As we have seen previously, simple chemical reactions can be characterized by how fast they occur (their rate) and how far they proceed (towards equilibrium). While you will learn much more about reactions if you continue on in chemistry, that is not something we will pursue here - rather we will consider the behavior of systems of reactions and their behavior, particularly when they have not reached equilibrium. This is a situation common in open systems, systems in which energy and matter are flowing in and out.

9.1 Reaction systems
9.2 Buffered systems
9.3 Activation energy

While, previously we have considered single reactions which we have perturbed, either by adding or taking away matter (reactants or products) or energy (heating or cooling the reaction), now it is time to look at what happens when reactions are coupled - that is: the products of one reaction are the starting materials for other reactions, occurring in the same system.

Take for example the coupled system introduced above - the pair of reactions that are linked by the formation and reaction of carbonic acid.
H₂O + CO₂ ↔ H₂CO₃ and H₂CO₃ + H₂O ↔ HCO₃– + H₃O+

These coupled reactions are important for a number of reasons, including transport of excess carbon dioxide to the lungs, and for buffering the pH of blood. Carbon dioxide enters the blood stream by dissolving in the plasma, however it can also react with water, in a reaction where the water acts as a nucleophile and the carbon dioxide acts an an electrophile.

The formation of carbonic acid is thermodynamically unfavorable, the equilibrium constant for hydration of carbon dioxide is 1.7 x 10–3. The standard free energy change for the reaction (ΔGº = –RTlnK), so at physiological temperatures (37º C) ΔGº is 16.4 kJ.

This means that the amount of carbonic acid in blood plasma is quite low; most carbon dioxide is just dissolved in the plasma (rather than reacted with the water). That said, as soon as carbonic acid is formed, it can react with water

H₂CO₃ + H₂O ↔ HCO₃– + H₃O+

to produce bicarbonate (HCO₃–); the rate of this reaction is increased by the enzymatic catalyst carbonic anhydrase. In this buffer system the carbonic acid can react with any base that enters the bloodstream, and the bicarbonate with any acid. This buffering system is more complex than the isolated ones we considered earlier, since one of the components (carbonic acid) is also part of another equilibrium reaction. In essence, this means that the pH of the blood is dependent of the amount of carbon dioxide in the bloodstream.
H₂O + CO₂ ↔ H₂CO₃ + H₂O ↔ HCO₃– + H₃O+

If we remove water from the equations (for the sake of clarity) we can (hopefully) see the connection better.
CO₂ + H₂CO₃ ↔ HCO₃– + H₃O+

The pK_a of carbonic acid is 6.37, and the pH of blood is typically 7.2-7.4, which does fall (just) within the buffering range.

Under normal circumstances this buffer system can handle most changes but for larger changes, other systems are called into play to help regulate the pH. So for example, if you exert yourself, one of the products generated is lactic acid, (which we will denote as LacOH)192. When it finds its way into the bloodstream it lowers the pH (increasing the amount of H3O+), through the reaction: LacOH + H2O ↔ H3O+ + LacO–

If we use Le Chatelier’s principle, you can see that increasing the H₃O+ shifts the equilibrium towards the production of carbon dioxide in the buffer system. As the concentration of CO₂ increases, a process known as chemoreception activates nervous systems that in turn regulate (increase) heart and respiratory rates, which in turn leads to an increase in the rate of CO₂ and oxygen exchange in the lungs - as you breathe in O₂ you breathe out CO₂ (removing it from your blood). In essence - Le Chatelier’s principle explains why we pant when we exercise! Conversely, when some people get excited they breathe too fast (hyperventilate); too much CO₂ is removed from the blood, which reduces the H₃O+ concentration and increases the pH. This can lead to fainting (which slows down the breathing), a rather drastic way to return your blood to its correct pH. An alternative, non-fainting approach is to breathe into a closed container. Since you are now breathing expelled CO₂ (and a lower level of O₂), this also leads to an increase in blood pH.

While we invoke Le Chatelier’s principle to explain the effect of rapid or slow breathing, this response is one based on what are known as adaptive and homeostatic systems. Biological systems are characterized by many such, often interconnected, regulatory mechanisms, that have evolved to maintain a stable chemical internal environment essential for life. Similar coupled regulatory systems lie at the heart of immune and nervous system function. Understanding the behavior of these coupled systems is at the forefront of many research areas. At their base, they rely on chemical systems to measure the levels of various chemicals (a process known as chemoreception), recognize and respond to foreign molecules (in the case of the immune system), and respond to stimuli from both the outside world (light, sound, smell, touch) and internal factors (in the case of the nervous system). Downstream of these ”sensory” systems, are networks of genes, proteins and other molecules whose interactions are determined by the thermodynamics of the chemical system. While they were formed by evolutionary processes, and are often baroque in their details, they are understandable in terms of the molecular interactions, chemical reactions, and their accompanying energy changes.

