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Conformations and Translocations of DNA Molecules

Abstract

In this study, molecular dynamics simulations are utilized to analyse the interactions and conformations of a DNA molecule as it passes through a membrane pore under an applied electric field. By changing the properties, specifically the charge of the pore and nature of the DNA, it is possible to explore how the conformations and translocations of various DNA molecules are altered in varying applied electric fields.

The study establishes that all DNA formed some type of non-linear conformation as it translocated, with no change in the orientation from entering to exciting the pore.

The research also proved that positive point groups placed in the pore have a significant effect on how the DNA translocates; with an electrostatic tethering mechanism that stops the DNA fully translocating.

It was also demonstrated that changing the orientation of the DNA also alters the mechanisms for DNA translocation, with the data illustrating that a positively charged ring would produce the opposite translocating effect with no tethering mechanism. Lastly, it was confirmed that differing lengths of DNA alters how the DNA passes through the pore, with a reduction in any electrostatic effect noted.

Overall, the results illustrate how changing the charge of the pore, type of molecule and the applied electric field can have a significant impact on the DNA conformation, mechanism and rate of translocation. This study has therefore confirmed the trends described in previous experimental and computational studies, whilst building on these results by determining novel trends involving DNA translocation.

Introduction

Nanopore sequencing technology has the potential to greatly advance the field of single molecule and DNA sensing. Detecting individual molecules has become an essential research tool within the modern scientific community. 1-3  Individual molecule detection research has also helped in developing the next-generation of analytical tools.4

DNA sequencing has been an integral technology for the past 50 years, used in a wide variety of research applications. The order of nucleic acids within a polynucleotide chains contains the information for the fundamental characteristics of life, hence the ability to determine such sequences is essential to modern scientific research.5 The completion of the large scale mission: the Human Genome Project, is an example of the feats that can be achieved by applying new sequencing technologies.6, 7

The new generation of single molecule sensing technology is based around utilizing nanopores. Nanopore technology has been widely incorporated into the next generation of DNA sequencers, as compared to its predecessor, this type of technology is relatively inexpensive, faster and more portable. This relatively young technology has gained popularity due to the simplicity of its system.

The fundamentals of nanopore sequencing involves employing the nanopore as a biosensor. The nanopore within the system acts as the only aperture in which the ionic solution can pass through from the cis to the trans side of the membrane. Hence, the narrowest section of the pore serves as the sensing region for the system. The full schematic of the system is shown in figure 1. A constant voltage produces an ionic current through the nanopore and is the driving force for the molecule to pass through the pore. An enzyme is placed onto the polynucleotide, so that a step-wise ratcheting movement controls the movement of the molecule through the nanopore. If sequencing a DNA strand, this enzyme ratchets the nucleotides, one nucleobase at a time. The blockage of the molecule within the pore produces an ionic signal, which is uniquely associated with a single molecule. The four key read-out variables with which a molecule can be characterised in nanopore analytics are event frequency, event lifetime, event amplitude, and the event area.8-10

Figure 1- Fully labelled schematic of a nanopore system, describing the nanopore sequencing process (created by author)

Nanopore technology has expanded in recent years to include the ability to sense analytes including polymers, peptides, proteins, small molecules, and biomolecular complexes.11-14 The proliferation of this technology into common scientific use has been supplemented with an increased range of nanopore types.

Whilst initially most research was performed with natural wild type proteins; man-made organic and inorganic solid state nanopores have become more common. These artificially created proteins can either be made from organic polymers, modified wild type proteins or an inorganic derivative of silicone.15

The origin of nanopore sequencing can be traced back to the preceding technique of Coulter-counting, where microscale objects pass through a microscale aperture and cause short pulses of altered resistance.16 The frequency of these modulations could then be used to infer the number of particles within the system, whilst the magnitude of the variations is proportional to the size of the analyte. This relationship is significant as it surmises that individual molecules can be sensed when the aperture is of a similar size. Hence, nanopore sensing embodies this technique on the nano-scale.

Another central technology which contributed to the development of nanopore technology is single-channel current recording. Previous to the development of nanopore technology, natural, stimulus responsive ion channels were characterised using this technique.17. The technology used the current modulations of a single channel which was controlled by external stimuli, within a natural lipid bilayer membrane.

Although single channel and nanopore technologies seem comparable at first, there are fundamental differences which separate these processes; the first being that nanopores are embedded artificial membranes, additionally the current alterations within nanopores are directly caused by the analyte molecules via electrostatic or steric effects. The final and most major dissimilarity is that nanopores lack any ability to bind specifically to a molecule, unlike a biological channel. This element of nanopores is advantageous, as these ‘blank’ pores can be prepared with a range of artificial binding sites that can be attuned to a variety of analytes.

The first breakthrough in nanopore research was found 1996; by utilizing an electrical field it was proven that individual polynucleotide could pass through an HL pore.18 Further advancements proved that individual nucleotides could be distinguished, in various forms.19, 20 21 Further to this research, it was found that the signals can distinguish between the orientation of polynucleotide strands travelling 3’ to 5’ compared to passing through the nanopore 5’ to 3’.22-24 This development as well as successive findings that the nanopore can distinguish and differentiate between different bases of DNA on a homo- and hetero-polymeric DNA strand were critical to nanopore development.25-27

However, these developments in nanopore technology depended on the DNA being immobilized within the HL pore, held there to prevent the strand from completing the electrophoretically driven translocation through the pore. Hence, the nucleotides of the immobilised strand remained in a fixed position at the pore’s sensing region, which greatly improved the signal-to-noise ratio, making it possible to distinguish individual nucleobases.  The next wave of research has therefore focused on finding a method for a controlled translocation of molecules through the pore. One method for this controlled translocation was to examine the use of processive control of DNA through the pore utilizing a variety of enzymes, with the most successful experiments using the enzyme phi29 DNAP.28

Another principal area in nanopore sequencing was based around utilizing the structure of the wild type HL pore. The HL pore is the most commonly used biological channel within nanopore research, with its popularity is due to a variety of features. Firstly, HL lacks any moving parts and has a robust structure, so is able to withstand drastic mutagenic changes and harsh purification conditions.29 Additionally, the HL pore is a ‘blank’ pore and therefore does not have any specificity for analytes. However, the ability to bind to specific analytes can be engineered into the pore due to the final feature, which is that the channel walls are responsive to design alterations using genetic and chemical methods.

