mechanism of dna transport through pores

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Mechanism of DNATransport Through Pores

Murugappan Muthukumar

Polymer Science and Engineering Department, University of Massachusetts, AmherstMassachusetts 01003; email: [email protected]

Annu. Rev. Biophys. Biomol. Struct. 2007.36:43550

First published online as a Review in Advance onFebruary 20, 2007

The Annual Review of Biophysics and BiomolecularStructure is online at biophys.annualreviews.org

This articles doi:10.1146/annurev.biophys.36.040306.132622

Copyright c 2007 by Annual Reviews.All rights reserved

1056-8700/07/0609-0435$20.00

Key Words

entropic barrier, nucleation, translocation, Brownian dynamics

Abstract

The transport of electrically charged macromolecules such as DNAthrough narrow pores is a fundamental process in life. When poly-

mer molecules are forced to navigate through pores, their transportis controlled by entropic barriers that accompany their conforma-

tional changes.During thepast decade, exciting results haveemerged

from single-molecule electrophysiology experiments. Specificallythe passage of single-stranded DNA/RNA through alpha-hemolysin

pores and double-stranded DNA through solid-state nanopores hasbeen investigated. By a combination of these results with theentropic

barrier theory of polymer transport and macromolecular simula-tions,an understanding of the mechanism of DNAtransport through

pores has emerged.

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Translocation: theprocess of transportof a polymer througha pore

HL: -hemolysin

ss-DNA:single-strandedDNA

ds-DNA:double-strandedDNA

Contents

INTRODUCTION... . . . . . . . . . . . . . . 436CENTRAL CONCEPT

OF TRANSLOCATION......... 438TRANSLOCATION OF

SINGLE-STRANDED

DNA/RNA . . . . . . . . . . . . . . . . . . . . . . 440Experimental Facts . . . . . . . . . . . . . . . 440Theoretical Considerations . . . . . . . 441

Simulation Studies . . . . . . . . . . . . . . . 442

TRANSLOCATION OFDOUBLE-STRANDED DNA . . . 446

Experimental Facts . . . . . . . . . . . . . . . 446Theory and Simulations . . . . . . . . . . 447

CO N CL U S IO N S . . . . . . . . . . . . . . . . . . . 4 4 7

INTRODUCTION

The transport of electrically charged polymermolecules, such as polynucleotides and pro-

teins, from one region of space to another incrowded electrolytic media is one of the most

crucial elementary processes of life. Exam-ples of biological phenomena, for which poly-

mer translocation is crucial, include passageof mRNA through nuclear pore complexes,

injection of DNA from a virus head into ahost cell, gene swapping through pili, andprotein translocations across biological mem-

branes through channels. Although polymertranslocation is ubiquitous in biology, in vivo

polymer translocations are too complex to di-rectly monitor one long molecule undergoing

migration in its totality.Fortunately, the societal need to sequence

enormous numbers of genomes immediatelyand inexpensively has recently stimulated a

spurt of exciting single-molecule electrophys-iology experiments (3, 5, 8, 12, 14, 16, 17,

2022, 32, 33). In these experiments, translo-

cation of single molecules of DNA/RNA ismonitored, through ionic current traces, as

the DNA/RNA molecules pass through pro-tein channels and solid-state nanopores un-

der an external electric field. These experi-

ments, although couched in the premise of

sequencing technology, serendipitously offera wealth of data to enable a fundamenta

understanding of the physical mechanism ofpolymer translocation in biology. Through

these single-molecule electrophysiology mea-surements, which are far simpler than the

in vivo biological translocations, the mech-anism of DNA transport through pores hasemerged.

In this review, we address the conceptualadvances that have recently been achieved

and the ongoing challenges in the con-texts of the following two areas: (a) translo-

cation of single-stranded (ss)-DNA/RNAmolecules through a protein channel, -

hemolysin (HL), and (b) translocation ofdouble-stranded (ds)-DNA through solid-

state nanopores. Sketches of these scenariosare given in Figure 1. Figure 1a shows the

pore as a heptameric self-assembly ofHL

which is incorporated into a membrane sepa-rating a donor (cis) chamber from an acceptor

(trans) chamber. Each chamber is filled with abuffered salt solution. TheHL pore consists

of a vestibule on the cisside and a transmem-brane -barrel on the trans side. The length

of the channel is 10 nm. The opening ofthe vestibule at the cis side is 2.9 nm and

the diameter of the vestibules cavity is

4.1nm. The average internal diameter of the -

barrel is 2 nm. The two domains of thepores lumen are separated by a constriction

of1.4 nm. The length of DNA that is passed

through HL can be as long as 1000 nm.In the case of solid-state nanopores, the di-

ameter is in the tunable range of 3 to 10 nmand the length is of order of 10 nm or more

(Figure 1b). The length of DNA can easily bemicrons.