Question to answer:

• If the pK_a of carbonic acid is 6.35 and the pH of blood is over 7, what do you think the relative amounts of carbonic acid and bicarbonate are? Why?
• Draw out the series of reactions that occur when lactic acid is introduced into the blood stream and explain why this would affect the concentration of carbon dioxide in the blood stream.
• If the amount of carbon dioxide in the atmosphere increases, what effect do you think it would have on oceans and lakes?
• If carbon dioxide dissolves in water to give carbonic acid, what do you think nitrogen dioxide (NO₂) will dissolve in water to give? How about sulfur dioxide? What effect will this have on the pH of the water it dissolves in?
  

Energetics and coupling

We have seen that for systems of coupled reactions, changing the concentration of one of the components in the system will affect all the other components, even if they are not directly reacting with the one that is changed. Now let us turn to another aspect of coupled reactions, in which we can use the same principles to explain why it is possible to make reactions that are thermodynamically unfavorable “go”. We will consider a fairly simple example and then move on to see how this works in biological systems.

Many metals are not found in their elemental form. For example copper, is an important metal used for a wide range of applications (from wires to roofs). It is often found as chalcocite, an ore containing copper as copper sulfide. We could imagine a “simple” chemical reaction,
Cu₂S(s) ↔ 2Cu(s) + S(s) ΔGº = 86.2 kJ/mol

that would allow us to separate the copper from the sulfide. Note that this reaction is a redox reaction in which the Cu+ ion is reduced to Cu by the addition of an electron (from the sulfide S₂– which is oxidized to sulfur with an oxidation state of 0). Unfortunately, since the free energy change for this reaction is positive, at equilibrium the system will be composed mostly of Cu₂S(s). How can we get copper out of copper sulfide?

One possibility to exploit the reaction between sulfur and oxygen:
S(s) + O₂(g) ↔ SO₂ (g), for which ΔGº = –300.1 kJ/mol

This reaction is highly favorable and “goes” toward the production of SO₂. It is basically the burning of sulfur (analogous to the burning of carbon) - and is another redox reaction in which the sulfur is oxidized (from an oxidation state of 0 to +4).

If we take Cu₂S(s) together with O₂(g), we have a system composed of two reactions:

Cu₂S(s) ↔ 2Cu(s) + S(s) [reaction 1]     and      S(s) + O₂(g) ↔ SO₂ (g) [reaction 2].

Since these two reactions share a common component (S(s)), they are coupled. Imagine what happens when the reaction 1 proceeds, even a little. The S(s) produced can then react with the O₂(g) present. As this reaction proceeds toward completion, S(s) is removed, leaving Cu (s) and SO₂ (g). Based on Le Chatelier's principle, reaction 1 is now out of equilibrium, and so will generate more S(s) (and Cu(s)). Reaction 1 which would, in isolation, produce relatively little copper or sulfur, is dragged toward the products by reaction 2, a favorable reaction that removes sulfur from the system. If we assume that there are no other reactions occurring within the system, we can calculate the ΔGº for the coupled reactions 1 and 2. Under standard conditions, we simply add the reactions together.

So, the ΔGº for the coupled reaction is -213.9kJ/mol. This same basic logic applies to any coupled reaction system. Note that the common intermediate, by which these two reactions are linked is sulfur (S). However it is not always so simple to identify the common intermediate; and in this system, we are tacitly assuming that O₂ and SO₂ do not react with either Cu₂S or SO₂. If they did, these reactions would also need to be considered in our analysis - in fact, we will always need to consider all of the reactions that are possible with a system. While this is normally not a big issue with simple chemical systems that contain relatively small numbers of different types of molecules (sometimes called species), it is a significant concern when we consider biological or ecological systems, which contain many thousands of different types of molecules, which can interact and react in a number of ways.

For example, you may have learned (in biology) that the molecule adenosine triphosphate (ATP) is used to store and provide energy for cellular processes. What exactly does this mean? First, let us look at the structure of ATP, it is composed of a base, adenine, a sugar ribose, and three phosphate units. For our purposes, the structures base and sugar together (which are called adenosine) are irrelevant - they do not change during most of the reactions in which ATP takes part. They are organic “blobs” with functional groups that allow them to interact with other components in the cell for other functions (for example in RNA and DNA). For the energy transfer purposes we can just use “A” (adenosine) to stand in for their structure. The important bit for our purposes are the phosphates hooked together by the P–O–P (phosphoanhydride) linkages.

At physiological pH most (if not all) of the oxygens of the phosphate esters are deprotonated. This means that there is a fairly high concentration of charge in this tri-ester side chain, which acts to destablize it. The bonds holding it together are relatively weak, and the molecule will react with any available entity to relieve some of this strain, and form even more stable bonds.

For example ATP is unstable in water and will react (hydrolyze) to form adenosine diphosphate (ADP) and inorganic phosphate (HPO4) (which is often written as Pi ). This reaction is written as ATP + H2O ↔ ADP + Pi.

