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Li R, Todd BA. Diffusion-limited encounter rate in a three-dimensional lattice of connected compartments studied by Brownian-dynamics simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:032801. [PMID: 25871151 DOI: 10.1103/physreve.91.032801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2014] [Indexed: 06/04/2023]
Abstract
We considered the rate at which a diffusing particle encounters a target in a three-dimensional lattice of compartments with semipermeable walls. This work expands a previous theory [Li et al., Phys. Rev. Lett. 113, 028303 (2014)] for the encounter rate in the dilute limit of targets to the general case of any density of targets. We also used Brownian dynamics simulations to evaluate the approximations in the analytical theory. We find that the largest errors in the analytical theory are on the order of 10%. This work therefore demonstrates an analytical theory capable of describing the encounter rates in compartmentalized environments for any level of confinement and any target density.
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Affiliation(s)
- Ran Li
- School of Electrical and Computer Engineering and Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Brian A Todd
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
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2
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Alonso S, Bär M. Modeling domain formation of MARCKS and protein kinase C at cellular membranes. ACTA ACUST UNITED AC 2014. [DOI: 10.1140/epjnbp14] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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3
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Kinsey ST, Locke BR, Dillaman RM. Molecules in motion: influences of diffusion on metabolic structure and function in skeletal muscle. J Exp Biol 2011; 214:263-74. [PMID: 21177946 PMCID: PMC3008633 DOI: 10.1242/jeb.047985] [Citation(s) in RCA: 63] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 08/25/2010] [Indexed: 12/23/2022]
Abstract
Metabolic processes are often represented as a group of metabolites that interact through enzymatic reactions, thus forming a network of linked biochemical pathways. Implicit in this view is that diffusion of metabolites to and from enzymes is very fast compared with reaction rates, and metabolic fluxes are therefore almost exclusively dictated by catalytic properties. However, diffusion may exert greater control over the rates of reactions through: (1) an increase in reaction rates; (2) an increase in diffusion distances; or (3) a decrease in the relevant diffusion coefficients. It is therefore not surprising that skeletal muscle fibers have long been the focus of reaction-diffusion analyses because they have high and variable rates of ATP turnover, long diffusion distances, and hindered metabolite diffusion due to an abundance of intracellular barriers. Examination of the diversity of skeletal muscle fiber designs found in animals provides insights into the role that diffusion plays in governing both rates of metabolic fluxes and cellular organization. Experimental measurements of metabolic fluxes, diffusion distances and diffusion coefficients, coupled with reaction-diffusion mathematical models in a range of muscle types has started to reveal some general principles guiding muscle structure and metabolic function. Foremost among these is that metabolic processes in muscles do, in fact, appear to be largely reaction controlled and are not greatly limited by diffusion. However, the influence of diffusion is apparent in patterns of fiber growth and metabolic organization that appear to result from selective pressure to maintain reaction control of metabolism in muscle.
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Affiliation(s)
- Stephen T Kinsey
- Department of Biology and Marine Biology, University of North Carolina Wilmington, 601 South College Road, Wilmington, NC 28403-5915, USA.
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4
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Reits E, Griekspoor A, Neijssen J, Groothuis T, Jalink K, van Veelen P, Janssen H, Calafat J, Drijfhout JW, Neefjes J. Peptide diffusion, protection, and degradation in nuclear and cytoplasmic compartments before antigen presentation by MHC class I. Immunity 2003; 18:97-108. [PMID: 12530979 DOI: 10.1016/s1074-7613(02)00511-3] [Citation(s) in RCA: 240] [Impact Index Per Article: 10.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Antigenic peptides generated by the proteasome have to survive a peptidase-containing environment for presentation by MHC class I molecules. We have visualized the fate and dynamics of intracellular peptides in living cells. We show that peptides are distributed over two different but interconnected compartments, the cytoplasm and the nucleus, and diffuse rapidly through and between these compartments. Since TAP is excluded from the nuclear face of the nuclear envelope, nuclear peptides have to leave the nucleus to contact TAP. Thereby, these peptides encounter cytosolic peptidases that degrade peptides within seconds unless bound to chromatin. Since peptide degradation is far more efficient than translocation, many peptides will be lost for antigen presentation by MHC class I molecules.