The length and timescales relevant tothe full translocation of DNA through pores

are several orders of magnitude larger thanthose pertinent to one nucleotide, one amino

acid unit, or one water molecule. A system-atic development of atomic forces among the

constituent molecules of large structures rele-

vant to DNA transport is impossible with the

436 Muthukumar


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present computational and theoretical capa-

bilities. It is therefore essential to seek thebig picture of DNA translocation by coarse-

graining (i.e., integrating out) local atomisticdetails and addressing global properties such

as therelativedependence of the translocation

time on the lengths of the DNA molecules

that undergo translocation. Such an approachdoes not have the capacity to specify the func-tional properties of a few specified atoms in-

volved in the transport phenomena. The basisof this coarse-grained approach is polymer

physics, in which the key concepts associatedwith the polymeric nature of the molecules

were harnessed over five decades and basedon synthetic polymers.

The basic conceptual attributes of electri-cally charged polymer molecules (called poly-

electrolytes) are the following. (a) The con-formational entropy S of a molecule is highowing to the ability of the molecule to adopt

an enormous number of conformations N.The actual value ofN depends on the various

potential interactions among the constituentmonomers of the molecules and on the na-

ture of the medium. In addition, the backbonestiffnessplaysaroleindictatingtheconforma-

tional entropy. Whereas ss-DNA moleculesare flexible and as a result can adopt many

conformations, the ds-DNA molecules of thesame contour length are stiffer and adopt

lesser conformations. (b) The counterions of

the polymer hover around the backbone ofthe polymer and significantly reduce the ef-

fective local electrostatic potential and the ef-fective charge of the polymer. (c) The mobil-

ity of a polyelectrolyte such as DNA under aconstant electric field in dilute salty solutions

is independent of the length of DNA. Thisremarkable feature is a result of the balance

between the hydrodynamic drag of the poly-mer and the opposing counterion forces. This

feature is distinct to polyelectrolytes and can-not be superficially surmised from laws valid

for the transport of unchargedpolymers. Fail-

ure to recognize these fundamental laws (23)of polyelectrolytes can only lead to confusing

conjectures for DNA transport.

Figure 1

(a) Sketch ofHL pore and a translocating ss-DNA. (b) Sketch of ds-DNAat a solid-state nanopore.

The transport of DNA and other polymer

molecules can be broadly classified into threegroups onthe basis of the ratio of the radius of

gyration (R) of the polymer to the radius ()of the pore (Figure 2). In this review we focus

only on the single-file transport correspond-ing to the case of R and the hairpin-like

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Figure 2Different regimesof polymerconfinement by thepore.

translocationsforR,

is pertinent to transport through wider chan-nels and is not reviewed here. For the situa-

tions under consideration, the narrowness ofthe pores reduces the conformational entropy

Entropicbarrier

F3

F1

F

I

I

Distance

III

III

II

II

F2

Figure 3

Genesis of entropic barrier for DNA transport through pores.

significantly, which in turn forms the basis of

the transport mechanism.The transport mechanism of ds-DNA can

be qualitatively different from that of ss-DNAowing to the differences in the backbone stiff-

ness. We discuss these differences in separate

sections.

CENTRAL CONCEPTOF TRANSLOCATION

When a polymer is forced through a narrow

pore the molecule is subjected to an entropicbarrier (6, 7, 9, 15, 2428, 34). The dynamics

of the polymer subjected to this entropic bar-rier constitutes the central concept of translo-

cation of DNA through pores. One of the

inherent properties of an isolated flexiblepolymer chain in solutions is its ability to as-

sume a large number of conformations N. Asa result, the chain entropy (kB lnN; kB is the

Boltzmann constant) can be high, and its freeenergy F is given by F = E-TS = EkBT

ln N, where E is the energy of interactionbetween monomers and the surrounding sol-

vent molecules and T is the absolute tempera-ture. There can be additional entropic contri-

butions to F due to a reorganization of solventmolecules accompanying the conformational

changes of the chain. When such a chain is

exposed to a restricted environment such as apore, the number of conformations that can

otherwise be assumed by the chain is reducedand as a result the chain entropy decreases and

the chain free energy increases. This effect isdepicted in Figure 3.

