Enzymes are proteins that catalyze (i.e. accelerate) chemical reactions. In these reactions, the molecules at the beginning of the process are called substrates, and the enzyme converts them into different molecules, the products. Almost all processes in a biological cell need enzymes in order to occur at significant rates. Since enzymes are extremely selective for their substrates and speed up only a few reactions from among many possibilities, the set of enzymes made in a cell determines which metabolic pathways occur in that cell.

Like all catalysts, enzymes work by lowering the activation energy (ΔG‡) for a reaction, thus dramatically accelerating the rate of the reaction. Most enzyme reaction rates are millions of times faster than those of comparable uncatalyzed reactions. As with all catalysts, enzymes are not consumed by the reactions they catalyze, nor do they alter the equilibrium of these reactions. However, enzymes do differ from most other catalysts by being much more specific. Enzymes are known to catalyze about 4,000 biochemical reactions. Not all biochemical catalysts are proteins, since some RNA molecules called ribozymes also catalyze reactions.

 Enzymes are protein molecules that are tailored to recognize and bind specific reactants and speed their conversion into products. These proteins are responsible for increasing the rates of all of the many thousand of reaction taking place inside cells.

All enzymatic proteins have several characteristics.

1.         Enzymes combine briefly with reactants during an enzyme-catalyzed reaction.

2.         Enzymes are released unchanged after catalyzing the conversion of reactants to Product

3.         Enzymes are specific in their activity; each enzyme catalyzes the reaction of a single type of molecules or a group of closely related molecules.

4.         Enzymes are saturated by high substrate concentrations.

5.         Many enzymes contain nonproteins groups called cofactors, which contribute to their activity. Inorganic cofactors are all metallic ions. Organic cofactors, called coenzymes, are complex groups derived from vitamins.

6.         Many enzymes are pH and temperature sensitive

The rate of combination and release, known as the turnover number, lies near 1000 per second for most enzymes. Some enzymes have turnover numbers as small as 100 per second or as large as 10 million per second. As a result of enzyme turnover, a relatively small number of enzyme molecules can catalyze a large number of reactant molecules.

The part of an enzyme that combines with substrate molecule is the active site. In most enzymes the active site is located in a cavity or pocket on the enzyme surface, frequently within a cleft marking the boundary between two or more major domains. Within the cleft or pocket, amino acid side groups are situated to fit and bind parts of substrate molecules that are critical to the reaction catalyzed by the enzyme. The active site also separates substrate molecules from the surrounding solutions and place them in environments with unique characteristics, including partial or complete exclusion of water.

How Enzymes Lower the Energy of Activation

The mechanisms by which enzymes lower the energy of activation are still not totally understood. However, the mechanisms are believed to be directly or indirectly related to achievement of what is known as the transition state for a reaction. During any chemical interaction the reactants briefly enter a state in which old chemical bonds are incompletely broken and new ones are incompletely formed. In this transition state electron orbital assume intermediate positions between their locations in the reactants and their positions in the products. The transition state is highly unstable and can easily move in either direction with little change in energy - forward toward products ore back ward toward reactants. In effect, achievement of the transition state places a reacting system in a poised and precariously balanced position at the top of the activation energy barrier.

For example, in the transfer of a phosphate group from one molecule to another, a transition state is set up in which both molecules (shown as X and Y in Figure 2) link to the phosphate group a fraction of a second via transitory bonds (dotted lines). This unstable state can change readily in the direction of either products or unchanged reactants.

Enzymes as Biological Catalysts

In cells and organisms most reactions are catalyzed by enzymes, which are regenerated during the course of a reaction. These biological catalysts are physiologically important because they speed up the rates of reactions that would otherwise be too slow to support life. Enzymes increase reaction rates--- sometimes by as much as one millionfold, but more typically by about one thousand fold. Catalysts speed up the forward and reverse reactions proportionately so that, although the magnitude of the rate constants of the forward and reverse reactions is are increased, the ratio of the rate constants remains the same in the presence or absence of enzyme. Since the equilibrium constant is equal to a ratio of rate constants, it is apparent that enzymes and other catalysts have no effect on the equilibrium constant of the reactions they catalyze.