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Affiliation(s)
- Eric Reits
- Department of Tumor Biology and Cell Biology, The Netherlands Cancer Institute, Plesmanlaan 121, 1066 CX Amsterdam, The Netherlands
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Reits EA, Neefjes JJ. From fixed to FRAP: measuring protein mobility and activity in living cells. Nat Cell Biol 2001; 3:E145-7. [PMID: 11389456 DOI: 10.1038/35078615] [Citation(s) in RCA: 448] [Impact Index Per Article: 18.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Experiments with fluorescence recovery after photobleaching (FRAP) started 30 years ago to visualize the lateral mobility and dynamics of fluorescent proteins in living cells. Its popularity increased when non-invasive fluorescent tagging became possible with the green fluorescent protein (GFP). Many researchers use GFP to study the localization of fusion proteins in fixed or living cells, but the same fluorescent proteins can also be used to study protein mobility in living cells. Here we review the potential of FRAP to study protein dynamics and activity within a single living cell. These measurements can be made with most standard confocal laser-scanning microscopes equipped with photobleaching protocols.
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Affiliation(s)
- E A Reits
- Division of Tumor Biology, The Netherlands Cancer Institute, Plesmanlaan 121, 1066 CX Amsterdam, The Netherlands
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6
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Kholodenko BN, Brown GC, Hoek JB. Diffusion control of protein phosphorylation in signal transduction pathways. Biochem J 2000; 350 Pt 3:901-7. [PMID: 10970807 PMCID: PMC1221325] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/17/2023]
Abstract
Multiple signalling proteins are phosphorylated and dephosphorylated at separate cellular locations, which potentially causes spatial gradients of phospho-proteins within the cell. We have derived relationships that enable us to estimate the extent to which a protein kinase, a phosphatase and the diffusion of signalling proteins control the protein phosphorylation flux and the phospho-protein gradient. Two different cellular geometries were analysed: (1) the kinase is located on one planar membrane and the phosphatase on a second parallel planar membrane, and (2) the kinase is located on the plasma membrane of a spherical cell and the phosphatase is distributed homogeneously in the cytoplasm. We demonstrate that the control contribution of protein diffusion is potentially significant, given the measured rates for protein kinases, phosphatases and diffusion. If the distance between the membranes is 1 microm or greater, the control by diffusion can reach 33% or more, with the rest of the control (67%) shared by the kinase and the phosphatase. At distances of less than 0.1 microm, diffusion does not limit protein phosphorylation. For a spherical cell of radius 10 microm, a protein diffusion coefficient of 10(-8) cm(2). s(-1) and rate constants for the kinase and the phosphatase of approx. 1 s(-1), control over the phosphorylation flux resides mainly with the phosphatase and protein diffusion, with approximately equal contributions of each of these. The ratio of phospho-protein concentrations at the cell membrane and the cell centre (the dynamic compartmentation of the phospho-protein) is shown to be controlled by the rates of the protein phosphatase and of diffusion. The kinase can contribute significantly to the control of the absolute value of the phospho-protein gradient.
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Affiliation(s)
- B N Kholodenko
- Department of Pathology, Anatomy and Cell Biology, Thomas Jefferson University, 1020 Locust St, Philadelphia, PA 19107, USA.
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7
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Foucault G, Vacher M, Cribier S, Arrio-Dupont M. Interactions between beta-enolase and creatine kinase in the cytosol of skeletal muscle cells. Biochem J 2000; 346 Pt 1:127-31. [PMID: 10657248 PMCID: PMC1220831] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/15/2023]
Abstract
We studied interactions in vivo between the cytosolic muscle isoform of creatine kinase (M-CK) and the muscle isoform of 2-phospho-D-glycerate hydrolyase (beta-enolase) in muscle sarcoplasm by incubating glycerol-skinned fibres with FITC-labelled beta-enolase in the presence or absence of free CK. A small amount of bound beta-enolase was observed in the presence of large concentrations of CK. The mobility of enolase was measured in cultured satellite cells by modulated-fringe-pattern photobleaching. FITC-labelled beta-enolase was totally mobile in both the presence and the absence of CK but its diffusion coefficient was slightly lower in the presence of CK. This suggests a weak interaction in vivo between enolase and CK.