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F1, F2, and F3 are the free energies of the

chain in regions I, II, and III, respectively.Owing to the reduction of conformations in

region III, F3 is higher than F1 and F2. Wecall F3-F1 the entropic barrier to the passage

of the chain out of region I. Although this

barrier is called the entropic barrier, it is in-

deed a free-energy barrier because additionalenthalpic contributions to F3 can arise fromthe interactions between the polymer and the

pore. In general, the environment of the chainin region II can be different from that in re-

gion I (due to different electrochemical po-tentials in these regions), so that F2 is not

necessarily equal to F1. The net driving po-tential for polymer transport from region I to

region II is (F1-F2). The polymer chain must

negotiate the entropic barrier in order for it

to successfully arrive at the opposite side ofthe pore.Is such a simple idea applicable to the ap-

parently complex transport of DNA throughpores? Without the knowledge of actual ex-

perimental data in this context, a computersimulation (25) was originally carried out in

the following manner. A flexible polyelec-trolyte chain was first equilibrated inside a

closed sphere at a prescribed ionic strengthby using the screened Coulomb potential and

the Monte Carlo simulation method. Then,a single hole, just big enough to allow only

one monomer at a time, was made on the

surface of the sphere at the start of a clock.The expulsion of the chain from the sphere

into the outside world was followed as a func-tion of time. As expected, the chain was try-

ing to exit as soon as one of the two ends ap-proached the hole, by ejecting a few of the

end monomers. Remarkably, the chain thenwent back inside the sphere instead of pro-

ceeding with the ejection. Once the chainwent back into the sphere, the process started

all over again. After rattling inside the spherefor a while, one of the two ends approached

the hole again, and some monomers were

put outside and then the whole chain wentback in again. After about 300 such attempts,

the chain put out enough monomers in the

Entropic barrier:creation of anunfavorable freeenergy by areduction in thenumber of possibleconformations of thepolymer due to

spatial restrictionsNucleation:initiation of a procesrequiring a thresholdamount of freeenergy

Figure 4

Simulated polymer escape demonstrates the analogy with nucleation andgrowth. t, time in arbitrary units.

outside world and completely got out of the

sphere. This sequence of the events is given inFigure 4, where trepresents time in arbitrary

units.Such a sequence of events is typical of the

nucleation and growth mechanism encoun-tered in the kinetic evolution of a metastable

state into an equilibrium state separated by afree-energy barrier. The results of Figure 4

are the manifestation of this nucleation andgrowth mechanism for the translocation of

one polymer chain negotiating the entropic

barrier of Figure 3. In addition to demon-strating the applicability of the central idea,

the simulation showed that the theoreticaltechnology that has been in place for eight

decades to describe the kinetics of first-order



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phase transformations could be readily imple-

mented for the transport of DNA throughpores. Therefore, the key issues that arise

are (a) how to compute/measure the entropicbarriers and (b) how to describe the trans-

port of highly correlated objects such as poly-

mers across free-energy barriers. Before we

address these issues, let us review some keyexperimental facts.

Lifetime ( s)

1

2

4000

Numberofblockades

2000

00 1000 2000

3

Peak

1

2

3

Lifetime (s)

92

290

1288

Blockades (s1)

0.9

2.3

1.5

I II

N - m

b

a

m

Figure 5

(a) Experimental histogram of translocation time. (b) Coarse-grained porein theoretical considerations.

TRANSLOCATION OFSINGLE-STRANDED DNA/RNA

Experimental Facts

When an external voltage is applied across amembranecontaining theHLpore,thepore

allows passage of small ions, and the resulting

ionic current is measured (14) in the geome-try ofFigure 1a. When this experiment is re-

peated with ss-DNA/RNA originally presentin the cischamber, the measured ionic current

decreases significantly by an amount Ib when-ever the polynucleotide transits through the

protein pore. Detailed experimental protocols(14) have revealed that the translocation time, for one molecule to go from the cisside tothe transside can be inferred from the dura-

tion of a current blockade. One of the key fea-

tures of theexperimental results is that there isa broad distribution in the values of and Ibalthough chemically identical molecules are

undergoing translocation events.

