Journal of Statistical Theory and Practice

, Volume 2, Issue 2, pp 173–182 | Cite as

Efficiency of Protein Production from mRNA

  • Marc A. SuchardEmail author
  • Kenneth Lange
  • Janet S. Sinsheimer


Adapting arguments from queuing theory, we investigate a mathematical model for protein production efficiency from mRNA. Our model involves six parameters: the mRNA length, the clearance distance a ribosome must travel from the initiation site before another ribosome can attach, the ribosomal attachment rate, the ribosomal traveling speed along the mRNA, the mRNA degradation rate, and the probability that a ribosome prematurely disengages from the mRNA. The model allows for different mechanisms of mRNA degradation; the more complicated mechanisms postulate a functional role for the mRNA poly A tail. We determine the probability generating function of the number N of fully formed proteins from a single mRNA. This function yields the moments of N exactly and the entire distribution of N numerically via the finite Fourier transform. Using biologically plausible estimates, we examine the sensitivity of protein production to the model parameters and degradation mechanisms. Model predictions are most sensitive to the degradation and attachment rates, two parameters which are poorly measured in vivo.


Genetics mRNA translation ribosome Poisson process queuing theory finite Fourier transform 

AMS Subject Classification

60G55 60K25 92B05 92C40 


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  1. Beelman, C., Parker, R., 1995. Degradation of mRNA in Eukaryotes. Cell, 81:179–183.CrossRefGoogle Scholar
  2. Christensen, A., Bourne, C., 1999. Shape of large bound polysomes in cultured fibroblasts and thyroid cells. Anatomical Record, 255, 116–129.CrossRefGoogle Scholar
  3. Curtis, D., Lehmann, R., Zamore, P., 1995. Translational regulation in development. Cell, 81, 171–178.CrossRefGoogle Scholar
  4. Feller, W., 1968. An Introduction to Probability Theory and Its Applications, Vol. 1. 3rd edition, Wiley, New York.Google Scholar
  5. Feller, W., 1971. An Introduction to Probability Theory and its Applications, Vol. 2. 2nd edition, Wiley, New York.Google Scholar
  6. Greenberg, J., 1972. High stability of messenger RNA in growing cultured cells. Nature, 240, 102–104.CrossRefGoogle Scholar
  7. Hargrove, J., Hulsey, M., Beale, E., 1991. The kinetics of mammalian gene expression. BioEssays, 13, 667–674.CrossRefGoogle Scholar
  8. Henrici, P., 1979. Fast Fourier transform methods in computational complex analysis. SIAM Review, 21, 481–527.MathSciNetCrossRefGoogle Scholar
  9. Jacobson, A., Peltz, S., 1996. Interrelationships of the pathways of mRNA decay and translation in eukaryotic cells. Annual Review of Biochemistry, 65, 693–739.CrossRefGoogle Scholar
  10. Jacobson, A., Peltz, S., 1999. Tools for turnover: methods for analysis of mRNA stability in eukaryotic cells. Methods: Companion to Methods in Enzymology, 17, 1–2.CrossRefGoogle Scholar
  11. Jorgensen, F., Kurland, C., 1990. Processing errors of gene expression in Escherichia coli. Journal of Molecular Biology, 215, 511–521.CrossRefGoogle Scholar
  12. Karlin, S., Taylor, H., 1975. A First Course in Stochastic Processes. 2nd edition, Academic Press, New York.zbMATHGoogle Scholar
  13. Karlin, S., Taylor, H., 1981. A Second Course in Stochastic Processes. Academic Press, New York.zbMATHGoogle Scholar
  14. Lange, K., 1999. Numerical Analysis for Statisticians. Springer-Verlag, New York.zbMATHGoogle Scholar
  15. Lewin, B., 1997. Genes VI. Oxford University Press, Oxford, United Kingdom.Google Scholar
  16. Mangus, D., Jacobson, A., 1999. Linking mRNA turnover and translation: assessing the polyribosomal association of mRNA decay factors and degradative intermediates. Methods: Companion to Methods in Enzymology, 17, 28–37.CrossRefGoogle Scholar
  17. Menninger, J., 1976. Peptidyl-transfer RNA dissociates during protein synthesis from ribosomes of E. coli. Journal of Biological Chemistry, 251, 3392–3398.Google Scholar
  18. Pavlov, M., Ehrenberg, M. (1996). Rate of translation of natural mRNAs in an optimized in vitro system. Archives of Biochemistry and Biophysics, 328, 9–16.CrossRefGoogle Scholar
  19. Pederson, S., 1984. Escherichia coli ribosomes translate in vivo with variable rate. EMBO Journal, 3, 2895–2898.CrossRefGoogle Scholar
  20. Ross, J., 1996. Control of messenger RNA stability in higher Eukaryotes. Trends in Genetics, 12, 171–175.CrossRefGoogle Scholar
  21. Singh, U., 1996. Polyribosome dynamics: size-distribution as a function of attachment, translocation and release of ribosomes. Journal of Theoretical Biology, 179, 147–159.CrossRefGoogle Scholar
  22. Voet, D., Voet, J., 1995. Biochemistry. 2nd edition, John Wiley and Sons, New York.Google Scholar
  23. Wells, S., Hillner, P., Vale, R., Sachs, A., 1998. Circularization of mRNA by eukaryotic translation initiation factors. Molecular Cell, 2, 135–140.CrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2008

Authors and Affiliations

  • Marc A. Suchard
    • 1
    Email author
  • Kenneth Lange
    • 2
  • Janet S. Sinsheimer
    • 1
  1. 1.Departments of Biomathematics, Biostatistics, Human GeneticsUniversity of CaliforniaLos AngelesUSA
  2. 2.Departments of Biomathematics, Human Genetics and StatisticsUniversity of CaliforniaLos AngelesUSA

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