Enzyme Regulation in Metabolic Pathways E-Book

Lloyd Wolfinbarger

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 348

Veröffentlichungsjahr: 2017

Beschreibung

Enzyme Regulation in Metabolic Pathways shows the reader how to understand the roles of enzymes and their kinetic constants in intermediary metabolism. It provides a means of correlating data obtained in experimental studies to multiple possible mechanisms through which some enzyme may catalyze the conversion of a substrate to a product. Although not the most appropriate means of determining some potential kinetic mechanism, quasi-equilibrium assumptions are used throughout the book, keeping the rate equation derivations simple. Actual metabolic pathways with known (presumed) positive and negative regulation events are linked to these potential kinetic mechanisms using both rate equation derivations and data plots illustrating how the rate equation derivations can be used to explain the data plots. This book will be a valuable reference for students in biological sciences and biochemistry majors required to take a core course in enzymology.

Leseprobe

Table of Contents

Cover

Title Page

Preface

Author’s Review

Part I

1 Characteristics of Enzymes

Thermodynamics

Enzyme Nomenclature

Activity Coefficients

2 Self‐Assembly of Polymers

3 Beginnings of Equations

Secondary Data Plots

4 Metabolite Distribution Systems

5 Modification of Enzymatic Activity

Competitive Modifiers

Noncompetitive Modifiers

Uncompetitive Modifiers

6 Modification of Metabolite Flow Through Metabolic Pathways

7 Which is the Real Substrate?

8 Non‐Quasi‐Equilibrium Assumptions

9 Underlying Attributes of Assessing Enzymatic Activities

Primary Data Plots

Secondary Data Plots

Part II

10 Breakdown of the Michaelis–Menten Equation (or Complex Enzyme Mechanisms)

11 Rate Equation Derivation by the King–Altman Method

Assignment of Values to Kinetic Constants: Ordered Two‐Substrate/Two‐Product Mechanism

12 Modification of Enzyme Mechanisms

Role of the Binding Constants of Modifiers

13 What Are These “Rate Constants” We Have Been Dealing With?

The Concentration Factor(s)

Bending the Data Curve Downward in Figure 13.2

Bending the Data Curve Upward in Figure 13.2

Other Factors Influencing Kinetic (Rate) Constants in Enzyme Mechanisms

Index

End User License Agreement

List of Tables

Chapter 01

Table 1.1 The relationships between entropy and enthalpy in determining whether or not some chemical reaction will be spontaneous or nonspontaneous.

List of Illustrations

Chapter 01

Figure 1.1 Illustration of the role of bound water versus nonbound water in the translational movement of a molecule of substrate into the substrate‐binding site of an enzyme.

Chapter 02

Figure 2.1 Sugar comprised of five molecules of “CO

2

” covalently linked to a second sugar with loss of a molecule of water.

Figure 2.2 Illustration of the use of five molecules of cyanide to form the base adenine.

Figure 2.3 Cartoon to illustrate the roles of base stacking and strong electronegative repulsion in determining why nucleic acids are helical.

Figure 2.4 Illustration of the role dehydration has in the formation of peptide bonds in proteins. The diagram is applicable to peptide bond formation whether it be by chemical or enzyme‐mediated reaction.

Figure 2.5 An “X/Y” data plot to illustrate two differing groups of molecules possessing two differing average energy levels permitting the demonstration of how increasing the average energy levels of such a population will impact on the concentration of substrate molecules possessing sufficient energy to be “unstable” and thus chemically reactive. The graph is designed to illustrate the population distributions of substrate molecules with differing levels of energy where the average energy levels are present at two different values. The vertical line illustrates the numbers of molecules presenting sufficient energy to be described as being “unstable” and likely to chemically change from one molecular form to another molecular form, that is, undergo conversion from a “substrate” to a “product” as described later in this book.

Chapter 03

Illustration 3.1

Figure 3.1 Typical velocity versus substrate concentration data plot showing the measured velocity asymptotically approaching maximal velocity at infinitely high concentrations of substrate.

