## Matter and Energy in Biology

### Matter and Energy

The concepts of matter and energy are essential to all scientific disciplines. Yet, while ubiquitous and fundamental, these concepts are often among the most confounding for students. Take the concept of energy. The term is used in a variety of contexts in everyday life:

• “Can we move the couch tomorrow? I don’t have the energy.”
• “Hey dude! Turn the light off. We need to conserve energy.”
• “This is a great energy drink.”

In some sciences classes, students are told that energy comes in different forms (i.e. kinetic, thermal, electrical, potential, etc.). This can sometimes make it difficult to understand exactly what energy “is”. The concept of energy is also associated with many different equations, each with different variables, but that somehow all seem to end up having units of work. Hold on! Work? I thought we were talking about energy?!

Given all the different contexts and sometimes seemingly contradictory treatments and definitions, it’s easy to understand why these topics seem challenging for many students and in some cases end up turning them off of the topics and even fields that make heavy use of these ideas. While the concepts of matter and energy are most often associated with chemistry and physics, they are nevertheless central ideas in biology and we don’t hide from this in BIS2A. In this respect, our instructional goals are to help students develop a framework that help them use the concepts of matter and energy to:

• successfully describe biological reactions and transformations;
• create models and hypotheses for “how things work” in biology that explicitly include matter and energy and;
• be scientifically correct and transfer these ideas to new problems as well as other disciplines.

While there may be a couple of energy-related equations to learn and use in BIS2A, the main focus of the course will be on the robust development of the concepts of energy and matter and their use in the interpretation of biological phenomena.

### Motivation for Learning About Matter and Energy

Discussions about matter and energy make some BIS2A students a little apprehensive. After all, aren’t these topics that belong in chemistry or physics? However, the transformations of matter and energy transfer are not phenomena reserved for the chemists and physicists or even scientists and engineers more generally. Understanding, conceptualizing, and doing some basic accounting of transformations of matter and transfers of energy are fundamental skills regardless of occupation or academic training. The scientist may need more rigorous and systematic descriptions of these transformations than the artist but both make use of these skills at various points of their personal and or professional lives. Take the following examples:

Example 1: Matter and Energy Transformation in Global Warming

Let us for a moment consider a topic that affects us all, global warming. At its core lies a relatively simple model that is based on our understanding of energy in solar radiation, the transfer of this energy with matter on the Earth, and the role and cycling of key carbon containing gases in the Earth's atmosphere. In simple terms, solar energy hits the earth and transfers energy to its surface, heating it. Some of this energy is transferred back into space. However, depending on the concentration of carbon dioxide (and other so-called greenhouse gases) different amounts of this energy may become “trapped” in the Earth’s atmosphere. Too little carbon dioxide and relatively little energy/heat is trapped - the Earth freezes and becomes inhospitable for life. Too much carbon dioxide and too much heat is trapped - the Earth overheats and becomes inhospitable for life. It stands to reason, therefore, that mechanisms (biological or other) that influence the levels of carbon dioxide in the atmosphere may be important to consider in the story of global warming and that developing a good understanding of global warming phenomena requires one to trace the flow of the carbon and oxygen (matter) through their different forms and the mechanisms by which energy is transferred to and from different components of the system.

Example 2: Muscle Contraction

Let us now consider a more personal example, the flexing of an arm starting from an extended position and ending in a flexed position. Like most processes, this one can be described and understood at various levels of detail: from the anatomical point of view where the system consists of muscles, skin, and bones to the molecular point of view where the system is composed of individual interacting biomolecules. At whatever level of detail, if we want to create a story describing this process we know that: (a) the description must include an accounting for what happened to the matter in the system (this includes the change in position of the molecules making up the various parts of the arm and the fuel “burned” to move it) and (b) that some fuel was burned to initiate the movement and therefore, that any description of the process must also include an accounting change in the energy of the system. In simpler terms, this is really just saying that if you want to describe a process where something has happened, you need to describe what happened to the “stuff” in the system and what happened to the energy in the system to make the process happen.

We can't possibly cover all examples of matter and energy transfer in BIS2A. But, we will explore these issues often and practice describing transformations that happen in Nature with a structured and explicit attention to what is happening to the matter and energy in a system as it changes. We will do this exercise across different structural levels in biology, from the molecular level (like a single chemical reaction) to more large-scale and abstracted models like nutrient cycling in the environment. We will practice this skill by using a pedagogical tool we call “The Energy Story”. Be prepared to participate!

