In recent years there has been a call to biologists and biological teachers to start a new initiative of biology, termed the “New Biology” which has become the new standard that we are working towards as scientists and educators. This “New Biology” interprets concepts from chemistry, physics, computer science, and engineering to incorporate the new age of biology. This allows biologists to keep up with the fast growing and changing subfields of biology. One of these fields would include synthetic biology.

The goal for this project was to bring about the idea of modeling biological systems to high school AP biology teachers. This will enable students at a young age to enter the world of biology with a notion of how to intertwine the concepts of these different subjects. The students are doing a project with genetically modified arabidopsis plants. There is one plant that is a wild type with another that had a mutation in one of the enzymes of a metabolic pathway. The enzyme can be chemically induced to be produced and the plant will grow as the wild type grows. The exact pathways are explained in Dr. Chappel's Slides.

The presentation was to explain the basics of modeling simple biological systems. As synthetic biologists, we have all experienced the importance and difficulty of modeling biological systems. These systems are rarely at steady state with all of the individual aspects having a large dependence on one another. The mathematical equations become quickly very difficult requiring math skills above the level of most AP biology students. The goal was to explain how to define a system along with the inputs and outputs. This introduces the idea of biology integrated with engineering taking students one step closer to synthetic biology.

The first step was to use a simple word problem that includes a familiar, everyday occurrence to introduce the ideas of defining systems, identifying inputs and outputs, and setting up basic mathematical equations.

1. Learning Objectives

The lab that the teachers use has a list of learning objectives for the students. After reading through this, we picked out which of these learning objectives this presentation covers. These are listed below:

• Explain how biological systems use free energy to maintain organization, to grow, and to reproduce
• Free energy is required for living systems to maintain organization, to grow, or to reproduce, but that multiple strategies exist in different living systems
• Apply mathematical routines to quantities that describe interactions among living systems and their environment, which result in the movement of matter or energy
• Predict the effects of a change of matter or energy availability on communities
• Basic accounting or budgeting skills – quantifying the inputs and resolving the outputs
• Constructing energy flow diagrams
• Calculating, recording, and diagramming energy dynamics in a simple model system
2. Example of Grocery Store

The purpose starting with an example of a grocery store is to be able to link something familiar with the new concepts introduced in the lab. In this way, the idea of modeling can be fully explained before delving into the biological concepts explained by the lab.

Problem Statement

Assume that there is a farmer who grew 15 flats of strawberries in one season. She sells the strawberries at $1.50/quart. Each quart container costs her $0.50 each. She then sells the strawberries by the flat to the grocer who wants 15 flats (each flat container has 8 quarts). The grocer then sells the strawberries by the quart for $3.00 each. The grocer has to pay the cashier to work to sell the strawberries at $1.00 a quart. The consumer(s) buy 15 flats of strawberries for $3.00 each. Model this system.

1. Draw a Picture


In this picture, the barn represents the farmer, the store represents the grocer, and the people with the cart are the consumer(s).

2. Determine the System


The dotted line in the picture above represents the system boundary. Anything that crosses this line is something that is leaving or entering the system. The picture below shows what is entering and leaving the system. Notice that anything occurring within the farm is not being shown.



Defining the system is an important first step in understanding the governing equations of the whole problem.

3. Calculations

Here I explain the balance equation (in - out +generation - consumption = accumulation. In this equation any time something crosses the boundary of the system it is either in the "in" or "out" term. Anything that is made within the system is considered a "gem" term where anything used by the system is in the "con" term. Whatever is left over by the system is "accum."



Here the converision of quarts to flats is given (8quart/1flat), the money goes into the system when a quart is sold ($1.50), and it is shown that 15 flats are generated then go out of the system. Consumption is the money needed to pay for each quart. Finally, it is calculated that $120 is accumulated by the farmer.

I also showed what would happen if the farmer grew 20 flats instead of only 15, but the farmer still only sold 15 flats. The calculations for this are shown below:



This example shows that if the farmer generates more flats than are leaving the system, the farmer will end up accumulating less money as well as more flats.

4. Repeat Steps 2 and 3 for Grocer and Consumer

During the presentation, we went through how to do the calculations for all three systems. These can be seen in the following document:*input link*.

5. Connect to Mass and Energy Balances

It was important to make the connection between the strawberries and money and mass and energy. This is so that the teachers can explain to students that this same process can be used to track mass and energy through a biological system. It is assumed that strawberries are the mass and energy is money. In this way the equations can be split up to mass and energy balances. These two balances are shown below:


6. Whole System

When looking at the system as a whole, there are several important things to point out:

• It costs more to buy strawberries the further through the chain you go
• Energy required increases through a food chain
• Everything comes at a cost
• Energy is always requried
• In the real world there is also shrink or idea that inventory is actually smaller than accounted for due to products lost or stolen
• Energy is lost to the surroundings, therefore, nothing is 100% efficient
• Everything balances out
• Energy and mass are both conserved
3. Model Given by Lab Handout

The following model was found in the teacher's handout (http://media.collegeboard.com/digitalServices/pdf/ap/APBioTeacherLabManual2012_2ndPrt_lkd.pdf). It has many simplifications that make it difficult to understand at a high school level. The main assumption is that there is no separation of energy and mass. It is assumed that the two are related by a conversion factor. This conversion factor is not explained, though it is a very simplified idea of higher heating value. This is a concept that most teachers and students won't have a background in to understand. The model is depicted below:



The incoming arrow represents kcal light energy. The outgoing arrows represent biomass, kcal energy lost due to respiration, and kcal waste energy. None of these are explained in the lab for the teachers or the students.

4. New Model

Because we wanted to show the teachers how to set up their own models of biological systems, we had the teachers try brainstorming what would go into the system and what would come back out of the system. After much debate this is the final model:



The following calculations were done:



5. Relation to Other Topics

Because the ultimate goal is to be able to show students that biology relates multiple fields, it was also important to show the teachers how this lab relates to other classes high school students might be taking. These include (but are not limited to):

• Physics
• What are the different types of energy? How are they found in this lab?
• • Potential Energy - found in the form of chemical potential within the bonds of the molecules in the plant
  • Kinetic Energy - found in the movement of the molecules
• Chemistry
• Gibbs Free Energy - the energy required for a chemical reaction such as the respiration that is taking place
• Engineering
• Modeling of systems and calculating mass and energy balances
• Biology
• Why is all of this important on a cellular level?
• Reactions are taking place in every cell of the plant. This same mass/energy balance can be done on a single cell with respiration. Gibbs free energy determines whether the reaction will be spontaneous or not. The energy in the bonds determines how much light energy and chemical energy is needed to break and form bonds in the chemical process.

Through this workshop with high school AP biology teachers, we were able to convey not only how to model systems, but also the importance of taking a look at the "New Biology." The teachers were very responsive to the ideas, and enjoyed the examples for how to explain these complex concepts to their students. Hopefully they will bring these ideas into their classroom, and we will see a new budding generation of synthetic biologists!