The standard free energy change for this reaction ΔGº = – 29 kJ/mol (at pH 7) - this is a highly exergonic reaction. Both the enthalpy and entropy changes for this reaction are favorable - that is: ΔH is negative and ΔS is positive. It makes sense that the entropy change is positive - after all we are producing two molecules from one. The enthalpy change also makes sense. We have already mentioned that ATP is unstable, and the loss of one of the phosphate groups relieves some of the strain caused by the charge repulsion between the three negatively charged phosphate groups in ATP. The bond energies in the product are stronger than the bond energies in the reactants and thus the reaction is exothermic. (this is all somewhat complicated - just like everything in living systems - by the presence of other substances in the cellular fluids, such as metal ions, Ca²⁺, Mg²⁺ - and changes in pH - but the explanation is still valid). Make sure that you do not fall prey to the commonly held misconception that it is the breaking of the P-O bond that releases energy - ON THE CONTRARY - it is the formation of more stable (stronger) bonds that releases energy.

If we go one step further and look at the actual free energy change ΔG (as opposed to the standard change), using typical cellular concentrations of ATP, ADP and Pi, and ΔG = ΔGº + RTlnQ (where Q = [ADP][Pi]/[ATP]), we can calculate that ΔG = – 52 kJ/mol (assuming that typically [ATP] is about ten times [ADP], and that Pi is about 0.001M). That is - in real conditions in the cell the free energy change is much higher than the standard free energy change. This energy is not wasted - but is used to drive other reactions that would not otherwise occur. However, this energy cannot be used to drive any random reaction, the reactions have to be coupled (just like the carbon dioxide carbonate system) by common intermediates.
A typical reaction scenario is the transfer of that terminal phosphate group to another biomolecule. This transfer occurs with lipids and proteins - but typically the reacting group is an alcohol (ROH) or sometimes a carboxylic acid (RCOOH). The reaction that takes place is almost the same as the hydrolysis reaction - except that the incoming nucleophile has much more “stuff” attached to the oxygen.

The formation of these phosphate esters makes the original functional group more reactive, so for example the formation of an amide bond, which is the major bond that holds proteins together, is normally exergonic (about + 2 to 4 kJ/mol). That is, the formation of amide bonds is not spontaneous (you might want to think about what this means for the amide bonds in the proteins that make up a good portion of you). So protein synthesis is coupled with ATP hydrolysis, as is the production of many biomolecules, sugars, lipids, RNA and DNA. While the reactions are complex, each of these are driven by series of individual reactions that are linked by common intermediates.

Question to answer:

• Can you draw the protonated form of ATP?
• Can you draw the unprotonated form of ATP showing how the negative charge is stabilized by the surrounding cellular fluids? (hint: mainly water)
• The pKas of phosphoric acid (H₃PO₄) are 2.15, 7.2 and 12.35. Would you predict that in the cellular environment ATP is protonated or deprotonated?
• Write out a hypothetical sequence of two reactions that would result in the production of a thermodynamically unfavorable product.
• How can you tell whether two reactions are coupled?
• Why do biological systems rely on coupled reactions?
• If ATP is unstable, how is it possible that there is ATP can exist (at high concentrations) within the cell?
  

Now the question you might be asking is if ATP is so unstable how does it get formed in the first place and how can it be found at such high concentrations? The short answer involves two ideas that we have encountered before. First, while ATP is unstable (like wood in the presence of O₂2), its hydrolysis does involve overcoming an activation energy, and so under physiological conditions, that means an enzyme (and ATPase). Second, ATP is formed through coupled reactions that link the oxidation of molecules such as glucose or the direct absorption of energy in the form of light (photosynthesis). When glucose reacts with oxygen it forms carbon dioxide and water.

C₆H₁₂O₆ + 6O₂ ↔ 6CO₂ + 6H₂O

The overall standard free energy change ΔGº = – 2870 kJ/mol. The reasons for this high negative free energy change are that ΔSº is positive (why do you think this is?), and there is a large negative ΔHº change. Remember that ΔHº can be approximated by looking at the changes in bond energy from reactants to produces. A major reason for this high enthalpy change is that the bond energies in carbon dioxide are very high (a C=O bond takes 805 kJ/mol to break), and therefore when a C=O bond is formed a large amount of energy is released. When one mole of glucose is completely oxidized to CO₂ and H₂O the energy produced is harnessed to ultimately produce ~36 moles of ATP (from ADP and Pi).

While the mechanism(s) involved in this process are complex (involving intervening ion gradients and rotating enzymes), the basic principle remains. The reactions are coupled by common, and often complex intermediate processes that we will for your biological studies.

But the major point to emphasize is that the synthesis and reaction of ATP (and ADP) is governed by the same principles as much simpler reactions. Whether the dominant species in any cellular compartment is ATP or ADP depends upon the conditions, and what substrates are present to react with.

9.1 Reaction systems
9.2 Buffered systems
9.3 Activation energy

Question to answer:

• If you are trying to determine whether two reactions are coupled, what would you look for?
• Coupling allows unfavorable reactions to occur, why does this not violate the laws of thermodynamics?
• Assume that you have a set of five coupled reactions, what factors could complicate the behavior of the system?
• How could you insure that an “unfavorable” reaction continued to occur at a significant (useful) rate?