HL is an homoheptameric protein, with a transmembrane 14-stranded β-barrel domain, linked to an extra-membranous cap, with an internal channel. The external dimensions of the pore are 10 x 10 nm and it has a 5nm stem with an internal channel diameter which varies from ~1.4 nm to ~2.4 nm, depending on the volume of the amino acid side chains projecting into the channel cylinder.30 A representation of the HL pore is seen in figure 2. This protein pore is formed by self-assembly of seven identical polypeptides from Staphylococcus aureus. Experiments using the wild type HL pore and DNA strands demonstrated that the all nucleobases within the stem of the pore contributed to the measured current levels, therefore obscuring any individual readings.31 A solution to this issue was to engineer a HL with a sensing region shorter than 5nm, which was demonstrated to individually resolve the four canonical nucleobases within DNA strands.25-27

Figure 2 – Representation of wild type HL pore from Staph Aureus, created from PDB file 7AHL30, using PyMol and coding each polypeptide a different colour

Utilizing the advances in nanopore technology, ONT was founded in 2005, with the aim of continuing nanopore sensing research for commercial use. ONT’s research cumulated in the release of the MinION device in 2014. The MinION is portable and compact, weighing ~100g. The design includes a flow cell with 2,048 individual protein nanopores, each embedded in a separate stable membrane. Preparation for this machine includes a hairpin loop to one end of a ds-DNA fragment. During the analytical process, the helicase enzyme unwinds the strand to form a ss-DNA which is drawn through the pore, producing a characteristic readout. Due to the hairpin bend within the molecule, both stands of the original ds-DNA molecule can be analysed, further improving the base characterisation accuracy. Common fragment lengths are in the range of 6,000 to 48,000 bases.32 ONT has successfully been used in a range of projects globally, demonstrating the utility of the MinION for general scientific use.33, 34 However, two issues still endure in nanopore DNA sequencing technology; the first being that enzyme turnover is stochastic, consequently the enzyme has a variable ratcheting speed, where the intervals between the advancement of DNA are inconstant. Within these time intervals the nanopore current identifies the individual bases, therefore inconsistent intervals produces an unreliable output, usually expressed in deletions.32 The second problem is that several nucleobases cumulatively contribute to the measured current level, this base multiplicity reduces the signal-to-noise ratio used for determining bases, meaning only the most likely sequence can be determined by applying dynamic programming.35 Hence, the issues of inconsistent and too fast DNA translocation are producing an unreliable readout, obstructing the progress of this technology. Consequently, producing a reliable ratcheting speed and translocation speed through the pore is essential to the reading accuracy.

Recent efforts have therefore largely focused on attempting to slow down the translocation of DNA through a nanopore. One approach to solve the issue of translocation speed is to research alternative enzymes such as exonuclease enzymes which cleave the DNA bases in succession, so the base can pass through the pore singularly.36, 37 Another approach is to engineer the pore itself, to introduce artificial binding sites for analytes. Three methods to create molecular recognition sites have been established. The first approach is to use amino acid replacement or substitution; this technique has been applied to alter the properties of the recognition points within the HL pore via substitutions of features such as amino acids. 38 39 The second approach involves covalently attaching non-proteinogenic receptors to the pore via one or more engineered cysteines. The final method of creating recognition binding sites is mainly used for small analyses and utilizes non-covalent adapters.

A vital tool in understanding the mechanisms of nanopores is MD, this area of research provides a means of examining nanopores and their conformational dynamics at an atomic resolution, in environments that mimic experimental conditions, with easily controlled variables. Within all atoms MD, a molecular system is modelled by a group of virtual atoms interacting according to the molecular force field applied. This molecular field was produced and calibrated to quantitatively model the physical properties of a simulated system. 40 To model the transport of molecules through nanopores, an all-atom model of the experimental system must be produced using known structures of all the key materials within this system. This close approximation of the experimental conditions gives MD the advantage that direct comparisons between the simulation and experiment are possible.41 However this approach is limited to a timescale of several microseconds, restricting the processes that can be investigated using this method.42

By using MD analysis and utilizing the dynamical simulation software GROMACS43, previous studies have concentrated on examining the lumen of HL and its associated interactions with DNA. As the character of the pore was changed, the DNA translocation altered, implying that the interaction between the pore and DNA molecule is fundamental in process of translocation.44 More recent work has concentrated on mutations of the HL pore, to identify the most favourable mutations that can slow the translocation rate and increase the base resolution. These studies identified a binding/sliding mechanism DNA translocation mechanism involving the arginine side groups within a mutated HL pore. Interactions between a positive molecule within the lumen of pore and DNA have been proven to slow down the translocation rate. Another finding was that DNA strands were shown to form non-linear conformations within the HL pores, due to the ssDNA-nanopore interactions, which is problematic for a DNA sequencing technology. 45, 46

The key principle examined in this study is how the pore design interacts and affects the behaviour of the ions and DNA within the system. This project has the overall objective of understanding which mechanisms are the most effective in slowing down and linearizing DNA translocation.

To achieve this aim, three questions were asked. Firstly, how does the alteration of the pore affect the flow of ions?

Secondly, what characteristics of the pore interact with a DNA molecule and what are the underlying mechanisms of these interactions?

Thirdly, how does altering the DNA type change the mechanisms of translocation?

By answering the questions outlined above, this study has probed how DNA translocation can be affected with changes to the pore, electrical field and DNA types.

This study used the GROMACS software to perform all atom MD analysis, running up to 5ns. Whilst many of the previous studies referenced have concentrated on modifying HL pore with mutations to examine this concept, this research took a reverse approach in the pore design. By starting with a blank aperture in a membrane, then adding specific characteristics, it was possible to probe the features of the pore and interactions with the DNA. The advantage of this system design was the ability to definitively determine the fundamentals of these interactions without any of the conventional limitations afforded by modelling a complex HL pore. This simplistic charge modelling approach is analogous to the previously cited idea of changing the amino acids found within the pore; however, instead of using amino acids, simplified point groups were modified instead. Although this study does not use a mutated HL pore, it is still imperative to recognise the links between the research carried out in this study and previous studies which employed the HL pore. Therefore, it is important to compare previous theoretical and experimental research using an HL pore to the results of this study, and understand how the findings from this research relate to more realistic pore systems.

