Using LEGO bricks and paper springs to illustrate helical chemical structures

by Dean J. Campbell* and Ali Patel, Bradley University, Peoria, Illinois

Helical model essentials

Helical structures can be found in a variety of areas in chemistry and related fields. These helical structures can be modeled with simple physical media such as interconnected building blocks and paper. Helical structures have chirality, that is, they have non-superimposable mirror images. The chirality of a helical structure arises from the orientation of its twist. As one progresses along the main axis of a right-handed helix, the helix will appear to twist clockwise, moving to the right along the top edge of its circle of rotation. The threads of most screws are right-handed helices.¹ The non-superimposable mirror image of a right-handed helix is a left-handed helix, twisting in a counter-clockwise direction as one progresses along the main axis of the helix.

Chiral shapes can be easily made from LEGO bricks and folded paper. Most single LEGO bricks, like the 1 peg x 2 peg brick in Figure 1, are achiral if the word “LEGO” at the tops of the brick pegs are excluded from consideration. Two LEGO bricks connected at an angle can produce a chiral structure. A very simple two-brick structure and its mirror image are shown in Figure 1. Similarly, some pieces of paper containing a single fold are achiral, but two of the folded paper pieces interleaved at an angle can produce a chiral structure, Figure 1. These simple chiral structural elements can be the bases of larger helical structures. Stacks of LEGO bricks can be used to make helices. For example, helical stacks of LEGO bricks have been used to model liquid crystal structures.² Paper springs, built from interfolded paper strips, are essentially helical stacked interleaved paper folds.

Figure 1. (TOP) A single 1 peg x 2 peg LEGO brick is achiral, but two 1 peg x 2 peg bricks connected at an angle are chiral with non-superimposable mirror images. (BOTTOM) A single folded paper rectangle is achiral, but two paper rectangles interfolded at an angle are chiral with non-superimposable mirror images.

 

Light polarization

One type of helical structure with connection to chemistry is circularly polarized light. This type of light can be thought of as having an electric field vector that rotates in a helix wrapped around the linear direction in which the light is traveling. The helical structure can be thought of as being the sum of two orthogonal light waves that are out of phase with each other.³ Depending on how the waves are out of phase, light with either right- or left-handed polarization can be produced. These ideas can be modeled with LEGO bricks. One way to model a wave with LEGO bricks is to stack them in the pattern:

2 peg x 1 peg, 4 peg x 1 peg, 4 peg x 1 peg, 2 peg x 1 peg

oriented in one direction, followed by the same pattern oriented in the opposite direction. In Figure 2, at the left of each image, are shown sets of these LEGO wave models aligned orthogonally to each other and out of phase. The orthogonal waves can be brought together by alternating bricks from each wave, and shown in the middle of each image. Finally, at the right of each image is a helical LEGO structure made from connecting the ends of 4 peg x 1 peg bricks and 1 peg x 1 peg bricks in an alternating pattern. The helical pattern is created by turning each 4 peg x 1 peg brick by 45° (or 1/8 of a circle) in the same direction relative to the previous 4 peg x 1 peg brick. Each helix in Figure 2 is comprised of sixteen 4 peg x 1 peg bricks and sixteen 1 peg x 1 peg bricks.

Figure 2. LEGO model of summation of light waves at 90° angles and out of phase to produce circularly polarized light with (TOP) left-handed and (BOTTOM) right-handed rotation.

 

Paper springs have been used to illustrate the sum of two orthogonal light waves to produce circular polarization.⁴ The left side of Figure 3 shows two strips of folded paper. The strips contain arrows to indicate the electric field orientation within the waves and red lines to represent wave maxima. Interleaving the offset strips produces a paper spring at the right side of Figure 3 where the red line of field orientation forms a right-handed helix. The same strips of paper can be used to produce left- and right-handed helices. The difference is the order in which the strips are folded. To change the handedness of a helix, unfold it and begin folding again with the opposite paper strip first.

Figure 3. Paper spring model of summation of light waves at 90° angles and out of phase to produce circularly polarized light with right-handed rotation.

