Skip to main content
Log in

Computational models of molecular self-organization in cellular environments

  • Original Paper
  • Published:
Cell Biochemistry and Biophysics Aims and scope Submit manuscript

Abstract

The cellular environment creates numerous obstacles to efficient chemistry, as molecular components must navigate through a complex, densely crowded, heterogeneous, and constantly changing landscape in order to function at the appropriate times and places. Such obstacles are especially challenging to self-organizing or self-assembling molecular systems, which often need to build large structures in confined environments and typically have high-order kinetics that should make them exquisitely sensitive to concentration gradients, stochastic noise, and other non-ideal reaction conditions. Yet cells nonetheless manage to maintain a finely tuned network of countless molecular assemblies constantly forming and dissolving with a robustness and efficiency generally beyond what human engineers currently can achieve under even carefully controlled conditions. Significant advances in high-throughput biochemistry and genetics have made it possible to identify many of the components and interactions of this network, but its scale and complexity will likely make it impossible to understand at a global, systems level without predictive computational models. It is thus necessary to develop a clear understanding of how the reality of cellular biochemistry differs from the ideal models classically assumed by simulation approaches and how simulation methods can be adapted to accurately reflect biochemistry in the cell, particularly for the self-organizing systems that are most sensitive to these factors. In this review, we present approaches that have been undertaken from the modeling perspective to address various ways in which self-organization in the cell differs from idealized models.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Adair, G. S. (1928). A theory of partial osmotic pressures and membrane equilibria, with special reference to the application of Dalton’s law to haemoglobin solutions in the presence of salts. Proceedings of the Royal Society of London Series A, 120, 573–603.

    Article  CAS  Google Scholar 

  2. Arkin, A., Ross, J., & McAdams, H. H. (1998). Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. Genetics, 149, 1633–48.

    PubMed  CAS  Google Scholar 

  3. Barocas, V. H., & Tranquillo, R. T. (1997a). An anisotropic biphasic theory of tissue-equivalent mechanics: The interplay among cell traction, fibrillar network deformation, fibril alignment, and cell contact guidance. Journal of Biomechanical Engineering-Transactions of the Asme, 119, 137–145.

    CAS  Google Scholar 

  4. Barocas, V. H., & Tranquillo, R. T. (1997b). A finite element solution for the anisotropic biphasic theory of tissue equivalent mechanics: The effect of contact guidance on isometric cell traction measurement. Journal of Biomechanical Engineering-Transactions of the Asme, 119, 261–268.

    CAS  Google Scholar 

  5. Bartol, T. M., & Stiles, J. R. (1997). MCell Quick Reference Guide: Version 1.21.

  6. Bartol, T. M., & Stiles, J. R. (1999). MCell Quick Reference Guide: Version 2.36.

  7. Bass, M. D., & Humphries, M. J. (2002). Cytoplasmic interactions of syndecan-4 orchestrate adhesion receptor and growth factor receptor signalling. TheBiochemical Journal, 368, 1–15.

    CAS  Google Scholar 

  8. Berg, O. G., Paulsson, J., & Ehrenberg, M. (2000). Fluctuations and quality of control in biological cells: zero-order ultrasensitivity reinvestigated. The Biophysical Journal, 79, 1228–36.

    CAS  Google Scholar 

  9. Bitan, G., et al. (2003). Amyloid beta -protein (Abeta) assembly: Abeta 40 and Abeta 42 oligomerize through distinct pathways. Proceedings of the National Academy of Science of the United States of America, 100, 330–5.

    Article  CAS  Google Scholar 

  10. Bookchin, R. M., Balazs, T., Wang, Z., Josephs, R., & Lew, V. L. (1999). Polymer structure and solubility of deoxyhemoglobin S in the presence of high concentrations of volume-excluding 70-kDa dextran. Effects of non-s hemoglobins and inhibitors. Journal of Biological Chemistry, 274, 6689–97.

    Article  PubMed  CAS  Google Scholar 

  11. Brion, J. P. (1992). The pathology of the neuronal cytoskeleton in Alzheimer’s disease. Biochimica et Biophysica Acta, 1160, 134–42.

    PubMed  CAS  Google Scholar 

  12. Brion, J. P. (1999). [Neurofibrillary tangles and early modification of the neuronal cytoskeleton in Alzheimer’s disease and in experimental models]. Bulletin et Memories de l’ Academie Royale de Medecine de Belgique, 154, 287–94.

