Skip to main content
SpringerLink
Log in

Kinetics of Dimension-Restricted Conditions

  • Chapter
Introduction to Systems Biology

Abstract

The intracellular environment is crowded with skeletal proteins, organelle membranes, ribosomes, and so on. When molecular movement is restricted by such environments, some biochemical reaction processes cannot be represented by classical models, which assume that reactions occur in simple Newtonian fluids. Dimension-restricted reaction kinetics (DRRK) modeling is a method that can represent dimension-restricted reactions. We introduce the methods of DRRK in each case of reaction type. DRRK has another advantage in that it can be quantitatively evaluated by biochemical experiments. We also introduce the procedure of applying it for experimental results. This modeling method may provide the basis for in vivo-oriented modeling.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Fulton AB. How crowded is the cytoplasm? Cell 1982;30:345–347.

    Article  PubMed  CAS  Google Scholar 

  2. Medalia O. et al. Macromolecular architecture in eukaryotic cells visualized by cryoelectron tomography. Science 2002;298:1209–1213.

    Article  PubMed  CAS  Google Scholar 

  3. Smoluchowski MV. Versuch einer mathematischen Theorie der Koagulationskinetik koloider Losungen. Phys Chem 1917;92:129–168.

    Google Scholar 

  4. Michaelis L, Menten LM. Die Kinetik der Invertinwirkung. Biochem Z 1913;49:333–369.

    CAS  Google Scholar 

  5. Segel IH. Enzyme kinetics. Behavior and analysis of rapid equilibrium and steady-state enzyme systems. New York: John Wiley & Sons, Inc; 1993.

    Google Scholar 

  6. Berg OG, Winter RB, von Hippel PH. Diffusion-driven mechanisms of protein translocation on nucleic acids. 1. Models and theory. Biochemistry 1981;24:6929–6948.

    Article  Google Scholar 

  7. Jelstch A, Pingoud A. Kinetic characterization of linear diffusion of the restriction endonuclease EcoRV on DNA. Biochemistry 1998;37:2160–2169.

    Article  Google Scholar 

  8. Stanford NP, Szczelkun MD, Marko JF, et al. One-and three-dimensional pathways for proteins to reach specific DNA sites. EMBO J 2000;1:6546–6557.

    Article  Google Scholar 

  9. Gowers DM, Halford SE. Protein motion from non-specific to specific DNA by three-dimensional routes aided by supercoiling. EMBO J 2003;17:1410–1418.

    Article  Google Scholar 

  10. Jeltsch A, Urbanke C. Sliding or hopping? How restriction enzymes find their way on DNA. In: Pngoud A, ed. Nucleic Acids and Molecular Biology: Restriction Endonuclease, vol. 14. Heidelberg: Springer-Verlag; 2004:95–110.

    Google Scholar 

  11. Einstein A. Investigations on the Theory of the Brownian Movement. New York: Dutton; 1926.

    Google Scholar 

  12. von Smoluchowski M. Drei Vorträgeüber Diffusion, Brownische Molekularbewegung und Koagulation von Kolloidteilchen. Phys Z 1916;17:557–571, 585–599.

    Google Scholar 

  13. Frish HI, Hammersly JM. Percolation process and related topics. J Soc Indust Appl Math 1963;11:894–918.

    Article  Google Scholar 

  14. Kopelman R, Argyrakis P. Diffusive and percolative lattice migration: Excitons. J Chem Phys 1980;72:3053–3060.

    Article  CAS  Google Scholar 

  15. Klymko PW, Kopelman R. Fractal reaction kinetics: exciton fusion on clusters. J Phys Chem 1983;87:4565–4567.

    Article  CAS  Google Scholar 

  16. Kopelman R, Klymko PW, Newhouse JS, et al. Reaction kinetics on fractals: random-walker simulations and exciton experiments. Phys Rev B 1984;29:3747–3748.

    Article  CAS  Google Scholar 

  17. Kopelman R. Fractal reaction kinetics. Science 1988;241:1620–1626.

    Article  PubMed  CAS  Google Scholar 

  18. Kopelman R. Exciton microscopy and reaction kinetics in restricted spaces. In: Glass WA, Varma MN, ed. Physical and Chemical Mechanisms in Molecular Radiation Biology. New York: Plenum Press; 1991:475–502.

    Google Scholar 

  19. Turner TE. Stochastic and deterministic approaches to modelling in vivo biochemical kinetics [masters thesis]. Trinity, England: University of Oxford; 2003.

    Google Scholar 

  20. Savageau MA. Influence of fractal kinetics on molecular recognition. J Mol Recognit 1993;4:149–157.

    Article  Google Scholar 

  21. Savageau MA. Michaelis-Menten mechanism reconsidered: implications of fractal kinetics. J Theor Biol 1995;176:115–124.

    Article  PubMed  CAS  Google Scholar 

  22. Savageau MA. Development of fractal kinetic theory for enzyme-catalysed reactions and implications for the design of biochemical pathways. Biosystems 1998;47:9–36.

    Article  PubMed  CAS  Google Scholar 

  23. Schnell S, Turner TE. Reaction kinetics in intracellular environments with macromolecular crowding: simulations and rate laws. Biophys Mol Biol 2004;85:235–260.

    Article  CAS  Google Scholar 

  24. Vlad MO, Popa VT, Segal E, et al. Multiple rate-determining steps for nonideal and fractal kinetics. J Phys Chem 2005;109:2455–2460.

