Download Interactive Computer Program: Packaging DNA into Chromosomes

Interactive Computer Program: Packaging DNA into
Chromosomes
Xiaoli Yang1, Yifan Cai1 and Charles Tseng2
1
Department of Electrical and Computer Engineering
2
Department of Biological Sciences
Purdue University Calumet
Hammond, IN, USA
Abstract - As part of the interactive program for teaching and
learning genetics, the module on packaging DNA into
chromosomes involves the simultaneous coordination of eyes,
mind, and hands for visualization, cognitive feedback, and
manipulation, respectively. Computer modeling of various
chromatin structures during packaging is based on OpenTKOpenGL on .Net Platform, which is coupled with an inquiry
based content design to enhance the efficiency of teaching and
learning. The prototype has been successfully tested in a
genetics class at Purdue University Calumet. It should also be
applicable to a number of undergraduate biology courses.
Keywords: DNA, Chromosomes, Modeling, Computer
Program
1
Introduction
From its central role in real-life forensic investigations
to being the basis of major biotechnological applications in
medicine, agriculture, and the environment, DNA based
genetics is an essential discipline in the life sciences. As
fascinating as the subject is, however, teaching and learning
genetics has often been fraught with difficulty [1-3].
Confronted with intricate molecular structures, complex
packaging schemes, and elaborate mechanisms of action, both
teacher and student are frequently at a loss – the teacher in
how to convey this material in a clear and understandable
way, and the student in how to assimilate all the information
usefully. To be sure, the abstract and intangible nature of
much of the material is the source of the problem.
Traditional methods of teaching genetics, employing
classroom
lectures,
textbook
readings,
homework
assignments, and laboratory exercises, have not proven to be
very effective [4, 5]. Recently, efforts have been made to
integrate computer visualization technologies into pedagogy
to enhance the learning process [6-8]. Current computerbased tools, however, do not stress cognitive feedback in their
designs. The present paper describes an innovative approach
to teaching and learning genetics, in which students can
visualize a real-time, interactive DNA model, as well as
actively control the dynamic process of packaging DNA into
a compact metaphase chromosome.
The objectives of the program are to 1) develop, as part
of a web-based interactive program, a DNA packaging
module suitable for a wide range of college courses and 2)
serve as a model for STEM (science, technology, engineering,
and mathematics) education via distance learning.
2
Model Development
Models of various structures were developed based on
the following system: OpenTK-OpenGL on .Net Platform.
The Open Tool Kit (OpenTK) is a free project that allows
developers to use OpenGL, OpenGL|ES, OpenCL, and
OpenAL APIs from a managed language (e.g. VB.NET).
Features include:
• Written in cross-platform C# and usable by all managed
languages (F#, Boo, VB.Net, C++/CLI).
• Consistent, strongly typed bindings, suitable for RAD
development.
• Usable
standing
alone
or
integrated
with
Windows.Forms, GTK#, and WPF.
• Cross-platform binaries that are portable on .Net and
Mono without recompilation.
• Wide platform support: Windows, Linux, and Mac OS
X, with iPhone port in process.
2.1
3D model of double helix DNA
DNA is modeled as a double helix. The model is
specified by l, the length of the helix, r, the radius of the helix,
and w and h, the width and the thickness of one strand of the
double helix, respectively (Fig. 1). These parameters generate
a group of points, which are used to construct the DNA
model. The points are linked together to form a sketch of the
double helix. After shading the sketch, a 3D DNA model is
created. The double helix model is calculated during runtime
based on the equations below:
,0
∗ sin
∗ cos
∗ ∗
(1)
Where t is the length variable along x-axis, r the radius of
the helix. the angle increment, controlling the smoothness
of the helix. We chose
6 from the experiment to make the
model smooth. determines the initial angle. We chose
0
45 from the experiment to generate double helical
shapes.
∗ ∈ 0, 2! . From the above equations,
,
,
determine the Cartesian coordinates x, y and
z in 3D space.
By calculating the position of all the points, a helical line
can be generated (Fig. 2, left). The quadrupling of the line
(Fig. 2, right) is generated by replicating the original line four
times.
