# MapAI: Precision in Building Segmentation

Sander Riisøen Jyhne
The Norwegian Mapping Authority
University of Agder
Grimstad, Norway
<EMAIL_ADDRESS>
Morten Goodwin
Centre for Artificial Intelligence Research
University of Agder
Grimstad, Norway
<EMAIL_ADDRESS>
Per Arne Andersen
Centre for Artificial Intelligence Research
University of Agder
Grimstad, Norway
<EMAIL_ADDRESS>
Ivar Oveland
The Norwegian Mapping Authority
Kristiansand, Norway
<EMAIL_ADDRESS>
Alexander Salveson Nossum
Norkart
Kristiansand, Norway
Karianne Ormseth
AI:Hub
Grimstad, Norway
Mathilde Ørstavik
Norkart
Oslo, Norway
Andrew C. Flatman
SDFI
Denmark

###### Abstract

MapAI: Precision in Building Segmentation is a competition arranged with the
Norwegian Artificial Intelligence Research Consortium (NORA)
111https://nora.ai in collaboration with Centre for Artificial Intelligence
Research at the University of Agder (CAIR)222https://cair.uia.no, the
Norwegian Mapping Authority333https://kartverket.no,
AI:Hub444https://aihub.no/, Norkart555https://www.norkart.no, and the Danish
Agency for Data Supply and Infrastructure666https://eng.sdfi.dk/. The
competition will be held in the fall of 2022. It will be concluded at the
Northern Lights Deep Learning conference focusing on the segmentation of
buildings using aerial images and laser data. We propose two different tasks
to segment buildings, where the first task can only utilize aerial images,
while the second must use laser data (LiDAR) with or without aerial images.
Furthermore, we use IoU and Boundary IoU [1] to properly evaluate the
precision of the models, with the latter being an IoU measure that evaluates
the results’ boundaries. We provide the participants with a training dataset
and keep a test dataset for evaluation.

_K_ eywords artificial intelligence; machine learning; deep learning; computer
vision; remote sensing; semantic segmentation

_K_ eywords First keyword $\cdot$ Second keyword $\cdot$ More

##  1 Introduction

Buildings are an essential component of information regarding population,
policy-making, and city management [2]. Using computer vision technologies
such as classification, object detection, and segmentation has proved helpful
in several scenarios, such as urban planning and disaster recovery [2, 3].
Segmentation is the most precise method and can give detailed insights into
the data as it highlights the area of interest.

Acquiring accurate segmentation masks of buildings is challenging since the
training data derives from real-world photographs. As a result, the data often
have varying quality, large class imbalance, and contains noise in different
forms. The segmentation masks are affected by optical issues such as shadows,
reflections, and perspectives. Additionally, trees, powerlines, or even other
buildings may obstruct the visibility [4]. Furthermore, small buildings have
proved to be more difficult to segment than larger ones as they are harder to
detect, more prone to being obstructed, and often confused with other classes
[5]. Lastly, different buildings are found in several diverse areas, ranging
from rural to urban locations. The diversity poses a vital requirement for the
model to generalize to the various combinations. These hardships motivate the
competition and our evaluation method, detailed in Evaluation Methodology.

This competition follows mostly the same strategy as previous NORA
competitions [6, 7].

##  2 Dataset Details

For the competition, we provide the participants with a dataset containing
aerial images, laser data, and ground truth masks for the buildings. We split
the dataset into a training dataset and a test dataset. The training dataset
is released at the start of the competition, while the test dataset will be
kept hidden until the competition is over. When the competition is complete,
we will release the full dataset.

The training dataset consists of several different locations in Denmark. Area
variability ensures a diverse dataset with several different environments and
building types. The test dataset consists of seven locations in Norway,
comprising urban and rural cities.

The data is derived from real-world data. As a result, there are cases where
the buildings in the aerial image do not correspond to a ground truth mask. In
addition, the ground truths in the test dataset are generated using a DTM,
which skews the top of the buildings in images compared to the ground truths.
The training dataset is generated using a DSM, which does not skew the top of
the buildings. In Figure LABEL:fig:dataexample, we can see examples of the
different datatypes present in the training dataset.

Figure 1: Aerial image sample from the training dataset Figure 2: Lidar sample
from the training dataset Figure 3: Mask sample from the training dataset

##  3 Task Descriptions

We present two subtasks; (1) an aerial image segmentation task and (2) laser
data segmentation task. The participants are encouraged to submit for both
tasks; however, it is not mandatory. Note that both tasks contribute equal
weight to the final score, i.e., 50% each. You can only reach the maximum
score by a separate submission for both tasks

###  3.1 Task 1: Aerial Image Segmentation Task

The aerial image segmentation task aims to solve the segmentation of buildings
only using aerial images. Segmentation using only aerial images is helpful for
several scenarios, including disaster recovery in remote sensing images where
laser data is unavailable. We ask the participants to develop machine learning
models for generating accurate segmentation masks of buildings solely using
aerial images.

###  3.2 Task 2: Laser Data Segmentation Task

The laser data segmentation task aims to solve the segmentation of buildings
using laser data. Segmentation using laser data is helpful for urban planning
or change detection scenarios, where precision is essential. We ask the
participants to develop machine learning models for generating accurate
segmentation masks of buildings using laser data with or without aerial
images.