Figure 3.2 Typical Lineweaver–Burk data plot where the reciprocal of the velocity at the reciprocal of each substrate concentration is plotted. The values of

V

max

and

K

m

are calculated by extrapolation of where the data line crosses the

x

and

y

axes for 1/Velocity and 1/Substrate concentration.

Figure 3.3 Typical velocity versus substrate concentration data plot showing the measured velocity asymptotically approaching maximal velocity at infinitely high concentrations of substrate (black data circles) and where the measured velocities do not asymptotically approach a maximal velocity, but rather turn upward (option 1) or downward (option 2) (open circle data points).

Figure 3.4 Typical Lineweaver–Burk data plot where the reciprocal of the velocity at the reciprocal of each substrate concentration is plotted. The values of

V

max

and

K

m

are calculated by extrapolation of where the data line crosses the

x

and

y

axes for 1/velocity and 1/substrate concentration (black circles) and for data plots that would be obtained from Options 1 and 2 from Figure 3.3 (open circles).

Figure 3.5 Typical velocity versus substrate concentration data plot showing the measured velocity asymptotically approaching maximal velocity at infinitely high concentrations of substrate (black data circles for one enzyme and open circles for a second enzyme).

Chapter 04

Figure 4.1 A diagrammatic illustration of a hypothetical water distribution system such as may have been in operation in ancient Rome. The water in this hypothetical system comes from some water source high in the mountains surrounding Rome and is delivered via an aqueduct into a water distribution system that feeds water to homes and public facilities in the city. Pipes A through D are intended to represent volumes of water that might be delivered based on two aspects of the distribution system: 1) the diameter, and thus carrying capacity, of the pipe feeding the home or public facility; and 2) the height of the pipes relative to other pipes in the water distribution system and thus the social/political stature of the owner of that home.

Figure 4.2 Cartoon to illustrate the role of enzymes (i.e., enzymes A, B, C, and D corresponding to horizontal pipes A, B, C, and D in Figure 4.1) in mediating the flow of substrate entering into a common “compartment” within the intermediary metabolism of a cell. The respective

K

m

and

V

max

values of each enzyme dictate which metabolic pathway receives metabolite and hence makes its specific product.

Figure 4.3 A diagram illustrating a metabolic pathway whereby two substrate molecules are metabolized to compound X via enzymes a, b, and c. Compound X is metabolized to compound Y by enzyme d. Compound Y is metabolized to compounds Z and A by enzymes e and f, respectively. Compound Z is metabolized to product P

1

by enzyme g, and compound A is metabolized to products P

2

and P

3

by enzymes h and i, respectively.

Figure 4.4 Pathway as shown in Figure 4.3, but with specific molecules in this aromatic amino acid biosynthetic pathway substituted for the symbols used in Figure 4.3. Prephenate is actually metabolized to either phenylpyruvate prior to formation of phenylalanine, or to parahydroxyphenylpyruvate prior to formation of tyrosine, but these intermediates were left out of this figure in order to emphasize the enzyme steps relevant (important) to regulation of this metabolic pathway and to aid in comprehension.

Figure 4.5 Diagram of the aromatic amino acid biosynthetic pathway showing the enzymatic steps in the pathway at which tyrosine (P

3

) modifies enzymatic activity via positive and negative regulatory events.

Figure 4.6 Diagram of the aromatic amino acid biosynthetic pathway showing the enzymatic steps in the pathway at which phenylalanine (P

2

) modifies enzymatic activity via positive and negative regulatory events.

Figure 4.7 Diagram of the aromatic amino acid biosynthetic pathway showing the enzymatic steps in the pathway at which tryptophan (P

1

) modifies enzymatic activity via positive and negative regulatory events.

Figure 4.8 Cartoon illustrating three binding sites for end‐product regulation and one catalytic site for the enzyme 3‐deoxyarabinoheptulosonate‐7‐phosphate synthetase.

Chapter 05

Figure 5.1 Lineweaver–Burk data plot showing a nonmodified enzymatic reaction (dark circles) and two modified enzymatic reactions (clear circles) where one modified reaction is classified as an inhibited enzymatic reaction (

K

m

value is increased) and the second modified reaction is classified as an activated enzymatic reaction (

K

m

value is decreased) relative to the

K

m

of the nonmodified enzymatic reaction.

