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Biophysical Reviews

, Volume 11, Issue 6, pp 851–872 | Cite as

Understanding biochemical processes in the presence of sub-diffusive behavior of biomolecules in solution and living cells

  • Sujit BasakEmail author
  • Sombuddha Sengupta
  • Krishnananda Chattopadhyay
Review

Abstract

In order to maintain cellular function, biomolecules like protein, DNA, and RNAs have to diffuse to the target spaces within the cell. Changes in the cytosolic microenvironment or in the nucleus during the fulfillment of these cellular processes affect their mobility, folding, and stability thereby impacting the transient or stable interactions with their adjacent neighbors in the organized and dynamic cellular interior. Using classical Brownian motion to elucidate the diffusion behavior of these biomolecules is hard considering their complex nature. The understanding of biomolecular diffusion inside cells still remains elusive due to the lack of a proper model that can be extrapolated to these cases. In this review, we have comprehensively addressed the progresses in this field, laying emphasis on the different aspects of anomalous diffusion in the different biochemical reactions in cell interior. These experiment-based models help to explain the diffusion behavior of biomolecules in the cytosolic and nuclear microenvironment. Moreover, since understanding of biochemical reactions within living cellular system is our main focus, we coupled the experimental observations with the concept of sub-diffusion from in vitro to in vivo condition. We believe that the pairing between the understanding of complex behavior and structure-function paradigm of biological molecules would take us forward by one step in order to solve the puzzle around diseases caused by cellular dysfunction.

Keywords

Anomalous diffusion Macromolecular crowding Protein stability Conformational equilibria Protein–protein interaction Biological functions Gene expression 

Notes

Acknowledgments

We would like to thank members of Krish lab for their critical inputs and their help. KC thanks CSIR for the funding.

