DNA Barcodes using a Cylindrical Nanopore
DDNA Barcodes using a Cylindrical Nanopore
Swarnadeep Seth and Aniket Bhattacharya ∗ Department of Physics, University of Central Florida, Orlando, Florida 32816-2385, USA (Dated: February 9, 2021)We report an accurate method to determine DNA barcodes from the dwell time measurement ofprotein tags (barcodes) along the DNA backbone using Brownian dynamics simulation of a modelDNA and use a recursive theoretical scheme which improves the measurements to almost 100%accuracy. The heavier protein tags along the DNA backbone introduce a large speed variation inthe chain that can be understood using the idea of non-equilibrium tension propagation theory.However, from an initial rough characterization of velocities into “fast” (nucleotides) and “slow”(protein tags) domains, we introduce a physically motivated interpolation scheme that enables usto determine the barcode velocities rather accurately. Our theoretical analysis of the motion of theDNA through a cylindrical nanopore opens up the possibility of its experimental realization andcarries over to multi-nanopore devices used for barcoding.
A DNA barcode consists of a short strand of DNAsequence taken from a targeted gene like COI or cox I(Cytochrome C Oxidase 1) [1] present in the mitochon-drial gene in animals. The unique combination of nu-cleotide bases in barcode allows us to distinguish onespecies from another. Unlike relying on the traditionaltaxonomical identification methods, DNA barcoding pro-vides an alternative and reliable framework to catego-rize a wide variety of specimens obtained from the nat-ural environment. Though researchers relied on DNAsequencing techniques for the identification of unknownspecies for a long time, in 2003, Hebert et al. [2] pro-posed the mictocondrial gene (COI) region barcoding toclassify cryptic species [3] from the entire animal popu-lation. Since then, several studies have shown the po-tential applications of barcoding in conserving biodiver-sity [4], estimating phyletic diversity, identifying diseasevectors [5], authenticating herbal products [6], unambigu-ously labeling the food products [7, 8], and protectingendangered species [4]. Traditional sequencing methodsbased on chemical analysis are widely used in the bio-logical community to determine the barcodes. Nanoporebased sequencing methods [9] are being explored in adual nanopore system for a cost effective, high through-put, chemical-free, and real time barcode generation.The possibility of determining DNA barcodes havebeen demonstrated in a dual nanopore device, by scan-ning a captured dsDNA multiple times by applying a netperiodic bias across the two pores [9–12]. Theoretical andsimulation studies have also been reported in the con-text of a double nanopore system [13–15]. In this article,we investigate a similar strategy in silico in a cylindricalnanopore and demonstrate that a cylindrical nanoporecan have a competitive advantage over a dual nanoporesystem. By studying a model dsDNA with barcodes us-ing Brownian dynamics we establish an important resultthat it is due to the disparate dwell time and speed of ∗ Author to whom the correspondence should be addressed;[email protected]
ExtendedWalls t pore t pore σ f U f D T T
1 2 TT T T T T a.b. FIG. 1. Schematics of a model dsDNA captured in cylindri-cal nanopore of diameter d = 2 σ and thickness t pore , where σ is the diameter of each monomer (purple beads). Protein tags(barcodes) of the same diameter but of different colors (onlythree are shown in here) interspersed along the dsDNA back-bone. Opposite but unequal forces (cid:126)f U and (cid:126)f D are appliedto straighten the dsDNA as it translocates in the directionbias net ±| ∆ (cid:126)f UD | = ±| (cid:126)f U − (cid:126)f D | through the nanopore. (b)Positions of the protein tags along the contour length of themodel dsDNA of length L = 1024 σ which represents an ac-tual dsDNA of 48500 base pairs. The location of the tags arelisted in Table-I. the barcodes (“tags”) compared to the nucleotide seg-ments (“monomers”) the current blockade time informa- TABLE I. Tag positions along the dsDNA
