1.7: Equilibrium vs. Homeostasis

Chemical Reactions

Chemical reactions occur when two or more atoms bond together to form molecules or when bonded atoms are broken apart. The substances that "go in" to a chemical reaction are called the reactants (by convention these are usually listed on the left side of a chemical equation), and the substances found that "come out" of the reaction are known as the products (by convention these are usually found on the right side of a chemical equation). An arrow linking the reactants and products is typically drawn between them to indicate the direction of the chemical reaction. By convention, for reactions in which the net flow is in a particular direction, we draw a single-headed arrow.

\[\ce{2 H2O2 -> 2 H2O + O2}\]

Note:

Practice: Identify the reactants and products of the reaction involving hydrogen peroxide above.

Note:

Possible discussion: When we write H₂O₂ to represent the molecule hydrogen peroxide it is a model representing an actual molecule. What information about the molecule is immediately communicated by this molecular formula? That is, what do you know about the molecule just by looking at the term H₂O₂?

What information is not explicitly communicated about this molecule by looking only at the formula?

Some chemical reactions, such as the one shown above, proceed mostly in one direction. However, all reactions are technically proceeding in both directions- individual molecules may be heading "backward", but the bulk flow of the reaction described above is from left to right. In a chemistry experiment we often dump a reagent or two into a test tube, allow them to react, and then come back later and see what we've got. Often the reactants are rapidly turned into products, but as the concentration of products builds up, the reverse reaction will start to occur also. When a certain relative balance between reactants and products occurs, one in which the rate of the reverse reaction (the frequency of product molecules becoming reactants)— matches the rate of the forward reaction, we reach a state called equilibrium. Some chemical reactions proceed strongly in in one direction until virtually everything become Product, at equilibrium- these are sometimes, perhaps a little loosely, referred to as "irreversible" reactions. Other reactions reach equilibrium when the relative concentration of product to reactant is relatively low. As we'll discuss later, the balance between products and reactants at equilibrium depends on the difference between them in the potential energy associated with their molecular structure.

Note:

Use of vocabulary: You may have realized that the terms "reactants" and "products" are relative to the direction of the reaction. If you have a reaction that is reversible, though, the products of running the reaction in one direction become the reactants of the reverse reaction. You can label the same compound with two different terms. That can be a bit confusing. So, what is one to do in such cases? The answer is that if you want to use the terms "reactants" and "products" you must be clear about the direction of reaction that you are referring to.

Let's look at an example of a reversible reaction in biology. In human blood, excess hydrogen ions (H⁺) bind to bicarbonate ions (HCO₃^-) forming an equilibrium state with carbonic acid (H₂CO₃). This reaction is readily reversible. If carbonic acid were added to this system, some of it would be converted to bicarbonate and hydrogen ions as the chemical system approached equilibrium.

\[\ce{HCO3^{-} + H^{+} -> H2CO3 }\]

The examples above examine "idealized" chemical systems as they might occur in a test-tube (a closed system). In biological systems, however, equilibrium for a single reaction is rarely obtained as it might be in the lab. In biological systems reactions do not occur in isolation. In some cases (for example, the detoxification of a poison by the liver), the concentrations of the reactants and/or products are changing. In others, the concentration of products and reactants is held at a constant value (steady state), but this value is not necessarily at equilibrium. In this class, we'll encounter many example of "biochemical pathways", in which a product of one reaction becomes a reactant for another reaction i.e., ...A -> B -> C -> D... As we'll discover, just as your body maintains its temperature at a level that is not in equilibrium with the air around you, and living things maintain the concentrations of various metabolites at ideal relative concentrations tuned to make reactions "go" in the direction that required. This ability of living things to maintain many aspects of metabolism, temperature, pH, and dissolved gas levels within a relatively narrow, often nonequilibrium range is referred to as homeostasis.

In a previous reading ("Matter and Energy") we discussed the concept of Gibbs free energy- the energy that can be derived from a chemical reaction. We'll see soon how Life harvests and stores this energy. For now, let's discuss the two most relevant components (for Biologists) that contribute to our consideration of whether a reaction will a) proceed as written (in the direction of our arrow) and b) produce energy that Life might possibly use to perform work (such as moving a muscle, or building a complex molecule). Both a and b will be always true at the same time, as reactions only proceed spontaneously from a state of higher to a state of lower potential energy (in other words, ∆G is a negative number). Life may not always be prepared to harvest that potential energy difference, however.

Many things affect the ∆G (change in free energy) of a reaction, but fortunately for us, as students of biology, we can choose to ignore most of them, because Life exists within fairly narrow range of temperature, pressure, and pH. The most important variables for us will be the intrinsic structures (the inherent potential energy) of the molecules, and their relative concentrations. These variables are summarized in the equation:

\[∆G = ∆G^{o'} + RT\ln Q\]

where Q is the ratio of concentration of products divided by the concentration of reactants. For example, if A -> B, then Q is simply [B]/[A]. If the reaction is instead 2A -> B, then you need include both molecules of A, so Q = [B]/[A]². If, in a different example, A breaks down to form B and C, Q would be [B][C]/[A]. Again, luckily for us, we will be discussing fairly steady-state concentrations. While the cell is processing A into B, A is being replaced from upstream chemical reactions, and B is being broken down by downstream reactions. We'll see that Life has tricks for regulating the flow of metabolites, and for stopping that flow (by stopping the production of upstream chemicals) when the biochemical pathway is not required.

R is a constant, and we'll essentially treat T (temperature) as one too, though this is a bit lazy on our part, as Life can be found living in a range from just below freezing to well above boiling (see thermophiles). Note that the ∆G˚' refers to the difference in inherent energy due to the structure of the reactants and products, at biologically standard conditions (which are not the same as the standard conditions employed by chemists.). These conditions are: pH 7.0, 1 atm pressure, an aqueous environment, and 25˚C. Note water, while often a product or reactant, is not included in our calculation of Q. The presence of plenty of liquid water is assumed as part of standard conditions and is already taken care of in our ∆G˚' term in the equation written above.

Practice:

1) Remember that the natural log of (ln) values greater than one is a positive number, while the natural log of values less than 1 is a negative number (see graph below). Knowing this, what is the effect on the ∆G of the reaction A -> B when the concentration of B is greater than the concentration of A? How would this affect the cell's ability harvest energy from a reaction, in comparison to a situation in which [A] = [B]?

2) As we will see when we study respiration, Life can harvest energy simply by allowing molecules to move from a high concentration compartment to a low concentration compartment. This energy is derived purely from the decrease in concentration- there is no change in chemical bonds. How is this negative ∆G related to the equation above?

Y = ln(X)