A typical example of the histogram P()forthe distribution of the occurrence of a partic-

ular value of is given in Figure 5a. Thisexhibits three peaks. The first peak with the

smallest translocation time can be attributedconfidently to events in which the polymer

only partially enters or collides with the pore

The second and third peaks represent fulltranslocation events, and the origin of theoccurrence of two peaks has been mysteri-

ous. However, if the two peaks were deconvo-luted, the average translocation time for each

of these two peaks would be proportional to

N/V, where N is the number of bases in thepolymer and V is the applied voltage differ-

ence. While the average obeys the expectedlaw of proportionality between the time to

pull a chain and the chain length, and the in-verse relation betweenandthe applied force

the breadth of the distribution has been sur-prising given the uniformity of the polymer

molecules. Nevertheless, different polymersequences showed different average translo-

cation times and raised the prospect of fastDNA sequencing to a new higher level. Fur-

thermore, a threshold of applied voltage was

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needed to thread DNA through HL, before

realizing the asymptoticrelation ofN/V.The value of the threshold voltage depends on

whether the polymer is pulled from the cissideor the transside.

Theoretical Considerations

In order to implement the entropic barriermodel to describe the translocation kinetics of

DNA through the HL pore, it is necessaryto assess the nature of the entropic barrier. In

thespiritof thecoarse-grainedapproach usingpolymer physics ideas, the barrier is evaluated

as follows. Let us make the big assumption(24) that the HL pore, with all its chemical

decorations and physical constrictions, can berepresented equivalently by a hole in a wall

(which represents the membrane), as sketchedin Figure 5b. This implies that a DNA chainduring its passage through the pore can be

imagined as two strands hanging from an im-penetrable wall, with one end of each strand

at the wall. The free energy of such strands iswell known in the polymer literature, and it is

straightforward to calculate the free energy ofa chain when a certain number of monomers

have been brought from the cis to the transchamber. Thus the free-energy landscape can

be calculated for different extents of translo-cation, and the calculations show that there

exists a free-energy barrier.

The kinetics of the translocation throughthe calculated free-energy barrier is described

by following the standard theoretical proce-dure for thekinetics of first-order phase trans-

formations. An additional assumption is thatthe polymer relaxes as fast as the transloca-

tion time, allowing the calculation of the dis-tribution of the translocation time, and the

average translocation time, in terms of onlyone parameter representing the friction of a

monomer at the pore. The resultant equa-tion is in the same universality class as the

drift-diffusion equation. The applied electric

field is responsible for the drift of the poly-mer, and the chain connectivity is responsi-

ble for the diffusive back-and-forth motion

of the polymer at the experimentally rele-

vant temperatures. In terms of the only phe-nomenological parameter for the monomer

friction, analytical formulas can be derived forthe translocation time and its distribution. Re-

markably, is proportional to N/V, as wasfound in experiments. The shape of the his-

tograms of the deconvoluted peaks is also re-produced. Furthermore, the theory predictedthat must be proportional to N2 for short

DNA chains, as wasconfirmed by experiments(22).

Several variations (13, 18) of the theoret-ical method given above, in which the chain

entropy and its consequent barrier play ratherminor roles, have been reported in the liter-

ature. While these calculations are certainlyof use under special circumstances, the con-

formational entropy of DNA is its inherentproperty and its role is a necessary componentof DNA transport. One of the extensions (15,

27) of the above theory is in the context ofgene translocation through pili. The translo-

cation kinetics of DNA from one sphericalcavity to another spherical cavity through an

oppositely charged pore of prescribed lengthhas been analytically calculated for the geom-

etry sketched in Figure 6. The free-energylandscape for this process consists of five im-

portant stages. The first stage, which is en-tropically most unfavorable, is the placement

of one of the ends of the chain at the gate of

the donor chamber. The second stage corre-sponds to filling the pore with the polymer.

This step is energetically favorable due to theopposite charges of the polymer and the pore.

