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Quantifying epistatic interactions among the components constituting the protein translation system.

Matsuura T, Kazuta Y, Aita T, Adachi J, Yomo T - Mol. Syst. Biol. (2009)

Bottom Line: Analyses of the data measured using various combinations of component concentrations indicated that the contributions of larger than 2-body inter-component epistatic interactions are negligible, despite the presence of larger than 2-body physical interactions.These findings allowed the prediction of protein synthesis activity at various combinations of component concentrations from a small number of samples, the principle of which is applicable to analysis and optimization of other biological systems.Moreover, the average ratio of 2- to 1-body terms was estimated to be as small as 0.1, implying high adaptability and evolvability of the protein translation system.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioinformatics Engineering, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka, Japan.

ABSTRACT
In principle, the accumulation of knowledge regarding the molecular basis of biological systems should allow the development of large-scale kinetic models of their functions. However, the development of such models requires vast numbers of parameters, which are difficult to obtain in practice. Here, we used an in vitro translation system, consisting of 69 defined components, to quantify the epistatic interactions among changes in component concentrations through Bahadur expansion, thereby obtaining a coarse-grained model of protein synthesis activity. Analyses of the data measured using various combinations of component concentrations indicated that the contributions of larger than 2-body inter-component epistatic interactions are negligible, despite the presence of larger than 2-body physical interactions. These findings allowed the prediction of protein synthesis activity at various combinations of component concentrations from a small number of samples, the principle of which is applicable to analysis and optimization of other biological systems. Moreover, the average ratio of 2- to 1-body terms was estimated to be as small as 0.1, implying high adaptability and evolvability of the protein translation system.

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Results of Bahadur expansion analysis of the experimental data. (A) Bahadur coefficients determined from the data shown in Figure 2B. The heights of the bars labeled mi and mi–mj on the horizontal axis indicate the 1st order coefficient of module mi and the 2nd order coefficient of the interaction between module mi and mj, respectively. (B, C) R2 values for each Bahadur coefficient from the results shown in Figure 2B (B) and Figure 2C (C). Insets show the R2 values calculated by each order truncation of equation (m4). The results of two independent trials are shown.
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f3: Results of Bahadur expansion analysis of the experimental data. (A) Bahadur coefficients determined from the data shown in Figure 2B. The heights of the bars labeled mi and mi–mj on the horizontal axis indicate the 1st order coefficient of module mi and the 2nd order coefficient of the interaction between module mi and mj, respectively. (B, C) R2 values for each Bahadur coefficient from the results shown in Figure 2B (B) and Figure 2C (C). Insets show the R2 values calculated by each order truncation of equation (m4). The results of two independent trials are shown.

Mentions: The calculated Bahadur coefficients are shown in Figure 3A. The absolute values of the coefficients became smaller as the order increased for both ‘0000 × 1111' and ‘1111 × 2222.' Note that if the activities are assigned as random numbers for all sequences, then all coefficients obtained using Bahadur expansion take an identical weight on average as with white noise. These results indicate that higher order terms make less of a contribution to the activity. Next, the coefficient of determination (R2) was calculated for each Bahadur coefficient (Figure 3B). The R2 value for each Bahadur coefficient is equivalent to the R2 (square of the correlation coefficient R) of regression analysis between the calculated and experimental activities, in which the calculated value was obtained from equation (2) by setting all other coefficients to 0. We confirmed that higher order terms make smaller contributions to the activity. Furthermore, the activity for each sequence was calculated using the obtained coefficients but by truncating equation (2) at the 1st, 2nd, 3rd, and 4th order, respectively. The inset of Figure 3B shows R2 values for the correlations between the calculated and experimental data. These R2 values are equivalent to those obtained by cumulating the elemental R2 values up to the 1st, 2nd, 3rd, and 4th order, respectively. The R2 value reached more than 0.96 even with truncation at the 3rd and 4th order, indicating that truncation at the 2nd order is sufficient to explain the experimental results. That is, larger than 2-body interactions among the modules can be approximated to zero.