    CAS  Google Scholar 

  13. Dallon, J. C., & Sherratt, J. A. (1998). A mathematical model for fibroblast and collagen orientation. Bulletin of Mathematical Biology, 60, 101–129.

    Article  PubMed  CAS  Google Scholar 

  14. Dallon, J. C., Sherratt, J. A., & Maini, P. K. (1999). Mathematical modelling of extracellular matrix dynamics using discrete cells: Fiber orientation and tissue regeneration. Journal of Theoretical Biology, 199, 449–471.

    Article  PubMed  CAS  Google Scholar 

  15. Dallon, J., Sherratt, J., Maini, P., & Ferguson, M. (2000a). Biological implications of a discrete mathematical model for collagen deposition and alignment in dermal wound repair. Ima Journal of Mathematics Applied in Medicine and Biology, 17, 379–393.

    Article  PubMed  CAS  Google Scholar 

  16. Dallon, J. C., & Sherratt, J. A. (2000b). A mathematical model for spatially varying extracellular matrix alignment. Siam Journal on Applied Mathematics, 61, 506–527.

    Article  CAS  Google Scholar 

  17. Denhez, F., et al. (2002). Syndesmos, a syndecan-4 cytoplasmic domain interactor, binds to the focal adhesion adaptor proteins paxillin and Hic-5. Journal of Biological Chemistry, 277, 12270–4.

    Article  PubMed  CAS  Google Scholar 

  18. Edelstein-Keshet, L. (1998). A mathematical approach to cytoskeletal assembly. European Biophysics Journal, 27, 521–31.

    Article  PubMed  CAS  Google Scholar 

  19. Eggers, D. K., & Valentine, J. S. (2001). Crowding and hydration effects on protein conformation: a study with sol-gel encapsulated proteins. Journal of Molecular Biology, 314, 911–22.

    Article  PubMed  CAS  Google Scholar 

  20. Ellis, R. J., & Minton, A. P. (2006). Protein aggregation in crowded environments. Biological Chemistry, 387, 485–97.

    Article  PubMed  CAS  Google Scholar 

  21. Franchini, K. G., Torsoni, A. S., Soares, P. H., & Saad, M. J. (2000). Early activation of the multicomponent signaling complex associated with focal adhesion kinase induced by pressure overload in the rat heart. Circulation Research, 87, 558–65.

    PubMed  CAS  Google Scholar 

  22. Fukae, M., & Mechanic, G. L. (1980). Maturation of collagenous tissue. Temporal sequence of formation of peptidyl lysine-derived cross-linking aldehydes and cross-links in collagen. Journal of Biological Chemistry, 255, 6511–8.

    PubMed  CAS  Google Scholar 

  23. GIllespie, D. (1975). Exact Method for Numerically Simulating Stochastic Coalescence Process in a Cloud. Journal of The Atmospheric Sciences, 32, 1977–1989.

    Article  Google Scholar 

  24. Gabdoulline, R. R., & Wade, R. C. (2002). Biomolecular diffusional association. Current Opinion in Structural Biology, 12, 204–13.

    Article  PubMed  CAS  Google Scholar 

  25. Galan, A., et al. (2001). Excluded volume effects on the refolding and assembly of an oligomeric protein. GroEL, a case study. Journal of Biological Chemistry, 276, 957–64.

    Article  PubMed  CAS  Google Scholar 

  26. Gibson, M., & Bruck, J. (2000). Efficient exact stochastic simulation of chemical systems with many species and many channels. Journal of Physical Chemistry A, 104, 1876–1889.

    Article  CAS  Google Scholar 

  27. Grima, R. & Schnell, S. (2006). A systematic investigation of the rate laws valid in intracellular environments. Biophysical Chemistry.

  28. Gross, S. P. (2004). Hither and yon: a review of bi-directional microtubule-based transport. Physical Biology, 1, R1–11.

    Article  PubMed  CAS  Google Scholar 

  29. Gupta, P., Hall, C. K., & Voegler, A. C. (1998). Effect of denaturant and protein concentrations upon protein refolding and aggregation: a simple lattice model. Protein Science, 7, 2642–52.