Compliance with ethical standards

Conflict of interest

Sujit Basak declares that he has no conflict of interest. Sombuddha Sengupta declares that he has no conflict of interest. Krishnananda Chattopadhyay declares that he has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Abad E, Yuste SB, Lindenberg K (2010) Reaction-subdiffusion and reaction-superdiffusion equations for evanescent particles performing continuous-time random walks. Phys Rev E Stat Nonlinear Soft Matter Phys.  https://doi.org/10.1103/PhysRevE.81.031115
  2. Aguzzi A, Calella AM (2009) Prions: protein aggregation and infectious diseases. Physiol Rev.  https://doi.org/10.1152/physrev.00006.2009 PubMedGoogle Scholar
  3. Akcasu AZ, Corngold N, Duderstadt JJ (1970) Theory of self-diffusion in classical fluids: the Van Hove self-correlation function Gs(r, t). Phys Fluids.  https://doi.org/10.1063/1.1693227 Google Scholar
  4. Alenghat FJ, Golan DE (2013) Membrane protein dynamics and functional implications in mammalian cells. Curr Top MembrGoogle Scholar
  5. Ando T, Skolnick J (2010) Crowding and hydrodynamic interactions likely dominate in vivo macromolecular motion. Proc Natl Acad Sci.  https://doi.org/10.1073/pnas.1011354107 Google Scholar
  6. Babu MM (2016) The contribution of intrinsically disordered regions to protein function, cellular complexity, and human disease. Biochem Soc Trans.  https://doi.org/10.1042/bst20160172 PubMedPubMedCentralGoogle Scholar
  7. Balbo J, Mereghetti P, Herten DP, Wade RC (2013) The shape of protein crowders is a major determinant of protein diffusion. Biophys J.  https://doi.org/10.1016/j.bpj.2013.02.041 PubMedPubMedCentralGoogle Scholar
  8. Banks DS, Fradin C (2005) Anomalous diffusion of proteins due to molecular crowding. Biophys J.  https://doi.org/10.1529/biophysj.104.051078 PubMedPubMedCentralGoogle Scholar
  9. Basak S, Chattopadhyay K (2013) Fluorescence correlation spectroscopy study on the effects of the shape and size of a protein on its diffusion inside a crowded environment. Langmuir.  https://doi.org/10.1021/la4031987 PubMedGoogle Scholar
  10. Basak S, Chattopadhyay K (2014) Studies of protein folding and dynamics using single molecule fluorescence spectroscopy. Phys Chem Chem PhysGoogle Scholar
  11. Berry H, Soula HA (2014) Spatial distributions at equilibrium under heterogeneous transient subdiffusion. Front Physiol.  https://doi.org/10.3389/fphys.2014.00437
  12. Best RB, Hummer G (2010) Coordinate-dependent diffusion in protein folding. Proc Natl Acad Sci.  https://doi.org/10.1073/pnas.0910390107 Google Scholar
  13. Bilsel O, Matthews CR (2000) Barriers in protein folding reactions. Adv Protein ChemGoogle Scholar
  14. Bouchaud JP, Georges A (1990) Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys RepGoogle Scholar
  15. Boyer D, Romo-Cruz JCR (2014) Solvable random-walk model with memory and its relations with Markovian models of anomalous diffusion. Phys Rev E Stat Nonlinear Soft Matter Phys.  https://doi.org/10.1103/PhysRevE.90.042136
  16. Bronshtein I, Kepten E, Kanter I et al (2015) Loss of lamin a function increases chromatin dynamics in the nuclear interior. Nat Commun.  https://doi.org/10.1038/ncomms9044
  17. Bu Z, Callaway DJE (2011) Proteins move! Protein dynamics and long-range allostery in cell signaling. Adv Protein Chem Struct BiolGoogle Scholar
  18. Chavent M, Duncan AL, Sansom MSP (2016) Molecular dynamics simulations of membrane proteins and their interactions: from nanoscale to mesoscale. Curr Opin Struct BiolGoogle Scholar
  19. Chechkin A V., Metzler R, Klafter J, Gonchar VY (2008) Introduction to the theory of Lévy flights. In: anomalous transport: foundations and applicationsGoogle Scholar
  20. Chechkin AV, Hofmann M, Sokolov IM (2009) Continuous-time random walk with correlated waiting times. Phys Rev E Stat Nonlinear Soft Matter Phys.  https://doi.org/10.1103/PhysRevE.80.031112
  21. Checkley S, Maccallum L, Yates J et al (2015) Bridging the gap between in vitro and in vivo: dose and schedule predictions for the ATR inhibitor AZD6738. Sci Rep.  https://doi.org/10.1038/srep13545
  22. Chen H, Larson DR (2016) What have single-molecule studies taught us about gene expression? Genes DevGoogle Scholar
  23. Chou T (2003) Ribosome recycling, diffusion, and mRNA loop formation in translational regulation. Biophys J.  https://doi.org/10.1016/S0006-3495(03)74518-4 PubMedPubMedCentralGoogle Scholar
  24. Conte E, Vincelli G, Schaaper RM et al (2012) Stabilization of the Escherichia coli DNA polymerase III ε subunit by the θ subunit favors in vivo assembly of the pol III catalytic core. Arch Biochem Biophys.  https://doi.org/10.1016/j.abb.2012.04.013 PubMedPubMedCentralGoogle Scholar
  25. Coquel AS, Jacob JP, Primet M et al (2013) Localization of protein aggregation in Escherichia coli is governed by diffusion and nucleoid macromolecular crowding effect. PLoS Comput Biol.  https://doi.org/10.1371/journal.pcbi.1003038 PubMedPubMedCentralGoogle Scholar
  26. Corrigan AM, Tunnacliffe E, Cannon D, Chubb JR (2016) A continuum model of transcriptional bursting. eLife.  https://doi.org/10.7554/elife.13051