Figure 5.2 Lineweaver–Burk data plot showing a nonmodified enzymatic reaction (dark circles) and two modified enzymatic reactions (clear circles) where one modified reaction is classified as an inhibited enzymatic reaction (

V

max

value is decreased) and the second modified reaction is classified as an activated enzymatic reaction (

V

max

value is increased) relative to the

V

max

of the nonmodified enzymatic reaction.

Figure 5.3 Lineweaver–Burk data plot showing a nonmodified enzymatic reaction (dark circles) and two modified enzymatic reactions (clear circles) where one modified reaction is classified as an inhibited enzymatic reaction (

V

max

value is decreased and

K

m

value is decreased) and the second modified reaction is classified as an activated enzymatic reaction (

V

max

value is increased and the

K

m

value is increased) relative to the

V

max

and

K

m

values of the nonmodified enzymatic reaction.

Figure 5.4 A Lineweaver–Burk data plot showing a nonmodified enzymatic reaction (dark circles) and one modified enzymatic reaction (clear circles) where the modified reaction is classified as either an inhibited enzymatic reaction (

K

m

value is increased relative to the nonmodified reaction) or as an activated enzymatic reaction (

V

max

value is increased) relative to the

V

max

of the nonmodified enzymatic reaction.

Figure 5.5 A Lineweaver–Burk data plot showing a nonmodified enzymatic reaction (dark circles) and one modified enzymatic reaction (clear circles) where some modified reactions would be classified as an inhibited enzymatic reaction (measured velocities are reduced relative to nonmodified enzyme velocities), but other modified reactions would be classified as an activated enzymatic reaction (measured velocities are increased relative to nonmodified enzyme velocities). Both calculated

V

max

and

K

m

values of the modified enzymatic reaction are changed relative to the

V

max

and

K

m

values of the nonmodified enzymatic reaction, that is, an uncompetitive modification mechanism.

Chapter 06

Figure 6.1 A diagrammatic illustration, also shown in Figure 4.1, of a hypothetical water distribution system such as may have been in operation in ancient Rome. The water in this hypothetical system is delivered via an aqueduct from some water source high in the mountains surrounding Rome and enters a water distribution system that feeds water to homes and public facilities in Rome. Pipes A through D are intended to represent volumes of water that might be delivered based on two aspects of the distribution system: 1) the diameter, and thus carrying capacity, of the pipe feeding the home or public facility; and 2) the height of the pipes relative to other pipes in the water distribution system.

Figure 6.2 A second diagrammatic illustration of a hypothetical water distribution system such as may have been in operation in ancient Rome. However this water system has been changed to reflect changes in the horizontal pipes compared with those same pipes in Figure 6.1. The water in this hypothetical system is delivered via an aqueduct from some water source high in the mountains surrounding Rome and enters a water distribution system that feeds water to homes and public facilities in Rome. Pipes A through D are intended to represent volumes of water that might be delivered based on two aspects of the distribution system: 1) the diameter, and thus carrying capacity, of the pipe feeding the home or public facility; and 2) the height of the pipes relative to other pipes in the water distribution system.

Figure 6.3 Diagram illustrating a metabolic pathway whereby two substrate molecules are metabolized to compound X via enzymes a, b, and c. Compound X is metabolized to compound Y by enzyme d. Compound Y is metabolized to compounds Z and A by enzymes e and f, respectively. Compound Z is metabolized to product P

1

by enzyme g and compound A is metabolized to products P

2

and P

3

by enzymes h and i, respectively.

Chapter 07

Figure 7.1 Graphic illustrating the four molecular species of aspartic acid as a function of changing pH and ionization of the three ionizable groups.

Figure 7.2 Graphic to illustrate how the concentrations of each of the four molecular forms (species) of aspartic acid change as a function of pH.

Chapter 08

Figure 8.1 Velocity versus substrate concentration data plot for a nonmodified and a modified enzyme to illustrate changes to kinetic constants.

Chapter 09

Figure 9.1 A hypothetical data plot showing a decrease in absorbance by substrate over time at a given concentration of substrate and a given concentration of enzyme.