Specific characteristics examined within this study include altering the pore membrane polarity, the charges within the aperture of the pore, and the nature of the DNA including differing lengths and orientations. A total of 14 simulations were run, all with different environments, including runs with and without DNA. These simulations were further split by the force of electric field applied, meaning that 42 discrete models were run in total. From this, a variety of measurements were taken, focusing on recording the movement of both the ions and DNA, when applicable.

Experimental

Methods

To achieve the aim of this project, all atom MD analytical methods were utilized. All simulations were performed using GROMACS software and VMD analysis. The model used for this study is based upon a 3nm deep methane membrane-memetic slab with a 3nm diameter pore embedded within, the model used can be seen in figure 3. The system was solvated with 1M NaCl, using the Genion function of GROMACS, which corresponds to approximately experimental concentrations used. The charged ring systems were produced by addition of 13 positive (figure 4) or negative point group molecules (figure 5), equally spaced within the centre of the pore’s aperture in the membrane.

Figure 3 – cross section of the membrane pore, created using VDW

Figure 5- cross section of the negatively charged membrane pore, with negative charges coded in orange, created using VDW

Figure 4- cross section of the positively charged membrane pore, with positive charges coded in purple, created using VDW

Three different types of DNA were used within this research; a 12mer ssDNA with a 5’(cis)-3’(trans) orientation (relative to the cis entrance of the pore), a 12mer ssDNA with a reversed 3’(cis)-5’(trans) orientation and finally a 48mer ssDNA molecule. These DNA molecules within the system can be seen respectively in figures 6, 7, and 8.

Figure 8- 48mer ssDNA placed within cross section of the membrane pore, created using VDW (pore) and liquorice

Figure 7- 3′-5′ DNA placed within cross section of the membrane pore, created using VDW (pore) and liquorice (DNA)

Figure 6- 5′-3′ DNA placed within cross section of the membrane pore, created using VDW (pore) and liquorice (DNA)

The properties of the pore and DNA were altered, creating 14 differing simulations, listed in table 1. To clearly reference these simulations, they will be hereafter cited by their assigned simulation code; ranging from A to N. To these simulations, an Ef in the z direction was applied with 3 intensities; 0 mV, 450 mV, 900 mV.  This created 42 models overall, each with different characteristics to each other.

DNA type Orientation of DNA Polarity of slab Simulation length Structure of pore Simulation code
ssDNA 12mer 5’(cis)- 3’(trans) Polar slab 1 ns No ring A
Non-polar slab 5 ns No ring B
Positive ring C
Negative ring D
3’(trans)- 5’(cis) Non-polar slab 1 ns No ring E
Positive ring F
Negative ring G
ssDNA 48mmer 5’(cis)- 3’(trans) Non-polar slab 5 ns No ring H
Positive ring I
Negative ring J
No DNA N/A Polar slab 1 ns No ring K
Non-polar slab 1 ns No ring L
Positive ring M
Negative ring N

Table 1 – complete list of all simulations performed, with differing environments

For each of these simulations, the models were run correspondingly. The full system comprised of 1 DNA molecule (when applicable), ∼300 Na+ and Cl ions, ∼2500 methane slab molecules (with 13 of these being altered into a ring of charged molecules when applicable) and ∼10,000 water molecules.  The box diameter was 6.2nm-6.2nm-12.4nm (x-y-z), forming a cuboid shaped container.

The 12mer ssDNA, if included within the simulation, was pre-threaded over the entrance of the pore (cis edge). The 12mmer DNA has a starting length of 4.55 nm, whilst the 48mmer has an initial length of approximately 20nm (including the extended 5’ section). Due to the extended length of the 48mmer ssDNA, this was pre-inserted, using extended 5’ end, through the pore to facilitate translocation of the DNA molecule effectively. Each simulation performed lasted either 1 or 5 ns, depending on the translocation events and length of DNA. A varied Ef was applied of either 0, 450 and 900mV over the entire membrane. The reasoning for this range of applied Ef was to simulate a higher than usual array of applied Ef. Using the GROMACS 53a6 forcefield14, the simulations were run at 300K and 1 bar pressure, using the Berendsen thermostat47 and barostat with Electrostatics treated with particle mesh Ewald.48

To accurately measure these simulations, a total of 9 methods were employed to analyse the simulations. These measurements can broadly be categorised into two classifications, one involving the translocation of DNA, the other concerning the movement of other molecules within the system, the full list is referred to in table 2.

Table 2- complete list of all analysis performed

Category of analysis Type of analysis
All DNA Translocation events
Translocation time
 DNA distance travelled
Translocation speed
12mer ssDNA only Range of DNA length
DNA hairpin analysis
All simulations (DNA and non-DNA) Cumulative ion (Na+ and Cl) flux
Cumulative water flux
Centre of mass tracking of ion (Na+ and Cl molecules)

These measurements were chosen as they represent the four measurements characterised in nanopore analytics. Event frequency and event lifetime of the DNA translocation can be compared to the analysis concerning the trajectory, speed and shape of the DNA. Whilst the area and amplitude of the event is analogous to the tracking of flux and individual molecules.

Translocation results: all DNA simulations

The results concerning the movement of the DNA can broadly be categorised into two subdivisions; one concerning how far the DNA travelled and at what speed, the other regarding the shape and length of DNA throughout the simulation.

Table 3 details all the results which concern the DNA’s movement including; the translocation events, time taken for the DNA to translocate, the speed, and the total distance travelled of the DNA molecule. As the results of table 3 show, the distance and speed of the molecule and whether it translocates through the pore are closely interconnected. The DNA translocation events were determined by observing how far the DNA had travelled by the end of the simulation and whether it was ‘stuck’ in any section of the pore. This was completed using visual analysis and the ending screenshots, found in appendix V1 to V10. From this, the simulation was correspondingly labelled with its translocation event. Similarly, the translocation time was recorded by observing at what time step the DNA has fully left the pore. From this, the translocation speed could be determined by dividing the time taken by the distance travelled of the DNA, the full calculations are in appendix C1. A general trend was identified in the data; as the applied Ef increases, so does the likelihood that the DNA would fully translocate.

Table 3- DNA translocation results including detailed translocation description, time and speed as well as total DNA distance travelled. Supporting data for this can be found in appendices C1 and D1-10.