&
$
1 ( * , 1, 1
)
3 ( , 3, 3
)
*
) 0./0* 1./1*
%, * ( * , * , * 2
$ -3/-4 ) 03/04 13/14
#, * ( * , * , * 2
-./-*
(2)
The result is a complete DNA model (Fig. 5).
Fig. 1. Parameters for a helix (perpendicular views)
Fig. 2. Left: helical line; Right: doubling of line
After further duplicating the strand with a different
value and shading the sketch, two DNA strands of different
colors are created (Fig. 3).
Fig. 3. DNA double helix structure with shading
2.2
3D model of nucleotide bases
We use line segments (cuboid) of different colors to
represent DNA bases. The points that form the DNA strands
(determined above) are used to calculate the points
representing the line segments (bases). Assume that p1 (x1,
y1, z1) and p2 (x2, y2, z2) are corresponding points on
different strands generated by the same t value, but different
θ values, p3 (x3, y3, z3) and p4 (x4, y4, z4) are the points
next to p1 and p2, respectively, w is the length of the side, pc1
is the midpoint between p1 and p2, and pc2 is the midpoint
between p3 and p4 (Fig. 4).
Fig. 5. Screen snapshot of DNA model from the program
2.3
3D model of histone octomer
The histone octomer is represented by an elongated
ball, which is described by the following equations:
∗ sin5 ∗ cos
6
∗ cos 5 7 , 5 9 0
∗ cos 5
8
*
8
*
,5 : 0
(3)
∗ sinφ ∗ sinθ
,
determine the Cartesian coordinate x, y and
z in a 3 dimensional space, where r is the radius of the
histone; 5 the angle between the diameter and z-axis,
= =
5 ∈ <7 , >;
the angle between the projection of the
* *
diameter on the plane and the x-axis. , ∈ 0, 2! and h the
height of the elongated ball (Fig. 6).
,
Fig. 6. Sphere coordinate system
Fig. 4. Parameters used to calculate the position and shape of
bases.
Then all 8 points needed to describe a cuboid can be
calculated as follows.
These points generate a sketch of the histone octomer.
Shading the sketch with a color completes the model (Fig. 7).
Fig. 7. Left: sketch of histone octomer;
Right: shaded histone octomer
2.4
DNA wrapping-formation of core
nucleosome
In this step, DNA is simplified as a line, which can be
wrapped around the histone octomer. Fig. 8 shows how to
calculate the position of the binding points.
implemented this function by adjusting camera position when
we developed the model. The camera was located on the
surface of sphere with the target at the center of sphere, so
that the distance between camera and target never changes. In
other words, the size of the target remains the same, so that
the model size does not change. Camera position (a point on
the surface of sphere) is described by φ , θ and r, where r is
the radius of sphere. While the value of r never changes, φ
and θ are variable. Changing φ and θ changes the camera
position, and they are changed by moving the mouse. Moving
the mouse produces component values dx and dy along the xand y-axis, respectively. Therefore, mapping dx and dy to φ
and θ is an effective way to adjust camera position.
3
Fig. 8. Calculation for DNA-protein binding position
The histone octomer is projected on the xz-plane as a
circle. Assume that O is the center of the circle, P is outside
the circle, r is the radius of the circle, dx and dy are the
differences between O and P in x and y components,
respectively, D is the distance between P and O, Pb is the
binding point,α is the angle between line P0 and the vertical
line, and β is the angle between line P0 and the line PbO.
Then α and β can be calculated as follows:
D
arcsin
arctan
C
F0
F-
(4)
270° 7 7 D
(5)
Finally, Pb is represented by (x,y), where
∗ sin
∗ cos
(6)
When DNA binds to a histone octomer, it starts to wrap
around the octomer. After Pb is determined, the points on the
spiral nearest to it can be calculated (Fig. 9).
The value of
is
Fig. 9. Wrapping of DNA around histone octomer. Left:
sketch; Right: shaded
2.5
Camera position adjustment
In the interactive module, users can view the model
from different angles by dragging the mouse. Our program
The Program Content Design
The design of module focuses on inquiry based methods
with cognitive feedback and interactive experiences as
important components [9]. In every section, a question is
followed by observations and measurements, hands-on
experiments, and conclusions. In each of the learning steps,
dynamic models of DNA molecules, chromatin fibers, and
metaphase chromosomes are presented for interaction through
visualization, cognition, and operation. Completion of the
program requires comprehension of the entire concept and
thus ensures the success of the learning experience. The
computer-based content is summarized below:
3.1
DNA and chromosomes in prokaryotes and
eukaryotes
Inside the cell, DNA molecules are packaged, with helped
of proteins, into thread-like structures called chromosomes.