In the third stage, the rest of the monomersleft behind in the donor chamber are trans-

ferred to the acceptor chamber by the en-tropic barrier mechanism. The fourth stage

corresponds to peeling off the polymer stuckinside the pore so that the pore is emptied,

and this step is an unfavorable process. In thefifth stage, the polymer is kicked into the re-

cipient chamber to fully realize the low free

energy of the final state. The free energy ofconfinement of polyelectrolytes in spherical

cavities is identical to that of a polyelectrolyte



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1

R1

R2

Freeenergy

a

b

1

1

2 3

4

5

2 3 4

Extent of translocation ()

Figure 6

(a) Key steps oftranslocationbetween tworeservoirs throughan interactive poreand (b) theaccompanyingfree-energylandscape.

solution, andscaling argumentsvalidfor pores

and channels cannot be casually extended.The agreement between the analytically

derived formulas and the general experimen-tal results shows that the entropic barrier

model enables researchers to understand themacromolecular basis of polymer transloca-

tion. The advantage of such a model and

phenomenological theories is their ability tooffer simple analytical formulas. These for-

mulas allow researchers to design experimen-tal geometries in order to realize various de-

sired translocation times for DNA. In spiteof this success, the entropic barrier model

is incapable of explaining the occurrence ofmultiple peaks in the experimentally observed

histograms (Figure 5a). Further, the specificeffects of particular nonblocky sequences of

DNA on the translocation histograms can-notbe adequately addressedin theseanalytical

calculations, although nonblocky sequences

can readily be addressed through molecularmodeling. To address these nonuniversal fea-

tures of DNA transport, we must resort tomolecular modeling.

Simulation Studies

Even with the modern computational facili-ties, it is impossible to perform ab initio cal-

culations of all atomic forces to follow thetranslocation events of DNA molecules that

occur at the timescale of hundreds of mi-

croseconds. Therefore, it is necessary to per-form coarse-graining of atomistic details butnot to throw away the chemical identity of

the building units such as the nucleotidessugar, and phosphate moieties. Building on

the expertise cultivated in polymer physics,Muthukumar & Kong (29) have recently used

Brownian dynamics simulations to model the

translocation of DNA through the HL poreand nanotubes. Through a description of the

ss-DNApolymerandtheHLporeasunited-

atom models, as depicted in Figure 7, confor-mations of the polymer have been monitoredas it is pulled by an externally imposed electric

field across the pore (which is embedded in amembrane).

In these simulations, the base, sugar, andphosphate moieties of the polymer and the

442 Muthukumar


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Figure 7

Coarse-graineddescription of (a) theHL pore, (b) a

nanopore, and (c) apolynucleotide.

various amino acid residues of the protein

are treated as effective beads with differingsizes and the appropriate charges. The en-

ergies associated with bond-stretch, bond-angle, torsion, Lennard-Jones, and screened

Coulomb interactions, among various unitedatoms, were taken into account. The base of

theDNA/RNA has a preferable tilt angle withrespect to the polymer backbone to allow the

monitoring of the 3 and 5 ends of the poly-

mer. The protein pore was taken as static, onthe basis of initial results of negligible con-

tributions arising from protein dynamics fortheissuesof translocation. Thedielectric con-

stant of the membrane and the interior of theunited atoms was taken to be 2, whereas the

aqueous medium was taken as a continuum

with a dielectric constant of 80. The con-formations of the polymer were monitored

in this medium of inhomogeneous dielectricconstant under the externally imposed elec-

tric field. This calculation was then coupled toa modified Poisson-Nernst-Planck procedure

to compute the ionic current as the polymerunderwent translocation.

Polymer conformations and the accompa-

nying ionic currents were calculated simul-taneously. The representative results (29) for

two trajectories are given in Figure 8. Thesesimulations were repeated thousands of times

and the histograms of P() were constructed.The simulations could reproduce almost all



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Figure 8

Simultaneouscalculation ofpolymerconformations andionic currents.(Top) A trajectoryof translocationwith longer , and

(bottom) a trajectoryof translocationwith shorter .

aspects of the experimental data. Remarkably,there are two peaks corresponding to translo-

cation, as seen in Figure 9a. By going back tothe chain conformations in all these simula-

tions, it was possible to find out why one par-ticular event took a particular time for translo-

cation. On the basis of these investigations, itwas concluded that the vestibule of the HL