Enzymes increase reaction rates by decreasing the amount of energy required to form a complex of reactants that is competent to produce reaction products. This complex is known as the activated state or transition state complex for the reaction. Enzymes and other catalysts accelerate reactions by lowering the energy of the transition state. The free energy required to form an activated complex is much lower in the catalyzed reaction. The amount of energy required to achieve the transition state is lowered; consequently, at any instant a greater proportion of the molecules in the population can achieve the transition state. The result is that the reaction rate is increased.

A number of mechanisms operate to contribute to formation of the transition state. One is bringing reacting molecules into close proximity. Many reactions involve combination or interaction of two or more reactant molecules. For the reaction to take place, the substrate molecule must collide. The required collisions may be rate among reactant molecules suspended in free solution, particularly if the substrates are present in low concentrations. Binding at the active site of an enzyme brings the reactants close together, raising their effective concentration in the active site to many time the concentration in the surrounding solution.

A second contribution mechanism is orienting reactants in positions favoring their interaction. Binding at the active site may bring substrate molecules into an arrangement in which they can collide ate exactly the correct positions and angles required for achievement of the transition state.

The third contributing mechanism is exposing reactant molecules to altered environments that promote their interaction. Enzyme-Substrate Interactions

The favored model of enzyme substrate interaction is known as the induced fit model. This model proposes that the initial interaction between enzyme and substrate is relatively weak, but that these weak interactions rapidly induce conformational changes in the enzyme that strengthen binding and bring catalytic sites close to substrate bonds to be altered. After binding takes place, one or more mechanisms of catalysis generates transition- state complexes and reaction products. The possible mechanisms of catalysis are four in number:

1. Catalysis by Bond Strain: In this form of catalysis, the induced structural rearrangements that take place with the binding of substrate and enzyme ultimately produce strained substrate bonds, which more easily attain the transition state. The new conformation often forces substrate atoms and bulky catalytic groups, such as aspartate and glutamate, into conformations that strain existing substrate bonds.


 2. Catalysis by Proximity and Orientation: Enzyme-substrate interactions orient reactive groups and bring them into proximity with one another. In addition to inducing strain, groups such as aspartate are frequently chemically reactive as well, and their proximity and orientation toward the substrate thus favors their participation in catalysis.


3. Catalysis Involving Proton Donors (Acids) and Acceptors (Bases): Other mechanisms also contribute significantly to the completion of catalytic events initiated by a strain mechanism, for example, the use of glutamate as a general acid catalyst (proton donor).


4. Covalent Catalysis: In catalysis that takes place by covalent mechanisms, the substrate is oriented to active sites on the enzymes in such a way that a covalent intermediate forms between the enzyme or coenzyme and the substrate. One of the best-known examples of this mechanism is that involving proteolysis by serine proteases, which include both digestive enzymes (trypsin, chymotrypsin, and elastase) and several enzymes of the blood clotting cascade. These proteases contain an active site serine whose R group hydroxyl forms a covalent bond with a carbonyl carbon of a peptide bond, thereby causing hydrolysis of the peptide bond.

Some reactions, for example, take place more readily in nonpolar environments. Active sites may create such an environment by binding reactants so closely that water molecules are excluded. Another important environmental change is creation of acidic or basic conditions by groups in the active site that release or take up H+ .

Cofactors and coenzymes

The functional role of coenzymes is to act as transporters of chemical groups from one reactant to another. The chemical groups carried can be as simple as the hydride ion (H+ + 2e-) carried by NAD or the mole of hydrogen carried by FAD; or they can be even more complex than the amine (-NH2) carried by pyridoxal phosphate.

Since coenzymes are chemically changed as a consequence of enzyme action, it is often useful to consider coenzymes to be a special class of substrates, or second substrates, which are common to many different holoenzymes. In all cases, the coenzymes donate the carried chemical grouping to an acceptor molecule and are thus regenerated to their original form. This regeneration of coenzyme and holoenzyme fulfills the definition of an enzyme as a chemical catalyst, since (unlike the usual substrates, which are used up during the course of a reaction) coenzymes are generally regenerated.

