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.
Similar content being viewed by others
References
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
Aguzzi A, Calella AM (2009) Prions: protein aggregation and infectious diseases. Physiol Rev. https://doi.org/10.1152/physrev.00006.2009
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
Alenghat FJ, Golan DE (2013) Membrane protein dynamics and functional implications in mammalian cells. Curr Top Membr
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
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
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
Banks DS, Fradin C (2005) Anomalous diffusion of proteins due to molecular crowding. Biophys J. https://doi.org/10.1529/biophysj.104.051078
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
Basak S, Chattopadhyay K (2014) Studies of protein folding and dynamics using single molecule fluorescence spectroscopy. Phys Chem Chem Phys
Berry H, Soula HA (2014) Spatial distributions at equilibrium under heterogeneous transient subdiffusion. Front Physiol. https://doi.org/10.3389/fphys.2014.00437
Best RB, Hummer G (2010) Coordinate-dependent diffusion in protein folding. Proc Natl Acad Sci. https://doi.org/10.1073/pnas.0910390107
Bilsel O, Matthews CR (2000) Barriers in protein folding reactions. Adv Protein Chem
Bouchaud JP, Georges A (1990) Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys Rep
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
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
Bu Z, Callaway DJE (2011) Proteins move! Protein dynamics and long-range allostery in cell signaling. Adv Protein Chem Struct Biol
Chavent M, Duncan AL, Sansom MSP (2016) Molecular dynamics simulations of membrane proteins and their interactions: from nanoscale to mesoscale. Curr Opin Struct Biol
Chechkin A V., Metzler R, Klafter J, Gonchar VY (2008) Introduction to the theory of Lévy flights. In: anomalous transport: foundations and applications
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
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
Chen H, Larson DR (2016) What have single-molecule studies taught us about gene expression? Genes Dev
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
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
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
Corrigan AM, Tunnacliffe E, Cannon D, Chubb JR (2016) A continuum model of transcriptional bursting. eLife. https://doi.org/10.7554/elife.13051
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
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
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
Das A, Makarov DE (2018) Dynamics of disordered proteins under confinement: memory effects and internal friction. J Phys Chem B
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
Debye P (2011) Reaction rates in ionic solutions. Trans Electrochem Soc. https://doi.org/10.1149/1.3071413
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
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
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
Dieker AB, Mandjes M (2003) On spectral simulation of fractional brownian motion. Probab Eng Inf Sci. https://doi.org/10.1017/s0269964803173081
Dill KA, Chan HS (1997) From levinthal to pathways to funnels. Nat Struct Biol
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
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
Ebbinghaus S, Gruebele M (2011) Protein folding landscapes in the living cell. J Phys Chem Lett
Einstein A (1956) Investigations on the theory of Brownian motion
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
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
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
Ellis RJ (2003) Protein folding: importance of the Anfinsen cage. Curr Biol
Engler AJ, Humbert PO, Wehrle-Haller B, Weaver VM (2009) Multiscale modeling of form and function. Science
Esadze A, Stivers JT (2018) Facilitated diffusion mechanisms in DNA base excision repair and transcriptional activation. Chem Rev
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
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
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
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
Felderhof BU (1990) Dynamics of hard sphere suspensions. Phys A: Stat Mech Appl. https://doi.org/10.1016/0378-4371(90)90213-C
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
Flory PJ (1953) Principles of polymer chemistry. Cornell University Press, Ithaca
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
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
Fulton TB (2011) Diffusion and transport across cell membranes. Cell. https://doi.org/10.1016/B978-0-12-664660-3.50009-0
Gershenson A (2014) Deciphering protein stability in cells. J Mol Biol
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
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
Golding I, Cox EC (2006) Physical nature of bacterial cytoplasm. Phys Rev Lett. https://doi.org/10.1103/PhysRevLett.96.098102
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
Hagen SJ (2010) Solvent viscosity and friction in protein folding dynamics. Curr Protein Pept Sci. https://doi.org/10.2174/1389210204267332037
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
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
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
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
Hoskins AA, Friedman LJ, Gallagher SS et al (2011) Ordered and dynamic assembly of single spliceosomes. Science. https://doi.org/10.1126/science.1198830
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
Jagannathan B, Marqusee S (2013) Protein folding and unfolding under force. Biopolymers
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
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
Jucker M, Walker LC (2013) Self-propagation of pathogenic protein aggregates in neurodegenerative diseases. Nature
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
Kapanidis AN, Uphoff S, Stracy M (2018) Understanding protein mobility in Bacteria by tracking single molecules. J Mol Biol
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
Kholodenko AL, Douglas JF (1995) Generalized stokes-Einstein equation for spherical particle suspensions. Phys Rev E. https://doi.org/10.1103/PhysRevE.51.1081
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
Kubo R (1966) The fluctuation-dissipation theorem. Rep Prog Phys. https://doi.org/10.1088/0034-4885/29/1/306
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
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
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
Langevin P (1908) Sur la théorie du mouvement brownien. C R Acad Sci. https://doi.org/10.1119/1.18725
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
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
Levine B, Kroemer G (2008) Autophagy in the pathogenesis of disease. Cell. https://doi.org/10.1016/j.cell.2007.12.018
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
Lippincott-Schwartz J, Snapp E, Kenworthy A. (2001) Studying protein dynamics in living cells. Macmillan Magazines Ltd
Liu Z, Tjian R (2018) Visualizing transcription factor dynamics in living cells. J Cell Biol
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
Luchko Y (2012) Anomalous diffusion: models, their analysis, and interpretation. Adv Appl Anal
Macháň R, Hof M (2010) Lipid diffusion in planar membranes investigated by fluorescence correlation spectroscopy. Biochim Biophys Acta Biomembr
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
