Mean velocity and effective diffusion constant for translocation of biopolymer chains across membrane. (English) Zbl 1459.92034
Summary: Chaperone-assisted translocation through a nanopore embedded in membrane holds a prominent role in the transport of biopolymers. Inspired by classical Brownian ratchet, we develop a theoretical framework characterizing such a translocation process through a master equation approach. In this framework, the polymer chain, provided with reversible binding of chaperones, undergoes forward/backward diffusion, which is rectified by chaperones. We drop the assumption of timescale separation and keep the length of a polymer chain finite, both of which happen to be key points in most of the previous studies. Our framework makes it accessible to derive analytical expressions for mean translocation velocity and an effective diffusion constant in a stationary state, which is the basis of a comprehensive understanding of the dynamics of such a process. Generally, the translocation of polymer chains across a membrane consist of three subprocesses: initiation, termination, and translocation of the main body part of a polymer chain, where the translocation of the main body part depends on both the binding/unbinding kinetics of chaperones and the diffusion of the biopolymer chain. This is the main concern of this study. Our results show that the increase of the forward/backward diffusion rate of a polymer chain and the binding/unbinding ratio of chaperones both raise the mean translocation velocity of a polymer chain, and the mean velocity finally reaches a saturation amount with an extremely rapid diffusion or extremely high binding/unbinding ratio. Roughly speaking, the dependence of effective diffusion constant on these two major processes achieves similar behavior. Besides, longer polymer chains employ higher velocity when the diffusion rate and binding/unbinding ratio are both large and similar results hold for polymer chains that are not too long in terms of the effects on the effective diffusion constant.
MSC:
| 92C40 | Biochemistry, molecular biology |
References:
| [1] | Simon S M and Blobel G 1991 A protein-conducting channel in the endoplasmic reticulum Cell65 371-80 · doi:10.1016/0092-8674(91)90455-8 |
| [2] | Simon S M and Blobel G 1992 Signal peptides open protein-conducting channels in E. coli Cell69 677-84 · doi:10.1016/0092-8674(92)90231-Z |
| [3] | Neupert W and Brunner M 2002 The protein import motor of mitochondria Nat. Rev. Mol. Cell Biol.3 555-65 · doi:10.1038/nrm878 |
| [4] | Rapoport T A 2007 Protein translocation across the eukaryotic endoplasmic reticulum and bacterial plasma membranes Nature450 663-9 · doi:10.1038/nature06384 |
| [5] | Neupert W 2015 A perspective on transport of proteins into mitochondria: a myriad of open questions J. Mol. Biol.427 1135-58 · doi:10.1016/j.jmb.2015.02.001 |
| [6] | Schatz G and Dobberstein B 1996 Common principles of protein translocation across membranes Science271 1519-26 · doi:10.1126/science.271.5255.1519 |
| [7] | Santos-Rosa H, Moreno H, Simos G, Segref A, Fahrenkrog B, Panté N and Hurt E 1998 Nuclear mRNA export requires complex formation between Mex67p and Mtr2p at the nuclear pores Mol. Cell Biol.18 6826-38 · doi:10.1128/MCB.18.11.6826 |
| [8] | Albert B, Johnson A, Lewis J, Raff M, Roberts K and Walter P 2008 Molecular Biology of the Cell 5th edn (New York: Garland Science) |
| [9] | Liu S, Chistol G, Hetherington C L, Tafoya S, Aathavan K, Schnitzbauer J, Grimes S, Jardine P J and Bustamante C 2014 A viral packaging motor varies its DNA rotation and step size to preserve subunit coordination as the capsid fills Cell157 702-13 · doi:10.1016/j.cell.2014.02.034 |
| [10] | Salman H, Zbaida D, Rabin Y, Chatenay D and Elbaum M 2001 Kinetics and mechanism of DNA uptake into the cell nucleus Proc. Natl Acad. Sci. USA98 7247-52 · doi:10.1073/pnas.121067698 |
| [11] | Chen I, Christie P J and Dubnau D 2005 The ins and outs of DNA transfer in bacteria Science310 1456-60 · doi:10.1126/science.1114021 |
| [12] | Allemand J F and Maier B 2009 Bacterial translocation motors investigated by single molecule techniques FEMS Microbiol. Rev.33 593-610 · doi:10.1111/j.1574-6976.2009.00166.x |
| [13] | Burton B and Dubnau D 2010 Membrane-associated DNA transport machines Cold Spring Harbin Perspect. Biol.2 a000406 · doi:10.1101/cshperspect.a000406 |
| [14] | Chen I and Dubnau D 2004 DNA uptake during bacterial transformation Nat. Rev. Microbiol.2 241-9 · doi:10.1038/nrmicro844 |