  27. Cote Y, Senet P, Delarue P et al (2012) Anomalous diffusion and dynamical correlation between the side chains and the main chain of proteins in their native state. Proc Natl Acad Sci.  https://doi.org/10.1073/pnas.1207083109 Google Scholar
  28. Cottrell D, Swain PS, Tupper PF (2012) Stochastic branching-diffusion models for gene expression. Proc Natl Acad Sci.  https://doi.org/10.1073/pnas.1201103109 Google Scholar
  29. Dao Duc K, Song YS (2018) The impact of ribosomal interference, codon usage, and exit tunnel interactions on translation elongation rate variation. PLoS Genet.  https://doi.org/10.1371/journal.pgen.1007166 PubMedPubMedCentralGoogle Scholar
  30. Das A, Makarov DE (2018) Dynamics of disordered proteins under confinement: memory effects and internal friction. J Phys Chem BGoogle Scholar
  31. De Sancho D, Sirur A, Best RB (2014) Molecular origins of internal friction effects on protein-folding rates. Nat Commun.  https://doi.org/10.1038/ncomms5307
  32. Debye P (2011) Reaction rates in ionic solutions. Trans Electrochem Soc.  https://doi.org/10.1149/1.3071413 Google Scholar
  33. Deich J, Judd EM, McAdams HH, Moerner WE (2004) Visualization of the movement of single histidine kinase molecules in live Caulobacter cells. Proc Natl Acad Sci.  https://doi.org/10.1073/pnas.0404200101 Google Scholar
  34. Denisov S, Zaburdaev V, Hänggi P (2012) Lévy walks with velocity fluctuations. Phys Rev E Stat Nonlinear Soft Matter Phys.  https://doi.org/10.1103/PhysRevE.85.031148
  35. Dey P, Bhattacherjee A (2018) Role of macromolecular crowding on the intracellular diffusion of DNA binding proteins. Sci Rep.  https://doi.org/10.1038/s41598-017-18933-3
  36. Dieker AB, Mandjes M (2003) On spectral simulation of fractional brownian motion. Probab Eng Inf Sci.  https://doi.org/10.1017/s0269964803173081 Google Scholar
  37. Dill KA, Chan HS (1997) From levinthal to pathways to funnels. Nat Struct BiolGoogle Scholar
  38. Dix JA, Hom EFY, Verkman AS (2006) Fluorescence correlation spectroscopy simulations of photophysical phenomena and molecular interactions: a molecular dynamics/Monte Carlo approach. J Phys Chem B.  https://doi.org/10.1021/jp055840k PubMedPubMedCentralGoogle Scholar
  39. Domański J, Marrink SJ, Schäfer LV (2012) Transmembrane helices can induce domain formation in crowded model membranes. Biochim Biophys Acta Biomembr.  https://doi.org/10.1016/j.bbamem.2011.08.021 Google Scholar
  40. Ebbinghaus S, Gruebele M (2011) Protein folding landscapes in the living cell. J Phys Chem LettGoogle Scholar
  41. Einstein A (1956) Investigations on the theory of Brownian motionGoogle Scholar
  42. Einstein A (2005) Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen [AdP 17, 549 (1905)]. Ann Phys.  https://doi.org/10.1002/andp.200590005 Google Scholar
  43. Elf J, Li GW, Xie XS (2007) Probing transcription factor dynamics at the single-molecule level in a living cell. Science.  https://doi.org/10.1126/science.1141967 PubMedPubMedCentralGoogle Scholar
  44. Ellery AJ, Baker RE, Simpson MJ (2016) Communication: distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice. J Chem Phys.  https://doi.org/10.1063/1.4948782 PubMedGoogle Scholar
  45. Ellis RJ (2003) Protein folding: importance of the Anfinsen cage. Curr BiolGoogle Scholar
  46. Engler AJ, Humbert PO, Wehrle-Haller B, Weaver VM (2009) Multiscale modeling of form and function. ScienceGoogle Scholar
  47. Esadze A, Stivers JT (2018) Facilitated diffusion mechanisms in DNA base excision repair and transcriptional activation. Chem RevGoogle Scholar
  48. Fan Y, Gao JH (2015) Fractional motion model for characterization of anomalous diffusion from NMR signals. Phys Rev E Stat Nonlinear Soft Matter Phys.  https://doi.org/10.1103/PhysRevE.92.012707
  49. Favard C (2018) Numerical simulation and FRAP experiments show that the plasma membrane binding protein PH-EFA6 does not exhibit anomalous subdiffusion in cells. Biomolecules.  https://doi.org/10.3390/biom8030090 PubMedCentralGoogle Scholar
  50. Fazal FM, Meng CA, Murakami K et al (2015) Real-time observation of the initiation of RNA polymerase II transcription. Nature.  https://doi.org/10.1038/nature14882 PubMedPubMedCentralGoogle Scholar
  51. Feig M, Yu I, Wang P-H et al (2017) Crowding in cellular environments at an atomistic level from computer simulations. J Phys Chem B 121:8009–8025.  https://doi.org/10.1021/acs.jpcb.7b03570 CrossRefPubMedPubMedCentralGoogle Scholar
  52. Felderhof BU (1990) Dynamics of hard sphere suspensions. Phys A: Stat Mech Appl.  https://doi.org/10.1016/0378-4371(90)90213-C Google Scholar
  53. Fierz B, Kiefhaber T (2007) End-to-end vs interior loop formation kinetics in unfolded polypeptide chains. J Am Chem Soc.  https://doi.org/10.1021/ja0666396 PubMedGoogle Scholar
  54. Flory PJ (1953) Principles of polymer chemistry. Cornell University Press, IthacaGoogle Scholar
  55. Friedel M, Baumketner A, Shea J-E (2006) Effects of surface tethering on protein folding mechanisms. Proc Natl Acad Sci.  https://doi.org/10.1073/pnas.0601210103 Google Scholar
