comparable between the stochastic calculation done with QSSA and mechanistic models as a function of mRNA population when KC (0.01) is small. As the KC value is increased systematically by keeping the mean value of total protein fixed at ~ 458 molecules, the differences between the CV values at the total protein level (as a function of mRNA abundance) increased between the stochastic calculations performed with the QSSA and mechanistic models (Fig 6B with KC = 0.1, Fig 6C with KC = 1.0 and Fig 6D with KC = 100.0). The qualitative nature of the variations in CV values remain identical in both the cases but quantitatively they again start to differ as a function of average number of mRNA molecules for KC>0.1. In this case too, it is quite clear from Fig 6E and 6F that if we change the absolute values of τP and τM (by keeping KC fixed), the stochastic results calculated from QSSA model can differ for KC = 0.01 (Fig 6E, τM = 0.1 min and τP = 10 min) and can be similar for KC = 100.0 (Fig 6F, τM = 700 min and τP = 7 min) as a function of mRNA number.


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

Sengupta D, Kar S - PLoS ONE (2015)

Plot of CV of total protein (X) versus mRNA (MP) abundance following approach 1 and approach 2 by keeping deterministic mean of X = 457.9 molecules for all the cases.(A) KC = 1E-02, τP = 700 min (approach 1), (B) KC = 1E-01, τP = 70 min (approach 1), (C) KC = 1.0, τP = 7 min (approach 1), (D) KC = 100.0, τP = 7.0E-02 min (approach 1). In all the cases we kept τM = 7 min. (E) KC = 1E-02, τP = 10 min, τM = 1E-01 min (approach 2). (F) KC = 100.0, τP = 7 min, τM = 700 min (approach 2).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0136668.g006: Plot of CV of total protein (X) versus mRNA (MP) abundance following approach 1 and approach 2 by keeping deterministic mean of X = 457.9 molecules for all the cases.(A) KC = 1E-02, τP = 700 min (approach 1), (B) KC = 1E-01, τP = 70 min (approach 1), (C) KC = 1.0, τP = 7 min (approach 1), (D) KC = 100.0, τP = 7.0E-02 min (approach 1). In all the cases we kept τM = 7 min. (E) KC = 1E-02, τP = 10 min, τM = 1E-01 min (approach 2). (F) KC = 100.0, τP = 7 min, τM = 700 min (approach 2).
Mentions: Following approach 1, we fixed the values of KC and kept the total protein level fixed at ~ 458 molecules in all the cases for the Fig 6A–6D (parameter values are given in the S5 Table). From Fig 6A it is evident that the CV calculated for the total protein level are comparable between the stochastic calculation done with QSSA and mechanistic models as a function of mRNA population when KC (0.01) is small. As the KC value is increased systematically by keeping the mean value of total protein fixed at ~ 458 molecules, the differences between the CV values at the total protein level (as a function of mRNA abundance) increased between the stochastic calculations performed with the QSSA and mechanistic models (Fig 6B with KC = 0.1, Fig 6C with KC = 1.0 and Fig 6D with KC = 100.0). The qualitative nature of the variations in CV values remain identical in both the cases but quantitatively they again start to differ as a function of average number of mRNA molecules for KC>0.1. In this case too, it is quite clear from Fig 6E and 6F that if we change the absolute values of τP and τM (by keeping KC fixed), the stochastic results calculated from QSSA model can differ for KC = 0.01 (Fig 6E, τM = 0.1 min and τP = 10 min) and can be similar for KC = 100.0 (Fig 6F, τM = 700 min and τP = 7 min) as a function of mRNA number.

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.