### The energy story

#### Overview of the energy story

Whether we know it or not, we tell stories that involve matter and energy everyday. We just don’t often use terminology associated with scientific discussions of matter and energy.

Example 1

The setup: a simple statement with implicit details
You tell your roommate a story about how you got to campus by saying, "I biked to campus today." In this simple statement are several assumptions that are instructive to unpack, even if they may not seem very critical to include explicitly in a casual conversation between friends over transportation choices.

An outsider's reinterpretation of the process
To illustrate this, imagine an external observer, such as an alien being watching the comings and goings of humans on Earth. Without the benefit of knowing much of the implied meanings and reasonable assumptions that are buried in our language, the alien's description of the morning cycling trip would be quite different than your own. What you described efficiently as "biking to campus" might be more specifically described by the alien as a change in location of a human body and its bicycle from one location (the apartment, termed position A) to a different location (the university, termed position B). The alien might be even more abstract and describe the bike trip as the movement of matter (the human body and its bike) between an initial state (at location A) to a final state (at location B). Furthermore, from the alien's standpoint, what you'd call "biking" might be more specifically described as the use of a two-wheeled tool that couples the transfer of energy from the electric fields in chemical compounds to the acceleration of the two-wheeled, tool-person combo that heats its environment. Finally, buried within the simple statement describing how we got to work is also the tacit understanding that the mass of the body and bike were conserved in the process (with some important caveats we’ll look at in future lectures) and that some energy was transfered around the system and environment to enable the movement of the body from position A to position B.

Note: possible discussion

Details are important. What if you owned a fully electric bike, and the person you were talking with didn’t know that? What important details might this change about the “everyday” story you told that the more detailed description would have cleared up? How would the alien’s story have changed? In what scenarios might these changes be relevant?

As this simple story illustrates, irrespective of many factors, the act of creating a full description of a process includes some accounting of what happened to the matter, what happened to the energy, and almost always some description of a mechanism that describes how changes in matter and energy of a system were brought about.

To practice this skill in BIS2A, we will make use of something we like to call the "Energy Story." You may be asked to tell an "energy story" in class, to practice telling energy stories on your lecture study guides, and to use the concept on your exams. In this section, we focus primarily on introducing the concept of an energy story and explaining how to tell one. It is worth noting that the term "energy story" is used almost exclusively in BIS2A (and has a specific meaning in this class). This precise term will not appear in other courses at UC Davis (at least in the short term), or if it appears, is not likely to be used in the same manner. You can think of “The Energy Story” as a systematic approach to creating a statement or story describing a biological process or event. Your BIS2A instructors have given this approach a short name (energy story) so that we can all associate it with the common exercise. That way, when the instructor asks the class to tell or construct an energy story, everyone knows what is meant.

Definition 1: energy story

An energy story is a narrative describing a process or event. The critical elements of this narrative are as follows:

1. Identify at least two states (e.g., start and end) in the process.
2. Identify and list the matter in the system and its state at the start and end of the process.
3. Describe the transformation of the matter that occurs during the process.
4. Account for the “location” of energy in the system at the start and end of the process.
5. Describe the transfer of energy that happens during the process.
6. Identify and describe mechanism(s) responsible for mediating the transformation of matter and transfer of energy.

A complete energy story will include a description of the initial reactants and their energetic states as well as a description of the final products and their energetic states after the process or reaction is completed.

Note: possible discussion

We argue that the energy story can be used to communicate all of the useful details that are required to describe nearly any process. Can you think of a process that cannot be adequately described by an energy story? If so, describe such a process.

Example 2: energy story example

Let us suppose that we are talking about the process of driving a car from "Point A" to "Point B" (see Figure 1).

Figure 1: This is a schematic of a car moving from a starting position, "Point A," to an end point, "Point B." The blue rectangle depicted in the back of the car represents the level of the gasoline; the purple, squiggly line near the exhaust pipe represents the exhaust; squiggly blue lines on top of the car represent sound vibrations; and the red shading represents areas that are hotter than at the start. Source: created by Marc T. Facciotti (own work)

Let's step through the Energy Story rubric:

1. Identify at least two states (e.g., start and end) in the process.

In this example, we can easily identify two states. The first state is the nonmoving car at "Point A," the start of the trip. The second state, after the process is done, is the nonmoving car at "Point B."

2. Identify and list the matter in the system and its state at the start and end of the process.

In this case, we first note that the "system" includes everything in the figure—the car, the road, the air around the car, etc.

It is important to understand the we are going to apply the physical law of conservation of matter. That is, in any of the processes that we will discuss, matter is neither created or destroyed. It might change form, but one should be able to account for everything at the end of a process that was there at the beginning.