Tag T T T T T T T T Position 154 369 379 399 614 625 696 901Separation 154 215 10 20 215 11 71 205 tion only is not enough and will lead to an inevitableunderestimation of the distance between the barcodes. a r X i v : . [ c ond - m a t . s o f t ] F e b Furthermore, using the ideas of the tension propagationtheory [16, 17], we demonstrate that information aboutthe fast-moving nucleotides in between the barcodes,- noteasily accessible experimentally is a key element to re-solve the underestimation. We suggest how to obtainthis information experimentally and provide a physicallymotivated “two-step” interpolation scheme for an accu-rate determination of barcodes, even when the separationof (unknown) tags has a broad distribution. • The Model System:
Our in silico coarse-grained (CG)model of a dsDNA consist of 1024 monomers interspersedwith 8 barcodes at different locations shown in Fig. 1 andTable-I is motivated by an experimental study by Zhang et al. on a 48500 bp long dsDNA with 75 bp long proteintags at random locations along the chain [10–12] usinga dual nanopore device. Here we explore if a cylindricalnanopore with applied biases at each end can resolve thebarcodes with similar accuracy or better. We purposelychoose positions of the 8 barcodes (Table-I) to study howthe effect of disparate distances among the barcodes af-fects their measurements. The tags T , T , T are closelyspaced and form a group. Likewise, another group con-sisting of T and T are put in a closer proximity to T .The tags T and T are further apart from the rest of thetags. The general scheme of the BD simulation strategyfor a translocating homo-polymer under alternate biashas been discussed in our recent publication [13, 14] andin the Appendix A.In this article, tags are introduced by choosing themass and friction coefficient at tag locations to be dif-ferent than the rest of the monomers along the chain.This requires modification of the BD algorithm as dis-cussed in the Appendix A. The protein tags used in theexperiments [10–12] translate to about three monomersin the simulation. The heavier and extended tags intro-duce a larger viscous drag. Instead of explicitly puttingside-chains at the tag locations, we made the mass andthe friction coefficient of the tags 3 times larger. Thiswe find enough to resolve the distance between the tags.Two forces (cid:126)f U and (cid:126)f D at each end of the cylinder in oppo-site directions keep the DNA straight inside the channeland allows translocation in the direction of the net bias(please see Fig. 1 and Fig. 2). • Barcodes from repeated scanning:
As potentiallycould be done in a nanopore experiments, we switchthe differential bias once the first tag or the last tag( T , T ) translocates through the nanopore duringup( U )/down( D ) → D/U translocation yet having endsegments inside the pore (please see Fig. 2) so that theDNA remains captured in the cylindrical pore and thebarcodes are scanned multiple times. The question weask: can we recover the actual barcode locations fromthese scanning measurements, so that the method canbe applied to determine unknown barcodes ? We mon-itor two important quantities, - the dwell time of each a. b. f U f D f U f D FIG. 2. Demonstration of the epoch when the bias voltage isflipped. (a) showing the last barcode is yet to translocate inthe downward direction when the net bias ∆ (cid:126)f DU = (cid:126)f D − (cid:126)f U >
0. (b) shows the situation after a later time when finally allthe barcodes crossed the cylindrical pore during downwardtranslocation with a portion of the end segment still remaininginside the pore. At this point the bias is flipped with anupward bias ∆ (cid:126)f UD = (cid:126)f U − (cid:126)f D >
0, translocation now occurs inthe upward direction. In this way, the DNA remains capturedall the time during repeated scans. t pore t pore ti U D (696) t f U D (696) W U D (696) = t f U D (696) t i U D (696) - T T8 T8T a. D U D U T7 T8 T8 T7 t pore t pore = τ mn U D t i U D (8) t i U D (7) - b. FIG. 3. (a) Demonstration of calculation of wait time for T which has the monomer of index m = 696. The dwellvelocity is then calculated using Eqn. 2. (b) Demonstrationof calculation of tag time delay τ U → D = t U → Di (8) − t U → Di (7)for tags T and T while they are moving downward. Pleasenote that similar quantity for upward translocation τ D → U = t D → Ui (7) − t U → Di (8) (cid:54) = τ U → D as there is no symmetry of thetags along the chain. monomer and the time delay of arrival of two successivemonomers at the pore as demonstrated in Fig. 3 and ex-plained below. For each up/down-ward scan we measurethe dwell times of the monomer m as follows: W U → D ( m ) = t U → Df ( m ) − t U → Di ( m ) , (1a) W D → U ( m ) = t D → Uf ( m ) − t D → Ui ( m ) . (1b)Here t U → Di ( m ) and t U → Df ( m ) are the arrival and exittimes of the monomer with index m as further demon-strated in Fig. 3(a). The corresponding dwell veloci-ties v U → Ddwell ( m ) and v D → Udwell ( m ) for the m th bead (eithera monomer or a tag) along the channel axis (please seeFig. 3(a)) can be obtained as follows. v U → Ddwell ( m ) = t pore /W U → D ( m ) , (2a) v D → Udwell ( m ) = t pore /W D → U ( m ) . (2b)In an actual experiment one measures the dwell veloci-ties of the tags only which are equivalent to the currentblockade times. • Non uniformity of the dwell velocity:
The presenceof tags with heavier mass ( m tag = 3 m bulk ) and largersolvent friction ( γ tag = 3 γ bulk ) introduces a large vari-ation in the dwell time and hence a large variation inthe dwell velocities of the DNA beads and tags (seeFig. 4). In general, there is no up-down symmetry forthe dwell time/velocity as tags are not located symmetri-cally along the chain backbone. Thus the physical quan-tities are averaged over U → D and D → U translo-cation data. The average dwell velocity ¯ v dwell ( m ) = (cid:2) v U → Ddwell ( m ) + v D → Udwell ( m ) (cid:3) clearly shows two different ve-locity envelopes - the tags residing at the lower envelope.Fig. 4 shows that the dwell velocities of the tags (green m/N Dw e ll V e l o c it y U � DD � U � UD � N = 1024 � = 3.0 FIG. 4. Dwell velocity of monomer in a cylindrical nanoporesystem. (cid:79) and (cid:77) represent downward and upward transloca-tion. ◦ are average of both directions. Filled triangles andcircles correspond to tag dwell velocities. circle ) are significantly lower than the velocity of thenucleotides in between the tags, which will underestimatethe barcode distances as explained later. We further no-tice that increasing the pore width resolves the barcodesbetter. • Barcode estimation using a cylindrical nanoporesetup:
If the dsDNA with barcodes were a rigid rod, then one could obtain the barcode distances d U → Dmn and d D → Unm between tags T m and T n from the following equations(shown for downward translocation only): d U → Dmn = v U → Dmn × τ U → Dmn where , (3a) v U → Dmn = 12 (cid:2) v U → Ddwell ( m ) + v U → Ddwell ( n ) (cid:3) , (3b) τ U → Dmn = (cid:0) t U → Di ( n ) − t U → Di ( m ) (cid:1) . (3c)Here τ U → Dmn is the time delay of arrivals of T m and T n for downward translocation (please see Fig. 3(b) whichexplains the special case when m = 7 and n = 8). SimilarEquations can be obtained by flipping D and m with U and n respectively. In other words, Eqn. 3 gives theshortest distance and not necessarily the contour length(the actual distance) between the tags. However, this isthe only data accessible through experiments and likelyto provide an underestimation of the barcodes. Fig. 5(a)shows the data for 300 scans. The average with error barsare shown in the 3 rd column of Table-II. Excepting for T these measurements grossly underestimate the actualpositions with large error bars. TABLE II. Barcodes from various methodsTag Relative Barcode Barcode BarcodeLabel Distance (Eqn. 3) (Method-I) (Method-II)w.r.t T × (cid:88) (cid:88) T
460 373 ±
122 459 ±
59 460 ± T
245 197 ±
67 250 ±
39 250 ± T
235 183 ±
63 237 ±
38 237 ± T
215 167 ±
54 211 ±
35 211 ± T T
11 11 ± ± ± T
82 68 ±
23 86 ±
23 86 ± T
287 230 ±
73 287 ±
65 287 ± • Tension Propagation (TP) Theory explains thesource of discrepancy and provides solution:
Unlike arigid rod, tension propagation governs the semi-flexiblechain’s motion in the presence of an external bias. InTP theory and its implementation in Brownian dynam-ics, the motion of the subchain in the cis side decouplesinto two domains [16, 17]. In the vicinity of the pore, thetension front affects the motion directly while the seconddomain remains unperturbed, beyond the reach of the TPfront. In our case, after the tag T m translocates throughthe pore, preceding monomers are dragged into the porequickly by the tension front, analogous to the uncoilingeffect of a rope pulled from one end. The onset of thissudden faster motion continues to grow and reaches itsmaximum until the tension front hits the subsequent tag T m ± , with larger inertia and viscous drag. At this time(called the tension propagation time [18]) the faster mo-tion of the monomers begins to taper down to the ve-locity of the tag T m ± . This process continues from onesegment to the other. Fig. 6 shows an example on howthe segment connecting T and T Relative Position F l o ss C oun t M e t hod I M e t hod II (a)(b)(d)(c)(e)(f) FIG. 5. (a) Barcodes generated using different methods. Ineach graph, the colored symbols/lines refer to the correspond-ing colors of the barcodes T , T , T , , T , T , T , T , and T respectively. The open and filled symbols represent bar-codes for U → D and D → U transolcation using (a) Eqn.3; (c) using method 1, and (e) using method 2. In (b), (d)and (e) the solid lines refer to the actual location of the bar-codes and the dashed lines correspond to the averages from(a), (c) and (e) respectively. The improved accuracy for thelatter two methods are readily visible in (d) and (f) where thesimulation and the actual data are almost indistinguishable. contour lengths of faster moving segments in between twobarcodes are not accounted for in Eqn 3. The experimen-tal protocols are limited in extracting barcode informa-tion through Eqn. 3 (measuring current blockade time)and therefore, likely to underestimate the barcodes, un-less the data is corrected to account for the faster movingmonomers in between two tags. • How to determine the barcodes correctly ?
Fig. 1(b) D U fastmovement slowmovement t pore t pore Tension front Tension front hits T a. b. v chain v dwell U D (7) v dwell U D (8) v dwell U D (7) v dwell U D (8)
U D U D v chain FIG. 6. Tension propagation (TP) through the chain back-bone connecting T and T
8. (a) Figure shows a sudden fastmovement of monomers right after T ’s passage through thepore. Due to the TP front’s influence (yellow blob region),subsequent monomers are sucked into the pore quickly. (b)TP front finally reaches T
8, leading to a slower translocationspeed due to the tag’s large inertia and higher viscous drag. and the 3 rd column of Table-II when looked closely pro-vide clues to the solution of the underestimated tag dis-tances. We note that locations of the isolated tags (suchas, T and T ) far from T have a larger error bar while T which is adjacent to T has the correct distance fromEqn. 3. It is simply because in the later case the con-tour length between T and T is almost equal to theshortest distance. Evidently, the error bars increase withincreased separation.To compare the barcodes obtained from Eqn. 3 withthe actual contour length (see 2 nd column of Table-II) be-tween tag pairs, we invoke the Flory theory to determinethe scaling exponent ν [19] which reveals the behavior ofthe segments under translocation. The heatmap in Fig. 7confirms that when the separation between the tag pairsis less compared to the DNA length, the connecting seg-ment behaves like a rigid rod ( ν > . ν < . Method 1 - Barcode from known end-to-end Tag dis-tance:
In order to measure the barcode distances accu-rately one thus needs the velocity of the entire chain. Ifthe distance between T and T ) d (cid:39) L , then the ve-locity of the segment d will approximately account forthe average velocity of the entire chain v chain and correctthe problem as demonstrated next. First we estimate thevelocity of the chain v U → Dchain ≈ v U → D = d /τ U → D , (4)assuming we know d and τ U → D is the time delay of ar-rival at the pore between T and T for U → D translo-cation. We then estimate the barcode distance d U → Dmn