###  3.3 Submission

We have developed a new template for competition participation and submission.
The contestants will have to fork a GitHub repository, create a folder for
their team and develop their methods in the folder. When the participants are
ready for submission, they push the changes to their fork and create a pull
request to the original repository. Automatic Github actions will test their
code and models and store their results. The GitHub repository and
instructions are found at https://github.com/Sjyhne/mapai-competition.

##  4 Evaluation Methodology

We evaluate both tasks with the same metrics described in the following
paragraphs. Overall there will be a first place and a second place winner of
MapAI, determined by the sum of the score $S$ from both tasks.

We use a combination of Intersection-over-Union (IoU) and Boundary
Intersection-over-Union (BIoU) to evaluate the submitted segmentation mask.
The formula for the evaluation score $S$ is presented in Eq. 1.

$S=\frac{BIoU+IoU}{2}$ (1)

The Intersection-over-Union (IoU), also known as the Jaccard Index, measures
the similarity between two samples, G (ground truth) and P (prediction), by
dividing the intersecting area by the total area, seen in Eq. 2.

$IoU=\frac{Intersection}{Union}=\frac{|G\cap P|}{|G|+|P|-|G\cap P|}$ (2)

The Boundary Intersection-over-Union (BIoU) calculates the IoU of the boundary
of the prediction and ground truth. A variable d determines the width of the
boundary used in the calculation. Fig 4 visualizes how we calculate the
Boundary IoU, where $G$ and $G_{d}$ denote the ground truth and the edge of
the ground truth with thickness d. Similarly to G, $P$ and $P_{d}$ denote the
predicted mask and the edge of the predicted mask with thickness d.

Figure 4: The Boundary Intersection-over-Union (BIoU) used to measure the
accuracy of the segmentation boundary [1]

The final score for the competition is the average of the score $S$ from both
tasks.

##  5 Summary

This paper presents the first version of MapAI: Precision in Building
Segmentation task. The competition aims to advance the remote sensing image
segmentation field by presenting two subtasks with an evaluation focused on
small buildings and segmentation boundaries. We hope the competition motivates
students to participate and contribute to advancing the field.

## References

  * [1] Bowen Cheng, Ross B. Girshick, Piotr Dollár, Alexander C. Berg, and Alexander Kirillov.  Boundary iou: Improving object-centric image segmentation evaluation.  CoRR, abs/2103.16562, 2021.
  * [2] Carmen Grecea, Alina Bălă, and S. Herban.  Cadastral requirements for urban administration, key component for an efficient town planning.  Journal of Environmental Protection and Ecology, 14:363–371, 01 2013.
  * [3] Wenjuan Sun, Paolo Bocchini, and Brian Davison.  Applications of artificial intelligence for disaster management.  Natural Hazards, 103:2631–2689, 09 2020.
  * [4] Schlosser Aletta, Gergely Szabo, Laszlo Bertalan, Zsolt Varga, Péter Enyedi, and Szilard Szabo.  Building extraction using orthophotos and dense point cloud derived from visual band aerial imagery based on machine learning and segmentation.  Remote Sensing, 12:2397, 07 2020.
  * [5] Michael Kampffmeyer, Arnt-Børre Salberg, and Robert Jenssen.  Semantic segmentation of small objects and modeling of uncertainty in urban remote sensing images using deep convolutional neural networks.  In 2016 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), pages 680–688, 2016.
  * [6] Steven Hicks, Debesh Jha, Vajira Thambawita, Pål Halvorsen, Bjørn-Jostein Singstad, Sachin Gaur, Klas Pettersen, Morten Goodwin, Sravanthi Parasa, Thomas de Lange, et al.  Medai: Transparency in medical image segmentation.  Nordic Machine Intelligence, 1(1):1–4, 2021.
  * [7] Tor-Arne Schmidt Nordmo, Ove Kvalsvik, Svein Ove Kvalsund, Birte Hansen, and Michael A Riegler.  Fish ai: Sustainable commercial fishing.  Nordic Machine Intelligence, 2(2):1–3, 2022.


] Author to whom the correspondence should be addressed

# How capture affects polymer translocation in a solitary nanopore

Swarnadeep Seth  Aniket Bhattacharya  [<EMAIL_ADDRESS>1Department of Physics, University of Central Florida, Orlando, Florida
32816-2385, USA

###### Abstract

DNA capture with high fidelity is an essential part of nanopore translocation.
We report several important aspects of the capture process and subsequent
translocation of a model DNA polymer through a solid-state nanopore in
presence of an extended electric field using the Brownian dynamics simulation
that enables us to record statistics of the conformations at every stage of
the translocation process. By releasing the equilibrated DNAs from different
equipotentials, we observe that the capture time distribution depends on the
initial starting point and follows a Poisson process. The field gradient
elongates the DNA on its way towards the nanopore and favors a successful
translocation even after multiple failed threading attempts. Even in the limit
of an extremely narrow pore, a fully flexible chain has a finite probability
of hairpin-loop capture while this probability decreases for a stiffer chain
and promotes single file translocation. Our in silico studies identify and
differentiate characteristic distributions of the mean first passage time due
to single file translocation from those due to translocation of different
types of folds and provide direct evidences of the interpretation of the
experimentally observed folds [M. Gershow et al., Nat. Nanotech. 2, 775 (2007)
& M. Mihovilovic et al. Phys. Rev. Letts. 110, 028102 (2013)] in a solitary
nanopore. Finally, we show a new finding, - that a charged tag attached at the
$5^{\prime}$ end of the DNA enhances both the multi-scan rate as well as the
uni-directional translocation ($5^{\prime}\rightarrow 3^{\prime}$) probability
that would benefit the genomic barcoding and sequencing experiments.