 

The plane of polarization of light can be thought of as arising from the sum of both right-handed and left-handed polarization of light that are in phase.⁵ Chiral substances can rotate the plane of polarization of light by shifting the differing circular polarizations of light with respect to each other. Figure 4 illustrates these ideas. In the middle of each panel is a tetrahedron built from five 2 peg x 2 peg LEGO bricks of differing colors. Each brick is attached by a corner to two top corners and two bottom corners of a central brick. The tetrahedron in the left panel has a superimposable mirror image and is achiral. It does not shift the differing circular polarizations of light relative to each other, and the plane of polarization represented at the bottom of the panel is vertical. The tetrahedra in the middle and right panels are non-superimposable mirror images of each other and are chiral. They do shift the differing circular polarizations of light relative to each other, and the planes of polarization represented at the bottom of the panels are no longer vertical.

Figure 4. (LEFT) LEGO model of summation of in-phase circularly-polarized light in achiral material to not rotate light polarization. (MIDDLE) LEGO model of summation of out-of-phase circularly-polarized light in dextrorotary chiral material to rotate light polarization clockwise. (RIGHT) LEGO model of summation of out-of-phase circularly-polarized light in levorotary chiral material to rotate light polarization counterclockwise. 

 

Figure 5 illustrates these ideas using paper springs. At the top of each panel is a tetrahedron built from molecular model kits. The tetrahedron in the left panel has a superimposable mirror image and is achiral. It does not shift the differing circular polarizations of light relative to each other. The tetrahedra in the middle and right panels are non-superimposable mirror images of each other and are chiral. They do shift the differing circular polarizations of light relative to each other.  

Figure 5. (LEFT) Paper model of summation of in-phase circularly-polarized light in achiral material to not rotate light polarization. (MIDDLE and RIGHT) Paper model of summation of out-of-phase circularly-polarized light in chiral material to rotate light polarization.

 

Chemical structures

The arrangement of atoms within structures can be represented by a variety of models,^6-9 and helical chemical structures can be represented using helical models. As noted above, helical stacks of LEGO bricks have been used to model liquid crystal structures.² The helical arrangement of dipoles associated with the liquid crystal molecules could be represented by the paper springs with the arrows printed on them as shown in Figure 3. Figure 6 shows 2 peg x 2 peg bricks connected by their corners into helical shapes. The left panel shows a single left-handed helix, like in the polysaccharide amylose starch.¹⁰ The ⍺-helices in proteins are typically right-handed.¹ The right panel shows two right-handed helices intertwined in an antiparallel arrangement, reminiscent of the strands of the most common forms of DNA.¹

Figure 6. (LEFT) LEGO model of left-handed helical structure. (RIGHT) LEGO model of double right-handed helices in an antiparallel arrangement.

 

Figure 7 shows paper springs in helical shapes. It is important to remember that the same strips of paper can be used to produce left- and right-handed helices, and that the difference is the order in which the strips are folded. The left panel shows a paper spring where the folds are highlighted with a chain of circles pattern to form a single left-handed helix, like in the polysaccharide amylose starch.¹⁰ The paper spring is partially unfolded to show the markings on each paper strip more clearly. Marks have been added to the centers of the squares in the paper springs to represent iodine trapped inside of the starch helix. The right panel shows a paper spring where the unfolded edges are colored with markers form the pattern of a right-handed triple helix, like in collagen.¹¹ The paper spring is partially unfolded to show the markings on each paper strip more clearly. In this case, it was easiest to make an unmarked paper spring, place preliminary marks on the edges of the structure, unfold the structure to complete the marks, and then fold the structure back together.

Figure 7. (LEFT) Folded paper spring with folds highlighted to produce a model of a left-handed helical structure. (RIGHT) Folded paper spring with non-fold edges highlighted in different colors to produce a model of a triple right-handed helical structure.

 

Connections

These models can be made from readily available materials and can be used in educational settings. A variation of the starch iodine paper spring model was made from part of a manila folder. It had fewer turns than the model in Figure 7, but was much wider for better visibility. It was passed around at a chemistry outreach event after first showing the audience the color change when starch is added to iodine. Additional connections might be made with a recent paper describing the Matilda Effect, describing “the shifting of identification of particular research efforts from the junior woman partner to the senior partner.”¹² The paper describes the efforts of Edith Humphrey, who worked with chiral inorganic compounds, and Florence Bell, who worked with X-ray diffraction of DNA.

