Using the DNA Triangle to Explain Complex Biology Concepts

Using the sine and cosine identities, we can calculate the sides and angles of any triangle. We call these identities” trigonometric identities.

Using Krogan06MATRIX, we found that themes in structural SDDI-PPI triangles consist of PPIs with similar function, process, or location involvements. This demonstrates that integrating with other complementary datatypes can help find protein complexes.


The triangle framework provides an intuitive and logical framework to help students understand complex biology concepts. For example, it provides a useful way to discuss meiosis and the DNA triangle: ploidy sits at the chromosomal level; homologous chromosomes reside at the molecular level; and the mechanism of homologous pairing connects the chromosomal and informational levels.

One feature of the triangle method that students might find helpful is its ability to create a universal triangle. This is accomplished by using the model to convert measured Tir into modeled Fr and Moisture availability (Mo). This transformation transforms the spatial distribution of moisture availability isopleths so that their coordinates are invariant for a given image, and thus allows trajectories toward different land surface conditions to be tracked over time without losing their relative positions within the triangle.

The transformation also makes the EF isopleths in Figure 2 relatively insensitive to ambient conditions, allowing trajectories to move toward higher Fr without changing Mo significantly, while still maintaining their position near the warm and cold edges of the triangle. This invariance is especially valuable for tracking changes in soil water content over time.


The central idea of molecular biology is that spontaneous chemical reactions that occur within cells release free energy. Cells use this free energy to drive nonspontaneous chemical reactions that generate proteins. This coupling of reactions is a fundamental aspect of life and, therefore, must be understood.

The chemists who developed the genetic code did so using clever biochemical tricks. They discovered that a certain sequence of bases in the DNA of one cell is translated to an amino acid sequence in the protein chain of another cell. This code enables cells to communicate with each other.

Application of the triangle g framework to topics like meiosis reveals that novices understand these concepts less completely than experts. For example, they often confuse the ploidy corner (C) with the homologous chromosomes and mechanism of homologous pairing corners (M and I). The middle/upper-level textbooks we reviewed describe meiosis mainly at the chromosomal and molecular levels but rarely at the informational level.


Biological processes such as meiosis require knowledge of DNA at different levels. The DNA triangle framework allows students to organize their thoughts about these complex topics.

The second-pass analysis of the interview data and written survey responses focused on codes related to the three apexes of the DNA triangle: C, chromosomal; M, molecular; and I, informational. For example, understanding the concept of ploidy requires knowledge of DNA at both the chromosomal and informational levels. Similarly, understanding homology and the mechanism of homologous pairing relies on knowledge of DNA at both the chromosomal (the physical interaction of complementary base sequences) and molecular (the chemical composition of DNA) levels.

A second finding from this work relates to how the DNA triangle model can be applied to other complex biology topics. For example, understanding the regulation of gene expression requires knowledge of DNA at both the chromosomal, molecular, and informational levels. This is also true when considering the cellular process of photosynthesis, in which energy from sunlight triggers a reaction that converts carbon dioxide and water to oxygen and glucose.


In addition to describing a process in terms of its components, biology also must describe those components at different levels of abstraction. This approach to science is sometimes called “symbolic biology.” The chemistry symbol delta () represents change. You may have seen this symbol used in a formula triangle, where two values are shown side by side and you multiply the bottom one by the top one to get your answer.

The second law of thermodynamics states that spontaneous chemical reactions, like cellular respiration, must release free energy (G). Cells use this free energy to drive non-spontaneous chemical reactions, such as protein synthesis, that cannot occur without an input of free energy.

Our framework of the DNA triangle could help students understand these concepts. For example, a student’s understanding of meiosis requires knowledge of DNA at all three corners of the triangle—chromosomal, molecular, and informational. The chromosomal level is the structure of chromosomes, which can be directly observed; the molecular level is the underlying sequence of nucleotide bases in a particular region of DNA; and the informational level is gene expression, the manifestation of hereditary material.

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