    PubMed  CAS  Google Scholar 

  30. Hall, D. (2002). On the role of the macromolecular phase transitions in biology in response to change in solution volume or macromolecular composition: action as an entropy buffer. Biophysical Chemistry, 98, 233–48.

    Article  PubMed  CAS  Google Scholar 

  31. Hancock, J. F. (2006). Lipid rafts: contentious only from simplistic standpoints. Nature Reviews in Molecular Cell Biology, 7, 456–62.

    Article  CAS  Google Scholar 

  32. Harrison, B., & Zimmerman, S. B. (1986). Stabilization of T4 polynucleotide kinase by macromolecular crowding. Nucleic Acids Research, 14, 1863–70.

    Article  PubMed  CAS  Google Scholar 

  33. Hill, T. L. (2002). Linear Aggregation Theory in Cell Biology. New York: Springer-Verlag.

    Google Scholar 

  34. Hlavacek, W. S., et al. (2006). Rules for Modeling Signal-Transduction Systems. Science STKE, 18, Pe18.

    Google Scholar 

  35. Istrail, S., Schwartz, R., & King, J. (1999). Lattice simulations of aggregation funnels for protein folding. Journal of Computational Biology, 6, 143–62.

    Article  PubMed  CAS  Google Scholar 

  36. Jamalyaria, F., Rohlfs, R., & Schwartz, R. (2005). Queue-based method for efficient simulation of biological self-assembly systems. Journal of Computational Physics, 204, 100–120.

    Article  Google Scholar 

  37. Janmey, P. A., et al. (1994). The mechanical properties of actin gels. Elastic modulus and filament motions. Journal of Biological Chemistry, 269, 32503–13.

    PubMed  CAS  Google Scholar 

  38. Kainov, D. E., Butcher, S. J., Bamford, D. H., & Tuma, R. (2003). Conserved intermediates on the assembly pathway of double-stranded RNA bacteriophages. Journal of Molecular Biology, 328, 791–804.

    Article  PubMed  CAS  Google Scholar 

  39. van Kampen, N. G. (1981). Stochastic Processes in Physics and Chemistry. New York: North-Holland Publishing Company.

    Google Scholar 

  40. Kidoaki, S., & Yoshikawa, K. (1999). Folding and unfolding of a giant duplex-DNA in a mixed solution with polycations, polyanions and crowding neutral polymers. Biophysical Chemistry, 76, 133–143.

    Article  PubMed  CAS  Google Scholar 

  41. Lee, V. M. (1995). Disruption of the cytoskeleton in Alzheimer’s disease. Current Opinion in Neurobiology, 5, 663–8.

    Article  PubMed  CAS  Google Scholar 

  42. Levenberg, K. (1944). A method for the solution of certain problems in least squares. The Quarterly of Applied Mathematics, 2, 164–168.

    Google Scholar 

  43. Lindner, R., & Ralston, G. (1995). Effects of dextran on the self-association of human spectrin. Biophysical Chemistry, 57, 15–25.

    Article  PubMed  CAS  Google Scholar 

  44. Lindner, R. A., & Ralston, G. B. (1997). Macromolecular crowding: effects on actin polymerisation. Biophysical Chemisttry, 66, 57–66.

    Article  CAS  Google Scholar 

  45. Liotta, L. A., Stracke, M. L., Aznavoorian, S. A., Beckner, M. E., & Schiffmann, E. (1991). Tumor cell motility. Semin Cancer Biol, 2, 111–4.

    PubMed  CAS  Google Scholar 

  46. Loew, L. M., & Schaff, J. C. (2001). The Virtual Cell: a software environment for computational cell biology. Trends in Biotechnology, 19, 401–406.

    Article  PubMed  CAS  Google Scholar 

  47. Loew, L. M. (2002). The virtual cell project. In Silico Simulation of Biological Processes, 247, 151–161.

    Article  Google Scholar 

  48. Lok, L., & Brent, R. (2005). Automatic generation of cellular reaction networks with Moleculizer 1.0. Nature Biotechnology, 23, 131–6.

    Article  PubMed  CAS  Google Scholar 

  49. Lopez de Heredia, M., & Jansen, R. P. (2004). mRNA localization and the cytoskeleton. Current Opinion in Cell Biology, 16, 80–5.