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pore acts as an additional entropic trap, as it

is sufficiently large to hold many segmentsof the polymer. The entropic trap generates

a resistive force against the translocation ofthe polymer. As a result, the polymer moves

slower while still maintaining the proportion-

ality of to N/V. Further, the translocation

time for such events is increased by roughly aconstant residence time inside the vestibule.Events mediated by the entropic trap of the

vestibule contribute to the peak with longer .On the other hand, there are events that avoid

the entropic trap of the vestibule by the ran-domness of the process. These events con-

tribute to the other peak with shorter .Whena nanotube (Figure 7b) is used instead of

the HL pore, only one peak is observed(Figure 9b) because the entropic trap of the

vestibule is now absent. However, this conclu-sion remains controversial, as an alternativeexplanation (19) has been offered in which

the two peaks are claimed to correspond totranslocations via 3 and 5 ends through the

pore. More work is needed to sort this issue.Attempts on explicit-atom molecular dy-

namics simulations (2, 11) have recently beenreported. More work is needed in order for

the reported results to be relevant to the ex-perimental situations, because the simulations

canbe carried outfor times only several ordersof magnitude shorter than the translocationtimes. However, these results are of immense

utility when calibrating the frictional forcesthat are used in the coarse-grained Brownian

dynamics simulations.Another direction where the modeling

should be extended is the role of secondarystructures of the polymer on the translocation

features. Polymer sequences and their abilityto spontaneously form secondary structures

influence their migration through nanopores.An excellent example (1) is the different types

of ionic current traces for poly C, poly dC,

and poly A. Although reasonable conjectureshave been proposed to explain these different

traces, full explanations are yet to be found.Finally, the structure of water in the HL

pore or any nanopore must be fully deter-

0.05

0

0.10

0.15

0.20

0.25

0.30

0 50 100 150

0 100 150

0

0.01

0.02

0.03

0.04

50

b

a

P(

)

P()

( s)

( s)

Figure 9

(a) Calculated histogram of translocation times. (b) The histogram for ananopore is much narrower than for the HL pore.

mined. Although there are simulation reportson the structure of water in nanopores, these

results were based on the potential betweenwater molecules in the bulk. When an inter-

face is created, for example, at the wall of thepore, dielectric discontinuity is created, and

forces from the image charges in turn mod-ify the force fields for water molecules under

confinement. Such calculations must be un-

dertaken before claims of description of the



12/18

role of explicit water molecules in DNA trans-

port through pores.

TRANSLOCATION OFDOUBLE-STRANDED DNA

Experimental Facts

One of the well-studied experimental systemsinvolving ds-DNAis thepackaging of theviral

genome within the capsid of a bacteriophage.Linear dimensions of capsids are typically

tens of nanometers, whereas the length of thegenome to be packaged is generally three to

four orders of magnitude longer. The persis-tence length, over which the chain contour

remains directionally correlated, is 50 nmin physiological conditions and is compara-

ble to the linear dimensions of the capsid.The bending required of the genome as itis wound tightly within the capsid leads to a

buildup of energy that is large compared withkBT. In addition, the presence of phosphate

links leads to high linear charge density alongthe DNA backbone and gives rise to large

repulsive energy inside the densely packedcapsid.

Thus, the process of viral genome packingis a conflict of scales, wherein a long molecule

must be compressed within a length scale onwhich it resists bending and to a density atwhich it must also overcome strong repul-

sive forces. Such a conflict leads to the gen-eration of tremendously large pressures in-

side the capsid. Several X-ray diffraction andcryo-transmission electron microscopy stud-

ies (4) have determined the three-dimensionalstructure of the packaged genome. The time-

dependent buildup of force as the genomeis packaged inside the 29 bacteriophage by

a motor protein has been investigated (31)by the single-molecule optical tweezers tech-

nique. From these two kinds of measure-

ments, details of the kinetics of genome pack-aging and of the final structure of the genome

inside the capsid are beginning to emerge.The other experimental system inves-

tigating the transport of ds-DNA is the

translocation of ds-DNA through solid-state

nanopores (Figure 1b). There has recentlybeen a tremendous advancement (16, 17, 32