  56. Friedman N, Cai L, Xie XS (2006) Linking stochastic dynamics to population distribution: an analytical framework of gene expression. Phys Rev Lett.  https://doi.org/10.1103/PhysRevLett.97.168302
  57. Fulton TB (2011) Diffusion and transport across cell membranes. Cell.  https://doi.org/10.1016/B978-0-12-664660-3.50009-0 Google Scholar
  58. Gershenson A (2014) Deciphering protein stability in cells. J Mol BiolGoogle Scholar
  59. Ghosh SK, Cherstvy AG, Grebenkov DS, Metzler R (2016) Anomalous, non-Gaussian tracer diffusion in crowded two-dimensional environments. New J Phys.  https://doi.org/10.1088/1367-2630/18/1/013027 Google Scholar
  60. Goiko M, De Bruyn JR, Heit B (2016) Short-lived cages restrict protein diffusion in the plasma membrane. Sci Rep.  https://doi.org/10.1038/srep34987
  61. Golding I, Cox EC (2006) Physical nature of bacterial cytoplasm. Phys Rev Lett.  https://doi.org/10.1103/PhysRevLett.96.098102
  62. Guigas G, Weiss M (2008) Sampling the cell with anomalous diffusion—the discovery of slowness. Biophys J.  https://doi.org/10.1529/biophysj.107.117044 PubMedGoogle Scholar
  63. Hagen SJ (2010) Solvent viscosity and friction in protein folding dynamics. Curr Protein Pept Sci.  https://doi.org/10.2174/1389210204267332037 Google Scholar
  64. Hänggi P, Talkner P, Borkovec M (1990) Reaction-rate theory: fifty years after Kramers. Rev Mod Phys.  https://doi.org/10.1103/RevModPhys.62.251 Google Scholar
  65. Harada R, Tochio N, Kigawa T et al (2013) Reduced native state stability in crowded cellular environment due to protein-protein interactions. J Am Chem Soc.  https://doi.org/10.1021/ja3126992 PubMedPubMedCentralGoogle Scholar
  66. Höfling F, Franosch T (2013) Anomalous transport in the crowded world of biological cells. Rep Prog Phys.  https://doi.org/10.1088/0034-4885/76/4/046602 PubMedGoogle Scholar
  67. Höfling F, Franosch T, Frey E (2006) Localization transition of the three-dimensional lorentz model and continuum percolation. Phys Rev Lett.  https://doi.org/10.1103/PhysRevLett.96.165901
  68. Hoskins AA, Friedman LJ, Gallagher SS et al (2011) Ordered and dynamic assembly of single spliceosomes. Science.  https://doi.org/10.1126/science.1198830 PubMedPubMedCentralGoogle Scholar
  69. Hou R, Cherstvy AG, Metzler R, Akimoto T (2018) Biased continuous-time random walks for ordinary and equilibrium cases: facilitation of diffusion, ergodicity breaking and ageing. Phys Chem Chem Phys 20:20827–20848.  https://doi.org/10.1039/C8CP01863D CrossRefPubMedGoogle Scholar
  70. Jagannathan B, Marqusee S (2013) Protein folding and unfolding under force. BiopolymersGoogle Scholar
  71. Jeon JH, Monne HMS, Javanainen M, Metzler R (2012) Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins. Phys Rev Lett.  https://doi.org/10.1103/PhysRevLett.109.188103
  72. Jin S, Haggie PM, Verkman AS (2007) Single-particle tracking of membrane protein diffusion in a potential: simulation, detection, and application to confined diffusion of CFTR Cl—channels. Biophys J.  https://doi.org/10.1529/biophysj.106.102244 PubMedPubMedCentralGoogle Scholar
  73. Jucker M, Walker LC (2013) Self-propagation of pathogenic protein aggregates in neurodegenerative diseases. NatureGoogle Scholar
  74. Jülicher F, Bruinsma R (1998) Motion of RNA polymerase along DNA: a stochastic model. Biophys J.  https://doi.org/10.1016/S0006-3495(98)77833-6 PubMedPubMedCentralGoogle Scholar
  75. Kapanidis AN, Uphoff S, Stracy M (2018) Understanding protein mobility in Bacteria by tracking single molecules. J Mol BiolGoogle Scholar
  76. Katz ZB, English BP, Lionnet T et al (2016) Mapping translation ‘hot-spots’ in live cells by tracking single molecules of mRNA and ribosomes. eLife.  https://doi.org/10.7554/eLife.10415.001
  77. Kholodenko AL, Douglas JF (1995) Generalized stokes-Einstein equation for spherical particle suspensions. Phys Rev E.  https://doi.org/10.1103/PhysRevE.51.1081 Google Scholar
  78. Klumpp S, Scott M, Pedersen S, Hwa T (2013) Molecular crowding limits translation and cell growth. Proc Natl Acad Sci.  https://doi.org/10.1073/pnas.1310377110 Google Scholar
  79. Kubo R (1966) The fluctuation-dissipation theorem. Rep Prog Phys.  https://doi.org/10.1088/0034-4885/29/1/306 Google Scholar
  80. Kühn T, Ihalainen TO, Hyväluoma J et al (2011) Protein diffusion in mammalian cell cytoplasm. PLoS One 6:e22962–e22962.  https://doi.org/10.1371/journal.pone.0022962 CrossRefPubMedPubMedCentralGoogle Scholar
  81. Kyoung M, Sheets ED (2008) Vesicle diffusion close to a membrane: intermembrane interactions measured with fluorescence correlation spectroscopy. Biophys J.  https://doi.org/10.1529/biophysj.108.128934 PubMedPubMedCentralGoogle Scholar
  82. Lampo TJ, Stylianidou S, Backlund MP et al (2017) Cytoplasmic RNA-protein particles exhibit non-Gaussian subdiffusive behavior. Biophys J.  https://doi.org/10.1016/j.bpj.2016.11.3208 PubMedPubMedCentralGoogle Scholar
  83. Langevin P (1908) Sur la théorie du mouvement brownien. C R Acad Sci.  https://doi.org/10.1119/1.18725 Google Scholar