FIG. 7. Flory exponent ( ν ) for the segment connecting a tagpair represented as a two dimensional heatmap array on thecolor scale ranging from blue to white. between tags T m and T n as d U → Dmn = v U → D × τ U → Dmn . (5)In the similar fashion one can calculate d D → Umn using v D → Uchain and τ U → Dmn information respectively. How do weknow d ? One can use d ≈ L scan and v chain ≈ ¯ v scan ,from Eqn. 6 where ¯ v scan is the the average velocity of thescanned length L scan from repeated scanning as discussedin the next paragraph. This method is effective for esti-mating the long-spaced barcodes but it overestimates thebarcode distance if multiple barcodes are close by as evi-dent in Fig. 5(d) and the 4 th column of table-II. Thus, weknow how to obtain barcode distances accurately whenthey are close by (from Eqn. 3) and for large separation(Eqn. 5). We now apply the physics behind these twoschemes to derive an interpolation scheme that will workfor all separations among the barcodes. Method 2 - Barcode using two-step method:
Averagescan time ¯ τ scan for the entire chain (which can be mea-sured experimentally) is a better way to estimate the av-erage velocity of the chain. L scan is the maximum lengthup to which the dsDNA segment remains captured in-side the nanopore gets scanned and denotes the theoreti-cal maximum beyond which the dsDNA will escape fromthe nanopore, thus, L ≈ L scan . For example, in our sim-ulation, scanning length L scan = 0 . L . We denote theaverage scan velocity as¯ v scan = 1 N scan N scan (cid:88) i =1 L scan /τ scan ( i ) , (6)where τ scan ( i ) is the scan time for the i th event, and N scan = 300. To proceed further, we use our establishedresults that the monomers of the dsDNA segments in be-tween the tags move with velocity ¯ v scan , while tags move with their respective dwell velocities v U → Dmn and v D → Umn (Eqn. 2). We then calculate the segment velocity betweentwo tags by taking the weighted average of the velocitiesof tags and DNA segment in between as follows.First, we estimate the approximate number ofmonomers N mn = d U → Dmn / (cid:104) b l (cid:105) ( (cid:104) b l (cid:105) is the bond-length)by considering the tag velocities only using Eqn. 3. Wethen calculate the segment velocity accurately by incor-porating weighted velocity contributions from both thetags and the monomers between the tags. v U → Dweight = 1 N mn (cid:104) v U → Ddwell ( m ) + v U → Ddwell ( n )+( N mn − v scan (cid:105) (7)The barcodes are finally estimated by multiplying thecalculated 2-step velocity in Eqn. 7 above by the tag timedelay as d U → Dmn = v U → Dweight × τ U → Dmn (8)for U → D translocation and repeating the procedurefor D → U translocation. This 2-step method accu-rately captures the distance between the barcodes whenthe two tags are in proximity or spaced apart from eachother. Table-II and Fig. 5 summarize our main resultsand claims. • Summary & Future work:
Motivated by the re-cent experiments we have designed barcode determina-tion experiment in silico in a cylindrical nanopore usingthe Brownian dynamics scheme on a model dsDNA withknown locations of the barcodes. We have carefully cho-sen the locations of the barcodes so that the separationsamong the barcodes span a broad distribution. We dis-cover that if we use the dwell time data only for thebarcodes from multiple scans of the dsDNA to calculatethe average velocities of the tags then the method under-scores the barcode distances for tags further apart. Oursimulation guides us to conclude that the source of thisunderestimation lies in neglecting the information con-tained in the faster moving DNA segments in betweenany two tags. We use non-equilibrium tension propaga-tion theory to explain the non-monotonic velocity of thechain segments where the barcodes lie at the lower boundof the velocity envelope as shown in Fig. 4. The emergingpicture readily shows the way how to rectify this error byintroducing an interpolation scheme that works well todetermine barcodes spaced apart for all distances whichwe validate using simulation data. We suggest how toimplement the scheme in an experimental setup. It isimportant to note that the interpolation scheme-basedconcept of the TP theory is quite general and we haveample evidence that this will work in a double nanoporesystem as well. • Conflicts of interest:
The authors declare no com-peting financial interest. • Acknowledgements:
The research at UCF has beensupported by the grant number 1R21HG011236-01 fromthe National Human Genome Research Institute at theNational Institute of Health. All computations were car-ried out at the UCF’s high performance computing plat-form STOKES.