In prokaryotes (such as bacteria), the chromosomal DNA,
when open, is often circular. The total length of a bacterial
chromosomal DNA (e.g., E. coli DNA) may be a thousand
times longer than the cell that contains it. Little is known
about the packaging of bacterial DNA, although a few major
DNA regions anchored by proteins at specific sites in the cell
have been noted.
In eukaryotes (such as animals and plants), DNA
molecules are linear. Each eukaryotic species has a fixed
number of chromosomes. For diploid species (species with 2
sets of chromosomes, one from each parent), chromosomes
are paired, so that the total number of chromosomes is always
even.
In humans, for example, the father provides a set (also
called a genome) of 23 different chromosomes (from sperm),
while the mother provides the other set (genome) of 23
different chromosomes (from egg). Thus, each of our somatic
(body) cells contains 46 (or 23 pairs) chromosomes.
3.2
How long is our DNA?
The DNA of each human genome is about 3.2 billion (3.2
x109) deoxyribonucleotides long. Each deoxyribonucleotide
is 3.4 A (0.34 nm), making the total length of human genomic
DNA (0.34 nm)(3.2 X 109) ≈1 m (meter) per genome. Since
there are 2 genomes per human cell, the total length of DNA
per human cell is 2 x 1 m = 2 m.
Assuming that an adult human body contains about 50
trillion (50 x 1012) cells, the total length of DNA in the human
body is (50 x 1012) 2 m = 100 x 1012 m (100 trillion meters of
DNA per human). The Sun is 150 x 109 m (150 billion
meters) from Earth. How many times can you stretch the
DNA from the Earth to the Sun? (100 x 1012)/ (150 x 109) =
666 times (Fig. 10). The distance between the Earth and the
Moon is about 3.84 x 108 m. Can you calculate the number of
times your DNA can stretch from the Earth to the Moon?
Level 2 - 10 nm chromatin fiber: The DNA of eukaryotic
cells is tightly bound to basic (positively charged) proteins
known as histones. This nucleoprotein complex is called
chromatin. The basic structural unit of chromatin is the
nucleosome. A nucleosome consists of a small segment of
DNA wrapped around histones. The core nucleosome
particle consists of two molecules each of the core histones
(H2A, H2B, H3, and H4), forming a histone octomer (Fig.
12), around which is wrapped approximately 146 base pairs
of DNA. The core particle is stabilized by a fifth histone
called H1 (also called a linker histone). DNA between the
core nucleosome particles is called linker DNA. The core
nucleosome particle plus the linker DNA is about 200 bases
long, as evidenced by digestion with the enzyme micrococcal
nuclease.
Fig. 10. The total length of human DNA
3.3
Can our genomic DNA fit into a nucleus?
Let’s examine the size of the human genome in the cell.
In the nucleus (G1 phase) of each cell in the human body are
46 chromosomes. Since a set of 23 chromosomes constitutes
a genome, there are 2 genomes per nucleus. Each genome
contains approximately 3 x 109 base pairs, so there are 6 x 109
base pairs per nucleus in the G1 phase. Each nucleotide of the
base pair measures approximately 3.4 x 10-10 m in length.
Therefore, the total length of DNA in each nucleus is:
(2)(3 x 109 nucleotides)(3.4 x 10-10 m/nucleotide) ≈ 2 m.
However, the diameter of an average nucleus is 10 x 10-6
m, making the total length of DNA in the nucleus 200,000
times longer than the diameter of the nucleus:
(2 m)/(10 x10-6 m) = 200,000. How can such a long strand of
DNA fit in such a small nucleus?
Cleary, the DNA must be folded. Let us examine how
much space the DNA occupies in the nucleus if it is somehow
folded so that it will fit. DNA exists in a double helix, which
can be approximated by a cylinder with diameter 20 x 10-10 m.