  84. Lapidus LJ, Steinbach PJ, Eaton WA et al (2002) Effects of chain stiffness on the dynamics of loop formation in polypeptides. Appendix: testing a 1-dimensional diffusion model for peptide dynamics. J Phys Chem B.  https://doi.org/10.1021/jp020829v Google Scholar
  85. Le Vot F, Abad E, Yuste SB (2017) Continuous-time random-walk model for anomalous diffusion in expanding media. Phys Rev E 96:32117.  https://doi.org/10.1103/PhysRevE.96.032117 CrossRefGoogle Scholar
  86. Levine B, Kroemer G (2008) Autophagy in the pathogenesis of disease. Cell.  https://doi.org/10.1016/j.cell.2007.12.018 PubMedPubMedCentralGoogle Scholar
  87. Levsky JM, Shenoy SM, Pezo RC, Singer RH (2002) Single-cell gene expression profiling. Science 297:836 LP–836840.  https://doi.org/10.1126/science.1072241 CrossRefGoogle Scholar
  88. Lippincott-Schwartz J, Snapp E, Kenworthy A. (2001) Studying protein dynamics in living cells. Macmillan Magazines LtdGoogle Scholar
  89. Liu Z, Tjian R (2018) Visualizing transcription factor dynamics in living cells. J Cell BiolGoogle Scholar
  90. Luby-Phelps K (2013) The physical chemistry of cytoplasm and its influence on cell function: an update. Mol Biol Cell.  https://doi.org/10.1091/mbc.e12-08-0617 PubMedPubMedCentralGoogle Scholar
  91. Luchko Y (2012) Anomalous diffusion: models, their analysis, and interpretation. Adv Appl AnalGoogle Scholar
  92. Macháň R, Hof M (2010) Lipid diffusion in planar membranes investigated by fluorescence correlation spectroscopy. Biochim Biophys Acta BiomembrGoogle Scholar
  93. Malchus N, Weiss M (2010) Anomalous diffusion reports on the interaction of misfolded proteins with the quality control machinery in the endoplasmic reticulum. Biophys J.  https://doi.org/10.1016/j.bpj.2010.06.020 PubMedPubMedCentralGoogle Scholar
  94. Mandelbrot BB, Van Ness JW (2005) Fractional Brownian motions, Fractional Noises and Applications. SIAM Rev.  https://doi.org/10.1137/1010093 Google Scholar
  95. Matsuda H, Putzel GG, Backman V, Szleifer I (2014) Macromolecular crowding as a regulator of gene transcription. Biophys J.  https://doi.org/10.1016/j.bpj.2014.02.019 PubMedPubMedCentralGoogle Scholar
  96. McGuffee SR, Elcock AH (2010) Diffusion, crowding & protein stability in a dynamic molecular model of the bacterial cytoplasm. PLoS Comput Biol.  https://doi.org/10.1371/journal.pcbi.1000694 PubMedPubMedCentralGoogle Scholar
  97. Metzler R, Jeon JH, Cherstvy AG, Barkai E (2014) Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking. Phys Chem Chem Phys.  https://doi.org/10.1039/c4cp03465a PubMedGoogle Scholar
  98. Metzler R, Jeon JH, Cherstvy AG (2016) Non-Brownian diffusion in lipid membranes: experiments and simulations. Biochim Biophys Acta BiomembrGoogle Scholar
  99. Minton AP (2015) How can biochemical reactions within cells differ from those in test tubes? J Cell Sci.  https://doi.org/10.1242/jcs.170183 PubMedGoogle Scholar
  100. Montroll EW, Weiss GH (1965) Random walks on lattices. II. J Math Phys.  https://doi.org/10.1063/1.1704269 Google Scholar
  101. Morelli MJ, Allen RJ, Rein Ten Wolde P (2011) Effects of macromolecular crowding on genetic networks. Biophys J.  https://doi.org/10.1016/j.bpj.2011.10.053 PubMedPubMedCentralGoogle Scholar
  102. Morrison JL, Breitling R, Higham DJ, Gilbert DR (2006) A lock-and-key model for protein-protein interactions. Bioinformatics.  https://doi.org/10.1093/bioinformatics/btl338 PubMedGoogle Scholar
  103. Mörters P, Peres Y, Schramm O, Werner W (2010) Brownian motionGoogle Scholar
  104. Mueller V, Ringemann C, Honigmann A et al (2011) STED nanoscopy reveals molecular details of cholesterol- and cytoskeleton-modulated lipid interactions in living cells. Biophys J.  https://doi.org/10.1016/j.bpj.2011.09.006 PubMedPubMedCentralGoogle Scholar
  105. Naganathan AN, Doshi U, Fung A, et al (2006) Dynamics, energetics, and structure in protein folding. BiochemistryGoogle Scholar
  106. Netz PA, Dorfmüller T (1995) Computer simulation studies of anomalous diffusion in gels: structural properties and probe-size dependence. J Chem Phys.  https://doi.org/10.1063/1.470018 Google Scholar
  107. Nixon GI, Slater GW (1999) Relaxation length of a polymer chain in a quenched disordered medium. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics.  https://doi.org/10.1103/PhysRevE.60.3170 Google Scholar
  108. Noguchi H, Gompper G (2006) Meshless membrane model based on the moving least-squares method. Phys Rev E Stat Nonlinear Soft Matter Phys.  https://doi.org/10.1103/PhysRevE.73.021903
  109. Notelaers K, Rocha S, Paesen R et al (2014) Analysis of α3 GlyR single particle tracking in the cell membrane. Biochim Biophys Acta, Mol Cell Res.  https://doi.org/10.1016/j.bbamcr.2013.11.019 Google Scholar
  110. Onuchic JN, Luthey-Schulten Z, Wolynes PG (1997) THEORY OF PROTEIN FOLDING: the energy landscape perspective. Annu Rev Phys Chem 48:545–600.  https://doi.org/10.1146/annurev.physchem.48.1.545 CrossRefPubMedGoogle Scholar
  111. Paul SS, Sil P, Chakraborty R et al (2016) Molecular crowding affects the conformational fluctuations, peroxidase activity, and folding landscape of yeast cytochrome c. Biochemistry.  https://doi.org/10.1021/acs.biochem.6b00053 PubMedGoogle Scholar