Quantifying epistatic interactions among the components constituting the protein translation system.

Matsuura T, Kazuta Y, Aita T, Adachi J, Yomo T - Mol. Syst. Biol. (2009)

Results of Bahadur expansion analysis of the experimental data. (A) Bahadur coefficients determined from the data shown in Figure 2B. The heights of the bars labeled mi and mi–mj on the horizontal axis indicate the 1st order coefficient of module mi and the 2nd order coefficient of the interaction between module mi and mj, respectively. (B, C) R2 values for each Bahadur coefficient from the results shown in Figure 2B (B) and Figure 2C (C). Insets show the R2 values calculated by each order truncation of equation (m4). The results of two independent trials are shown.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2736649&req=5

f3: Results of Bahadur expansion analysis of the experimental data. (A) Bahadur coefficients determined from the data shown in Figure 2B. The heights of the bars labeled mi and mi–mj on the horizontal axis indicate the 1st order coefficient of module mi and the 2nd order coefficient of the interaction between module mi and mj, respectively. (B, C) R2 values for each Bahadur coefficient from the results shown in Figure 2B (B) and Figure 2C (C). Insets show the R2 values calculated by each order truncation of equation (m4). The results of two independent trials are shown.
Mentions: The calculated Bahadur coefficients are shown in Figure 3A. The absolute values of the coefficients became smaller as the order increased for both ‘0000 × 1111' and ‘1111 × 2222.' Note that if the activities are assigned as random numbers for all sequences, then all coefficients obtained using Bahadur expansion take an identical weight on average as with white noise. These results indicate that higher order terms make less of a contribution to the activity. Next, the coefficient of determination (R2) was calculated for each Bahadur coefficient (Figure 3B). The R2 value for each Bahadur coefficient is equivalent to the R2 (square of the correlation coefficient R) of regression analysis between the calculated and experimental activities, in which the calculated value was obtained from equation (2) by setting all other coefficients to 0. We confirmed that higher order terms make smaller contributions to the activity. Furthermore, the activity for each sequence was calculated using the obtained coefficients but by truncating equation (2) at the 1st, 2nd, 3rd, and 4th order, respectively. The inset of Figure 3B shows R2 values for the correlations between the calculated and experimental data. These R2 values are equivalent to those obtained by cumulating the elemental R2 values up to the 1st, 2nd, 3rd, and 4th order, respectively. The R2 value reached more than 0.96 even with truncation at the 3rd and 4th order, indicating that truncation at the 2nd order is sufficient to explain the experimental results. That is, larger than 2-body interactions among the modules can be approximated to zero.

Bottom Line: Analyses of the data measured using various combinations of component concentrations indicated that the contributions of larger than 2-body inter-component epistatic interactions are negligible, despite the presence of larger than 2-body physical interactions.These findings allowed the prediction of protein synthesis activity at various combinations of component concentrations from a small number of samples, the principle of which is applicable to analysis and optimization of other biological systems.Moreover, the average ratio of 2- to 1-body terms was estimated to be as small as 0.1, implying high adaptability and evolvability of the protein translation system.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioinformatics Engineering, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka, Japan.

ABSTRACT
In principle, the accumulation of knowledge regarding the molecular basis of biological systems should allow the development of large-scale kinetic models of their functions. However, the development of such models requires vast numbers of parameters, which are difficult to obtain in practice. Here, we used an in vitro translation system, consisting of 69 defined components, to quantify the epistatic interactions among changes in component concentrations through Bahadur expansion, thereby obtaining a coarse-grained model of protein synthesis activity. Analyses of the data measured using various combinations of component concentrations indicated that the contributions of larger than 2-body inter-component epistatic interactions are negligible, despite the presence of larger than 2-body physical interactions. These findings allowed the prediction of protein synthesis activity at various combinations of component concentrations from a small number of samples, the principle of which is applicable to analysis and optimization of other biological systems. Moreover, the average ratio of 2- to 1-body terms was estimated to be as small as 0.1, implying high adaptability and evolvability of the protein translation system.

Show MeSH