###### pacs:

82.35.Pq, 87.15.rp, 87.14.gk, 87.50.C-, 36.20.-r, 87.85.Qr, 81.07.-b

##  I Introduction

Efficient capture of a dsDNA is the first step for its subsequent
translocation through the nanopore that is central for sequencing, genome
mapping, and other multiplexed nanopore sensing applications [1, 2, 3, 4, 5,
6]. A voltage is applied across the nanochannel to electrophoretically drive a
dsDNA or other biopolymer through the nanopore or a nanochannel. The
characteristic current blockade data is then deconvoluted to reconstruct the
translocated species [7]-[19]. The capture rate in a nanopore device is a
function of several adjustable parameters, the pH of the electrolyte, the
diameter and shape of the nanopore, the strength of the external electric
field, and the length of the biomolecule and its effective charge. Evidently,
a fundamental understanding of the dependencies of the capture rate on these
factors is essential to improve efficiency and quality of a nanopore device. A
large majority of these items have been addressed experimentally [21, 20, 23,
22, 24]. The theoretical studies have either concurred or validated some of
these dependencies [25, 26, 27]. Parallelly, simulation studies [28, 29, 30,
31, 32] have revealed more detailed picture of the capture process and helped
towards the construction of a unifying theory of capture and translocation.

Nanopore translocation consists of three distinct processes. Diffusion of a
polymer towards the pore which progressively acquires characteristics of a
drift as it approaches the pore, its eventual capture, often after multiple
attempts, and finally, the successful threading through the nanopore which we
call translocation. A large fraction of the earlier simulation studies were
done assuming the polymer is already captured at the pore entrance and that a
localized field exists only inside the pore that drives the biopolymer from
the cis to the trans side. One of the major focus of these theoretical and
computational studies were directed to find how the mean first passage time
$\langle\tau\rangle$ depends on the chain length assuming a power law
dependence $\langle\tau\rangle\sim N^{\alpha}$, where $\alpha$ is the
translocation exponent [5, 2]. However, the diffusion and the drift of the
polymer, and its eventual capture in the pre-translocation phase getting ready
to be translocated itself is very rich in physics as has been demonstrated in
recent experimental studies studies [20, 23, 22, 24]. Gershow and Golovchenko
studied Kilo-base-pair (kbp) long dsDNA and studied capture-recapture
probability as a function of the delay time (which approximately translates to
different distances from the pore) of the voltage reversal [20]. Mihovilovic
et al. made a detailed study of how capture of a folded configuration affects
its translocation property [22]. Wanunu et al. found that for a fixed
concentration, the capture rate increases with the contour length up to a
critical length beyond which it saturates [23]. They further observed that a
salt gradient increases the capture probability. Jeon and Muthukumar conducted
a similar study on the dependence of salt-concentration gradient and pore-
polymer interaction using a $\alpha$-haemolysin protein pore [24]. These
experimental studies have motivated more simulation studies on the capture
problem. Slater and co-workers used different approaches to define the capture
radius, studied the effect of the time dependent field [30, 31, 32] on the
capture process. Vollmer and deHaan studied the change in the shape of the
polymer as it approaches to the pore by the ratio of gyration radii along the
longitudinal and transverse direction [28].

In this article, we report a few new results on further details of the capture
process and how the capture affects the translocation properties of a
biopolymer. A few results have been influenced by and complement previous
studies and a few others which we believe add to our overall understanding of
the capture and translocation characteristics. We primarily consider three
factors; the extended electric field outside the pore, the initial release
point of the polymer, and the DNA persistence length on the capture and
translocation probability keeping the length and the field strength constant
and present the following key results. (i) We revisit the effect of the
electric field and demonstrate how an extended field influences the capture
process as opposed to a field that strictly resides inside the nanopore. The
polymer makes multiple attempts in presence of an extended field (Fig. 1),
similar to Kramer’s barrier crossing problem [38] and increases the capture
probability, as recently theoretically discussed by Grossberg [26, 27]. (ii)
Following Vollmer et al. we use the ratio of the gyration ellipses to monitor
the shape of the polymer which shows a signature as the diffusive motion
acquires characteristics of a drift as the polymer approaches the pore (Fig.
2). (iii) We further show that releasing the polymer close to the pore mouth
from stronger equipotentials has higher success rate of capture (Fig.3) and
shorter capture time (Fig. 4(a)-(d)) and that (iii) the release distance
affects the formation and translocation of hairpin structures (Fig. 4). (iv)
We provide further details and validate different modes of folded and unfolded
configurations from the reversal of the electric field (Fig. 5). We then
demonstrate that the single-file capture can be enhanced drastically by
stiffening the polymer (Fig. 6) and the hairpin translocation probability is
negligible after achieving a critical persistence length. (v). Finally, we
show that an effective way to increase the unidirectional capture rate is to
attach charged tags at one end the DNA which breaks the degeneracy promoting a
higher rate of unidirectional capture with the increasing stiffness (Fig.7),
often required for the nanopore sequencing experiments. Thus the manuscript
connects new results with those already published, reveals the details of the
experimentally observed modes of translocation, and provides a unifying
picture of how the capture occurs and how different captured configurations
eventually translocate through the nanopore.