  112. Pauwels K, Lebrun P, Tompa P (2017) To be disordered or not to be disordered: is that still a question for proteins in the cell? Cell Mol Life SciGoogle Scholar
  113. Perrin J (1909) Mouvement brownien et realité moléculaire. Ann Chim PhysGoogle Scholar
  114. Phillip Y, Schreiber G (2013) Formation of protein complexes in crowded environments-from in vitro to in vivo. FEBS LettGoogle Scholar
  115. Phillip Y, Sherman E, Haran G, Schreiber G (2009) Common crowding agents have only a small effect on protein-protein interactions. Biophys J.  https://doi.org/10.1016/j.bpj.2009.05.026 PubMedPubMedCentralGoogle Scholar
  116. Phillip Y, Kiss V, Schreiber G (2012) Protein-binding dynamics imaged in a living cell. Proc Natl Acad Sci U S A.  https://doi.org/10.1073/pnas.1112171109 Google Scholar
  117. Politz JC, Browne ES, Wolf DE, Pederson T (2002) Intranuclear diffusion and hybridization state of oligonucleotides measured by fluorescence correlation spectroscopy in living cells. Proc Natl Acad Sci.  https://doi.org/10.1073/pnas.95.11.6043 Google Scholar
  118. Pollak E, Talkner P (2005) Reaction rate theory: what it was, where is it today, and where is it going? Chaos.  https://doi.org/10.1063/1.1858782 Google Scholar
  119. Prabakaran S, Lippens G, Steen H, Gunawardena J (2012) Post-translational modification: Nature’s escape from genetic imprisonment and the basis for dynamic information encoding. Wiley Interdiscip Rev Syst Biol MedGoogle Scholar
  120. Prabhakar A, Puglisi EV, Puglisi JD (2019) Single-molecule fluorescence applied to translation. Cold Spring Harb Perspect Biol.  https://doi.org/10.1101/cshperspect.a032714 Google Scholar
  121. Raj A, van Oudenaarden A (2009) Single-molecule approaches to stochastic gene expression. Annu Rev Biophys.  https://doi.org/10.1146/annurev.biophys.37.032807.125928 PubMedPubMedCentralGoogle Scholar
  122. Ramadurai S, Holt A, Schäfer LV et al (2010) Influence of hydrophobic mismatch and amino acid composition on the lateral diffusion of transmembrane peptides. Biophys J.  https://doi.org/10.1016/j.bpj.2010.05.042 PubMedPubMedCentralGoogle Scholar
  123. Ramakrishnan V (2002) Ribosome structure and the mechanism of translation. CellGoogle Scholar
  124. Reverey JF, Jeon JH, Bao H et al (2015) Superdiffusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic Acanthamoeba castellanii. Sci Rep.  https://doi.org/10.1038/srep11690
  125. Rieckh G, Tkačik G (2014) Noise and information transmission in promoters with multiple internal states. Biophys J.  https://doi.org/10.1016/j.bpj.2014.01.014 PubMedPubMedCentralGoogle Scholar
  126. Ritz JB, Caltagirone JP (1999) A numerical continuous model for the hydrodynamics of fluid particle systems. Int J Numer Methods Fluids.  https://doi.org/10.1002/(SICI)1097-0363(19990830)30:8<1067::AID-FLD881>3.0.CO;2-6
  127. Roosen-Runge F, Hennig M, Zhang F et al (2011) Protein self-diffusion in crowded solutions. Proc Natl Acad Sci.  https://doi.org/10.1073/pnas.1107287108 Google Scholar
  128. Sabelko J, Ervin J, Gruebele M (2002) Observation of strange kinetics in protein folding. Proc Natl Acad Sci.  https://doi.org/10.1073/pnas.96.11.6031 Google Scholar
  129. Saenko VV (2016) The influence of the finite velocity on spatial distribution of particles in the frame of Levy walk model. Phys A: Stat Mech Appl.  https://doi.org/10.1016/j.physa.2015.10.046 Google Scholar
  130. Saffman PG, Delbrück M (1975) Brownian motion in biological membranes. Proc Natl Acad Sci U S AGoogle Scholar
  131. Samiotakis A, Wittung-Stafshede P, Cheung MS (2009) Folding, stability and shape of proteins in crowded environments: experimental and computational approaches. Int J Mol SciGoogle Scholar
  132. Sandev T, Metzler R, Tomovski Ž (2014) Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise. J Math Phys.  https://doi.org/10.1063/1.4863478 Google Scholar
  133. Satija R, Das A, Makarov DE (2017) Transition path times reveal memory effects and anomalous diffusion in the dynamics of protein folding. J Chem Phys.  https://doi.org/10.1063/1.4993228 PubMedGoogle Scholar
  134. Saxton MJ (1994) Anomalous diffusion due to obstacles: a Monte Carlo study. Biophys JGoogle Scholar
  135. Schurgers E, Kelchtermans H, Mitera T et al (2010) Discrepancy between the in vitro and in vivo effects of murine mesenchymal stem cells on T-cell proliferation and collagen-induced arthritis. Arthritis Res Ther.  https://doi.org/10.1186/ar2939 Google Scholar
  136. Schwarzl M, Godec A, Metzler R (2017) Quantifying non-ergodicity of anomalous diffusion with higher order moments. Sci Rep.  https://doi.org/10.1038/s41598-017-03712-x
  137. Schwille P, Korlach J, Webb WW (1999) Fluorescence correlation spectroscopy with single-molecule sensitivity on cell and model membranes. Cytometry.  https://doi.org/10.1002/(SICI)1097-0320(19990701)36:3<176::AID-CYTO5>3.0.CO;2-F
  138. Seisenberger G, Ried MU, Endreß T et al (2001) Real-time single-molecule imaging of the infection pathway of anadeno-associated virus. Science.  https://doi.org/10.1126/science.1064103 PubMedGoogle Scholar
