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7/31/2019 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.
435
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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
440 Muthukumar
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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
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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
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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
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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
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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
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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
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Fusion Pores and Fusion Machines in Ca2+-Triggered Exocytosis
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RNA Folding During Transcription
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Roles of Bilayer Material Properties in Function and Distribution of
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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
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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
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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
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