At the beginning of the process, the matter in the system consists of the following:
1. The car and all the stuff in it
2. The fuel in the car (a special thing in the car)
3. The air (including oxygen) around the car.
5. The driver

At the end of the process, the matter in the system is distributed as follows:
1. The car and all the stuff in it is in a new place (let's assume, aside from the fuel and position, that nothing else changed).
2. There is less fuel in the car, and it too is in a new place.
3. The air has changed; it now has less molecular oxygen, more carbon dioxide, and more water vapor.
4. The road did not change (let's assume it didn't change—other than a few pebbles that moved around).
5. The driver did not change (let's assume she didn't change—though we'll see by the end of the term that she did, at least a little). However, the driver is now in a different place.

3. Describe the transformation of the matter that occurs during the process.

What happened to the matter in this process? Thanks to a lot of simplifying assumptions, we see that two big things happened. First, the car and its driver changed positions—they went from "Point A" to "Point B." Second, we note that some of the molecules in the fuel, which used to be in the car as a liquid, have changed forms and are now mostly in the form of carbon dioxide and water vapor (purple blob coming out of the tailpipe). Some of the oxygen molecules that used to be in the air are now also in a new place as part of the carbon dioxide and water that left the car.

4. Account for the “location” of energy in the system at the start and end of the process.

It is again important to understand that we are going to invoke the physical law of conservation of energy. That is, we stipulate that the energy in the system cannot be created or destroyed, and therefore, the energy that is in the system at the start of the process must still be there at the end of the process. It may have been redistributed, but you should be able to account for all the energy.

At the beginning of the process, the energy in the system is distributed as follows:
1. The energy is tied up in the associations between atoms that make up the matter of the car.
2. The energy is tied up in the associations between atoms that make up the fuel.
3. The energy is tied up in the associations between atoms that make up the air.
4. The energy is tied up in the associations between atoms that make up the road.
5. The energy is tied up in the associations between atoms that make up the driver.
6. For all the things above, we can also say that there is energy in the molecular motions of the atoms that make up the stuff.

At the end of the process, the energy in the system is distributed as follows:
1. The energy is tied up in the associations between atoms that make up the matter of the car.
2. The energy is tied up in the associations between atoms that make up the fuel.
3. The energy is tied up in the associations between atoms that make up the air.
4. The energy is tied up in the associations between atoms that make up the road.
5. The energy is tied up in the associations between atoms that make up the driver.
6. For all the things above, we can also say that there is energy in the molecular motions of the atoms that make up the stuff.

This is interesting in some sense, because the lists are about the same. We know that the amount of energy stored in the car has decreased, because there is less fuel. Something must have happened.

5. Describe the transfer of energy that happens during the process.

In this particular example, it is the transfer of energy among the components of the system that is most interesting. As we mentioned, there is less energy stored in the gas tank of the car at the end of the trip, because there is now less fuel. We also know intuitively (from real-life experience) that the transfer of energy from the fuel to something else was instrumental in moving the car from "Point A" to "Point B." So, where did this energy go? Remember, it didn't just disappear. It must have moved somewhere else in the system.

Well, we know that there is more carbon dioxide and water vapor in the system after the process. There is energy in the associations between those atoms (atoms that used to be in the fuel and air). So some of the energy that was in the fuel is now in the exhaust. Let's also draw from real-life experience again, and state that we know that parts of our car have gotten hot by the end of the trip (e.g., the engine, transmission, wheels/tires, exhaust, etc.). For the moment, we'll just use our intuition, and say that we understand that making something hot involves some transfer of energy. So we can reasonably postulate that some of the energy in the fuel went (directly or indirectly) into heating the car, parts of the road, and the exhaust—and thus the environment around the car. An amount of energy also went into accelerating the car from zero velocity to whatever speed it traveled at, but most of that energy eventually became heat when the car came to a stop.

This is a bit of a hand-wavy explanation, and we'll learn how to do a better job throughout the quarter. The main point is that we should be able to add all the energy of the system at the beginning of the process (in all the places it is found) and at the end of the process (in all the places it is found), and those two values should be the same.

6. Identify and describe mechanism(s) responsible for mediating the transformation of matter and transfer of energy.

Finally, it is useful to try understanding how those transformations of matter and transfers of energy might have been facilitated. For the sake of brevity, we might just say that there was a complicated mechanical device (the engine) that helped facilitate the conversion of matter and transfer of energy about the system and coupled this to the change in position of the car. Someone interested in engines would, of course, give a more detailed explanation.