    CAS  Google Scholar 

  25. Duran J, Pelle F, Portella MT. Fractal kinetics of multiparticle diffusion. J Phys C: Solid State Phys 1986;19:6185–6194.

    Article  Google Scholar 

  26. Berry H. Monte Carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation. Biophys J 2002;83:1891–1901.

    PubMed  CAS  Google Scholar 

  27. Aon MA, Cortassa S. On the fractal nature of cytoplasm. FEBS Lett 1994;344:1–4.

    Article  PubMed  CAS  Google Scholar 

  28. Aon MA, O’Rourke B, Cortassa S. The fractal architecture of cytoplasmic organization: scaling, kinetics and emergence in metabolic network. Mol Cell Biochem 2004;256/257:169–184.

    Article  CAS  Google Scholar 

  29. Briggs GE, Haldane JBS. A note on the kinetics of enzyme action. Biochem J 1925;19:338–339.

    PubMed  CAS  Google Scholar 

  30. Kulkarni RP, Wu DD, Davis ME, Fraser SE. Quantitating intracellular transport of polyplexes by spatio-temporal image correlation spectroscopy. Proc Natl Acad Sci USA 2005;102:7523–7528.

    Article  PubMed  CAS  Google Scholar 

  31. Burack WR, Shaw AS. Live cell imaging of ERK and MEK. J Biol Chem 2005;280:3832–3837.

    Article  PubMed  CAS  Google Scholar 

  32. Phair RD, Misteli T. High mobility of proteins in the mammalian cell nucleus. Nature 2000;404:604–609.

    Article  PubMed  CAS  Google Scholar 

  33. Lillemeier BF, Köster M, Kerr IM. STAT1 from the cell membrane to the DNA. EMBO J 2001;20:2508–2517.

    Article  PubMed  CAS  Google Scholar 

  34. Kabata H, Okada W Washizu M. Single-molecule dynamics of the EcoRI enzyme using stretched DNA: its application to in situ sliding assay and optical DNA mapping. Jpn J Appl Phys 2000;39:7164–7171.

    Article  CAS  Google Scholar 

  35. Seidel R, van Noort J, van der Scheer C, et al. Real-time observation of DNA translocation by the type I restriction modification enzyme EcoR124I. Nat Struct Biol 2004;11:838–843.

    Article  CAS  Google Scholar 

  36. Solovjeva L, Svetlova M, Stein G, et al. Conformation of replicated segments of chromosome fibers in human S-phase nucleus. Chromosome Res 1998;6:595–602.

    Article  PubMed  CAS  Google Scholar 

  37. Maly IV, Vorobjev IA. Centrosome-dependent anisotropic random walk of cytoplasmic vesicles. Cell Biol Int 2002;26:791–799.

    Article  PubMed  CAS  Google Scholar 

  38. Orci L, Ravazzola M, Volchuk A, et al. Anterograde flow of cargo across the Golgi stack potentially mediated via bidirectional “percolating” COPI vesicles. Proc Natl Acad Sci USA 2000;97:10400–10405

    Article  PubMed  CAS  Google Scholar 

  39. Axelrod D, Koppel DE, Schlessinger J, et al. Mobility measurement by analysis of fluorescence photobleaching recovery kinetics. Biophys J 1976;16:1055–1069.

    Article  PubMed  CAS  Google Scholar 

  40. Verkman AS. Solute and macromolecule diffusion in cellular aqueous compartments. Trends Biochem Sci 2002;27:27–33

    Article  PubMed  CAS  Google Scholar 

  41. Halford SE, Marco JF. How do site-specific DNA-binding proteins find their targets? Nucleic Acid Res 2004;32:3040–3052.

    Article  PubMed  CAS  Google Scholar 

  42. Kitano H, Funahashi A, Matsuoka Y, Oda K. The process diagram for graphical representation of biological networks. Nat Biotechnol 2005;23:961–966.

    Article  PubMed  CAS  Google Scholar 

  43. Hiroi N, Funahashi A, Kitano H. Kinetics for dimension restricted reactions. Submitted; 2005.

    Google Scholar 

  44. Hiroi N, Funahashi A, Kitano H. Two numerical model analysis for the movement of a restriction enzyme. Foundations of Systems Biology in Engineering (FOSBE 2005). Santa Barbara, CA, USA. August 2005.

    Google Scholar 

  45. Hiroi N, Funahashi A, Kitano H. Analysis for dimension restriction kinetics with bacterial endonuclease movement. The 2005 WSEAS International Conference on Cellular and Molecular Biology—Biophysics and Bioengineering. Athens, Greece. July 2005.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ERATO-SORST Kitano Symbiotic Systems Project, Japan Science and Technology Agency, Shibuya-ku, Tokyo, Japan

    Noriko Hiroi & Akira Funahashi

Authors
  1. Noriko Hiroi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Akira Funahashi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Biological Sciences, Ajou University, Suwon, Korea

    Sangdun Choi PhD

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Humana Press Inc.

About this chapter

Cite this chapter

Hiroi, N., Funahashi, A. (2007). Kinetics of Dimension-Restricted Conditions. In: Choi, S. (eds) Introduction to Systems Biology. Humana Press. https://doi.org/10.1007/978-1-59745-531-2_14

Download citation

Publish with us

Policies and ethics

Search

Navigation