  139. Semenov AN, Meyer H (2013) Anomalous diffusion in polymer monolayers. Soft Matter 9:4249–4272.  https://doi.org/10.1039/C3SM27839E CrossRefGoogle Scholar
  140. Seu KJ, Cambrea LR, Everly RM, Hovis JS (2006) Influence of lipid chemistry on membrane fluidity: tail and headgroup interactions. Biophys J.  https://doi.org/10.1529/biophysj.106.084590 PubMedPubMedCentralGoogle Scholar
  141. Shin Y, Brangwynne CP (2017) Liquid phase condensation in cell physiology and disease. ScienceGoogle Scholar
  142. Shinkai S, Nozaki T, Maeshima K, Togashi Y (2016) Dynamic nucleosome movement provides structural information of topological chromatin domains in living human cells. PLoS Comput Biol.  https://doi.org/10.1371/journal.pcbi.1005136 PubMedPubMedCentralGoogle Scholar
  143. Slater GW, Yan Wu S (1995) Reptation, entropic trapping, percolation, and rouse dynamics of polymers in “random” environments. Phys Rev Lett.  https://doi.org/10.1103/PhysRevLett.75.164 PubMedGoogle Scholar
  144. Smoluchowski Mv (1907) Zur kinetischen Theorie der Brown’schen Molekularbewegungen und der Suspensionen. W. Zeitschr f Chem und Ind der Kolloide.  https://doi.org/10.1007/bf01813736 Google Scholar
  145. Smoluchowski M (2017) Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen. Z Phys Chem.  https://doi.org/10.1515/zpch-1918-9209
  146. Sokolov IM (2012) Models of anomalous diffusion in crowded environments. Soft MatterGoogle Scholar
  147. Soranno A, Koenig I, Borgia MB et al (2014) Single-molecule spectroscopy reveals polymer effects of disordered proteins in crowded environments. Proc Natl Acad Sci.  https://doi.org/10.1073/pnas.1322611111 Google Scholar
  148. Spiess C, Meyer AS, Reissmann S, Frydman J (2004) Mechanism of the eukaryotic chaperonin: protein folding in the chamber of secrets. Trends Cell BiolGoogle Scholar
  149. Sung BJ, Yethiraj A (2006) Lateral diffusion and percolation in membranes. Phys Rev Lett.  https://doi.org/10.1103/PhysRevLett.96.228103
  150. Sung BJ, Yethiraj A (2008) Lateral diffusion of proteins in the plasma membrane: spatial tessellation and percolation theory. J Phys Chem B.  https://doi.org/10.1021/jp0772068 PubMedGoogle Scholar
  151. Tabatabaei F, Lenz O, Holm C (2011) Simulational study of anomalous tracer diffusion in hydrogels. Colloid Polym Sci.  https://doi.org/10.1007/s00396-011-2393-0 Google Scholar
  152. Taloni A, Chechkin A, Klafter J (2010) Generalized elastic model yields a fractional langevin equation description. Phys Rev Lett.  https://doi.org/10.1103/PhysRevLett.104.160602
  153. Tanner NA, van Oijen AM (2010) Visualizing DNA replication at the single-molecule level. Methods EnzymolGoogle Scholar
  154. Ten Wolde PR, Mugler A (2014) Importance of crowding in signaling, genetic, and metabolic networks. Int Rev Cell Mol BiolGoogle Scholar
  155. Theillet F-X, Binolfi A, Frembgen-Kesner T et al (2014) Physicochemical properties of cells and their effects on intrinsically disordered proteins (IDPs). Chem Rev.  https://doi.org/10.1021/cr400695p PubMedPubMedCentralGoogle Scholar
  156. Trimble WS, Grinstein S (2015) Barriers to the free diffusion of proteins and lipids in the plasma membrane. J Cell BiolGoogle Scholar
  157. Trovato F, Tozzini V (2014) Diffusion within the cytoplasm: a mesoscale model of interacting macromolecules. Biophys J.  https://doi.org/10.1016/j.bpj.2014.09.043 PubMedPubMedCentralGoogle Scholar
  158. Uphoff S, Reyes-Lamothe R, Garza de Leon F et al (2013) Single-molecule DNA repair in live bacteria. Proc Natl Acad Sci.  https://doi.org/10.1073/pnas.1301804110 Google Scholar
  159. Valastyan S, Weinberg RA (2011) Tumor metastasis: molecular insights and evolving paradigms. Cell.  https://doi.org/10.1016/j.cell.2011.09.024 PubMedPubMedCentralGoogle Scholar
  160. Venters BJ, Pugh BF (2009) How eukaryotic genes are transcribed. Crit Rev Biochem Mol Biol.  https://doi.org/10.1080/10409230902858785 PubMedPubMedCentralGoogle Scholar
  161. Vilar JMG, Saiz L (2013) Systems biophysics of gene expression. Biophys JGoogle Scholar
  162. Vitali S, Sposini V, Sliusarenko O et al (2018) Langevin equation in complex media and anomalous diffusion. J R Soc Interface.  https://doi.org/10.1098/rsif.2018.0282 PubMedCentralGoogle Scholar
  163. Wang W, Chen C (2016) Tracking translation of single mRNA molecule in live cells. Sci Bull.  https://doi.org/10.1007/s11434-016-1116-9 Google Scholar
  164. Wang Y, Benton LA, Singh V, Pielak GJ (2012a) Disordered protein diffusion under crowded conditions. J Phys Chem Lett.  https://doi.org/10.1021/jz3010915 PubMedPubMedCentralGoogle Scholar
  165. Wang Y, Sarkar M, Smith AE et al (2012b) Macromolecular crowding and protein stability. J Am Chem Soc.  https://doi.org/10.1021/ja305300m PubMedGoogle Scholar
  166. Wang Y, Liu J, Huang BO et al (2015) Mechanism of alternative splicing and its regulation. Biomed Rep.  https://doi.org/10.3892/br.2014.407 PubMedPubMedCentralGoogle Scholar
  167. Wang C, Han B, Zhou R, Zhuang X (2016a) Real-time imaging of translation on single mRNA transcripts in live cells. Cell.  https://doi.org/10.1016/j.cell.2016.04.040 PubMedPubMedCentralGoogle Scholar
