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Formulation of the protein synthesis rate with sequence information

  • * Corresponding author: Jinzhi Lei

    * Corresponding author: Jinzhi Lei
This work is supported by National Natural Science Foundation of China (91430101 and 11272169).
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  • Translation is a central biological process by which proteins are synthesized from genetic information contained within mRNAs. Here, we investigate the kinetics of translation at the molecular level by a stochastic simulation model. The model explicitly includes RNA sequences, ribosome dynamics, the tRNA pool and biochemical reactions involved in the translation elongation. The results show that the translation efficiency is mainly limited by the available ribosome number, translation initiation and the translation elongation time. The elongation time is a log-normal distribution, with the mean and variance determined by the codon saturation and the process of aa-tRNA selection at each codon binding site. Moreover, our simulations show that the translation accuracy exponentially decreases with the sequence length. These results suggest that aa-tRNA competition is crucial for both translation elongation, translation efficiency and the accuracy, which in turn determined the effective protein production rate of correct proteins. Our results improve the dynamical equation of protein production with a delay differential equation that is dependent on sequence information through both the effective production rate and the distribution of elongation time.

    Mathematics Subject Classification: 92C45.


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  • Figure 1.  Kinetic scheme of RNA translation. Re-drawn from [6]

    Figure 2.  Translation kinetics of a single mRNA sequence. (a) Positions of each ribosome on the sequence. (b) Numbers of protein products. The black solid line represents all protein products, and the red dashed line represents the correctly translated proteins (no incorrect amino acid added by near-cognate aa-tRNAs). Here, the sample sequence is the gene YAL003W from the SGD yeast coding sequence, with a sequence length $L = 621 nt$. The simulation time, on Mac Pro with $2\times 3.06$ GHz 6-Core Intel Xeon and 16 GB memory, was about 3 min. Parameters are $R=20$ and $F=0.03$. For other parameters refer to Table 1

    Figure 3.  Distribution of the elongation time per codon during the translation of YAL003W. All parameters are the same as described in Fig. 2. The red curve is the fit with the normal distribution $\ln \mathcal{N}(-1.6, 1.69)$

    Figure 4.  Dependence of the $ETC$ of yeast coding sequences on tRNA usage. Dots represent the mean (upper panel) and variance (bottom panel) of the logarithm of $ETC$ with cognate tRNA usage $F_{\mathrm{cog}}$, near-cognate tRNA usage $F_{\mathrm{near}}$ and non-cognate tRNA usage $F_{\mathrm{non}}$. Dashed lines show the linear fitting. Simulations of 1000 yeast coding sequences are shown; each dot corresponds to one sequence. All parameters are the same as described in Fig. 2

    Figure 5.  Dependence of the elongation time on the available ribosome number $R$. (a) Average $ETC$ versus $R$. (b) Ribosome distance (in codons) versus $R$. The sequence and parameters are the same as described in Fig. 2

    Figure 6.  Dependence of the $ETC$ on total tRNA number represented by the factor $F$. The mean (left hand ordinate, blue circles connected with a dashed line) and variance (right hand ordinate, red triangles connected with a dotted line) of the logarithm of $ETC$ are shown as a function of the factor $F$. The sequence and parameters are the same as described in Fig. 2

    Figure 7.  Dependence of translation efficiency on the maximum number of available ribosomes $R$. The dashed lines represent show the two-phase dependence following Eq. 11. The sequence and parameters are the same as described in Fig. 2

    Figure 8.  Translation kinetics. (a) Translation efficiency versus sequence length for 1000 yeast coding sequences. Red line shows the fitting with $TE = \dfrac{0.195}{1+0.0033 n}$. (b) Translation accuracy versus sequence length for 1000 yeast coding genes. Red line shows the fitting with $e^{-0.0042 n}$. Here, $n=L/3$ represents the protein chain length. Data were obtained from the simulation shown in Fig. 4

    Figure 9.  Sensitivity analysis of translation efficiency. Bars show changes in the logarithm of translation efficiencies induced by changes in a single parameter $\ln(TE^*/TE_0)$, where $TE^*$ and $TE_0$ represent the $TE$ for modified and default parameters, respectively. Blue bars correspond to the increase of a parameter by $10\%$, and yellow bars correspond to the decrease of a parameter by $10\%$. For parameters refer to Table 1, the parameters $\mathrm{ke02}$, $\mathrm{ke3}$, $\mathrm{ke5}$, $\mathrm{ke7}$, and $\mathrm{keT}$ for values of $\mathrm{k02}$, $\mathrm{k3}$, $\mathrm{k5}$, $\mathrm{k7}$, and $\mathrm{kT}$ of near-cognate tRNAs (second column in Table 1), respectively, and $\mathrm{kn01}$ for the parameter $\mathrm{k01}$ of the non-cognate tRNAs (third column in Table 1). The sequence and default parameters are the same as described in Fig. 2

    Figure 10.  $ETC$ of the translation for different samples. Distributions of the mean and variance of the logarithm of $ETC$ for yeast coding RNAs (a), yeast noncoding RNAs (b), human coding RNAs (c) and human noncoding RNAs (d). Here, the results of 500 random sequences with lengths of $200 nt < L< 1000 nt$ for each sample are shown. Red stars show the average values for each sample; the values are provided in the table. The parameters are $R=20, F=0.03$; for other parameters, refer to Table 1

    Table 1.  Values of kinetic rate constants ($s^{-1}$) (refer to [6])

    Parameters Values Cognate Near-cognate Non-cognate
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    Table 2.  tRNA pool composition (refer to [5,6]). Also refer to [6] for the anti-codons for the tRNAs

    tRNA Molecules/cell tRNA Molecules/cell tRNA Molecules/cell
    Gln1764Met f11211Thr4916
    Gln2881Met f2715Trp943
    Glu24717Met m706Tyr1769
     | Show Table
    DownLoad: CSV
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