Code & 

simulation time

Applied Ef (mV) Translocation events Trans-location time (ns) Trans- location speed (ns/nm) total distance travelled (nm)
A (1ns) 0 None 0.55
450 None 0.16
900 Full and non-linear 0.49 14.10 6.43
B (5ns) 0 None 1.04
450 Full and non-linear 1.07 6.54 5.95
900 Full and non-linear 0.42 16.67 22.03
C (5ns) 0 Partial, tethered and non-linear 2.91
450 Partial, tethered and non-linear 6.13
900 Partial, tethered and non-linear 7.68
D (5ns) 0 None 1.89
450 Full and non-linear 1.7 4.18 6.45
900 Full and non-linear 1.08 6.48 17.85
E (1ns) 0 None 0.508
450 Partial and non-linear 5.00
900 Full and non-linear 0.53 13.20 5.20
F (1ns) 0 None 0.43
450 Full and non-linear 0.94 7.45 4.89
900 Full and non-linear 0.66 10.61 4.84
G (1ns) 0 None -0.74
450 Partial and non-linear 1.75
900 Full and non-linear 0.41 17.07 6.42
H (5ns) 0 Partial and non-linear  –  – 1.28
450 Full and non–linear 2.36 1.36 16.73
900 Full, 3 cycles and non –linear 0.81 8.15 42.12
I (5ns) 0 Partial and non-linear 1.61
450 Full and non-linear 3.55 1.86 6.13
900 Full, 3 cycles and non –linear 0.77 8.57 44.58
J (5ns) 0 Partial and non-linear 1.13
450 Full and non-linear 2.51 2.63 15.43
900 Full, 3 cycles and non –linear 0.9 7.33 38.79

In terms of translocation events: none refers to the fact that the DNA did not enter the pore. Partial denotes that the DNA did not fully exit the pore. Tethered signifies the DNA strand was ‘stuck’ onto the pore and therefore unable to progress. Full refers to the DNA passing through the pore. Non-linear indicates that the DNA was not in its linear sequence whilst exiting the pore. Cycling refers to the amount of times the DNA cycles through the simulation.

To calculate the total distance that the DNA travelled, multiple approaches were considered. One approach examined was to track the distance between the DNA molecule and membrane pore using the VMD bond distance tool. However, this method did not consider the DNA’s trajectory, which can include cycling through the simulation box. Hence, this measurement does not assess the total distance of the DNA, therefore is not appropriate for tracking the DNA’s progress.

To effectively track the DNA, it was decided that tracking the centre of mass of the DNA molecule was the most suitable method. This process involved using a tcl script (see appendix S1to track the specified centre of mass in the z (cis to trans) direction throughout the simulation. By calculating the distance from the initial starting point, it was possible to follow the centre of mass from its point of origin and measure the total distance travelled by the DNA. DNA is inherently a flexible polymer, therefore there were concerns that taking the entire centre of mass of a DNA molecule may give an inaccurate result due to the potential changes in shape and therefore centre of mass during the simulation. To address this concern, two different centre of masses were taken for simulations B, C and D. One centre of mass was spanning the entirety of the DNA molecule including all 12 bases, whilst the other covered the only centre of the DNA molecule, from base pair 5 to 7. Comparing these data sets using the standard deviation, mean and coefficient of variance demonstrated that the data sets were of low variance (see appendix C2) and therefore closely related. Although both centres of masses yielded accurate results, it was decided that the smaller centre of mass would be used within this study. This was mainly due to the reasoning that the smaller centre of mass would be less affected if the DNA altered shape, hence marginally more accurate than the larger centre of mass. The key results for simulations A-J are displayed in table 3. To calculate the total distance travelled, it was key to tally the cumulative distance travelled, so that the accurate distance was recorded. The graphs shown in figure 9 and 10 illustrates the difference between the initial non-continuous and final cumulative data sets.

A more extensive set DNA travelled by the DNA, taken for simulations A-J, can be found in in appendix D1-10.

Figure 9- Graph illustrating total distance travelled by DNA in simulation B, with no cumulative analysis. The dip for 900 mV is due to the centre of mass of the DNA passing through the pore, hence becoming a negative distance from the initial centre of mass.

Figure 10- Graph illustrating total distance travelled by DNA in simulation B, with cumulative analysis. With this analysis, there is no negative dip as the negative distance travelled is cumulatively included within the data set.

DNA shape analysis results: 12mer ssDNA only

The next set of data involved qualitatively tracking how the DNA shape alters over time, specifically, how the DNA length and shape alters over the simulations. The first measureable analysis for this was tracking the minimum and maximum length of the DNA via VMD’s bond distance tool, with figure 11 showing the resulting graph (see appendix D11-17 for full data sets).

However, as the 48mer ssDNA joins to form a continuous loop when simulated, it was impossible to track the molecules length and hair-pinning (see figure 12), hence there is no data available on the 48mer ssDNA molecule.  As the results show, all the 12mer ssDNA molecules stretched past their original length in the simulation. This stretching of the DNA is possibly due the system relaxing the DNA molecule into a less coiled structure after the 1st step of the simulation, hence all DNA molecules will stretch out to a point. The DNA molecules also all contract to smaller conformations then the initial structure. An important note on this measurement is that the DNA bond length was taken from each tip of the molecule, consequently the minimum lengths are more indicative of the DNA hair-pinning or forming smaller shapes, then any actual contractions in size.

Figure 11- Stacked bar graph of minimum and maximum DNA lengths over a range of applied Ef. The dotted line indicates the approximate initial length of the DNA molecule (4.55 nm).

Figure 12- Screenshot of 48mer ssDNA at end of simulation with an applied Ef of 0, 450 and 900 mV (left to right). Created using created using VDW (pore) and liquorice (DNA).

The final measurement regarding DNA was to track the shape of the DNA molecule; specifically, whether the DNA hair-pins and if so, for how long. A stem or hairpin-loop is a pattern that occurs in ssDNA, and is characterised by the base pairs forming a double helix that ends in an unpaired loop.41, 49-51 For this study, a hairpin within the 12mer ssDNA was defined as the point when the ends of the DNA formed a loop shape, with both ending base pairs forming an intramolecular link. This was measured by observing the shape of the DNA during its simulation, if the DNA formed a closed U-shape, then this was recorded alongside the time this conformation lasted. The full results are detailed in figure 13, screenshots of these hairpins and the full data is found in appendix D18 and V11-17. The graph illustrates how the time and length of hairpin events are closely linked to the applied Ef, with a hairpin event never untangling once formed. As the data shows, generally a higher Ef will cause a hairpin event to occur sooner. For all simulations, when the hairpin event has occurred, it persists for the remainder of the simulation.

