Enzyme Regulation in Metabolic Pathways

Part I

Beyond this point there be dragons.

Admonition on old seafaring maps

1

Characteristics of Enzymes

At university, Enzymology was the class that most biochemistry or biology majors dreaded taking. Those students who liked the class were typically math majors who took the class for the thrill of solving complex rate equation derivations. Those students who had to take the class against their will were those who might need to understand the role of enzymes as they pertained to other aspects of biochemistry, but otherwise had little desire to sit through boring lectures involving lots of equations and the occasional molecular structures on the white board. As a professor teaching biochemistry to undergraduate and graduate students the task fell to me to keep my students’ attention, so they didn’t fall asleep, yet challenge them to understand why what I was teaching them could be both fun and useful.

I started teaching traditional enzymology as it was presented in the textbooks of the day (and I’m sorry to say is still being presented today). I found my students were passing the tests, but failing to understand how to interpret data and more importantly how to fit the data they were obtaining in their research into something meaningful and exciting. I eventually adopted a strategy of engaging the minds of my students with challenging, but improbable, enzymatic mechanisms and found that steady state kinetics, while more relevant, hindered the understanding of some of the more basic principles associated with enzyme kinetics. I finally hit upon the use of quasi‐equilibrium assumptions and my students began to question and challenge my lectures—I had finally arrived as a professor.

Enzymology can be the study of enzymes as protein molecules with specific folding patterns of the amino acid polymer and unique binding sites wherein intra‐ and inter‐molecular distances define the specificity of the molecule to attract, bind to, and change some substrate molecule. Computer‐aided molecular modeling is a wonderful aspect of both biochemistry and enzymology in providing visuals essential to understanding, but does little to help with data analysis. Alternatively, enzymology can be the study of how these protein molecules control and mediate the flow of metabolites through intermediary metabolism affecting what we call metabolic viability to life forms. It is this latter study of enzymes that will be the focus of this book.

Enzymes are mostly proteins that are of variable length (with respect to amino acid sequences) and molecular weight. These amino acid polymers typically fold into some conformation that is most energetically favored based on the nature of the amino acids making up the protein and the aqueous environment in which they find themselves. For the most part, hydrophobic amino acids such as leucine or phenylalanine, as examples, are to be found in what might be called the hydrophobic core of the protein, whereas the hydrophilic amino acids such as histidine or aspartic acid, again as examples, will preferentially be found on those surfaces of the protein more exposed to an aqueous (hydrophilic) environment. The arrangement of hydrophobic and ionizable side groups of these hydrophilic amino acids is typically described as being present in some molecular organization that forms a region complementary to some low molecular weight solute. This region of the protein is generally regarded as constituting the substrate‐ (or modifier‐) binding site. Whether this binding site tends to bind an unstable form of the substrate, stabilizing the unstable intermediate, and in so doing promoting its conversion to product; or whether this binding site tends to bind a stable form of the substrate and in so doing causes the substrate to shift into some less stable configuration promoting its conversion to product, will be discussed in detail. We will enter into this aspect of the basics of enzymology in detail in Chapter 2. For now, I only wish to stipulate that this enzyme with a substrate‐binding site will be referred to as free enzyme (E) in subsequent sections. When free enzyme (E) binds with the substrate, it will be referred to as the enzyme/substrate complex (ES). As the enzyme facilitates the conversion of substrate to product via some unknown or unspecified mechanism, the product (P) released from the substrate‐binding site will result in the (ES) complex reverting to free enzyme (E). Thus within the context of this book, the sum of the concentration of free enzyme (E) and enzyme/substrate complex (ES) will be referred to as the total amount (or quantity) of enzyme (Et). When introducing modifiers of enzyme activity, I will use the simple connotation of a modifier (M) being either an activator (Ma) or an inhibitor (Mi). Modifiers will typically bind to free enzyme (E) to form a modified enzyme as either (MaE) or (MiE). Where substrate (S), enzyme (E), substrate/enzyme complex (ES), and so forth, are bracketed with square brackets, such as [S], the intent will be to express the molecule as some concentration. I will try to restate this point throughout the text, more to remind and help you than to irritate you with what will appear as my being overly redundant. Repetition is a good learning tool.

I would also like to emphasize one more point. I will make reference to saturating concentrations of substrate or modifier in the text. As you will see in later figures, as you add increasing concentrations of substrate (or modifier) to an enzymatic reaction, the rate of conversion of substrate to product will gradually increase until such time as that concentration approaches the capacity of that enzyme to bind to substrate converting it to product. At such a time where increasing the concentration of substrate no longer significantly increases the rate of conversion to product, it is generally assumed (described) as a saturation of enzyme by substrate. This will make more sense later, but I also want to emphasize that we will operate under the premise that the amount of substrate at any given concentration of that substrate will be inexhaustible. This means basically that you can crystallize salt out of sea water, but you will never run out of sea water where there is an infinite amount of salt. This is the difference between the concentration of salt in sea water and the amount of salt in the sea.

I shall take a rather simplistic approach to the overall mathematical equation subject with respect to enzymes by defining a few selected terms. As you get deeper into the study of enzymes and enzymology you will have an opportunity to learn that in seeking generalities, one must frequently stretch the truth a bit in order to understand the why when it comes to enzymes as mediators of intermediary metabolism. I will work almost exclusively under what is generally referred to as quasi‐equilibrium assumptions, rather than the more probable and ultimately more useful steady‐state assumptions to describe enzyme kinetic mechanisms and associated rate constants. Later on in your studies, you can move onto steady‐state assumptions, but for now I will take a bit of poetic license and work under quasi‐equilibrium assumptions.

