Computer Simulation of Single Molecule Diffusion
David E. Pederson, Bryon S. Drown, Dr. Daniel Burden
Wheaton College, Chemistry Department
Wheaton, IL 60187
Abstract: Computers can simulate the diffusion of a single particle as it moves in solution. The system that the particle diffuses through contains a separating membrane,
an alpha-hemolysin nanopore and .1 M KCl or NaCl solution. Oxford Nanopore Technologies proposed that the system can be used for an efficient genome sequencing
technique. The forces of electrophoretic flow, electroosmotic flow and random diffusion determine the movement of the particle in solution. Our model suggests that
decomposition of the system at the high potentials required to produce high capture rates inhibits actualization of the proposed genome sequencing technique.
Preliminary results from investigation into complex situations that have been suggested to increase the capture rate confirm that genome sequencing is inhibited by
decomposition of the system. Future research will continue to investigate particle motion in solution and transport dynamics promising systems and to help explain
experimental results of transport dynamics.
Computer Simulation of Single
Molecule Diffusion
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Nucleotide is simulated as a
charged particle
Particle is released above alphahemolysin embedded in membrane
Three forces determine particle
motion
Results of Particle Simulation
Three Forces
Electrophoretic
Flow
Electroosmotic
Flow
Random Diffusion
Electrophoretic force is
the force of the electric
field on the charged
particle.
Electroosmotic flow is
the force induced by
solvated ions flowing
through the pore.
Random diffusion
simulates the many
random interactions that
the particle experiences in
solution.
Particle experiences a random walk
based on molecular forces
Our results say that an extreme
potential would have to be applied
across the pore in order to attain
capture rates acceptable for genome
sequencing (>99%). The proposed
system of alpha-hemolysin has a
maximum capacity of approximately 1
V before decomposition.Our results
state that about 8 V of potential would
be required to increase the capture
rates to >99% in favorable transport
conditions. Preliminary testing using
COMSOL finite element analysis
maps suggest that the required
potential for >99% transport would be
even greater. Future investigation will
investigate more complex, promising
systems.
The equation above constrains
the magnitude of the random
diffusion step size.
Proposed Genome sequencing
method attaches enzyme to pore to
sequentially release nucleotides
Time to Capture Results
Alpha Hemolysin
The time to capture results are more favorable for genome
sequencing, suggesting that nucleotides that are captured are
likely to be captured in order due to the fast transport from
release to the hit point. We came to the conclusion that
captured particles were most likely captured within the first
100 ns of release. We also determined that there is a local
maximum in the average time that particles take to be
captured at different applied potential. We hypothesize that as
potential increases to 3.5 V more particles which diffused for
a long time further away are drawn into pore. At potentials
above 3.5 V, the particles are all drawn into the pore quickly
without having the chance to diffuse far from the pore.
Physical Properties include:
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Heptomeric structure
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10 nanometer long tube
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2.5 nanometer wide opening
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Large vestibule inside opening
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Beta-cyclodextrin constriction point Perspectival view of alpha-
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The figure above shows the direction of the
combined electrophoretic and electroosmotic forces
in the different regions.
The image above shows the
position of particles as they are
allowed to diffuse for 3 ns.
Surrounded by .1 M ionic solution hemolysin from release point
COMSOL Finite Element Analysis
Single Molecule Diffusion Simulation (SMDS)
SMDS is a program that releases particles one at a time
above a nanopore and simulates the the molecular forces
that act on the particle, generating a random walk through the
pore or out into solution.
COMSOL Multiphysics is a program designed to solve
difficult differential equations describing complex
physics based systems. In our application, we solve for
the electric field at points, or nodes, in the alphahemolysin, lipid and water system. COMSOL then
generates a map of all the node locations and their
corresponding electric voltage which can be fitted to
our single molecule diffusion simulator to dictate
electrophoretic flow. The advantage of COMSOL is
that we can create large maps of complex geometries.
FIgure above shows COMSOL
mesh for basic pore geometry.
Figure below shows a more
complex, accurate geometry.
Special Thanks
NAMD Molecular Dynamics Simulator
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The figure above
demonstrates a random
walk. It shows a two
dimensional projection of
a particle's path above
and into the simulated
pore. Snapshots of the
particle's position are
taken every .25
nanoseconds.
This image shows the
cumulative density of particle
position on a logarithmic
binning scale as particles are
allowed to diffuse around a
custom electrophoretic flow
map. The upper red spot
shows the release point. The
map is generated from
molecular dynamics data.
This summer, we experimented with NAMD to improve
force calculation in the system. NAMD is a molecular
dynamics simulator meaning it models all of the
molecules in a system and all of their interactions with
the rest of the system over time. Molecular dynamics
simulations produce wealth of information about the
forces present around and inside the pore. NAMD
accurately models increased complexities in the system
such as ion gradients which have been shown to
increase the probability of analyte capture. Figures on
the left show (above) alpha-hemolysin alone and
(below) alpha-hemolysin embedded in a lipid bilayer
surrounded with NaCl solution.
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The Alumni Association
The National Science Foundation
Wheaton College
Chemistry Department of Wheaton College
Bibliography
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(http://www.nanoporetech.com/technology/introduction-to-nanopore-sensing/introduction-to-nanopore-sensing)
Molecular structure images were made with made with VMD. Graphs produced on Origin Pro. Mesh images were made using
COMSOL. Particle path image and flow diagram were made using MATLAB graphing utilities.