A                 B                  C                D                  E                  F                G

Figure 13- table illustrating time and length of hairpin conformation for each simulation A-G

Ion tracking and flux results: all simulations

The other main set of data analysed involved all the simulations, and included tracking the flux and movement of water and ions. The cumulative flux for all the simulations are illustrated in figure 14 to 19, divided by length of simulation. The ion and water cumulative flux were both measured by pore crossing events, by utilizing a python script (instructions in appendix S2), with the full data set in appendix D19 to 75.  The cumulative flux events proceed in a linear manner, with the flux rate constantly increasing in similar increments. The pore crossing events are measured by counting the individual upwards and downwards events across the pore. Most upwards and downwards flux occurrences have a similar number of events, with less than a 10% digression. The only exceptions to this trend occurs within systems with low flux events. Overall, these low flux systems have less than 150 total cumulative (upwards and downwards) crossing events, with a negligible flow which produces an imbalance in the overall ratio of flux events.

Whilst the order of flux events alters between the ion and water flux, both sets of data illustrates similar trends in crossing events. In general, the cumulative water and ion flux of simulations correspond to the translocation events (see table 3), with lower flux levels agreeing with either full or partial translocation events and vice-versa.

Figure 14- Graph illustrating cumulative water flux events for all 1 ns simulations. Blue bars represent simulations with DNA included, whilst red bars represent simulations with no DNA.

Figure 15- Graph illustrating cumulative water flux events for all 5 ns simulations. Blue bars represent simulations with DNA included.

Figure 16-  Graph illustrating cumulative Na+ and Cl flux events for all 1 ns simulations. Blue (Na+) and orange (Cl) bars represent simulations with DNA included, whilst purple (Na+) and red (Cl) bars represent simulations with no DNA.

Figure 17- Graph illustrating cumulative Na+ and Cl flux events for all 5 ns simulations. Blue (Na+) and orange (Cl) bars represent simulations with DNA included.

Figure 18- Graph illustrating cumulative ion flux events for all 1 ns simulations. Blue bars represent simulations with DNA included, whilst red bars represent simulations with no DNA.

Figure 19- Graph illustrating cumulative ion flux events for all 5 ns simulations. Blue bars represent simulations with DNA included.

The final measurement involved tracking the centre of mass of an ion (Na+/Cl) molecule in the z direction throughout the simulations (see figure 20 and 21). As the Na and Cl (resID’s: X6536/X6852) data points were identical when compared, the mass that was tracked can be labelled as a general ion (Na+ or Cl). Due to the cycling nature of the simulation box, some anomalous data points had to be removed for the data set, when the ion travelled across the box boundaries. The general trend of increased movement with increased applied Ef can be seen, however it is less observable within this set of data. This may be due to the random walk effect the ion experiences as it travels across the simulation box. Still, this data is useful as a representation of an individual movement of an ion and as a comparison of the different simulations.

Figure 20- Graph illustrating total distance travelled by an ion molecule for all 1 ns simulations. Blue bars represent simulations with DNA included, whilst red bars represent simulations with no DNA.

Figure 21- Graph illustrating total distance travelled by an ion molecule for all 5 ns simulations. Blue bars represent simulations with DNA included.

Discussion

When discussing this research, the overall results will be broken down into individual simulations, before examining the trends observed. Once these trends have been explored, it will be possible to compare the results to external studies; as well as investigating how these results relate back to the original aims. However, before examining individual simulations, it’s important to outline how these models are hypothesised to behave. By describing the predicted trends and the theories behind them, it allows results to be discussed only when they have significant, unusual or anomalous results, compared to the theorised results. It also enables a comparison between the hypothesised trends and the results, and measures how closely this study agrees to previous work completed.

Predictions of general trends

Firstly, the expected general trends for all systems will be described. It is hypothesized that with increasing Ef there will be a higher cumulative number of water and ion flux events and a larger distance travelled by the ion. This is due to the applied Ef increasing the effective energy of the system, causing the molecules to move more and for a longer period.

It is also theorised that the flux of Na+ will be consistently higher than Cl. This discrepancy will be due to the relative sizes of the ions, with Na+ having a smaller ionic radius then Cl. This means more Na+ ions could pass though due to less steric interactions, compared to a Cl molecule. Consequently, it is expected that the negative rings will have the highest flux out of all possible ring configurations, as the negative rings will attract the most Na+ ions through the pore.

Next, the predicted trends for the DNA translocation will be described. It is believed that with increasing Ef (hence increasing energy in the system) there will be: a higher likelihood of a translocation event occurring, a longer distance that the DNA travels and higher speed that the DNA travels. This is due to the same reasoning explained above. This increase in applied Ef will also force the DNA to interact with itself to minimise its energy, forming a kink within the DNA as it aligns with the applied Ef. 41, 49, 51, 52 Therefore, it is believed that the DNA will form non-linear, hairpin conformations quicker with increasing Ef.

The partial or full translocation of DNA has been predicted to also lower the water and ion flux events and distance travelled by the ion. This would occur because there would be a blockage in the pore, which would form a characteristic dip in the flux and movement of the ions.

Another key predicted trend is that the positive ring will tether the DNA and hold it within the aperture, whilst the negative ring will accelerate the DNA through the pore. This was theorised to occur because the positive charge of a DNA molecule will theoretically be electrostatically attracted to the positive point group and form an ionic type bond. However, the negative group will repulse the DNA molecule, pushing it through the pore.

The final trend theorised is that the reversed DNA (3’(trans)- 5’(cis)) will have a slower translocation rate compared to the non-reversed DNA, causing lower flux events. This is because the orientation of the reversed DNA is more symmetrical compared to the 5’(cis)-threaded molecule. The reversed DNA will experience smaller effective friction through the pore and will not have to alter shape significantly, consequently it will pass through the pore at a slower rate. Therefore, the effectiveness of the translocation will reduce, due to the reversed configuration and lack of shape alteration. This was shown to occur form previous research, where the threaded 3’-5’ DNA was significantly slower than the usual 5’-threaded configuration. 22

Analysis of models without any DNA included

The first set of simulation results which will be discussed are models without any DNA, which include: K, L, M and N. The initial simulation under review is the non-polar, uncharged membrane, coded as L, which lacks a DNA molecule or a charged ring. Within this model, the water flux rate at 0 and 450 mV is abnormally low (figure 11), this suggests that a vacuum has been created within the pore, this event was not predicted. A similar trend was seen within the ion flux, with a negligible flow at 0 and 450 mV (figure 15). This was further confirmed by the lack of water and ions in the pore seen visually, shown in figure 22.