The exoskeletons of some beetles reflect left-handed circularly polarized light. Some 3D glasses utilize circularly polarized light to produce the illusion of three-dimensional images. Viewing the beetles through different lenses of the 3D glasses makes the beetles appear different colors. For example, green June beetles and Japanese beetles appear to reflect green without the glasses, as well as through one of the lenses of the glasses. When viewed through the other lens of the glasses, the green color is absorbed and cannot be viewed, Figure 8. The exoskeletons of the beetles contains chitin in structures called microfibrils, which lie flat in layers. The orientation of the microfibrils is rotated from layer to layer, creating helix-like structures that reflect left-handed circularly polarized light.¹³ Though this polarization does not appear to arise from chirality at the molecular level, the structures resemble some liquid crystals as examples of control of light polarization by helical ensembles of molecules.

 

Figure 8. Japanese beetle viewed through two different lenses of pair of 3D movie glasses.
 

Safety Small children could possibly swallow LEGO bricks. Consider the hand-eye coordination of individuals being asked to cut paper strips to make springs.

 

Acknowledgements This work was supported by Bradley University and the Mund-Lagowski Department of Chemistry and Biochemistry with additional support from the Illinois Heartland Section of the American Chemical Society. The material contained in this document is based upon work supported by a National Aeronautics and Space Administration (NASA) grant or cooperative agreement. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of NASA. This work was supported through a NASA grant awarded to the Illinois/NASA Space Grant Consortium.

 

References

1. Elgi, M.; Zhangh, S. Making Sense of Helices: Right and Wrong Models in Science and Art. Molec. Front. J., 2023, 7, 1, https://structbio.vanderbilt.edu/~eglim/journals/284.pdf (accessed June, 2024).
2. Campbell, D. J.; et al. Exploring the Nanoworld with LEGO Bricks [Online]; Bradley University, Peoria, IL, 2011. https://chem.beloit.edu/edetc/LEGO/PDFfiles/nanobook.PDF (accessed June, 2024).
3. Introduction to Polarization. Edmund Optics. https://www.edmundoptics.com/knowledge-center/application-notes/optics/i... (accessed June, 2024).
4. Campbell, D. J. Paper Springs as Demonstrations of Chiral Objects and Circular Polarization. https://personalpages.bradley.edu/~campbell/chiralpapersprings.pdf (accessed June, 2024).
5. Paschotta, R. Optical Activity. RP Photonics Encyclopedia. https://www.rp-photonics.com/optical_activity.html (accessed June, 2024).
6. Campbell, D. “Modeling Unit Cells and Layer Sequences of Solar Cell Materials using Dimpled Packaging.” Green Chemistry Teaching and Learning Community. https://gctlc.org/modeling-unit-cells-and-layer-sequences-solar-cell-mat... (accessed June, 2024).
7. Campbell, D. “Tissue Paper Banners Connected to Chemistry.” ChemEd Xchange. https://www.chemedx.org/blog/tissue-paper-banners-connected-chemistry (accessed December, 2023).
8. Campbell, D. J.; Walls, K.; Steres, C. “Paper Snowflakes to Model Flat Symmetrical Molecules.” ChemEd Xchange. April 6, 2022. https://www.chemedx.org/blog/paper-snowflakes-model-flat-symmetrical-mol... (accessed December, 2023).
9. Robinson, K. F.; Nguyen, P. N.; Applegren, N.; Campbell, D. J. “Illustrating Close-Packed and Graphite Structures with Paper Snowflake Cutouts.” The Chemical Educator, 2007, 12,163-166.
10. Pesek, S.; Lehene, M.; Brânzanic, A. M. V.; Silaghi-Dumitrescu, R. On the Origin of the Blue Color in The Iodine/Iodide/Starch Supramolecular Complex. Molecules, 2022, 27, 8974, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9784209/ (accessed June, 2024).
11. Shoulders, M. D.; Raines, R. T. Collagen Structure and Stability. Ann. Rev. Biochem., 2009, 78, 929-958, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2846778/ (accessed June, 2024).
12. Rayner-Canham, M.; Rayner-Canham, G. The Matilda Effect: Some British Chemistry Case Studies (I). Bull. Hist. Chem., 2024, 49, 5-14.
13. Berthier, S.; Thomé, M.; Simonis, P. Circular Polarization in Nature: Factual, Theoretical and Experimental Summary. Mat. Today: Proc., 2014, 1, 145–154.

 

Supporting Information

Attached is a PowerPoint file of paper spring models for chemistry, that, when printed double-sided, can be used to produce paper springs to model circularly polarized light and helical molecular structures.