33) in sculpting solid-state nanopores withapertures ranging from 3 to 10 nm with con-

trollable thicknesses. Excellent progress hasbeen made in passing ds-DNA through these

nanopores under a voltage bias and record-ing signatures of ionic current trace unique tothe polymer undergoing translocation. The

most striking feature of the passage of ds-DNA through solid-state nanopores is the

tremendous heterogeneityin the distributionsof the blocked ionic current and transloca-

tion time, even though identical moleculesare passing by. The results reported so far

on the dependencies of these distributions onDNA length, applied voltage, pore diame-

ter, and pore length are bewildering. How-ever, some major conclusions can be drawn

from these data. The DNA molecule translo-

cates through the pore in quantized config-urations, such as a single-file chain with one

hairpin, even if the pore diameter is one or-der of magnitude smaller than the persistence

length of ds-DNA. The relative propensity ofsingle-file (unfolded) events increased non-

linearly with the voltage bias and decreasedwith the DNA length. To explain these ob-

servations, an electric field extending beyond2 m from the pore and the accompanying

conformationalchanges of DNA was invokedThis conjecture requires scrutiny, because for

the ionic strengths used in the experiments

the range of the electric field from the porecan be over only a few nanometers and not

microns.The experimental results on ds-DNA

transport through pores from different labo-ratories are sometimes contradictory. For ex-

ample, in one laboratory (15), the observedmobility of the polymer was independent

of polymer length and applied voltage. Inanother laboratory (33), the average translo-

cation time was found to depend on the poly-mer length with a 1.26-power law, in con-

tradiction with the other result, although

the pore diameters in these two experiments

446 Muthukumar


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Figure 10

Modeling of packingof ds-DNA into a T7bacteriophage.

are comparable. In addition, the theoretical

explanation offered for the 1.26-power lawviolates the known laws of polyelectrolyte hy-

drodynamics. In general, the experimental sit-uation appears murky and the data from dif-

ferent laboratories are inconsistent.

Theory and Simulations

Although there have been several theoreticalattempts to describe the experimental obser-

vations on the packaging of genomes in bacte-riophages, none is satisfactory so far. To gain

insight into the relative importance of the var-ious competing forces involved in packaging

of genomes, Forrey & Muthukumar (10) per-formed a coarse-grained Brownian Dynam-

ics simulation. As the genome is pushed intoan icosahedral capsid under the influence of a

motor protein, the internal buildup of energyand the resultant forces and the evolution ofstructure were monitored. A typical trajectory

of genome packing for a T7 bacteriophageis given in Figure 10. The simulations can

qualitatively reproduce experimental resultson force profiles, X-ray diffraction, and cryo-

transmission electron microscopy. Analysis ofthe detailed forces present during the packag-

ing process reveals that the genome packingprocess is fundamentally different from the

previously popular inverse spool model andthat it is dominatedby entropy associated with

polymer dynamics.Theory and modeling of the translocation

of ds-DNA through nanopores have yet to be

undertaken in a rigorous way. Unlike flexi-ble chains such as ss-DNA, it is not enough

for semiflexible polyelectrolytes such as ds-

DNA to have one of their ends at the pore

entrance in order for translocation to pro-ceed. The end must approach the pore with

the correct orientation as well. The calcula-tion of entropic barriers with additional con-

straints on the orientational degrees of free-dom is a difficult task (30). Nevertheless, this

exercise should be pursued. However, coarse-

grained simulations such as those performedfor the genome packaging in bacteriophages

can readily be performed for the translocationof ds-DNA through pores. These simulations

enable researchers to investigate the effectsof pore geometries, applied voltage bias, and

polymer length on the way in which ds-DNAmolecules pass through the pores. Further-

more, the role of patterned chemical decora-tion of the pores inner walls on the translo-

cation characteristics can easily be explored.

Although the hydrodynamic interactionsamong the polymer segments inside narrow

pores are expected to be screened, the effectof the electro-osmotic flow arising from the

coupling between the interface charges andhydrodynamics has yet to be systematically

investigated.

CONCLUSIONS

We have summarized the current status ofthe translocation of DNA through the HL

pore and solid-state pores in terms of ma-

jor experimental results, theoretical concepts,and macromolecular modeling. For the case

of flexible polyelectrolytes such as ss-DNAundergoing translocation through the HL

pore, most of the experimental results are



14/18

well understood and the theoretical frame-

work is satisfactory. The same cannot besaid about the current status of the trans-

port of ds-DNA through pores. Inconsistentresults are reported from different labora-

tories. More careful measurements on well-

calibrated, solid-state nanopores are needed.

On the theoretical side, the challenge lies

in the proper treatment of local chain stiff-ness and the conformational changes of semi-

flexible polyelectrolytes accompanying thetranslocation through pores under an exter-

nal field. Nevertheless, progress is likely to be

made soon by using computer simulations.