Figure 22- Final screenshots of 0, 450 and 900 mV simulations for L (left to right respectively). Notice the vacuums formed within 0 and 450 mV. Na+ and Cl molecules are coded purple and blue respectively. Created using VDW and lines.

The theorised reason for this vacuum forming is the hydrophobicity of the membrane. Without any applied electric field or charges, this two-state liquid-vapour water behaviour has been previously demonstrated within MD for nanopores up to a 2nm diameter53-55. However, this is a larger pore then previously tested, inferring this two-state effect continues past the previously tested thresholds. This is possibly because a larger, consequently, more hydrophobic membrane is used within this study.  Once the current is increased up to the threshold of 900 mV, the water flux increases considerably. The hypothesis is that a dipole moment had now formed within the water molecules, moving it though the pore. It also further supports the argument that this is a liquid-vapour system. Therefore, the change in behaviour at 900 mV is due to the Ef overcoming the energetic threshold, thus allowing the molecules to move through the systems by breaking the previously stated vacuum energetic barrier. Interestingly, as shown in figure 18, the ion still travels some distance within a vacuum system at 0 and 450 mV. However, in this instance, the difference is not as significant as the flux data. This may infer that the ion is moving away from the pore in the simulation box, as it repulsed from the vacuum, which further confirms the hypothesis of an energetic barrier for the molecule.

Once a charged ring is added into the pore in simulations M and N, the flux returns to a more consistent, higher flow (see appendices D23-34). This indicates that the addition of a charged element within the pore overcomes the energetic limitation of the water to the membrane and attracts the water. Simulations M and N have a similar level of water flux and follow the expected trend of increasing Ef producing an increased flow. For simulation N, the negatively charged ring has a higher level of ion flux compared to M, this was previously predicted and is demonstrated by looking at the individual Na+ and Cl fluxes in figure 15. This theory is further proved by examining the distances travelled by the ion, simulation N has a higher distance travelled by the ion compared to M. Another interesting trend to note is that simulation M is the only occurrence when the ion distance decreases with increasing Ef. This effect is most likely due to the ion becoming tethered to some component within the simulation system and hence not progressing.

For simulation K, the flux data is significantly higher than for the non-polar membrane simulations L, M and N, with this trend continuing across all polar pore systems. The cumulative flux data also follows the same overall trend of increased flux when the applied Ef is increased, which is expected to occur with a system that have no obstructions within them. However, unlike its non-polar counterpart, the polar membrane does not form any type of vacuum when a low Ef is applied (see figure 23). The difference in flux events suggest that the polar pore membrane allows ions to flow through effectively. The theory for this difference is that the hydrophilic membrane attracts the waters and ion molecules, producing a higher overall flow due to the increased attraction. This is the opposite effect to the vacuum formed in simulation L, and caused by a reversing of the polarity of the membrane.

Figure 23- Final screenshots of 0, 450 and 900 mV simulations for L (left to right respectively). No vacuums formed within these simulations. Na+ and Cl molecules are coded purple and blue respectively. Created using VDW and lines

 

Analysis of models with 12mer ssDNA in a 5’(cis)- 3’(trans) orientation

The next section of results that will be analysed includes ssDNA in a 5’(cis)- 3’(trans) orientation and involves the simulations A-D.  Simulations B to D were run for 5ns, to get a more extensive DNA translocation representation.

B includes a non-polar, non-charged pore with the DNA molecule placed in the cis entrance to the pore. Table 3 details the translocation events for this simulation, with no Ef producing no translocation events whilst applied Efs of 450 and 900 mV yielded a full translocation of the DNA through the pore, with an applied Ef of 900 mV giving the fastest translocation out of this entire block of simulations (see B, C and D in table 3). Moving past the translocation speed into the shape analysis, the DNA simulation B does not translocate in a linear fashion, as expected. These results indicate that the DNA has changed configuration to a shorter structure. This shortening of the DNA is further supported by the hairpin analysis, which shows that the DNA hairpins quickly whilst in the simulation; at 900 mV, the DNA hairpins at 0.4 ns and holds this shape until the end of the 5ns simulation (figure 13).

There is no cumulative water flux at 0 mV, again suggesting a vacuum is in place. However, the introduction of DNA into a pore with no ring seems to reduce the vacuum threshold to ∼450mV, compared to in simulation L where it was in place until 900 mV. This divergence could be due to the same effect previously seen in simulations M and N, as a charged element is added to the pore, it reduces the energetic barrier. In this case, the charged component is the DNA passing through the pore. There is no significant water flux difference between 450 and 900 mV, which is unexpected. However, the ion flux results follow the expected trend, as the cumulative ion flux dips for 450 mV. This is theorised to occur because the DNA was within the molecule for a longer period compared to at 900 mV, hence blocking it for longer and reducing the flow of ions.

The final component of this system to analyse are the ion distance results. Superficially, these trends are in opposition to the previously explained trends, as the highest distance travelled occurs at 0mV.  However, this reversal in trends is hypothesised to occur due to the vacuum effect. Like simulation L, at 0 mV, the ion is ‘pushed’ away from the membrane, hence flows backwards up the simulation box. Comparatively at 450 mV the ion can only partially translocate and hence travels the shortest distance, whilst at 900 mV it can fully pass through the pore, travelling an expected distance away.

Comparing these results to simulation C, the positive ring has an attracting and tethering effect to the DNA molecule, which was previously theorised. At 0 mV, the DNA is attracted to the pore and partially translocates into the pore before becoming ‘stuck’ onto the positive charged ring; at 450 mV and 900 mV this trend continues with partial translocations in all cases. The distance travelled by the DNA increases as the applied Ef increases, however this effect is not influential enough to untether the DNA from the positively charged ring. Like simulation B, the DNA is non-linear as it passes through the pore, and forms a hairpin in all simulations.

In terms of flux events, the DNA seems to prevent any vacuum from occurring within either of the charged rings, hence meaning water and ion flux are both high across both simulations. Another interesting note is that neither the water or ion flux decreases significantly with the DNA stuck in the pore, suggesting that the tethering event is not a full blockage of the pores aperture.