Mandelbrot BB, Van Ness JW (2005) Fractional Brownian motions, Fractional Noises and Applications. SIAM Rev. https://doi.org/10.1137/1010093
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
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
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
Metzler R, Jeon JH, Cherstvy AG (2016) Non-Brownian diffusion in lipid membranes: experiments and simulations. Biochim Biophys Acta Biomembr
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
Montroll EW, Weiss GH (1965) Random walks on lattices. II. J Math Phys. https://doi.org/10.1063/1.1704269
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
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
Mörters P, Peres Y, Schramm O, Werner W (2010) Brownian motion
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
Naganathan AN, Doshi U, Fung A, et al (2006) Dynamics, energetics, and structure in protein folding. Biochemistry
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
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
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
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
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
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
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 Sci
Perrin J (1909) Mouvement brownien et realité moléculaire. Ann Chim Phys
Phillip Y, Schreiber G (2013) Formation of protein complexes in crowded environments-from in vitro to in vivo. FEBS Lett
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
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
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
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
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 Med
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
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
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
Ramakrishnan V (2002) Ribosome structure and the mechanism of translation. Cell
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
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
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
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
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
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
Saffman PG, Delbrück M (1975) Brownian motion in biological membranes. Proc Natl Acad Sci U S A
Samiotakis A, Wittung-Stafshede P, Cheung MS (2009) Folding, stability and shape of proteins in crowded environments: experimental and computational approaches. Int J Mol Sci
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
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
Saxton MJ (1994) Anomalous diffusion due to obstacles: a Monte Carlo study. Biophys J
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
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
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
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
Semenov AN, Meyer H (2013) Anomalous diffusion in polymer monolayers. Soft Matter 9:4249–4272. https://doi.org/10.1039/C3SM27839E
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
Shin Y, Brangwynne CP (2017) Liquid phase condensation in cell physiology and disease. Science
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
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
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
Smoluchowski M (2017) Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen. Z Phys Chem. https://doi.org/10.1515/zpch-1918-9209
Sokolov IM (2012) Models of anomalous diffusion in crowded environments. Soft Matter
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
Spiess C, Meyer AS, Reissmann S, Frydman J (2004) Mechanism of the eukaryotic chaperonin: protein folding in the chamber of secrets. Trends Cell Biol
Sung BJ, Yethiraj A (2006) Lateral diffusion and percolation in membranes. Phys Rev Lett. https://doi.org/10.1103/PhysRevLett.96.228103
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
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
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
Tanner NA, van Oijen AM (2010) Visualizing DNA replication at the single-molecule level. Methods Enzymol
Ten Wolde PR, Mugler A (2014) Importance of crowding in signaling, genetic, and metabolic networks. Int Rev Cell Mol Biol
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
Trimble WS, Grinstein S (2015) Barriers to the free diffusion of proteins and lipids in the plasma membrane. J Cell Biol
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
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
Valastyan S, Weinberg RA (2011) Tumor metastasis: molecular insights and evolving paradigms. Cell. https://doi.org/10.1016/j.cell.2011.09.024
Venters BJ, Pugh BF (2009) How eukaryotic genes are transcribed. Crit Rev Biochem Mol Biol. https://doi.org/10.1080/10409230902858785
Vilar JMG, Saiz L (2013) Systems biophysics of gene expression. Biophys J
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
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
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
Wang Y, Sarkar M, Smith AE et al (2012b) Macromolecular crowding and protein stability. J Am Chem Soc. https://doi.org/10.1021/ja305300m
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
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
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
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
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
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
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
Wong E, Cuervo AM (2010) Autophagy gone awry in neurodegenerative diseases. Nat Neurosci
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
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
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
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
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
Zaburdaev V, Denisov S, Klafter J (2015) Lévy walks. Rev Mod Phys. https://doi.org/10.1103/RevModPhys.87.483
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
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
Zhivotovsky B, Orrenius S (2010) Cell cycle and cell death in disease: past, present and future. J Intern Med
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
Zhou HX (2004) Protein folding and binding in confined spaces and in crowded solutions. J Mol Recogn
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
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
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
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
Zwanzig R (1997) Two-state models of protein folding kinetics. Proc Natl Acad Sci U S A
Zwanzig R (2004) Theoretical basis for the Rouse-Zimm model in polymer solution dynamics. J Chem Phys. https://doi.org/10.1063/1.1681433
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
Acknowledgments
We would like to thank members of Krish lab for their critical inputs and their help. KC thanks CSIR for the funding.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
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.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Basak, S., Sengupta, S. & Chattopadhyay, K. Understanding biochemical processes in the presence of sub-diffusive behavior of biomolecules in solution and living cells. Biophys Rev 11, 851–872 (2019). https://doi.org/10.1007/s12551-019-00580-9
Received:
Accepted:
Published:
Issue date:
DOI: https://doi.org/10.1007/s12551-019-00580-9