##  II Coarse-grained model & Langevein dynamics simulation:

Our CG model of a dsDNA consists of 256 beads of diameter of $\sigma$, that
mimics a $4\mu$m long $\lambda$-phage DNA with $48$ bp resolution associated
with a single bead. We use a short range Lennard-Jones (LJ) potential

$\displaystyle U_{\mathrm{LJ}}(r)$ $\displaystyle=$ $\displaystyle
4\epsilon\left[{\left(\frac{\sigma}{r}\right)}^{12}-{\left(\frac{\sigma}{r}\right)}^{6}\right]+\epsilon,\;\mathrm{for~{}~{}}r\leq
2^{1/6}\sigma;$ (1) $\displaystyle=$ $\displaystyle
0,\;\mathrm{for~{}~{}}r>2^{1/6}\sigma.$

to model the excluded volume interaction between two beads separated at a
distance $r$ where, $\epsilon$ is the strength of the LJ potential. The
connectivity between two neighboring monomers is constructed using the FENE
spring potential

$U_{\mathrm{FENE}}(r_{ij})=-\frac{1}{2}k_{F}R_{0}^{2}\ln\left(1-r_{ij}^{2}/R_{0}^{2}\right).$
(2)

Here, $r_{ij}=\left|\vec{r}_{i}-\vec{r}_{j}\right|$ is the distance between
two consecutive monomer beads $i$ and $j=i\pm 1$ at $\vec{r}_{i}$ and
$\vec{r}_{j}$, $k_{F}$ is the spring constant and $R_{0}$ is the maximum
allowed separation between two connected monomers. An angle dependent three
body interaction term is introduced between successive bonds which accounts
for the chain stiffness $\kappa$

$U_{\mathrm{bend}}(\theta_{i})=\kappa\left(1-\cos\theta_{i}\right)$ (3)

and $\theta_{i}$ is the angle between the bond vectors
$\vec{b}_{i-1}=\vec{r}_{i}-\vec{r}_{i-1}$ and
$\vec{b}_{i}=\vec{r}_{i+1}-\vec{r}_{i}$, respectively. For a homopolymer chain
the persistence length $\ell_{p}$ in three dimensions (3D) is given by

$\ell_{p}/\sigma=\kappa/k_{B}T.$ (4)

A cylindrical nanopore of diameter of $2\sigma$ is constructed by removing out
particles from the center of a $2\sigma$ thick wall consists of immobile LJ
particles. We use the Langevin dynamics simulation following the equations of
motion for the ith monomer

$m\ddot{\vec{r}}_{i}=-\nabla(U_{\mathrm{LJ}}+U_{\mathrm{FENE}}+U_{\mathrm{bend}}\\\
+U_{\mathrm{wall}})-\Gamma\vec{v}_{i}+\vec{\eta}_{i}.$ (5)

Here $\vec{\eta}_{i}(t)$ is the Gaussian white noise with zero mean at
temperature $T$, and satisfies the fluctuation-dissipation relation in $d$
physical dimensions (here $d=3$):

$<\,\vec{\eta}_{i}(t)\cdot\vec{\eta}_{j}(t^{\prime})\,>=2dk_{B}T\Gamma\,\delta_{ij}\,\delta(t-t^{\prime}).$
(6)

We express length and energy in units of $\sigma$ and $\epsilon$,
respectively. The parameters for the FENE potential in Eq. (2), $k_{F}$ and
$R_{0}$, are set to $k_{F}=30\epsilon/\sigma$ and $R_{0}=1.5\sigma$,
respectively. The friction coefficient and the temperature are set to
$\Gamma=0.7\sqrt{m\epsilon/\sigma^{2}}$ and $k_{B}T/\epsilon=1.0$. The
numerical integration of Equation (5) is implemented using the algorithm
introduced by Gunsteren and Berendsen [33].

Figure 1: A series of simulations snapshots (a)-(f) in progressive time show
the translocation process of the polymer in presence of localized force bias
applied in the nanopore thickness. $\tau$ is the total translocation time of
the chain. (g)-(l) The same polymer configuration is released from the
equipotentials surface $d=4.0$ away from the pore in presence of the electric
field which extends beyond the nanopore. During the capture process, the
polymer makes a few unsuccessful attempts shown in (h) and (j) before one end
threads into the nanopore. (k)-(l) show the translocation of the captured
polymer through the nanopore under the electric field gradient. Figure 2:
Polymer radius of gyration as a function of first monomer distance $r(N_{0})$
from the pore. The effective radius of gyration of the polymer at a distance
is represented by an ellipse having the major/minor is representing
transverse/longitudinal component respectively. The average $R_{g}$ is denoted
by the magenta dotted line. $R_{g}$ at different phases (a) diffusion
dominated (b) drift dominated and capture (c) translocation and escape are
presented in the inset ellipses and compared against a unit circle in black.
$e$ and $A$ denote the eccentricity and the area of the ellipses respectively.
The drift region is identified from the diffusion dominated region by marking
the inflection point of the $R_{g}$.