The other charged system from this section is simulation D, which includes a negatively charged pore. At 0 mV, there is no translocation of DNA, compared to at 450 and 900 mV when both fully translocate. The translocation speed increases in-line with increasing applied Ef, as expected, however it is not as quick compared to simulation B at 900 mV. All DNA translocated non-linearly, with hairpins occurring early for 450 and 900 mV. However, for 0 mV, the hairpin does not occur till the end, which is anomalous. The water and ion flux is consistently high throughout.

The final simulation examined was simulation A, with a polar pore and an uncharged pore, run for 1 ns. No translocation events occurred at 0 or 450 mV, with the DNA fully translocating at 900 mV. Reiteratively, the DNA forms a non-linear, hairpin conformation for all simulations. There was no vacuum formed, like K, and the flux is comparable to the values seen in B, C and D over a smaller time scale. The ion distance increases by increasing the applied Ef.

Analysis of models with 12mer ssDNA in a 3’(trans)- 5’(cis) reverse orientation

This section of results involves the simulations E, F and G, with a non-polar slab and reversed 3’(trans)-5’(cis) 12mer ssDNA molecule. Simulation E is slower than its non-reversed counterpart B, with only a partial translocation event occurring at 450 mV. This trend was previously predicted, as was the reduced water and ion flux events. For simulation E at 0 mV, there seems to be a vacuum forming, like B. However, simulation B has a much higher number of flux events at 450 and 900 mV, even after extrapolating E’s flux events for a 5ns timescale (assuming a linear progression, from graphs in appendix D19-74). However, it is important to note that the cumulative flux events for E are similar to the levels seen without any DNA. The shape analysis was also successfully predicted, with the DNA molecule for E-G extended into a longer shape compared to the non-reversed DNA strand (B, C and D). However, this extended DNA configuration still seems to hairpin at approximately the same rate as the non-reversed DNA molecule.

F includes a positive ring within the pore, unexpectedly and unlike simulation C, this addition does not tether the DNA to the pore. The DNA in simulation F does not interact with the positive charge at all, with full translocation events occurring at 450 and 900 mV. This uncharacteristic behaviour is theorised to occur because of the different, extended and reverse configuration of the DNA. It has been previously theorised that bases of a 5’-threaded has a more unsymmetrical configuration within a pore; however, it was not predicted that this alteration in shape would have such a significant effect on the translocation events. The reversed 3’ DNA configuration does not interact with the positive point groups in any substantial way, in comparison to the non-reversed DNA. A theory for this behaviour is that the reversed configuration is twisted, so that the negative phosphate groups do not interact with the positive ring and the DNA can fully translocate.

The final reversed DNA simulation was G. Again, this had a slower translocation profile compared to D (which contained a non-reversed DNA molecule). Within simulation G, the DNA did not hairpin during the entirety of the simulation at 0 and 450 mV. This effect is speculated to occur because of; its extended shape, the reversed configuration, or a combination of both explanations. However, it’s impossible to give a definite reason with the current data available.

Simulation E, F and G show the same trend of lower cumulative water flux, compared to a non-reversed DNA system. However, for simulation F and G there is no vacuum formed at 0 mV, which is analogous to simulations C and D. The ion flux for F events demonstrate the blockage caused by the full translocation at 450 and 900 mV, with a lower rate compared to 0 mV. However, this effect is less apparent in the ion flux results for G, possibly due to increased rate of ions flux for a negative ring.

Analysis of models with 48mer ssDNA in a 5’(cis)- 3’(trans) orientation

The simulations with 48mer ssDNA included are listed as H-J. Due to the length of the molecule, these simulations were run for 5ns. For these simulations, the DNA formed a continuous loop once simulated, making it impossible to accurately track the length or detailed shape of the DNA (figure 12). However, it was still possible to extrapolate whether the DNA was linear/non-linear via screenshots (see appendix V8-10) and visual analysis. Due to this loop effect and extended length of the DNA, the translocation events were recorded in cycles, depending on how many times the original 5’ end translocates through the pore.

Simulation H had no ring and included the 48mer DNA. At 0 mV, there was only a partial translocation, whilst at 450 mV the DNA fully cycled through once. At 900 mV, the DNA fully cycles through the pore 3 times. The speed of these translocations increase with applied Ef, hence the distance travelled also increases. The flux for H is low, as the DNA permanently blocks the pore. Hence, it was expected that the flux would be significantly reduced, as previously predicted. It was impossible for the DNA to fully hairpin within this system; however, the final screenshots in appendix V8-10 still illustrate how the DNA seems to curve to form exaggerated S and bunched shapes throughout the simulation. Consequently, it is still possible to extrapolate when the DNA is not passing through the pore in a linear fashion, instead forming clusters of DNA in a similar manner to a hairpin formation.

Simulation I and J included a positively and negatively charged ring respectively. However, even with these additions, both sets of results were like simulation H. The same translocation trends were observed in I and J, as well as the same non-linear shapes within the DNA being detected. The addition of charged rings did not have any significant effect on the translocation mechanism. The ionic and water flux were at low levels for both simulations.

 

 

 

Predicted trends compared to actual results

Overall, the data for all the simulations generally followed the expected trends laid out at the beginning of this section. Simulations with unobstructed pores measured a higher level of water and ion flux with increasing applied Ef. Negative rings in general gave the highest levels of ion flux.

However, the distance the ion travelled did not seem to linearly increase with increasing Ef, even when there was no DNA that could obstruct the pathway of the ion. This divergence could be due to a variety of reasons. The most credible theory, is that this ion has altered behaviour in every simulation; and the distance travels totally depends on whether it gets randomly ‘caught’ on any feature of the simulation and therefore cannot travel further. Hence this data set must be further investigated, as it may not be showing the true extent of ion movement within the system.

The likelihood and speed of translocation events increased with increasing applied Ef, as previously predicted. Also, the prediction that the length and occurrence of hairpin configurations would increase with higher Ef was proved. The DNA always left the pore in its original orientation, with no reversal of orientation occurring in the pore. The ion flux demonstrated blockages within the pore by DNA by a reduction in flow, which was expected. Conversely, the cumulative water flux did not show these obstructions; possibly due to the nature of the water molecule. Water is a polar molecule, but is not charged, unlike Naor Cl– ions. Hence, it is theorised that the water can pass through the pore more efficiently due to less potential interactions, which produces a higher flux rate, even with potential obstructions. The only exception to this water flux trend was in simulations H-J, where the pore was nearly totally blocked and a very low level of flux was possible.