    Article  CAS  Google Scholar 

  50. MacKenna, D. A., Dolfi, F., Vuori, K., & Ruoslahti, E. (1998). Extracellular signal-regulated kinase and c-Jun NH2-terminal kinase activation by mechanical stretch is integrin-dependent and matrix-specific in rat cardiac fibroblasts. Journal of Clinical Investigation, 101, 301–10.

    PubMed  CAS  Google Scholar 

  51. Macek, M., Hurych, J., & Chvapil, M. (1967). The collagen protein formation in tissue cultures of human diploid strains. Cytologia (Tokyo), 32, 426–43.

    CAS  Google Scholar 

  52. Maini, P. K., Olsen, L., & Sherratt, J. A. (2002). Mathematical models for cell-matrix interactions during dermal wound healing. International Journal of Bifurcation and Chaos, 12, 2021–2029.

    Article  Google Scholar 

  53. Mallik, R., & Gross, S. P. (2004). Molecular motors: strategies to get along. Current Biology, 14, R971–82.

    Article  PubMed  CAS  Google Scholar 

  54. Maly, I. V., & Borisy, G. G. (2001). Self-organization of a propulsive actin network as an evolutionary process. Proceedings of the National Academy of Science of the United States of America, 98, 11324–9.

    Article  CAS  Google Scholar 

  55. Maly, I. V. (2002a). Diffusion approximation of the stochastic process of microtubule assembly. Bulletin of Mathematical Biology, 64, 213–38.

    Article  PubMed  CAS  Google Scholar 

  56. Maly, I. V., & Borisy, G. G. (2002b). Self-organization of treadmilling microtubules into a polar array. Trends in Cell Biology, 12, 462–5.

    Article  PubMed  CAS  Google Scholar 

  57. Maly, I. V., Lee, R. T., & Lauffenburger, D. A. (2004). A model for mechanotransduction in cardiac muscle: effects of extracellular matrix deformation on autocrine signaling. Annals of Biomedical Engineering, 32, 1319–35.

    Article  PubMed  Google Scholar 

  58. Marquardt, D. (1963). An algorithm for the least-squares estimation of non-linear parameters. SIAM Journal of Applied Maths, 11, 431–441.

    Article  Google Scholar 

  59. Matsumoto, K., Ziober, B. L., Yao, C. C., & Kramer, R. H. (1995). Growth factor regulation of integrin-mediated cell motility. Cancer Metastasis Reviews, 14, 205–17.

    Article  PubMed  CAS  Google Scholar 

  60. Mazzag, B., Tignanelli, C. J., & Smith, G. D. (2005). The effect of residual Ca2+ on the stochastic gating of Ca2+-regulated Ca2+ channel models. Journal of Theoretical Biology, 235, 121–50.

    Article  PubMed  CAS  Google Scholar 

  61. McAdams, H. H., & Arkin, A. (1999). It’s a noisy business! Genetic regulation at the nanomolar scale. Trends in Genetics, 15, 65–9.

    Article  PubMed  CAS  Google Scholar 

  62. Meisinger, J., et al. (1997). Protein phosphatase-2A association with microtubules and its role in restricting the invasiveness of human head and neck squamous cell carcinoma cells. Cancer Letters, 111, 87–95.

    Article  PubMed  CAS  Google Scholar 

  63. Minton, A. P. (1998). Molecular crowding: Analysis of effects of high concentrations of inert cosolutes on biochemical equilibria and rates in terms of volume exclusion. Energetics of Biological Macromolecules, Pt B, 295, 127–149.

    Article  CAS  Google Scholar 

  64. Minton, A. P. (2001). The influence of macromolecular crowding and macromolecular confinement on biochemical reactions in physiological media. Journal of Biological Chemistry, 276, 10577–80.

    Article  PubMed  CAS  Google Scholar 

  65. Minton, A. P. (2006). How can biochemical reactions within cells differ from those in test tubes? Journal of Cell Science, 119, 2863–9.

    Article  PubMed  CAS  Google Scholar 

  66. Mirny, L., & Shakhnovich, E. (2001). Protein folding theory: from lattice to all-atom models. Annual Reviews in Biophysical and Biomolecular Structure, 30, 361–96.

    Article  CAS  Google Scholar 

  67. Muramatsu, N., & Minton, A. P. (1988). Tracer diffusion of globular proteins in concentrated protein solutions. Proceedings of the National Academy of Science of the United States of America, 85, 2984–8.