Enzyme Relative to Substrate Type

Although enzymes are highly specific for the kind of reaction they catalyze, the same is not always true of substrates they attack. For example, while succinic dehydrogenase (SDH) always catalyzes an oxidation-reduction reaction and its substrate is invariably succinic acid, alcohol dehydrogenase (ADH) always catalyzes oxidation-reduction reactions but attacks a number of different alcohols, ranging from methanol to butanol. Generally, enzymes having broad substrate specificity are most active against one particular substrate. In the case of ADH, ethanol is the preferred substrate.

Enzymes also are generally specific for a particular steric configuration (optical isomer) of a substrate. Enzymes that attack D sugars will not attack the corresponding L isomer. Enzymes that act on L amino acids will not employ the corresponding D optical isomer as a substrate. The enzymes known as racemases provide a striking exception to these generalities; in fact, the role of racemases is to convert D isomers to L isomers and vice versa. Thus racemases attack both D and L forms of their substrate.

As enzymes have a more or less broad range of substrate specificity, it follows that a given substrate may be acted on by a number of different enzymes, each of which uses the same substrate(s) and produces the same product(s). The individual members of a set of enzymes sharing such characteristics are known as isozymes. These are the products of genes that vary only slightly; often, various isozymes of a group are expressed in different tissues of the body. The best studied set of isozymes is the lactate dehydrogenase (LDH) system. LDH is a tetrameric enzyme composed of all possible arrangements of two different protein subunits; the subunits are known as H (for heart) and M (for skeletal muscle). These subunits combine in various combinations leading to 5 distinct isozymes. The all H isozyme is characteristic of that from heart tissue, and the all M isozyme is typically found in skeletal muscle and liver. These isozymes all catalyze the same chemical reaction, but they exhibit differing degrees of efficiency. The detection of specific LDH isozymes in the blood is highly diagnostic of tissue damage such as occurs during cardiac infarct.

Enzyme cofactors

Many enzymes require the presence of an additional, nonprotein, cofactor.

Some of these are metal ions such as Zn2+ (the cofactor for carbonic anhydrase), Cu2+, Mn2+, K+, and Na+.

Some cofactors are small organic molecules called coenzymes. The B vitamins

o          thiamine (B1)

o          riboflavin (B2) and

o          nicotinamide

are precursors of coenzymes.

Coenzymes may be covalently bound to the protein part (called the apoenzyme) of enzymes as a prosthetic group. Others bind more loosely and, in fact, may bind only transiently to the enzyme as it performs its catalytic act.

Lysozyme is a globular protein with a deep cleft across part of its surface. Six hexoses of the substrate fit into this cleft.

With so many oxygen atoms in sugars, as many as 14 hydrogen bonds form between the six amino sugars and certain amino acid R groups such as Arg-114, Asn-37, Asn-44, Trp-62, Trp-63, and Asp-101.

Some hydrogen bonds also form with the C=O groups of several peptide bonds.

In addition, hydrophobic interactions may help hold the substrate in position.

X-ray crystallography has shown that as lysozyme and its substrate unite, each is slightly deformed. The fourth hexose in the chain (ring #4) becomes twisted out of its normal position. This imposes a strain on the C-O bond on the ring-4 side of the oxygen bridge between rings 4 and 5. It is just at this point that the polysaccharide is broken. A molecule of water is inserted between these two hexoses, which breaks the chain. Here, then, is a structural view of what it means to lower activation energy. The energy needed to break this covalent bond is lower now that the atoms connected by the bond have been distorted from their normal position.

As for lysozyme itself, binding of the substrate induces a small (~0.75Å) movement of certain amino acid residues so the cleft closes slightly over its substrate. So the "lock" as well as the "key" changes shape as the two are brought together. (This is sometimes called "induced fit".)

The amino acid residues in the vicinity of rings 4 and 5 provide a plausible mechanism for completing the catalytic act. Residue 35, glutamic acid (Glu-35), is about 3Å from the -O- bridge that is to be broken. The free carboxyl group of glutamic acid is a hydrogen ion donor and available to transfer H+ to the oxygen atom. This would break the already-strained bond between the oxygen atom and the carbon atom of ring 4.

Now having lost an electron, the carbon atom acquires a positive charge. Ionized carbon is normally very unstable, but the attraction of the negatively-charged carboxyl ion of Asp-52 could stabilize it long enough for an -OH ion (from a spontaneously dissociated water molecule) to unite with the carbon. Even at pH 7, water spontaneously dissociates to produce H+ and OH- ions. The hydrogen ion (H+) left over can replace that lost by Glu-35.


