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: ∗ sin 5 ∗ 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 ∈ ; 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.

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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

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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.

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References

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Learning:

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