| [15] | Holowka E P, Sun V Z, Kamei D T and Deming T J 2007 Polyarginine segments in block copolypeptides drive both vesicular assembly and intracellular delivery Nat. Mater.6 52-7 · doi:10.1038/nmat1794 |
| [16] | Turner S W P, Cabodi M and Craighead H G 2002 Confinement-induced entropic recoil of single DNA molecules in a nanofluidic structure Phys. Rev. Lett.88 128103 · doi:10.1103/PhysRevLett.88.128103 |
| [17] | Kasianowicz J J, Brandin E, Branton D and Deamer D W 1996 Characterization of individual polynucleotide molecules using a membrane channel Proc. Natl Acad. Sci. USA93 13770-3 · doi:10.1073/pnas.93.24.13770 |
| [18] | Meller A, Nivon L, Brandin E, Golovchenko J and Branton D 2000 Rapid nanopore discrimination between single polynucleotide molecules Proc. Natl Acad. Sci. USA97 1079-84 · doi:10.1073/pnas.97.3.1079 |
| [19] | Sung W and Park P J 1996 Polymer translocation through a pore in a membrane Phys. Rev. Lett.77 783-6 · doi:10.1103/PhysRevLett.77.783 |
| [20] | Meller A, Nivon L and Branton D 2001 Voltage-driven DNA translocations through a nanopore Phys. Rev. Lett.86 3435-8 · doi:10.1103/PhysRevLett.86.3435 |
| [21] | Corsi A, Milchev A, Rostiashvili V G and Vilgis T A 2006 Field-driven translocation of regular block copolymers through a selective liquid-liquid interface Macromolecules39 7115-24 · doi:10.1021/ma060920n |
| [22] | Simon S M, Peskin C S and Oster G F 1992 What drives the translocation of proteins? Proc. Natl Acad. Sci. USA89 3770-4 · doi:10.1073/pnas.89.9.3770 |
| [23] | Peskin C S, Odell G M and Oster G F 1993 Cellular motions and thermal fluctuations: the Brownian ratchet Biophys. J.65 316-24 · doi:10.1016/S0006-3495(93)81035-X |
| [24] | Matlack K E S, Mothes W and Rapoport T A 1998 Protein translocation: tunnel vision Cell92 381-90 · doi:10.1016/S0092-8674(00)80930-7 |
| [25] | Elston T C 2000 Models of post-translational protein translocation Biophys. J.79 2235-51 · doi:10.1016/S0006-3495(00)76471-X |
| [26] | Matlack K E S, Misselwitz B, Plath K and Rapoport T A 1999 BiP acts as a molecular ratchet during posttranslational transport of prepro-α factor across the ER membrane Cell97 553-64 · doi:10.1016/S0092-8674(00)80767-9 |
| [27] | Hepp C and Maier B 2016 Kinetics of DNA uptake during transformation provide evidence for a translocation ratchet mechanism Proc. Natl Acad. Sci. USA113 12467-72 · doi:10.1073/pnas.1608110113 |
| [28] | Zandi R, Reguera D, Rudnick J and Gelbart W M 2003 What drives the translocation of stiff chains? Proc. Natl Acad. Sci. USA100 8649-53 · doi:10.1073/pnas.1533334100 |
| [29] | Ambjörnsson T and Metzler R 2004 Chaperone-assisted translocation Phys. Biol.1 77-88 · doi:10.1088/1478-3967/1/2/004 |
| [30] | Ambjörnsson T, Lomholt M A and Metzler R 2005 Directed motion emerging from two coupled random processes: translocation of a chain through a membrane nanopore driven by binding proteins J. Phys.: Condens. Matter17 S3945-64 · doi:10.1088/0953-8984/17/47/021 |
| [31] | D’Orsogna M R, Chou T and Antal T 2007 Exact steady-state velocity of ratchets driven by random sequential adsorption J. Phys. A: Math. Theor.40 5575-84 · Zbl 1139.92002 · doi:10.1088/1751-8113/40/21/009 |
| [32] | Krapivsky P L and Mallick K 2010 Fluctuations in polymer translocation J. Stat. Mech. P07007 · doi:10.1088/1742-5468/2010/07/p07007 |
| [33] | Abdolvahab R H, Metzler R and Ejtehadi M R 2011 First passage time distribution of chaperone driven polymer translocation through a nanopore: homopolymer and heteropolymer cases J. Chem. Phys.135 245102 · doi:10.1063/1.3669427 |
| [34] | Uhl M and Seifert U 2018 Force-dependent diffusion coefficient of molecular Brownian ratchets Phys. Rev. E 98 022402 · doi:10.1103/PhysRevE.98.022402 |
| [35] | Derrida B 1983 Velocity and diffusion constant of a periodic one-dimensional hopping model J. Stat. Phys.31 433-50 · doi:10.1007/BF01019492 |
| [36] | Gerland U, Moroz J D and Hwa T 2002 Physical constraints and functional characteristics of transcription factor-DNA interaction Proc. Natl Acad. Sci. USA99 12015-20 · doi:10.1073/pnas.192693599 |
| [37] | Kolomeisky A B and Phillips H 2005 Dynamic properties of motor proteins with two subunits J. Phys.: Condens. Matter17 S3887-99 · doi:10.1088/0953-8984/17/47/017 |
| [38] | Svoboda K, Mitra P P and Block S M 1994 Fluctuation analysis of motor protein movement and single enzyme kinetics Proc. Natl Acad. Sci. USA91 11782-6 · doi:10.1073/pnas.91.25.11782 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