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Affiliation(s)
- G Foucault
- Gènes et Protéines Musculaires, EP CNRS 1088, Centre scientifique d'Orsay, bâtiment 430, F 91405 Orsay cedex, France.
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Luby-Phelps K. Cytoarchitecture and physical properties of cytoplasm: volume, viscosity, diffusion, intracellular surface area. INTERNATIONAL REVIEW OF CYTOLOGY 1999; 192:189-221. [PMID: 10553280 DOI: 10.1016/s0074-7696(08)60527-6] [Citation(s) in RCA: 733] [Impact Index Per Article: 28.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/03/2022]
Abstract
Classical biochemistry is founded on several assumptions valid in dilute aqueous solutions that are often extended without question to the interior milieu of intact cells. In the first section of this chapter, we present these assumptions and briefly examine the ways in which the cell interior may depart from the conditions of an ideal solution. In the second section, we summarize experimental evidence regarding the physical properties of the cell cytoplasm and their effect on the diffusion and binding of macromolecules and vesicles. While many details remain to be worked out, it is clear that the aqueous phase of the cytoplasm is crowded rather than dilute, and that the diffusion and partitioning of macromolecules and vesicles in cytoplasm is highly restricted by steric hindrance as well as by unexpected binding interactions. Furthermore, the enzymes of several metabolic pathways are now known to be organized into structural and functional units with specific localizations in the solid phase, and as much as half the cellular protein content may also be in the solid phase.
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Affiliation(s)
- K Luby-Phelps
- Department of Physiology, University of Texas Southwestern Medical Center, Dallas 75235-9040, USA
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Abstract
If a protein is rapidly phosphorylated and dephosphorylated at separate cellular locations and protein diffusion is slow, then a spatial gradient of the phosphorylated form of the protein may develop within the cell. We have estimated the potential size of such gradients using measured values of protein diffusion coefficients and protein kinase and phosphatase activities. We analysed two different cellular geometries: (1) where the kinases is located on the plasma membrane of a spherical cell and the phospatase is distributed homogenously in the cytoplasm and (2) where the kinase is located on one planar membrane and the phosphatase on a second parallel planar membrane. The estimated gradients of phospho-proteins were potentially very large, which has important implications for cellular signalling.
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Affiliation(s)
- G C Brown
- Department of Biochemistry, University of Cambridge, Tennis Court Road, Cambrigde, UK.
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Foucault G, Vacher M, Merkulova T, Keller A, Arrio-Dupont M. Presence of enolase in the M-band of skeletal muscle and possible indirect interaction with the cytosolic muscle isoform of creatine kinase. Biochem J 1999; 338 ( Pt 1):115-21. [PMID: 9931306 PMCID: PMC1220032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
Abstract
Glycerol-skinned skeletal muscle fibres retain the defined sarcomeric structure of the myofibrils. We show here that a small fraction of two enzymes important for energy metabolism, the cytosolic muscle isoform of creatine kinase (EC 2.7.3.2), MM-creatine kinase (MM-CK), and enolase (EC 4.2.1.11), remains bound to skinned fibres. CK is slowly exchangeable, whereas enolase is firmly bound. Two-dimensional gel electrophoresis followed by Western blot analyses demonstrates that both alpha (ubiquitous) and beta (muscle-specific) subunits of enolase are present in these preparations. Enolase and CK were co-localized at the M-band of the sarcomeres, as observed by indirect immunofluorescence and confocal microscopy. Cross-linking experiments were performed on skinned fibres with three bifunctional succinimidyl esters of different lengths and yielded a protein complex of 150 kDa that reacted with antibodies directed against either M-CK or beta-enolase. The cross-linking efficiency was greatest for the longest reagent and zero for the shortest one. The length of the cross-linker giving a covalent complex between the two enzymes does not support the notion of a direct interaction between M-CK and enolase. This is the first demonstration of the presence of an enzyme of energy metabolism other than CK at the M-band of myofibres.