  168. Wang H, La Russa M, Qi LS (2016b) CRISPR/Cas9 in genome editing and beyond. Annu Rev Biochem.  https://doi.org/10.1146/annurev-biochem-060815-014607 PubMedGoogle Scholar
  169. Weigel AV, Simon B, Tamkun MM, Krapf D (2011) Ergodic and nonergodic processes coexist in the plasma membrane as observed by single-molecule tracking. Proc Natl Acad Sci.  https://doi.org/10.1073/pnas.1016325108 Google Scholar
  170. Weiss M, Hashimoto H, Nilsson T (2003) Anomalous protein diffusion in living cells as seen by fluorescence correlation spectroscopy. Biophys J.  https://doi.org/10.1016/S0006-3495(03)75130-3 PubMedPubMedCentralGoogle Scholar
  171. Weiss M, Elsner M, Kartberg F, Nilsson T (2004) Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells. Biophys J.  https://doi.org/10.1529/biophysj.104.044263 PubMedPubMedCentralGoogle Scholar
  172. Wieczorek G, Zielenkiewicz P (2008) Influence of macromolecular crowding on protein-protein association rates—a Brownian dynamics study. Biophys J 95:5030–5036.  https://doi.org/10.1529/biophysj.108.136291 CrossRefPubMedPubMedCentralGoogle Scholar
  173. Wong E, Cuervo AM (2010) Autophagy gone awry in neurodegenerative diseases. Nat NeurosciGoogle Scholar
  174. Wyłomańska A, Kumar A, Połoczański R, Vellaisamy P (2016) Inverse Gaussian and its inverse process as the subordinators of fractional Brownian motion. Phys Rev E.  https://doi.org/10.1103/PhysRevE.94.042128
  175. Xu L, Luo J (2018) Stochastic differential equations driven by fractional Brownian motion. Statist Probab Lett.  https://doi.org/10.1016/j.spl.2018.06.012 Google Scholar
  176. Yamamoto E, Kalli AC, Akimoto T et al (2015) Anomalous dynamics of a lipid recognition protein on a membrane surface. Sci Rep.  https://doi.org/10.1038/srep18245
  177. Yamamoto E, Akimoto T, Kalli AC et al (2017) Dynamic interactions between a membrane binding protein and lipids induce fluctuating diffusivity. Sci Adv.  https://doi.org/10.1126/sciadv.1601871 PubMedPubMedCentralGoogle Scholar
  178. Yan X, Hoek TA, Vale RD, Tanenbaum ME (2016) Dynamics of translation of single mRNA molecules in vivo. Cell.  https://doi.org/10.1016/j.cell.2016.04.034 PubMedPubMedCentralGoogle Scholar
  179. Zaburdaev V, Denisov S, Klafter J (2015) Lévy walks. Rev Mod Phys.  https://doi.org/10.1103/RevModPhys.87.483 Google Scholar
  180. Zhang Z, Chan HS (2012) Transition paths, diffusive processes, and preequilibria of protein folding. Proc Natl Acad Sci.  https://doi.org/10.1073/pnas.1209891109 Google Scholar
  181. Zhao ZW, White MD, Alvarez YD et al (2017) Quantifying transcription factor-DNA binding in single cells in vivo with photoactivatable fluorescence correlation spectroscopy. Nat Protoc.  https://doi.org/10.1038/nprot.2017.051 PubMedGoogle Scholar
  182. Zhivotovsky B, Orrenius S (2010) Cell cycle and cell death in disease: past, present and future. J Intern MedGoogle Scholar
  183. Zhou HX (1993) Brownian dynamics study of the influences of electrostatic interaction and diffusion on protein-protein association kinetics. Biophys J 64:1711–1726.  https://doi.org/10.1016/S0006-3495(93)81543-1 CrossRefPubMedPubMedCentralGoogle Scholar
  184. Zhou HX (2004) Protein folding and binding in confined spaces and in crowded solutions. J Mol RecognGoogle Scholar
  185. Zhou YL, Liao JM, Chen J, Liang Y (2006) Macromolecular crowding enhances the binding of superoxide dismutase to xanthine oxidase: implications for protein-protein interactions in intracellular environments. Int J Biochem Cell Biol.  https://doi.org/10.1016/j.biocel.2006.05.012 Google Scholar
  186. Zhou H-X, Rivas G, Minton AP (2008) Macromolecular crowding and confinement: biochemical, biophysical, and potential physiological consequences. Annu Rev Biophys.  https://doi.org/10.1146/annurev.biophys.37.032807.125817 PubMedPubMedCentralGoogle Scholar
  187. Zimmerman SB, Minton AP (1993) Macromolecular crowding: biochemical, biophysical, and physiological consequences. Annu Rev Biophys Biomol Struct.  https://doi.org/10.1146/annurev.bb.22.060193.000331 PubMedGoogle Scholar
  188. Zumofen G, Klafter J, Blumen A (1983) Long-time behavior in diffusion and trapping. J Chem Phys 79:5131–5135.  https://doi.org/10.1063/1.445637 CrossRefGoogle Scholar
  189. Zwanzig R (1997) Two-state models of protein folding kinetics. Proc Natl Acad Sci U S AGoogle Scholar
  190. Zwanzig R (2004) Theoretical basis for the Rouse-Zimm model in polymer solution dynamics. J Chem Phys.  https://doi.org/10.1063/1.1681433 Google Scholar
  191. Zwanzig R (2012) Hydrodynamic fluctuations and Stokes’ law friction. Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics.  https://doi.org/10.6028/jres.068b.019 Google Scholar

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© International Union for Pure and Applied Biophysics (IUPAB) and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Biochemistry and Molecular PharmacologyUniversity of Massachusetts Medical SchoolWorcesterUSA
  2. 2.Protein Folding and Dynamics Lab, Structural Biology and Bioinformatics, CSIR-Indian Institute of Chemical Biology (CSIR-IICB)KolkataIndia

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