##  III Results

Unless otherwise specified, we choose a polymer of length $N=256$ and each
monomer carries a charge $|q_{i}|=1.0$. We release the equilibrated polymers
from different equipotentials $\Phi$ referenced using the vertical distances
$d/\sigma=4,8,12,$ and $16$ from the pore (corresponding the equipotential
values $\Phi=0.322,0.157,0.101,$ and $0.071$ in MD units respectively, please
see Table-I). The release configuration of a polymer is such that the first
monomer stays on the equipotential $\Phi$ and rest of the chain conformation
remains in the lower equipotential levels away from the pore. The
equipotentials are calculated numerically but exactly with appropriate
boundary conditions and closely resemble those using the analytic expression
by Farahpour et al. [34]. Far away from the pore, the equipotentials are
almost concentric circles but close to the pore become elliptical. We consider
fully flexible chain and chains of persistence length corresponding to
$\kappa=3,6,$ and $9$ respectively. The initial locations of the polymer are
then chosen by uniform random sampling for a given equipotential. In addition,
for certain cases, we carried out simulation for a chain length $N=512$. For
the first translocation event, we choose the negative $y$-axis to be the
translocation axis (Fig. 1), the captures occur at $y=0$, and the electric
field deep inside the pore is directed along the $-y$ axis (Fig. 1(b)). Both
the diameter and width of the nanopore are chosen to be $2\sigma$ that also
allows translocation of the folded configurations. For the multiple scans the
electric field is reversed accordingly across the pore.

###  III.1 Translocation in a localized electric field:

All of our results excepting Fig. 1(a)-(f) are presented for an electric field
that extends beyond the pore. To contrast those results we show the results
for an equilibrated chain for four Rouse relaxation time with an initial
configuration placing a few beads inside the nanopore those experience the
localized electric field strictly inside the pore. At the start of the
translocation process, the beads inside the nanopore experience a downward
pulling force while the tension front [35] propagates through the chain
backbone in the opposite direction of translocation that first uncoils the
chain. The chain is quickly sucked into the pore when the tension front hits
the last bead [36]. This entire process is demonstrated in Fig. 1 ((a)-(f)).

###  III.2 Capture in an extended electric field:

However, the process in Fig. 1 ((a)-(f)) does not resemble an experimental
situation. In an experimental situation the polymer is first released into the
solution executes a drift-diffusive motion and gets captured aided by the
extended electric field beyond the pore shown in Fig. 1 ((g)-(l)). We use the
Finite Element method [37] to solve the Poisson equation to solve the electric
field around the solitary nanopore. Unlike the case of a localized E-field,
the extended E-field elongates the polymer polymer along the field vector. The
field gradient, which is strongest at and near the pore also helps the capture
process. Vollmer et al. have shown that the radius of gyration ellipse deforms
differently depending on the polymer size and the Péclet number [28]. We use
this idea, but monitor the average radius of gyration $\langle R_{g}\rangle$
for the entire processes from capture to translocation that shows the shape of
the polymer under the influence of an extended electric field. We characterize
this dynamic deformation process by comparing the transverse and longitudinal
radius of gyration as the polymer drifts towards the pore. We define the
longitudinal and the transverse gyration radii as in Eqn. 7a and 7b,

$\langle Rg_{||}\rangle=\sqrt{\langle R_{y}^{2}\rangle}$ (7a) $\langle
Rg_{\perp}\rangle=\sqrt{\langle Rg_{x}^{2}\rangle+\langle Rg_{z}^{2}\rangle}$
(7b) $\langle Rg_{||}\rangle/\langle Rg_{\perp}\rangle$ (7c)

and construct a radius of gyration ellipse using Eqn. 7c. Far away from the
pore, the polymer remains almost unaffected by the electric field, resembling
the equilibrium configuration with $\langle Rg_{||}\rangle\simeq\langle
Rg_{\perp}\rangle$. As polymer drifts along the field lines, $\langle
Rg_{||}\rangle$ extends over $\langle Rg_{\perp}\rangle$ enhancing the
eccentricity of the gyration ellipse as shown in Fig. 2. The gyration ellipse
eccentricity increases steadily until the polymer translocates through the
nanopore. Specifically, how the electric field affects the post-
translocational conformations are further discussed in Section E.

###  III.3 Polymer drift and capture at the nanopore

The process of capture requires the polymer to overcome the potential barrier
by adjusting its conformational entropy resembling Kramer’s escape problem
[38, 23]. The capture is a non-equilibrium process [35, 36, 39] where field
strength dominates over the diffusion near the pore. This leads to a directed
motion of either end of the polymer until the polymer gets captured. During
simulation, the equilibrated DNA polymers are released from different
equipotentials. To implement that we first determine the potential $\Phi$ at a
vertical distance $d$ from the nanopore orifice and locate other points on the
same equipotential surface. We use these equipotentials as the starting
locations of the DNA polymer as this would be easier to compare and perform in
the experiments. We define the capture probability $P_{cap}(\Phi,t)$ of a
polymer at the pore at time $t$ released from an equipotential $\Phi$ at time
$t=0$ as

$P_{cap}(\Phi,t)=\frac{N_{p}(\Phi,t)}{N_{p}(\Phi,0)},$ (8)

where $N_{p}(\Phi,t)$ is the number of polymers captured at time $t$ at the
pore and $N_{p}(\Phi,0)$ is the number released at the beginning at time $t=0$
from an equipotential $\Phi$. The capture of polymers at the pore from an
equipotential are independent events (as they are released sequentially one
after another), thus follows a “memoryless” Poisson process and time between
capture events resembles an exponential distribution. This has been measured
experimentally also in a single nanopore context [8]. Therefore, theoretically
the capture probability is the cumulative distribution function of the
exponential distribution

$P_{cap}(\Phi,t)=1-\exp\left(-\lambda_{cap}t\right).$ (9)