SUMMARY POINTS

1. Changes in the conformational entropy of polymer molecules, which accompany

their transport through pores, control the global properties of the transport such asthe dependencies of the translocation time on polymer length, driving forces, and

pore geometries.

2. Translocation of a single polymer molecule through pores is analogous to the nucle-

ation and growth mechanism for the kinetics of phase transformations.

3. Simple analytical formulas can be obtained for the global properties of polymer

translocation. In general, for long polymers and large driving forces, the translo-cation time is proportional to N/V, where N is the polymer length and V is the

applied voltage difference.

4. Macromolecular modeling is a useful tool that enables researchers to understand the

generic features of the experimental data on DNA transport through pores.

ACKNOWLEDGMENTS

It is a pleasure to thank C.Y. Kong and C. Forrey for their collaborations and the NIH (Grant

No. 1R01HG002776-01) for financial support.

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Annual Re

of Biophys

Biomolecu

Structure

Volume 35,

Contents

Frontispiece

Martin Karplus p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p xii

Spinach on the Ceiling: A Theoretical Chemists Return to Biology

Martin Karplus p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 1

Computer-Based Design of Novel Protein Structures

Glenn L. Butterfoss and Brian Kuhlman p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 49

Lessons from Lactose PermeaseLan Guan and H. Ronald Kaback p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 67

Evolutionary Relationships and Structural Mechanisms of AAA+Proteins

Jan P. Erzberger and James M. Berger p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 93

Symmetry, Form, and Shape: Guiding Principles for Robustness in

Macromolecular Machines

Florence Tama and Charles L. Brooks, III p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 115

Fusion Pores and Fusion Machines in Ca2+-Triggered Exocytosis

Meyer B. Jackson and Edwin R. Chapmanp p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p

135

RNA Folding During Transcription

Tao Pan and Tobin Sosnick p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 161

Roles of Bilayer Material Properties in Function and Distribution of

Membrane Proteins

Thomas J. McIntosh and Sidney A. Simon p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 177

Electron Tomography of Membrane-Bound Cellular Organelles

Terrence G. Frey, Guy A. Perkins, and Mark H. Ellisman p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 199

Expanding the Genetic CodeLei Wang, Jianming Xie, and Peter G. Schultz p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 225

Radiolytic Protein Footprinting with Mass Spectrometry to Probe the

Structure of Macromolecular Complexes

Keiji Takamoto and Mark R. Chance p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 251

v


18/18

The ESCRT Complexes: Structure and Mechanism of a

Membrane-Trafficking Network

James H. Hurley and Scott D. Emr p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 277

Ribosome Dynamics: Insights from Atomic Structure Modeling into

Cryo-Electron Microscopy Maps

Kakoli Mitra and Joachim Frank p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 299

NMR Techniques for Very Large Proteins and RNAs in SolutionAndreas G. Tzakos, Christy R.R. Grace, Peter J. Lukavsky, and Roland Riek p p p p p p p p p p 319

Single-Molecule Analysis of RNA Polymerase Transcription

Lu Bai, Thomas J. Santangelo, and Michelle D. Wang p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 343

Quantitative Fluorescent Speckle Microscopy of Cytoskeleton

Dynamics

Gaudenz Danuser and Clare M. Waterman-Storer p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 361

Water Mediation in Protein Folding and Molecular Recognition

Yaakov Levy and Jos N. Onuchic p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 389

Continuous Membrane-Cytoskeleton Adhesion Requires Continuous

Accommodation to Lipid and Cytoskeleton Dynamics

Michael P. Sheetz, Julia E. Sable, and Hans-Gnther Dbereiner p p p p p p p p p p p p p p p p p p p p p p p 417

Cryo-Electron Microscopy of Spliceosomal Components

Holger Stark and Reinhard Lhrmann p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 435

Mechanotransduction Involving Multimodular Proteins: Converting

Force into Biochemical Signals

Viola Vogel p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 459

INDEX

Subject Index p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 489

Cumulative Index of Contributing Authors, Volumes 3135 p p p p p p p p p p p p p p p p p p p p p p p p p p p 509

Cumulative Index of Chapter Titles, Volumes 3135 p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 512

ERRATA

An online log of corrections to Annual Review of Biophysics and Biomolecular Structurechapters (if any, 1997 to the present) may be found at

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mechanism of dna transport through pores

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