Figure 9.2 A hypothetical data plot showing an increase in absorbance by product over time at a given concentration of substrate and a given concentration of enzyme.

Figure 9.3 A hypothetical data plot showing change in absorbance of some compound, for example “product” as discussed in the text, versus concentration of that compound. As noted, not all absorbance data points will fall on a straight line as determined using regression analysis (normally any one or more data points that cause the

R

2

value associated with a regression analysis to become smaller is sufficient reason to exclude it from the regression line derived).

Figure 9.4 Typical velocity versus substrate concentration data plot showing the measured velocity asymptotically approaching maximal velocity at infinitely high concentrations of substrate.

Figure 9.5 A hypothetical data plot showing change in absorbance of product being produced by an enzymatic reaction as a function of time and at four different concentrations of substrate, [S

1

], [S

2

], [S

3

], and [S

4

], over four different intervals of time.

Figure 9.6 A hypothetical data plot showing change in absorbance due to appearance of product over time at some concentration of substrate and a fixed concentration of enzyme. The straight line going from zero to the black circle represents an experiment where a single data point is taken at some fixed time interval. The curved line going from zero to a point equivalent to the data point represented by the black circle represents multiple data points taken at that same concentration of enzyme and substrate. It is clear that the use of a single data point to determine the slope or rate of conversion of substrate to product can lead to an erroneous determination of the rate of conversion if for some reason, the time dependent conversion of substrate to product is not a liner function of time over the time chosen for the experimental determination of rate.

Figure 9.7 The Eadie–Hofstee plot. “

V

” stands for velocity, such as would be obtained from data like those shown in Figures 9.1 and 9.2, and [S] stands for substrate concentration.

Figure 9.8 Eadie–Hofstee data plot showing velocity versus velocity/substrate concentration values for nonmodified (open circles) enzyme and for modified enzymes being activated or inhibited “competitively” by some modifier (black circles).

Figure 9.9 Eadie–Hofstee data plot showing velocity versus velocity/substrate concentration values for nonmodified (open circles) enzyme and for modified enzymes being activated or inhibited “un‐competitively” by some modifier (black circles).

Figure 9.10 Eadie–Hofstee data plot (noncompetitive) showing velocity versus velocity/substrate concentration values for nonmodified (open circles) enzyme and for modified enzymes being activated or inhibited “noncompetitively” by some modifier (black circles).

Chapter 10

Figure 10.1 Pathway as previously shown in Figures 4.3 and 4.4, with specific molecules found in this aromatic amino acid biosynthetic pathway substituted for the symbols used in Figure 4.3. Prephenate is actually metabolized to either phenylpyruvate prior to formation of phenylalanine, or to parahydroxyphenylpyruvate prior to formation of tyrosine, but these intermediates were left out of this scheme in order to emphasize the enzyme steps relevant (important) to regulation of this metabolic pathway and to aid in comprehension.

Figure 10.2 Diagram of the aromatic amino acid biosynthetic pathway showing the enzymatic steps in the pathway at which phenylalanine (P

2

) modifies enzymatic activity via positive and negative regulatory events.

Figure 10.3 A typical Lineweaver–Burk data plot that plots the reciprocal of the velocity against the reciprocal of each substrate concentration. The values of

V

max

and

K

m

are calculated by extrapolation of where the data line crosses the

x

and

y

axes for 1/Velocity and 1/Substrate concentration. Note that I have applied “relative” numbers for velocity of reaction along the

y

axis (10 to 100 downwards) and 200 to 20 left to right on the negative side of the

x

axis to illustrate the essential complications of a double reciprocal data plot.

Figure 10.4 Repeated Figure 4.6. Diagram of the aromatic amino acid biosynthetic pathway showing the enzymatic steps in the pathway at which phenylalanine (P

2

) modifies enzymatic activity via positive and negative regulatory events.

Figure 10.5 Repeated Figure 4.4. Pathway as shown in Figure 4.3, but with specific molecules found in this aromatic amino acid biosynthetic pathway substituted for the symbols used in Figure 4.3. Prephenate is actually metabolized to either phenylpyruvate prior to formation of phenylalanine or to parahydroxyphenylpyruvate prior to formation of tyrosine, but these intermediates were left out of this figure in order to emphasize the enzyme steps relevant (important) to regulation of this metabolic pathway and to aid in comprehension.