Figure 3: (a) Capture probability $P_{cap}(\Phi,t)$ as a function of time for
the polymer released from different equipotentials $\Phi=0.322$ ( ), $0.157$
(${\color[rgb]{1,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,1}\pgfsys@color@cmyk@stroke{0}{1}{0}{0}\pgfsys@color@cmyk@fill{0}{1}{0}{0}{\bigtriangleup}}$),
$0.101$
(${\color[rgb]{1,.5,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,.5,0}{\Diamond}}$),
and $0.071$
(${\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}{\Diamond}}$).
In each case the solid colored line represents a fit to Eqn. 9 with
$\lambda_{cap}=\frac{1}{\mu}$ shown in Table-I. (b) Dependence of the capture
probability $P_{cap}(\Phi,t)$ as a function of the equipotential $\Phi$. The
line through the points is described by a function $A\tanh(\beta\Phi)$. The
graphs (c)-(f) show the capture time distributions for different
equipotentials. In each case, $\mu$ and $\sigma$ corresponds to the
distribution average and standard deviation respectively. The black envelops
show the exponential fits of the distributions with the averages marked by
dashed lines.

The cumulative capture probabilities for different equipotentials obtained
from BD simulation are shown in Fig 3 (a). $P_{cap}(\Phi,t)$ increases with
time and follows Eqn. 9. It is important to note that the values of the
prefactor $\tilde{\lambda}_{cap}$ to best fit the Eqn. 9 in Fig. 3(a) are
almost the same as the values $\lambda_{cap}=\frac{1}{\mu}$ obtained from the
capture time distributions (Fig. 3(c)-(f)) as shown in Table-1.

Figure 4: (a)-(d) show the rendition of the different ways a polymer threads through the nanopore and translocates. The capture location $x$ denotes the normalized monomer index $m/N$ which first threads into the nanopore; (a) The single file capture events where either of the ends gets captured are denoted as Type1 translocation. (b)-(c) show the Type2-1 events in which polymer is captured at any random location except at the ends and in the symmetric location. (d) Type2 events indicate the symmetrical capture cases. (e)-(h) denote the same using the actual coordinates from BD simulation for a fully flexible polymer. End to end distance $R_{end}$ distributions of a polymer at the moment of capture at the nanopore orifice after being released from four different equipotential distances $d=4.0$, $8.0$, $12.0$, and $16.0$ are shown in (i)-(l) sub-plots. The black envelops denote the exponentially modified Gaussian fits of the distributions. Average and standard deviation of the distributions are marked in $\mu$ and $\sigma$ respectively and corresponding $\langle R_{end}\rangle$ are shown in the colored dashed lines while the blue line represents the average end to end distances of the starting configurations. After capture, the mean first passage time histograms (m)-(p) follow Gaussian shape with average $\mu$ and standard deviation $\sigma$ are obtained from single file translocation (Type 1) events for the same equipotential release distances. The Type 2-1 translocations are faster than Type 1 events and are shown in silver histograms which are also predominant occurrences for higher $d$. Type 2 events are relatively rare and the bar plots in the insets represent the occurrence of these three types of capture events on a percentage scale.  $d$ |  $\Phi$ |  $\mu$ |  $\lambda_{cap}=\frac{1}{\mu}$ |  $\tilde{\lambda}_{cap}$
---|---|---|---|---
4 | 0.322 | 1361.76 | $7.343\times 10^{-4}$ | $7.618\times 10^{-4}$
8 | 0.157 | 2431.66 | $4.413\times 10^{-4}$ | $4.112\times 10^{-4}$
12 | 0.101 | 3636.57 | $2.749\times 10^{-4}$ | $2.858\times 10^{-4}$
16 | 0.071 | 5352.53 | $1.868\times 10^{-4}$ | $1.897\times 10^{-4}$
Table 1: The table represents the fit parameters for the capture probability
shown in Fig. 3(a). $d$ is the vertical distances from the pore for the
corresponding potentials $\Phi$. $\mu$ is the capture time distribution
average of the released polymers from the different equipotential surfaces
(Fig. 3(c)-(f)) The fit parameters $\lambda_{cap}$ shown in the fourth column
are used to fit the capture time graphs of Fig. 3(a). The last column
represent the best-fit parameters obtained numerically fitting
$P_{cap}(\Phi,t)$. Figure 5: The series of snapshots show the multi-capture
process of a single polymer by altering the voltage bias. (a) The first
attempt of threading from the cis side (b) hairpin capture (Type 2-1), and (c)
translocation from the cis side to the trans side. (d) After the reversal of
the E-field (e) the same polymer gets captured from the bottom side of the
pore. The hairpin loop structure is shown in the inset and at first both ends
translocate at the same time. (f) Single end translocation begins after the
unwinding of the loop.

Fig. 3 (a) also shows the dependence of the capture time on different
equipotentials. A larger value of the equipotential (closer to the pore) helps
a faster capture. To get an improved statistics we monitor the journey of
$1000$ independent fully flexible polymers after the initial release from
randomly chosen coordinates on an equipotential $\Phi$ until they translocate.
By increasing the release distance $d$ (lowering the strength of the
equipotential $\Phi$), our study shows that there is a finite probability
(shown in Fig. 3 (b)) that polymers drift away from the pore as the field
strength becomes weaker at the distant equipotential surfaces. One can use
this graph to define a capture radius [30].

Though a polymer is captured, its motion barely follows the curvature of a
single field line going straight through the nanopore. A successful capture
often requires multiple failed attempts but with an increasing number of
failed attempts, the probability of capture also gets enhanced as the polymer
gyration radius gets compressed by the E-field and remains in the vicinity of
the nanopore opening. Fig. 3((c)-(f)) show the capture time distributions
which sum up the polymer journey from release to capture including the failed
attempts. With increasing $d$, the average capture time increases which
suggests a longer wonder time when released from a weaker potential. The
process of capture is Poissonian in nature and the distribution follows the
shape of an exponential distribution where the mean and standard deviation is
almost identical. It is worth mentioning that the exponential distributions of
Fig. 3((c)-(f)) produced by the BD simulation are the same as observed
experimentally by Gershow and Golovchenko [20].