Thermodynamics

For now, let’s think about the role of an enzyme and what we need to think about when it comes to an enzyme performing that role. Enzymes, as proteins in solution, have three simplistic energies. They have vibrational energy, which is simply the tendency of atoms and groups of atoms to present energy dissipation or collection as more or less a degree of stability/instability without presenting as either of the two other forms of energy. They also have rotational energy, which is simply the tendency of a molecule (collection of atoms) to roll or spin in place when in solution. Finally, they have translational energy, which is simply the tendency of a molecule to move in some direction until events cause it to change that direction in favor of a second direction. Temperature has an impact on all three forms of energy in an enzyme, and we shall attempt to cover how all three forms of energy in an enzyme (as well as their substrates) factor into the role of an enzyme in speeding the rate of conversion of substrate to product without being consumed in the reaction. However, as I stated above, we will get more into this topic in Chapter 2. This chapter has more to do with trying to define terms than trying to explain how they help in describing how an enzyme functions.

Temperature has an obvious role in enzyme activities and a very complex role. Temperature changes directly impact on the vibrational energy of molecules such as substrates of enzymatic reactions. Using the brief description of vibrational energy in the previous paragraph, it is easy to suggest that as the temperature in which a substrate molecule (as well as an enzyme, but let’s leave the enzyme out for now) finds itself, the increased vibrational energy will tend to present as increased movement of atoms relative to their covalent bonds, as movements of electrons in possible orbits around their nuclei, and/or as overall changes in the structural conformation of the molecule (substrate in this instance). In some respects, increases in vibrational energy may represent the more significant aspect of what has been described as the energy of activation of some molecule necessary for that molecule to undergo a spontaneous chemical reaction becoming another molecule (perhaps a product for sake of my keeping in focus with this book). As a molecule becomes activated through the introduction of energy—in the form of increased temperature(s)—more of the substrate molecules will possess sufficient energy to acquire that energy of activation; and since the spontaneous chemical reaction will be defined as a concentration times some rate constant, the higher concentration of activated (energized) substrate will result in a faster rate of chemical change of that substrate into a product. You will encounter this issue again in Chapter 2 and Figure 2.4. However, this is a book about enzymes, and I would be remiss if I left the rather loose definition of energy of activation to apply only to vibrational energy of a molecule (substrate). Temperature also has effects on rotational and translational energies of molecules involved in some enzymatic reaction. As temperatures increase in some enzymatic reaction, molecules will tend to rotate and translate more freely, and while such rotational and translational energies may have less to do with the energy of activation component of a spontaneous chemical reaction, they most likely have more of an effect on the energy of activation associated with the enzyme‐driven spontaneous chemical reaction than vibrational energy. So, how to define energy of activation for how we wish it to be used in the context of this book? The first thing we have to understand is that the energy of activation of a molecule that will undergo a spontaneous chemical reaction is not the same energy of activation of a molecule that will undergo a spontaneous chemical reaction where the rate of that spontaneous chemical reaction is enhanced through mediation of an enzyme (catalyst?). The energy of activation of the latter reaction should thus include roles for temperature, solution effects, enzyme, substrate, vibrational energies, rotational energies, and translational energies (note the use of energies here in that both the substrate and the enzyme possess these characteristics).

Like temperature, the solution in which an enzyme (and its substrates) is dissolved has an impact on all three forms of energy in an enzyme, but this impact is far more complicated than the role of temperature, although as we will see later, temperature has considerable impact on the nature of the solution and how that nature of the solution bears on the three forms of energy and subsequent interactions of the enzyme with its substrate(s) (and formed products). Enzymes function naturally in an aqueous solution of water and various ions (and/or other solutes). Water consists of a unique molecule consisting of one oxygen and two hydrogen atoms. The hydrogen atoms are situated on one side of the oxygen atom, and both kinds of atoms share electrons such that the electrons tend to spend more time with the oxygen atom than with the corresponding hydrogen atom(s) giving the whole molecule a dipole moment. This dipole moment imparts a slight negative nature to the oxygen side of the water molecule and a slight positive nature to the hydrogen side of the water molecule. It is this dipole moment that gives the water solution characteristics relevant to the energies of the enzyme, the energies of the substrate (and formed product), and directly impacts on the energy of activation and the kinetics of the enzymatic reaction in the conversion of substrate to product by that enzyme.

Normally water molecules are oriented rather randomly (with respect to their dipole moments) in some aqueous solution. However, lowering the temperature begins to remove energy from those water molecules, and at some sufficiently low temperature the water molecules will begin to lose rotational and translational energy and begin to align themselves according to their dipole moment such that the more positively charged side will be attracted to the more negatively charged side of a second molecule; eventually the water molecules will assume a crystalline‐like structure where the dipole moments of the water molecules will all be oriented in mostly the same direction. This crystalline‐like (or paracrystalline) form of water is called ice; ice presents a solution of water molecules with a lower entropy (less fluidized) than a solution of water molecules randomly associated as in a more fluidized or liquid solution