In either case, the chain is broken, the two fragments separate from the enzyme, and the enzyme is free to attach to a new location on the bacterial cell wall and continue its work of digesting it.


Some enzymes do not need any additional components to show full activity. However, others require non-protein molecules to be bound for activity. Cofactors can be either inorganic (e.g., metal ions and iron-sulfur clusters) or organic compounds, (e.g., flavin and heme). Organic cofactors (coenzymes) are usually prosthetic groups, which are tightly bound to the enzymes that they assist. These tightly-bound cofactors are distinguished from other coenzymes, such as NADH, since they are not released from the active site during the reaction.


An example of an enzyme that contains a cofactor is carbonic anhydrase, and is shown in the ribbon diagram above with a zinc cofactor bound in its active site. These tightly-bound molecules are usually found in the active site and are involved in catalysis. For example, flavin and heme cofactors are often involved in redox reactions.


Enzymes that require a cofactor but do not have one bound are called apoenzymes. An apoenzyme together with its cofactor(s) is called a holoenzyme (i.e., the active form). Most cofactors are not covalently attached to an enzyme, but are very tightly bound. However, organic prosthetic groups can be covalently bound (e.g., thiamine pyrophosphate in the enzyme pyruvate dehydrogenase).




Space-filling model of the coenzyme NADH Coenzymes are small molecules that transport chemical groups from one enzyme to another. Some of these chemicals such as riboflavin, thiamine and folic acid are vitamins, this is when these compounds cannot be made in the body and must be acquired from the diet. The chemical groups carried include the hydride ion (H-) carried by NAD or NADP+, the acetyl group carried by coenzyme A, formyl, methenyl or methyl groups carried by folic acid and the methyl group carried by S-adenosylmethionine.


Since coenzymes are chemically changed as a consequence of enzyme action, it is useful to consider coenzymes to be a special class of substrates, or second substrates, which are common to many different enzymes. For example, about 700 enzymes are known to use the coenzyme NADH.

Coenzymes are usually regenerated and their concentrations maintained at a steady level inside the cell: for example, NADPH is regenerated through the pentose phosphate pathway and S-adenosylmethionine by methionine adenosyltransferase.

Factors Affecting Enzyme Action

The activity of enzymes is strongly affected by changes in pH and temperature. Each enzyme works best at a certain pH (left graph) and temperature (right graph), its activity decreasing at values above and below that point. This is not surprising considering the importance of

tertiary structure (i.e. shape) in enzyme function and

noncovalent forces, e.g., ionic interactions and hydrogen bonds, in determining that shape.


the protease pepsin works best as a pH of 1-2 (found in the stomach) while

the protease trypsin is inactive at such a low pH but very active at a pH of 8 (found in the small intestine as the bicarbonate of the pancreatic fluid neutralizes the arriving stomach contents).

Changes in pH alter the state of ionization of charged amino acids (e.g., Asp, Lys) that may play a crucial role in substrate binding and/or the catalytic action itself. Without the unionized -COOH group of Glu-35 and the ionized -COO- of Asp-52, the catalytic action of lysozyme would cease.

Hydrogen bonds are easily disrupted by increasing temperature. This, in turn, may disrupt the shape of the enzyme so that its affinity for its substrate diminishes. The ascending portion of the temperature curve (red arrow in right-hand graph above) reflects the general effect of increasing temperature on the rate of chemical reactions (graph at left). The descending portion of the curve above (blue arrow) reflects the

Biological function

Enzymes serve a wide variety of functions inside living organisms. They are indispensable for signal transduction and cell regulation, often via kinases and phosphatases. They also generate movement, with myosin hydrolysing ATP to generate muscle contraction and also moving cargo around the cell as part of the cytoskeleton. Other ATPases in the cell membrane are ion pumps involved in active transport. Enzymes are also involved in more exotic functions, such as luciferase generating light in fireflies.

Viruses can contain enzymes for infecting cells, such as the HIV integrase and reverse transcriptase, or for viral release from cells, like the influenza virus neuraminidase.