###  III.4 Modes of translocation

Dekker et al. introduced the nomenclatures for polymers threading into the
pore with three different conformations (Type 1, Type 2-1, Type 2) events,
depending on the relative location of the chain with respect to the pore [21].
Mihovilovic et al. further studied and quantified translocation of these
folded conformations [22]. We observed these separate events in our simulation
shown in Fig. 4((a)-(h)). In Type 1 events one end of the polymer threads
(Fig. 4(a,e)), while in Type 2-1 a random location capture occurs. The
symmetric threadings are Type 2 events (Fig. 4(b,f) & (c,g)). Not only we
observe these threading conformations in our simulation studies, in addition,
our simulation provides the fraction of events belonging to these three
categories shown Fig. 4((m)-(p)) insets. For a closer release from
$d=4.0~{}(\Phi=0.322)$, Type 1 capture percentage is marginally greater than
Type 2-1 events but for all the other cases $d\geq 6.0$, Type 2-1 is the most
abundant event. On the contrary, Type 2 events are rare occurrences ($\leq
2\%$) compared to the rest. These BD simulation results reveal further details
as well as validates earlier theoretical and studies experimental studies [39,
21, 20, 22].

Recent theories [39] indicate that translocation depends on the polymer’s
initial conformation and the degree of equilibration. The electric field and
its gradient also influence the polymer shape during capture. We calculate the
average end-to-end distance $\langle R_{end}\rangle$ of the polymer at the
instance of capture to study its effect on the translocation time. During the
pre-capture phase, a polymer undergoes stretching deformation due to the
unidirectional field gradient and $\langle R_{end}\rangle$ deviates from the
equilibrium end to end distance which is more prominent when starting from a
distant equipotential from the pore mouth. The $\langle R_{end}\rangle$
histograms in Fig. 4((i)-(l)) become slightly right skewed for higher $d$
(lower $\Phi$) and $\langle R_{end}\rangle$ increases by $5-20~{}\%$ from the
equilibrium average. However, the mean first passage time (MFPT) distributions
of $1000$ independently captured polymers show a counter intuitive outcome,
indicating a faster translocation time for higher $d$ where we previously
observed that $\langle R_{end}\rangle$ is large. This apparent contradiction
is resolved when we filter out Type 2-1 events from Type 1 events and plot the
translocation time histograms separately for each type of event as shown in
Fig. 4((e)-(h)). The translocation of Type 2-1 and Type 2 captured
configurations are inherently different and faster than a single file
translocation event as both ends of a hairpin loop configuration thread
through the nanopore simultaneously until one end translocates completely and
the loop unwinds. This phenomenon is also observed for the multi scan events
as depicted in Fig. 5(e) and in Section F. For Type 1 translocation event,
average MFPT and spread increase with $d$ (shown in the colored histograms in
Fig. 4((m)-(p)), while for the Type 2-1 events a faster MFPT is obtained
(silver histograms).

###  III.5 Post-translocation compression

Translocation being a faster process in presence of an electric field
gradient, the polymer configuration gets compressed in the post translocation
phage. Fig. 2 demonstrates the compression factor as the area of the gyration
ellipse decreases more than 20% compared to its pre-translocation stage. After
translocation, both the eccentricity and area of $\langle Rg\rangle$ ellipse
remain constant but the fluctuation in $\langle Rg\rangle$ increases (pink
cloud in Fig. 2) as it enters into the diffusive domain.

Figure 6: (a) Hairpin capture probability for different stiffnesses of the
polymer. By increasing the chain stiffness, the single file capture (Type 1
events) represented by the blue circles ( ) increases while reducing the Type
2-1 events denoted by the magenta triangles
(${\color[rgb]{1,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,1}\pgfsys@color@cmyk@stroke{0}{1}{0}{0}\pgfsys@color@cmyk@fill{0}{1}{0}{0}{\bigtriangleup}}$).
The symmetric capture rate (Type 2 events) remains non-zero up to the chain
persistence length $\ell_{p}=6$ and goes to zero for stiffer chains. (b)-(e)
figures show the distributions of capture locations (in reduced units) for
different persistence lengths. (b) For a fully flexible polymer, capture
distribution is broader, Type 2-1 event occurrence has finite translocation
probability along with the Type 1 events. The capture location distributions
for stiffer chains are shown in (c) $\ell_{p}=3.0$ (d) $\ell_{p}=6.0$ (e)
$\ell_{p}=9.0$ respectively. With the stiffening of the chain hairpin capture
probability significantly reduces down improving the single file capture rate.