The tethering effect associated with the positive ring was proven in simulation C; however, the reversed DNA in simulation F did not tether. This unexpected result was attributed to the difference in configuration between the two DNA molecules; however, it was not predicted that this difference would have such a significant effect on the translocation mechanism in simulation F.

The negative pore seemed to have no impact on the speed of the translocation event; the results showed that for most simulations the negative ring has a similar or lower speed compared to the systems without a ring. The only exemption to this trend was for the reversed DNA at 900 mV, the increased speed could be due to the altered configuration of the molecule.

Overall, the reverse DNA did have slower translocation times versus the non-reversed DNA. However, this trend was only seen in the systems without a charged ring, with the charged systems behaviour producing unexpected results, as previously mentioned.

Results compared to wider studies

A similar tethering effect to the one seen in simulation C has been observed in other computational studies. A binding/sliding mechanism for translocation was previously identified with basic side chains within a HL pore.45, 46 Interactions between a positive molecule within the lumen of pore and DNA have been proven to slow down (and occasionally stop) the translocation rate and non-linearize ssDNA within the pore. A key difference between these results and this study is the lack of any binding-sliding mechanism seen, as the DNA seems to be ‘stuck’ to the lumen. This could be because of the large number of positive, point molecules within the pore, increasing the tethering to the DNA. It also could be due to the length of the simulation, as research conducted in other studies allowed simulations to run up to 20 ns; whilst these simulations ran up to 5 ns.

Other trends found in wider research included the orientation bias, with Mathe et al22 proving a significant difference between DNA orientations; with a 3’-threaded end translocating up to 3 times slower through a HL pore. This trend was seen within this study, however there were unexpected translocation effects once the nature of the pore was changed. It was found that the positive charged pore did not have any type of tethering mechanism with the reversed orientated DNA.

The non-linear configurations adopted by all the DNA simulated have also been discovered in wider research.46 Previous studies have investigated these configurations with HL pores, and like the research conducted in this study, non-linear configurations were observed, with the original orientation being preserved. It is interesting to note that the only configurations that did not hairpin were the reversed DNA molecules, with a negative ring having the most significant effect. However, further research is needed to confirm that this is not an anomalous result.

Experimentally, the data reported by groups like Maglia et al56 on modified HL pores cannot be directly compared to the work completed, due the differences between the pores. However, this is still a useful benchmark into the translocation of modified pores. A similar trend is seen again within this data, with the higher percentage of basic side chains within the modified HL awarding a lower translocation rate. Other experimental research also proves how translocation of DNA molecules through the α-hemolysin protein nanopore can be slowed controllably by introducing positive charges. 44 Again, this exact trend is not observed, as it is more of a tethering rather than a slowing mechanism. However, this data is still vital, as it illustrates how the trends observed in this research are mirrored in other, experimental studies.

Conclusions

In conclusion, results have been obtained for the three questions, posed as part of the instruction. Firstly, altering the nature of the pore does affect the flow of ions, with a negative ring consistently having a higher ionic flux rate compared to the positive and non-charged systems.

Secondly, the characteristics of the pore do alter the behaviour of the DNA through the pore. It was demonstrated that altering the pore with positive charges does change the nature of the translocation event. This study illustrated how the DNA in a 5’-3’ configuration is tethered to the positive point groups via a strong electrostatic attraction, however when the DNA is reversed, this effect does not occur due to the altered configuration. The negative ring had a smaller effect on the translocation of the DNA then expected; there were no significant differences in the translocation process with a negative ring included.

Finally, by altering the type of DNA, the mechanisms of translocation changed considerably. When a longer 48mer DNA molecule was included it formed an effective continuous strand within the simulation, with DNA cycling events instead of discrete exiting occurrences. Consequently, the charged rings did not have such a significant effect, with no tethering mechanism being observed for the positive ring. The reversed orientation of the DNA also had a significant effect, with a more elongated shape being observed whilst the reverse DNA translocated. This alteration in shape directly affected the mechanisms of translocation, as previously mentioned.

Overall, whilst the data is not directly comparable to other sources, it is still important that these results yield similar trends to much larger, more complicated systems.  This research has explored a different range of pore alterations, with a higher than usual range of applied electric fields and a shorter simulation time. The number of charged molecules introduced was high, and the nature of their shape was a single molecular point, instead of a chain.

An interesting trend to note is the formation of a vacuum system, this can form within the membrane pore due to its hydrophobic nature and occurs across all non-polar membrane simulations. Whist this effect is usually seen in smaller nanopores, and without any applied electric field, it is important to note for future simulations that this can occur with a diameter of 3nm within this model.

The simplified pores created were found to reproduce the general trends of DNA translocation and ion flow that have been previously published for the -HL pore and its mutations. Furthermore, it has been demonstrated that charged molecules within a simple membrane pore system can have major conformational effects on a ssDNA as it moves through a nanopore, with an applied electric field. The positive molecules within the inside of the pore electrostatically interact with the DNA, altering the conformation of the DNA, propagating the tethering effect and causing the DNA to not completely translocate. Thus, these results suggest that for a full DNA translocation sequence, it is important that the nanopore limited positive point groups within the lumen, due to the strong tethering effect observed.

Considering the trends established in this study, it should possible to further propagate nanopore design. By introducing the conditions observed in this research into new pore designs, improved DNA sequencers could be produced, with a slower translocation event time.

 

 

 

 

 

 

 

Next steps

This study was restricted by the time per simulation (∼1ns/8hr) and therefore only a limited number of simulations could be run. The next steps would be to increase the simulation time for the models detailed above to 10-20 ns per simulation. Another important step would be to repeat the conditions of this study in different models, to confirm any trends observed.

Another parameter to be examined is the diameter of the pore, as well as further alterations to the design of the nanopore. The overall aim would be to build a more complex, realistic interpretation of a -HL pore, with the same elements present within this study. The overall charge of the point groups within the pore can also be further varied, to include more, less and mixed charges.

Finally, further research should be focused on comparing non-linear and linear translocation events. This study found that without any feeding of the DNA into the pore, it will form a non-linear configuration. Hence, it is important to simulate these types of ‘ratcheting’ mechanisms within the simulations, to get a more complete representation of DNA translocation events.

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