In this example, we made a bunch of simplifying assumptions to highlight the process and to focus on the transformation of the fuel. But that's fine. The more you understand about the processes, the finer details you can add. Note that you can use the Energy Story rubric for describing your understanding (or looking for holes in your understanding) of nearly any process (certainly in biology). In BIS2A, we'll use the Energy Story to get an understanding of processes as varied as biochemical reactions, DNA replication, the function of molecular motors, etc.

Important:

First: We will be working on many examples of the energy story throughout the course—do not feel that you need to have mastery over this topic today.

Second: While it is tempting to think all this is superfluous or not germane to your study of biology in BIS2A, let this serve as a reminder that your instructors (those creating the course midterm and final assessments) view it as core material. We will revisit this topic often throughout the course but need you to get familiar with some of the basic concepts now.

This is important material and an important skill to develop—do not put off studying it because it doesn't "look" like "biology" to you today. The academic term moves VERY quickly, and it will be difficult to catch up later if you don't give this some thought now.

## Energy

Energy is a central concept in all sciences. Energy is a property of a system. While it can be neither created nor destroyed, understanding the transfer of energy around physical systems is a key component of understanding how and why things change. In the following sections, we are going to explore some basic concepts associated with common transformations in biology and chemistry: the solubility of various biomolecules, the making and breaking of chemical bonds, the transfer of electrons, the transfer of energy to and from light, and the transfer of energy as heat. In class, many of the discussions will happen in the context of the Energy Story rubric, so when we consider a reaction of transformation, we will be interested in precisely defining the system in question and trying to account for all the various transfers of energy that occur within the system, making sure that we abide by the Law of Conservation of Energy.

There are plenty of examples where we use the concept of energy in our everyday lives to describe processes. A bicyclist can bike to get to campus for class. The act of moving herself and her bicycle from point A to point B can be explained to some degree by examining the transfers energy that take place. We can look at this example through a variety of lenses, but, as biologists, we more than likely want to understand the series of events that explain how energy is transferred from molecules of food, to the coordinated activity of biomolecules in a bicyclist's flexing muscle, and finally, to the motion of the bike from point A to point B. To do this, we need to be able to talk about various ways in which energy can be transferred between parts of a system and where it is stored or transferred out of the system. In the next section, we will also see the need to consider how that energy is distributed among the many microstates (molecular states) of the system and its surroundings.

### How we will approach conceptualizing energy

In BIS2A we will think about energy with a "stuff" metaphor. Note, however, that energy is NOT a substance, it is rather a property of a system. But we will think of it, in some sense, as property that can be stored in a part of a physical system and transferred or "moved" from one storage place to another. The idea is to reinforce the concept that energy maintains its identity when transferredit is not changing forms per se. This in turn also encourages us to make sure that energy always has a home and that we account for all of the energy in a system before and after a transformation; it does not just get "made" or get "lost" (both of these ideas contradict of the Law of Conservation of Energy). When energy is being transferred, we therefore must identify where it is coming from and where it is goingall of it! Again, we can't just have some getting lost. When energy is transferred, there must be some mechanism associated with that transfer. Let's think about that to help us explain some of the phenomena we're interested in. That mechanism is part of the "how" that we are often interested in understanding. Finally, if we talk about transfer, we must realize that both components, the part of the physical system that gave up energy and the part of the system that received that energy, are changed from their initial states. We should make sure that we are looking at all of the components of a system for changes in energy when examining a transformation.

### Energy sources

Ultimately, the source of energy for many processes occurring on the Earth's surface comes from solar radiation. But as we will see, biology has been very clever at tapping a variety of forms of energy to construct and maintain living beings. As we move through this course, we will explore a variety of energy sources and the ways in which biology has devised to transfer energy from these fuels.

## Free Energy

If we want to describe transformations, it is useful to have a measure of (a) how much energy is in a system, (b) the dispersal of that energy within the system and, of course, (c) how these factors change between the start and end of a process. The concept of free energy, often referred to as Gibbs energy or Gibbs enthalpy (abbreviated with the letter G), in some sense, does just that. Gibbs energy can be defined in several interconvertible ways, but a useful one in the context of biology is the enthalpy (internal energy) of a system minus the entropy of the system scaled by the temperature. The difference in free energy when a process takes place is often reported in terms of the change (Δ) of enthalpy (internal energy) denoted H, minus the temperature scaled change (Δ) in entropy, denoted S. See the equation below.