    Article  CAS  Google Scholar 

  68. Nagai, T., et al. (1999). Beta3–integrin-mediated focal adhesion complex formation: adult cardiocytes embedded in three-dimensional polymer matrices. American Journal of Cardiology, 83, 38H–43H.

    Article  PubMed  CAS  Google Scholar 

  69. Nguyen, H. D., & Hall, C. K. (2002). Effect of rate of chemical or thermal renaturation on refolding and aggregation of a simple lattice protein. Biotechnology and Bioengineering, 80, 823–34.

    Article  PubMed  CAS  Google Scholar 

  70. Niu, S., Matsuda, T., & Oka, T. (1991). Control of cellular orientation in two-dimensional tissue formation. Surface topologic effect of collagen fibers on endothelialization. ASAIO Trans, 37, M441–2.

    PubMed  CAS  Google Scholar 

  71. Nossal, R. (1988). On the elasticity of cytoskeletal networks. The Biophysical Journal, 53, 349–59.

    CAS  Google Scholar 

  72. Ogston, A. et al. (1973). Transport of Compact Particles through Solutions of Chain-Polymers. Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 333, 297–316.

    Article  CAS  Google Scholar 

  73. Olsen, L., Sherratt, J. A., & Maini, P. K. (1995). A Mechanochemical Model for Adult Dermal Wound Contraction and the Permanence of the Contracted Tissue Displacement Profile. Journal of Theoretical Biology, 177, 113–128.

    Article  PubMed  CAS  Google Scholar 

  74. Olsen, L., Sherratt, J. A., & Maini, P. K. (1996). A mathematical model for fibro-proliferative wound healing disorders. Bulletin of Mathematical Biology, 58, 787–808.

    Article  PubMed  CAS  Google Scholar 

  75. Olsen, L., Maini, P., & Sherratt, J. (1997a). A mechanochemical model for normal and abnormal dermal wound repair. Nonlinear Analysis-Theory Methods & Applications, 30, 3333–3338.

    Article  Google Scholar 

  76. Olsen, L., Sherratt, J. A., Maini, P. K., & Arnold, F. (1997b). A mathematical model for the capillary endothelial cell-extracellular matrix interactions in wound-healing angiogenesis. Ima Journal of Mathematics Applied in Medicine and Biology, 14, 261–281.

    Article  PubMed  CAS  Google Scholar 

  77. Olsen, L., Maini, P. K., & Sherratt, J. A. (1998). Spatially varying equilibria of mechanical models: Application to dermal wound contraction. Mathematical Biosciences, 147, 113–129.

    Article  PubMed  CAS  Google Scholar 

  78. Olsen, L., Maini, P. K., Sherratt, J. A., & Dallon, J. (1999). Mathematical modelling of anisotropy in fibrous connective tissue. Mathematical Biosciences, 158, 145–170.

    Article  PubMed  CAS  Google Scholar 

  79. van Oudenaarden, A., & Theriot, J. A. (1999). Cooperative symmetry-breaking by actin polymerization in a model for cell motility. Nature Cell Biology, 1, 493–9.

    Article  PubMed  CAS  Google Scholar 

  80. Patro, S. Y., & Przybycien, T. M. (1994). Simulations of kinetically irreversible protein aggregate structure. The Biophysical Journal, 66, 1274–89.

    CAS  Google Scholar 

  81. Patro, S. Y., & Przybycien, T. M. (1996). Simulations of reversible protein aggregate and crystal structure. The Biophysical Journal, 70, 2888–902.

    CAS  Google Scholar 

  82. Paulsson, J. (2004). Summing up the noise in gene networks. Nature, 427, 415–8.

    Article  PubMed  CAS  Google Scholar 

  83. Plopper, G. E., McNamee, H. P., Dike, L. E., Bojanowski, K., & Ingber, D. E. (1995). Convergence of integrin and growth factor receptor signaling pathways within the focal adhesion complex. Molecular Biology of the Cell, 6, 1349–65.

    PubMed  CAS  Google Scholar 

  84. Prevelige, P. E., Jr., Thomas, D., & King, J. (1993). Nucleation and growth phases in the polymerization of coat and scaffolding subunits into icosahedral procapsid shells. The Biophysical Journal, 64, 824–35.