###  III.6 Multiple recaptures of a translocated polymer

It is the faster speed of the translocating DNA in a solitary nanopore that
makes the current blockade measurements noisy for sequencing purposes. To
overcome this issue, multiple recaptures [20] of the same molecule can be a
viable option that relies on increased statistics, hence, enhancing the
accuracy of the measurement. In our simulation setup, we reverse the voltage
bias after a successful translocation as the center of mass of the polymer
moves $20\sigma$ away from the pore and study the polymer dynamics as a
function of its persistence length. During the multi-capture events statistics
are collected for six independent runs, each containing $100$ scans unless the
polymer drifts away. Fig. 5 demonstrates the recapture events for a polymer
having the persistence length $\ell_{p}=3.0$. Our study shows that even in the
extreme narrow nanopore limit (pore diameter of $2\sigma$), hairpin capture
probability dominates over the single file translocation events for semi-
flexible polymers (see the simulation movies). In addition, from Fig. 6(e) it
is evident that only beyond $\ell_{p}=6.0$, Type 1 capture probability is
higher than hairpin capture (Type 2-1 and Type 2) probability and
$\ell_{p}=6.0$ serves as a critical point between these two events. To
understand how the chain stiffness affects the capture process in presence of
a field gradient we have studied the capture location distributions shown in
detail in Fig. 6(a)-(d). For a fully flexible chain ($\ell_{p}=0$) all three
types of capture occur but with the increasing stiffness, as expected, the
single file captures become predominant. It is important to note that for
$\ell_{p}=3.0$; Fig. 6(c) - that corresponds to the persistence length of a
dsDNA under most experimental conditions the distributions of the capture
locations obtained from the BD simulation closely resemble those obtained
experimentally by Mihovilovic et.al. [22].

We further verify that for a longer chain with $N=512$, the capture location
distributions for different stiffness are qualitatively similar, however, the
probability of the Type 1 capture increases compared to the other two types of
events. This enhancement of Type 1 events with the increased chain length is
more prominent for the fully flexible polymer and does not alter the
distribution as such for the cases with higher persistence lengths, where Type
1 is the only predominant event.

###  III.7 Enhancement of capture rate by End Tagging

Attaching a “charged motif” to a dsDNA provides additional information about
its translocation dynamics through a nanopore [40, 41]. In our simulation, we
enhance the charge content of the last six monomers of one end (let’s call it
$5^{\prime}$ end) by three times of a normal monomer ($q_{tag}=3q$) and apply
the same recapture method to demonstrate the effect of end tagging on the
capture and translocation process. We first monitor the scan time duration
(capture time + translocation time) of a homopolymer varying its persistence
length. Fig. 7(a) (magenta circles) show that the scan time increases non-
linearly with an increase in the chain stiffness and the error bar in scan
time widens which signifies a large

Figure 7: (a) Figure shows the scan time duration of a homopolymer in magenta
circles ( ) and polymer with end tags in blue diamonds
(${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}{\Diamond}}$)
as a function of the polymer persistence length. (b) Homopolymers of different
stiffnesses are captured and scanned multiple times and the capture percentage
of $3^{\prime}$ and $5^{\prime}$ end terminus are shown in yellow and pink
bars. (c) The same bar diagrams are depicted for polymer with charged tags
located at the $5^{\prime}$ end.

variation in capture time for the stiffer chains. To reduce the uncertainties
of capture, we use the end tagging method (see the insets of Fig. 7) and blue
diamonds confirm that end tags not only conclusively lower the scan time for
the stiffer chains but the error range also gets reduced.

In reality, without the data post-processing, it is almost impossible to know
which end of the polymer threads into the pore during each recapture scan. By
charge tagging the $5^{\prime}$ end, we potentially break the degeneracy as
the tags with high charge content are prone to enter into the nanopore first
due to the stronger pull of the electric field. Fig. 7(b) shows that the
capture probability of the $3^{\prime}$ and $5^{\prime}$ ends are almost equal
for a homopolymer even with different stiffnesses, hence degenerate. Our
simulation confirms that these degeneracies are broken and $5^{\prime}$ end
has a significant higher probability of entrance when tags are present at the
$5^{\prime}$ end as shown in Fig. 7(c). This tagging prioritizes the
$5^{\prime}\rightarrow 3^{\prime}$ uni-directional translocations from either
side of the pore during multi-recapture and scan which can potentially benefit
the single nanopore barcoding and sequencing experiments where uni-directional
reads would be preferred. Moreover, one can make the end terminus oppositely
charged which would in principle further promote the uni-directional
translocations due to the favorable attractive interaction at one end and a
repulsive force on the other end in presence of an extended electric field.

##  IV Discussion and conclusion

In this article, we report the details of the capture and translocation of a
DNA polymer as it meanders its way to the pore entrance from different
equipotentials. Capture from different equipotentials affects the
conformations at the pore entry as well as the translocation speed. Our
studies reveal the details of multiple failed attempts and eventual success in
presence of an extended E-field, quantify and differentiate accurately
characteristics of translocation of both straight and folded conformations. We
analyze further details of the folded coordinates in reference to the entire
chain. Based on these results, we suggest how one can take advantage of it to
improve the accuracy of the experimental protocol using a solitary nanopore.
We also demonstrate the model is capable of reproducing all the details of an
actual experiment [20] and Mihovilovic et al. [22]. We introduce a charge tag
at one end of the dsDNA and demonstrate that the scan time and its variability
are significantly reduced especially for the stiffer chains and uni-
directional capture probability increases by lifting the degeneracy of which
end threads through the nanopore during the multi-capture process. We expect
this work will promote future experimental studies on repeated scanning of a
biopolymer through nanopore and can be useful for a large community involved
in various types of biopolymer translocations.

##  V Acknowledgment

The research has been supported by grant number 1R21HG011236-01 from the
National Human Genome Research Institute at the National Institute of Health.
All computations were carried out using STOKES High-Performance Computing
Cluster at UCF. The simulation movies are generated using the Visual Molecular
Dynamics package [42].

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