Appendix A: The Model and Brownian dynamicssimulation
Our BD scheme is implemented on a bead-springmodel of a polymer with the monomers interacting viaan excluded volume (EV), a Finite Extension NonlinearElastic (FENE) spring potential, and a bond-bending po-tential enabling variation of the chain persistence length (cid:96) p (Fig.A1). The model, originally introduced for a fullyflexible chain by Grest and Kremer [20], has been stud-ied quite extensively by many groups using both MonteCarlo (MC) and various molecular dynamics (MD) meth-ods [21]. Recently we have generalized the model for asemi-flexible chain and studied both equilibrium and dy-namic properties [18, 22, 23] and studied compression dy-namics of a model dsDNA inside a nanochannel [24, 25]. The mutual EV interaction among any two monomersare given by the truncated Lennard-Jones (LJ) potentialwith a cut-off radius 2 / σU LJ ( r ij ) = (cid:15) (cid:20)(cid:16) σr ij (cid:17) − (cid:16) σr ij (cid:17) (cid:21) + (cid:15), for r < / , otherwise (A1)where σ is the effective diameter of a monomer and (cid:15) is the interaction strength. To mimic the connectivitybetween two adjacent monomers, finite-extensible-non-linear elastic (FENE) potential i-1 i i+1 i+2 i+3 i b. a. t pore σ c. r( �� U (r)[ � � LJFENELJ + FENE
Equilibrium Bond Length (0.972±0.001 �� � FIG. A1. (a) Illustration depicts the monomers are inter-acting via LJ and FENE potential. The three body bendingpotential is calculated using the angle θ i between two adjacentbond vectors (cid:126)b i and (cid:126)b i +1 respectively. (b) Interaction poten-tial between two consecutive monomers is given by the greenline for a separation distance r in unit of σ . The blue dia-monds denote the LJ potential with a cutoff radius 2 / σ andthe magenta circles correspond to the FENE potential with aspring constant κ F = 30 . (cid:15)/σ . (c) A cylindrical nanopore ofdiameter 2 σ is dilled into a material of thickness t pore . Thewalls consist of purely repulsive LJ particles. U F ENE ( r ij ) = − κ F R ln (cid:34) − (cid:18) r ij R (cid:19) (cid:35) (A2)is used with the maximum bond-stretching length R =1 . σ and spring constant κ F = 30 (cid:15)/σ . Here, r ij = | (cid:126)r i − (cid:126)r j | is the separation distance between two adjacentmonomers i and j = i ± (cid:126)r i and (cid:126)r j respec-tively. Along with these two potentials, we introduce abending potential U bend ( θ i ) = κ (1 − cos ( θ i )) (A3)with bending rigidity κ . In three dimensions, for κ (cid:54) =0, the persistence length (cid:96) p of the chain is related to κ via [26] (cid:96) p = κk B T , (A4)where k B is the Boltzmann constant and T is thetemperature. Here θ i is the bond angle between twosubsequent bond vectors (cid:126)b i = (cid:126)r i +1 − (cid:126)r i and (cid:126)b i − = (cid:126)r i − (cid:126)r i − . A cylindrical nanopore of diameter 2 σ isdrilled through a solid material of thickness t pore con-sists of immobile and purely repulsive LJ particles. Ourmodel of DNA polymer consists 1016 monomer beadsalong with 8 heavier tags ( T - T ) located at po-sitions 154 , , , , , , m tag )three times heavier of a normal monomer to replicate thetags used in the experiments. We proportionally increasethe solvent friction of the tags Γ tag = 3Γ i . We use theBrownian dynamics to solve the equation of motion of amonomer i having a mass m i and solvent friction Γ i as m i ¨ (cid:126)r i = (cid:126) ∇ i [ U LJ + U F ENE + U bend + U wall ] − Γ i (cid:126)v i + η i (A5)where Γ i = 0 . (cid:112) m i (cid:15) /σ is the frictional coefficient aris-ing from solvent-monomer interaction. For the case ofa tag, m tag = 3 m i and Γ tag = 2 . (cid:112) m i (cid:15) /σ . TheGaussian white noise η i arising from thermal fluctua-tion is delta correlated and expressed as (cid:104) η i ( t ) .η j j ( t (cid:48) ) (cid:105) =2 dk B T Γ δ ij δ ( t − t (cid:48) ) with d = 3 in three dimension. Weexpress length and energy in units of σ and (cid:15) respectivelysuch that k B T /(cid:15) = 1 .
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