Chapter 11

Figure 11.1 An expected velocity versus substrate concentration data plot for substrate B illustrated in Equation 11.4 in the presence of saturating concentrations of substrate A.

Chapter 12

Figure 12.1 Diagram of the aromatic amino acid biosynthetic pathway showing the enzymatic steps in the pathway at which

tyrosine

(P

3

) modifies enzymatic activity via positive and negative regulatory events [Figure 4.5 repeated].

Figure 12.2 Diagram of the aromatic amino acid biosynthetic pathway showing the enzymatic steps in the pathway at which

phenylalanine

(P

2

) modifies enzymatic activity via positive and negative regulatory events [Figure 4.6 repeated].

Figure 12.3 Diagram of the aromatic amino acid biosynthetic pathway showing the enzymatic steps in the pathway at which

tryptophan

(P

1

) modifies enzymatic activity via positive and negative regulatory events [Figure 4.7 repeated].

Chapter 13

Figure 13.1 Hypothetical graph illustrating the rate of appearance of the “product” (in this case the enzyme–substrate complex as illustrated in Equation 13.1) by plotting the concentration of the enzyme–substrate complex ([ES]) as a function of the concentration of substrate ([S]). Theoretically the line would pass through zero, but this expectation is not shown here simply because the graph is hypothetical, and whether or not the line would pass through zero is speculative at best, but you can think more about that later.

Figure 13.2 A hypothetical graph illustrating the change in the concentration of the enzyme–substrate complex [ES] versus change in the concentration of free enzyme [E] associated with Equation 13.1.

Figure 13.3 Illustration of the role of bound water versus nonbound water in the translational movement of a molecule of substrate into the substrate‐binding site of an enzyme [Figure 1.1 repeated].

Figure 13.4 Illustration of the role of bound water versus nonbound water in the translational movement of a molecule of substrate into the substrate‐binding site of an enzyme where other solute(s) is present to aid in the disruption of the structure of bound water in close proximity to both enzyme and substrate.

Guide

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Enzyme Regulation in Metabolic Pathways

Lloyd Wolfinbarger, Jr.

Professor EmeritusOld Dominion University, Norfolk, Virginia, USA

This edition first published 2017© 2017 John Wiley & Sons, Inc.

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Library of Congress Cataloging‐in‐Publication Data

Names: Wolfinbarger, Lloyd, Jr.Title: Enzyme Regulation in Metabolic Pathways / Lloyd Wolfinbarger, Jr., Ph. D., professor emeritus, Old Dominion University, Norfolk, Virginia, USA.Description: Hoboken, NJ : John Wiley & Sons, Inc., 2017. | Includes bibliographical references and index.Identifiers: LCCN 2016053362 (print) | LCCN 2016055282 (ebook) | ISBN 9781119155386 (cloth) | ISBN 9781119155409 (pdf) | ISBN 9781119155416 (epub)Subjects: LCSH: Enzymes–Regulation. | Metabolism.Classification: LCC QP601.4 .W65 2017 (print) | LCC QP601.4 (ebook) | DDC 572/.7–dc23LC record available at https://lccn.loc.gov/2016053362

Cover design: WileyCover image: theasis/Gettyimages

Preface

This book was developed from courses in biochemistry and enzymology at the upper undergraduate and lower graduate level. I found that my students were quick at learning structures and metabolic pathways in biochemistry and at deriving rate equations for single‐substrate/single‐product as well as two‐substrate/two‐product enzyme‐catalyzed reactions, but neither group of students was getting a good understanding of how enzymes directed the flow(s) of metabolites through metabolic pathways and how these metabolites regulated which pathway managed to metabolize the most metabolites to some end product(s). All too often, they were too focused on passing the tests rather than trying to understand and to challenge what I was teaching them.