    CAS  Google Scholar 

  85. Puskar, K., Apelstein, L., Ta’asan, S., Schwartz, R., & LeDuc, P. (2004). Understanding Actin Organization in Cell Structure Through Lattice Based Monte Carlo Simulations. Mechanics and Chemistry of Biosystems, 1, 123–132.

    PubMed  Google Scholar 

  86. Puskar, K., Ta’asan, S., Schwartz, R., & LeDuc, P. (2006). Evaluating spatial contraints in cellular assembly processes using a Monte Carlo approach. Cell Biochemistry and Biophysics, 45, 195–201.

    Article  PubMed  CAS  Google Scholar 

  87. Rivas, G., & Minton, A. P. (1999a). Characterization of attractive and repulsive interactions between macromolecules via measurement of tracer sedimentation equilibrium. The Biophysical Journal, 76, A455–A455.

    Google Scholar 

  88. Rivas, G., Fernandez, J. A., & Minton, A. P. (1999b). Direct observation of the self-association of dilute proteins in the presence of inert macromolecules at high concentration via tracer sedimentation equilibrium: theory, experiment, and biological significance. Biochemistry, 38, 9379–88.

    Article  PubMed  CAS  Google Scholar 

  89. Rivas, G., Fernandez, J. A., & Minton, A. P. (2001). Direct observation of the enhancement of noncooperative protein self-assembly by macromolecular crowding: Indefinite linear self-association of bacterial cell division protein FtsZ. Proceedings of the National Academy of Sciences of the United States of America, 98, 3150–3155.

    Article  PubMed  CAS  Google Scholar 

  90. Roeder, B. A., Kokini, K., Sturgis, J. E., Robinson, J. P., & Voytik-Harbin, S. L. (2002). Tensile mechanical properties of three-dimensional type I collagen extracellular matrices with varied microstructure. Journal of Biomechanical Engineering, 124, 214–22.

    Article  PubMed  Google Scholar 

  91. Rosenfeld, N., Young, J. W., Alon, U., Swain, P. S., & Elowitz, M. B. (2005). Gene regulation at the single-cell level. Science, 307, 1962–5.

    Article  PubMed  CAS  Google Scholar 

  92. Saitoh, T., et al. (1992). Degradation of proteins in the membrane-cytoskeleton complex in Alzheimer’s disease. Might amyloidogenic APP processing be just the tip of the iceberg? Annals of the New York Academy of Sciences, 674, 180–92.

    Article  PubMed  CAS  Google Scholar 

  93. Sako, Y. (2006). Imaging single molecules in living cells for systems biology. Molecular Systems Biology, 2, 1–6.

    Article  Google Scholar 

  94. Schaff, J. C., Slepchenko, B., Moraru, I. I., Fortin, D., & Loew, L. M. (2002). The Virtual Cell project. Molecular Biology of the Cell, 13, 274a–274a.

    Google Scholar 

  95. Schlaepfer, D. D., Broome, M. A., & Hunter, T. (1997). Fibronectin-stimulated signaling from a focal adhesion kinase-c-Src complex: involvement of the Grb2, p130cas, and Nck adaptor proteins. Molecular Cell Biology, 17, 1702–13.

    CAS  Google Scholar 

  96. Sept, D., & McCammon, J. A. (2001). Thermodynamics and kinetics of actin filament nucleation. The Biophysical Journal, 81, 667–74.

    CAS  Google Scholar 

  97. Shea, J. E., & Brooks, C. L., (2001). 3rd. From folding theories to folding proteins: a review and assessment of simulation studies of protein folding and unfolding. Annual Reviews of Physical Chemistry, 52, 499–535.

    Article  CAS  Google Scholar 

  98. Sigmundsson, K., Masson, G., Rice, R., Beauchemin, N., & Obrink, B. (2002). Determination of active concentrations and association and dissociation rate constants of interacting biomolecules: an analytical solution to the theory for kinetic and mass transport limitations in biosensor technology and its experimental verification. Biochemistry, 41, 8263–76.

    Article  PubMed  CAS  Google Scholar 

  99. Smith, A. V., & Hall, C. K. (2001) Protein refolding versus aggregation: computer simulations on an intermediate-resolution protein model. Journal of Molecular Biology, 312, 187–202.