$ΔG=ΔH−TΔS \label{gibbs}$

The Gibbs energy is often interpreted as the amount of energy available to do useful work. With a bit of hand waving, we can interpret this statement by invoking the idea presented in the section on entropy, which states the dispersion of energy (required by the Second Law) associated with a positive change in entropy somehow renders some of the energy that is transferred less useful to do work. One can say that this is reflected in part in the $$T∆S$$ term of the Equation \ref{gibbs}.

To provide a basis for fair comparisons of changes in Gibbs energy amongst different biological transformations or reactions, the free energy change of a reaction is measured under a set of common standard experimental conditions. The resulting standard free energy change of a chemical reaction is expressed as an amount of energy per mole of the reaction product (either in kilojoules or kilocalories, kJ/mol or kcal/mol; 1 kJ = 0.239 kcal), when measured at a standard pH, temperature, and pressure conditions. Standard pH, temperature, and pressure conditions are generally standardized at pH 7.0, 25 degrees Celsius, and 100 kilopascals (1 atm pressure), respectively. It is important to note that cellular conditions vary considerably from these standard conditions, and so actual $$∆G$$ inside a cell will differ considerably from those calculated under standard conditions.

## Chemical Equilibrium—Part 2: Gibbs Energy

In a previous section, we began a description of chemical equilibrium in the context of forward and reverse rates. Three key ideas were presented:

1. At equilibrium, the concentrations of reactants and products in a reversible reaction are not changing in time.
2. A reversible reaction at equilibrium is not staticreactants and products continue to interconvert at equilibrium, but the rates of the forward and reverse reactions are the same.
3. We were NOT going to fall into a common student trap of assuming that chemical equilibrium means that the concentrations of reactants and products are equal at equilibrium.

Here we extend our discussion and put the concept of equilibrium into the context of Gibbs energy, also reinforcing the Energy Story exercise of considering the "Before/Start" and "After/End" states of a reaction (including the inherent passage of time).

Figure 1. Reaction coordinate diagram for a generic exergonic reversible reaction. Equations relating Gibbs energy and the equilibrium constant: R = 8.314 J mol-1 K-1 or 0.008314 kJ mol-1 K-1; T is temperature in Kelvin. Attribution: Marc T. Facciotti (original work)

The figure above shows a commonly cited relationship between ∆G° and Keq:

$∆G^o = -RT\ln K_{eq}.$

Here, G° indicates the Gibbs energy under standard conditions (e.g., 1 atmosphere of pressure, 298 K). This equation describes the change in Gibbs energy for reactants converting to products in a reaction that is at equilibrium. The value of ∆G° can therefore be thought of as being intrinsic to the reactants and products themselves. ∆G° is like a potential energy difference between reactants and products. With this concept as a basis, one can also consider a reaction where the "starting" state is somewhere out of equilibrium. In this case, there may be an additional “potential” associated with the out-of-equilibrium starting state. This “added” component contributes to the ∆G of a reaction and can be effectively added to the expression for Gibbs energy as follows:

$∆G = ∆G° + RT\ln Q,$

where $$Q$$ is called the reaction quotient. From the standpoint of BIS2A, we will use a simple (a bit incomplete but functional) definition for

$Q = \dfrac{[Products]_{st}}{[Reactants]_{st}}$

at a defined non-equilibrium condition, st. One can extend this idea and calculate the Gibbs energy difference between two non-equilibrium states, provided they are properly defined and thus compute Gibbs energy changes between specifically defined out-of-equilibrium states. This last point is often relevant in reactions found in biological systems as these reactions are often found in multi-step pathways that effectively keep individual reactions in an out-of-equilibrium state.

This takes us to a point of confusion for some. In many biology books, the discussion of equilibrium includes not only the discussion of forward and reverse reaction rates, but also a statement that ∆G = 0 at equilibrium. This can be confusing because these very discussions often follow discussions of non-zero ∆G° values in the context of equilibrium (∆G° = -RTlnKeq). The nuance to point out is that ∆G° is referring to the Gibbs energy potential inherent in the chemical transformation between reactants and products alone. This is different from considering the progress of the reaction from an out-of-equilibrium state that is described by

$∆G = ∆G^o + RT \ln Q.$

This expression can be expanded as follows:

$∆G = -RT\ln K_{eq} + RT\ln Q$

to bring the nuance into clearer focus. In this case note that as Q approaches Keq that the reaction ∆G becomes closer to zero, ultimately reaching zero when Q = Keq. This means that the Gibbs energy of the reaction (∆G) reaches zero at equilibrium not that the potential difference between substrates and products (∆G°) reaches zero.