Therefore, the volume the DNA occupies is:
π(r2)h = (3.14159)(10 x10-10 m)(2 m) = 6.4 x 10-18 m3
Assume that the diameter of an average nucleus is
approximately 10 x 10-6 m, making the volume of the
spherical nucleus:
(4/3)(π)(r3) = (4/3)(3.14159)(5 x 10-6 m)3 = 5.24 x 10-16 m3
Consequently, the fraction of the nucleus occupied by
DNA is:
[(6.4 x 10-18 m3) / (5.24 x 10-16 m3)] x 100 = 1.22%
There is clearly enough room in the nucleus for the DNA
– and for its activities including transcription, replication,
packaging and unpackaging. This leads to the our main topic:
How is the DNA packaged into chromosomes?
3.4
Levels of DNA packaging
DNA packaging can be considered at the following
levels:
Level 1 - Double helix: The double helical DNA molecule
has a width of about 20 A (2 nm) (Fig. 11)
Fig. 11. Screen snapshot of double helical DNA molecule
Fig. 12. Screen snapshot of histone octomer.
(blue: H3; green: H4; Yellow: H2A; red: H2B)
The linear chromatin fiber at this level is about 10 nm in
diameter (Fig. 13. a). This represents the state of most
chromosomal DNA during interphase and is known as
euchromatin. Genes that are actively transcribed (with
momentary detachment of histones) are in this less condensed
state.
Level 3 – 30 nm chromatin fiber:
Some of the 10 nm chromatin fibers can be packed into
30 nm fibers. To do this, the H1 histones, each attached to a
core nucleosome, interact with each other, turning inwards
and forming a new spiral structure known as a solenoid or 30
nm chromatin fiber (Fig. 13. b).
Each 6-8 nucleosomes
constitute one turn of the new spiral. In this state, the
chromatin is tightly packed and is referred to as
heterochromatin, a state in which DNA is genetically inactive
(no transcription or replication).
Higher levels of packaging - looping: The above levels
of DNA packaging mainly describe the G1 phase of the cell
cycle. If the cell is destined for division, the G1 phase is
followed by the S phase, where a DNA molecule replicates
semiconservatively to form two identical DNA molecules
before being packaged into chromatin fibers and entering the
G2 phase. In the early stages of mitosis (or meiosis), the two
replicated DNA molecules (in the form of chromatin fibers)
continue to condense, and the 30 nm fibers are folded into
loops (Fig. 14).
Fig. 15. Screen snapshot of DNA in sister chromatids of
metaphase chromosome
Fig. 13 a. 11 nm chromatin fiber
Fig. 16. Screen snapshot of metaphase chromosome
with centromere and telomeres
4
Fig. 13 b. 30 nm chromatin fiber
Fig. 14. Screen snapshot of looped chromatin fibers
The chromosome reaches its highest condensed state at
metaphase. Condensation is the result of the further folding
of the 30 nm fibers into different loops until a 700 nm
structure is reached (width of a chromatid). Therefore, a
metaphase chromosome, which consists of two sister
chromatids as thick as 1700 nm, is large enough to be clearly
seen under a light microscope (Fig. 15). Two specialized
structures, centromere and telomere, can be seen with special
staining technique (Fig. 16). Chromatin fibers decondense
through unpackaging and stretching as the cell returns to the
G1 phase.
Conclusions
This research uses computer technology to enhance life
science education. It is part of the interactive program for
genetics education [10-14]. The success of this interactive
computer program relies heavily on 1) innovative content
design that stimulates cognitive feedback through coordinated
hands-on interactions at key points of the learning process,
and 2) efficient computer programs that are capable of
demonstrating complex concepts and processes.
The computer learning modules involve the simultaneous
coordination of eyes, mind, and hands for visualization,
cognitive feedback, and manipulation, respectively. In this
way, complex concepts are scaffolded, reinforcing the
learning process. From a pedagogical standpoint, science is
essentially taught with the scientific method, with questions,
observations, experiments, and analysis. Science learned in
this way is more meaningful – and more memorable.
The DNA packaging module, utilizing these methods, is one
of a series of modules for learning genetics that can be
adopted for a number of biology courses at both college and
high school levels.
5
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