    Article  PubMed  CAS  Google Scholar 

  100. Smolle, J. (1992). [Biological basis of metastasis formation]. Hautarzt, 43, 55–64.

    PubMed  CAS  Google Scholar 

  101. St Johnston, D. (2005). Moving messages: the intracellular localization of mRNAs. Nature Reviews in Molecular Cell Biology, 6, 363–75.

    Article  CAS  Google Scholar 

  102. Takahashi, K., et al. (2003). E-Cell 2: multi-platform E-Cell simulation system. Bioinformatics, 19, 1727–9.

    Article  PubMed  CAS  Google Scholar 

  103. Taketomi, H., Ueda, Y., & Go, N. (1975). Studies on protein folding, unfolding and fluctuations by computer simulation. I. The effect of specific amino acid sequence represented by specific inter-unit interactions. International Journal of Peptide and Protein Research, 7, 445–59.

    Article  PubMed  CAS  Google Scholar 

  104. Terry, R. D. (1998). The cytoskeleton in Alzheimer disease. Journal of Neural Transmission Supplementum, 53, 141–5.

    PubMed  CAS  Google Scholar 

  105. Thattai, M., & van Oudenaarden, A. (2002). Attenuation of noise in ultrasensitive signaling cascades. The Biophysical Journal, 82, 2943–50.

    CAS  Google Scholar 

  106. Tomita, M., et al. (1999). E-CELL: software environment for whole-cell simulation. Bioinformatics, 15, 72–84.

    Article  PubMed  CAS  Google Scholar 

  107. Vadlamudi, R. K., Adam, L., Nguyen, D., Santos, M., & Kumar, R. (2002). Differential regulation of components of the focal adhesion complex by heregulin: role of phosphatase SHP-2. Journal of Cell Physiology, 190, 189–99.

    Article  CAS  Google Scholar 

  108. Wang, W., et al. (2002). Single cell behavior in metastatic primary mammary tumors correlated with gene expression patterns revealed by molecular profiling. Cancer Research, 62, 6278–88.

    PubMed  CAS  Google Scholar 

  109. Wilson, E., Sudhir, K., & Ives, H. E. (1995). Mechanical strain of rat vascular smooth muscle cells is sensed by specific extracellular matrix/integrin interactions. Journal of Clinical Investigation, 96, 2364–72.

    Article  PubMed  CAS  Google Scholar 

  110. Zaner, K. S. (1995). Physics of actin networks. I. Rheology of semi-dilute F-actin. The Biophysical Journal, 68, 1019–26.

    Article  CAS  Google Scholar 

  111. Zhang, T., Rohlfs, R., & Schwartz, R. (2005). in Winter Simulation Conference (ed. Kuhl, M. E., Steiger, N.M., Armstrong, F.B., and Joines, J.A.) 2223–2231 (Orlando, FL).

  112. Zhang, T., & Schwartz, R. (2006). Simulation study of the contribution of oligomer/oligomer binding to capsid assembly kinetics. The Biophysical Journal, 90, 57–64.

    Article  CAS  Google Scholar 

  113. Zimmerman, S. B., & Minton, A. P. (1993). Macromolecular Crowding - Biochemical, Biophysical, and Physiological Consequences. Annual Review of Biophysics and Biomolecular Structure, 22, 27–65.

    Article  PubMed  CAS  Google Scholar 

  114. van den Berg B., Wain R., Dobson C. M., & Ellis, R. J. (2000). Macromolecular crowding perturbs protein refolding kinetics: implications for folding inside the cell. The EMBO Journal, 19, 3870–3875.

    Google Scholar 

Download references

Acknowledgments

The authors would especially like to thank Ivan Maly at the University of Pittsburgh for helpful discussions and review of this manuscript. This work was supported in part by the National Science Foundation (CAREER, R.S., 0346981, and P.L., 0347191), National Academies Keck Foundation Futures Initiative, Pennsylvania Infrastructure Technology Alliance, the Department of Energy-Genome to Life, and the Beckman Young Investigators Award.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Philip LeDuc.

Rights and permissions

Reprints and permissions

About this article

Cite this article

LeDuc, P., Schwartz, R. Computational models of molecular self-organization in cellular environments. Cell Biochem Biophys 48, 16–31 (2007). https://doi.org/10.1007/s12013-007-0012-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12013-007-0012-y

Keywords

Navigation