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Affiliation(s)
- G Foucault
- Gènes et Protéines Musculaires, EP CNRS 1088, Centre scientifique d'Orsay, France.
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Merkulova T, Thornell LE, Butler-Browne G, Oberlin C, Lucas M, Lamandé N, Lazar M, Keller A. The beta enolase subunit displays three different patterns of microheterogeneity in human striated muscle. J Muscle Res Cell Motil 1999; 20:55-63. [PMID: 10360234 DOI: 10.1023/a:1005428328913] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
In higher vertebrates, the glycolytic enzyme enolase (2-phospho-D-glycerate hydrolyase; EC 4.2.1.11) is active as a dimeric protein formed from three subunits--alpha: ubiquitous, beta: muscle specific, and gamma: neuron specific--encoded by different genes. In the present study, we have shown that an antiserum previously produced against the mouse beta beta enolase is also a specific reagent for the muscle specific human enolase. Using this antiserum to study human muscles, we demonstrated novel patterns of the beta subunit microheterogeneity which are distinctive from those observed previously in rodents and which appear to be independent of age, gender and muscular activity. Two variants of the beta subunit differing by their size have been detected: one heavy form of 46 kDa (beta H) and one light form of 45 kDa (beta L). Muscle biopsies expressed either beta H or beta L or beta H + beta L, and all muscles of an individual expressed the same variants. The products of in vitro translation of RNA prepared from human muscle displayed beta subunit variants identical to those of the protein present in the biopsy. Therefore the differences observed between individuals reveal a difference already present at the level of the RNA transcripts. These observations suggest the existence of an yet undescribed polymorphism of the human beta enolase gene which could affect the coding sequence. Comparative immunocytochemical and histochemical analyses of biopsies demonstrated that the beta subunit was expressed in all fast fibres (type II), but not in slow fibres (type I). No difference was observed in the intensity of beta enolase immunolabelling between the various types (IIA, IIAB, IIB) of fast fibres. No significant difference in fibre type composition and histological appearance was visible between muscles presenting either one of the three patterns of microheterogeneity.
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Affiliation(s)
- T Merkulova
- Biochimie Cellulaire, CNRS UPR 9065, Collège de France, Paris, France
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Stolz M, Wallimann T. Myofibrillar interaction of cytosolic creatine kinase (CK) isoenzymes: allocation of N-terminal binding epitope in MM-CK and BB-CK. J Cell Sci 1998; 111 ( Pt 9):1207-16. [PMID: 9547297 DOI: 10.1242/jcs.111.9.1207] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
The molecular origin of the isoenzyme-specific interaction of cytosolic creatine kinase isoenzymes, muscle-type creatine kinase and brain-type creatine kinase, with myofibrillar structures has been studied by confocal microscopy in an functional in situ binding assay with chemically skinned, unfixed skeletal muscle fibers using wild-type and chimeric creatine kinase isoproteins. The specific interaction of both wild-type isoforms with the sarcomeric structure resulted in a stable, isoform-characteristic labeling pattern with muscle-type creatine kinase bound exclusively and tightly to the sarcomeric M-band while brain-type creatine kinase was confined to the I-band region. Chimeric proteins of both muscle-type and brain-type creatine kinases were constructed to localize the corresponding binding domain(s). Exchanged domains included the N-terminal part (residues 1–234), the region containing an isoenzyme ‘diagnostic box’ (residues 235–285) and the C-terminal part (residues 286–380). The purified recombinant proteins were all fully intact and enzymatically active. All chimeric proteins containing the N-terminal region (amino acid 1–234) of muscle-type or brain-type creatine kinase were always specifically targeted to the sarcomeric M-band or I-band, respectively. We therefore propose that the relevant epitope(s), determining the isoenzyme-specific targeting in skeletal muscle, are entirely located within the N-terminal regions of both cytosolic creatine kinase isoforms.
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Affiliation(s)
- M Stolz
- Swiss Federal Institute of Technology, Institute of Cell Biology, Zürich, Switzerland.
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