Enzymology is frequently taught in a standard biochemistry textbook, and the course in biochemistry using that book takes a fairly standard approach in covering energies of activation, steady state versus quasi‐equilibrium kinetics, and modes of modifier inhibition/activation of an enzymatic reaction. A typical enzymology course tends to focus on the differing kinds of enzymes and the kinds of reactions they catalyze, kinetic rate equation derivations, data plots obtained with different enzyme modifiers, and, in the more extensive texts, kinetic mechanisms by which an enzyme may catalyze a chemical reaction.

The basic premise of this book will be that there is a need for an easy means of correlating the data one actually obtains in experimental studies with multiple possible mechanisms through which some enzyme may catalyze the conversion of a substrate to a product. Although not the most appropriate means of determining some potential kinetic mechanism, quasi‐equilibrium assumptions will be used throughout the book in that these keep the rate equation derivations simple. Actual metabolic pathways with known (presumed) positive and negative regulation events are linked to these potential kinetic mechanisms using both rate equation derivations and data plots illustrating how the rate equation derivations can be used to explain the data plots.

Finally, I want to emphasize that it is not the purpose of this book to be technically accurate with respect to enzyme kinetics, nor is it the purpose of this book to teach you about metabolic pathways or the traditional ways in which metabolic pathways are thought to be regulated. I do not profess to be a hard core enzymologist devoted to teaching enzymology. Rather I propose to show you how I came to understand the roles of enzymes and their kinetic constants in intermediary metabolism, and thus the purpose of this book is to challenge you to think about what I convey to you and hopefully to get you to challenge my teachings. In challenging my teachings, you will achieve the purpose of this book. You will learn to think rather than learn to take notes so you can pass the next test.

The level and contents of this book should make it suitable as a reference text in biochemistry courses at the undergraduate level and as a textbook for a course in basic enzymology taken prior to a more advanced course in enzymology at the graduate level.

I acknowledge substantial help from my former students who over my 30 odd years as a professor constantly challenged my ideas and interpretation of data, and particularly to one of my former employees, Katrina Ruth, who challenged me to stay on track with what I wanted to write and greatly assisted me in writing what I wrote in a more clear and concise manner.

Author’s Review

Yes, I know that this book is repetitive, redundant, and tedious. I also know, and suggest to you, that if you expected this book to teach you about basic enzymology, you picked up the wrong book. I was a professor at a major State University for some 30 years over a time where computers were first beginning to make their appearance, and I retired when computers had pretty much taken over the thinking process once reserved for people. When I was a young Assistant Professor, I ran across a small paperback book entitled To Know a Fly written by Vincent G. Dethier. The book was easy to read, with cartoons no less, and described how the author learned how to ask the right questions in his conduct of research using the common housefly. He asked how did flies know when something was sweet (food), how did they land upside down on the ceiling, and other equally important questions. The answers, at least for me however, were not about learning how flies know when something is food, but rather about how to ask the right questions and come up with the proper experiments to answer a question. This is, I hope, what this book is about.

You will be dragged through pseudo‐thermodynamics, complex enzyme mechanisms, rate equation derivations that go nowhere, and through seemingly endless repetition to answers that are not absolute (only possible). But, somewhere in all of this, you will hopefully begin to think about what questions to ask when it comes to the study of enzyme function(s) and how to think about the vast numbers of possibilities you can devise in the way of answers (none, of course, that will be verifiable). If you are successful, you will realize that in all of this repetition, redundancy of writing, and tedious attention to details, it is not the answers that are important in life, it is the questions that you will learn to ask.

I quickly learned to use computers and to incorporate them into my teaching. However, I never lost sight of the importance of getting a small group of people together in a classroom where the sharing of creative (and frequently “ridiculous”) ideas led to understanding and knowledge with respect not only to biochemistry or enzymology, but also to all those other bits and pieces of information floating around in our heads that led us to new ideas and understanding.

I will leave you with the admonition that you should ignore the tedious, the repetition, and the redundancy and forge ahead into the book. Ignore the failings of the author and focus on creating those visual images of the “possibles” and how you arrived at those “possibles.” As is always said, it is the journey that is important, not the destination.

Part I

Beyond this point there be dragons.

Admonition on old seafaring maps

1Characteristics 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).