An important function of enzymes is in the digestive systems of animals. Enzymes such as amylases and proteases break down large molecules (starch or proteins, respectively) into smaller ones, so they can be absorbed by the intestines. Starch is inabsorbable in the intestine but enzymes hydrolyse the starch chains into smaller molecules such as maltose and eventually glucose, which can then be absorbed. Different enzymes digest different food substances. In ruminants which have a herbivorous diets, bacteria in the gut produce another enzyme, cellulase to break down the cellulose cell walls of plant fiber.

Several enzymes can work together in a specific order, creating metabolic pathways. In a metabolic pathway, one enzyme takes the product of another enzyme as a substrate. After the catalytic reaction, the product is then passed on to another enzyme. Sometimes more than one enzyme can catalyse the same reaction in parallel, this can allow more complex regulation: with for example a low constant activity being provided by one enzyme but an inducible high activity from a second enzyme.

Enzymes determine what steps occur in these pathways. Without enzymes, metabolism would neither progress through the same steps, nor be fast enough to serve the needs of the cell. Indeed, a metabolic pathway such as glycolysis could not exist independently of enzymes. Glucose, for example, can react directly with ATP to become phosphorylated at one or more of its carbons. In the absence of enzymes, this occurs so slowly as to be insignificant. However, if hexokinase is added, these slow reactions continue to take place except that phosphorylation at carbon 6 occurs so rapidly that if the mixture is tested a short time later, glucose-6-phosphate is found to be the only significant product. Consequently, the network of metabolic pathways within each cell depends on the set of functional enzymes that are present.

While it is clear that enzymes are responsible for the catalysis of almost all biochemical reactions, it is important to also recognize that rarely, if ever, do enzymatic reactions proceed in isolation. The most common scenario is that enzymes catalyze individual steps of multi-step metabolic pathways, as is the case with glycolysis, gluconeogenesis or the synthesis of fatty acids. As a consequence of these lock- step sequences of reactions, any given enzyme is dependent on the activity of preceding reaction steps for its substrate.

In humans, substrate concentration is dependent on food supply and is not usually a physiologically important mechanism for the routine regulation of enzyme activity. Enzyme concentration, by contrast, is continually modulated in response to physiological needs. Three principal mechanisms are known to regulate the concentration of active enzyme in tissues:

1. Regulation of gene expression controls the quantity and rate of enzyme synthesis.

 2. Proteolytic enzyme activity determines the rate of enzyme degradation.

3. Covalent modification of preexisting pools of inactive proenzymes produces active enzymes.

Enzyme synthesis and proteolytic degradation are comparatively slow mechanisms for regulating enzyme concentration, with response times of hours, days or even weeks. Proenzyme activation is a more rapid method of increasing enzyme activity but, as a regulatory mechanism, it has the disadvantage of not being a reversible process. Proenzymes are generally synthesized in abundance, stored in secretory granules and covalently activated upon release from their storage sites. Examples of important proenzymes include pepsinogen, trypsinogen and chymotrypsinogen, which give rise to the proteolytic digestive enzymes. Likewise, many of the proteins involved in the cascade of chemical reactions responsible for blood clotting are synthesized as proenzymes. Other important proteins, such as peptide hormones and collagen, are also derived by covalent modification of precursors.

Another mechanism of regulating enzyme activity is to sequester enzymes in compartments where access to their substrates is limited. For example, the proteolysis of cell proteins and glycolipids by enzymes responsible for their degradation is controlled by sequestering these enzymes within the lysosome.

In contrast to regulatory mechanisms that alter enzyme concentration, there is an important group of regulatory mechanisms that do not affect enzyme concentration, are reversible and rapid in action, and actually carry out most of the moment- to- moment physiological regulation of enzyme activity. These mechanisms include allosteric regulation, regulation by reversible covalent modification and regulation by control proteins such as calmodulin. Reversible covalent modification is a major mechanism for the rapid and transient regulation of enzyme activity. The best examples, again, come from studies on the regulation of glycogen metabolism where phosphorylation of glycogen synthase and glycogen phosphorylase kinase results in the stimulation of glycogen degradation while glycogen synthesis is coordinately inhibited. Numerous other enzymes of intermediary metabolism are affected by phosphorylation, either positively or negatively. These covalent phosphorylations can be reversed by a separate sub-subclass of enzymes known as phosphatases. Recent research has indicated that the aberrant phosphorylation of growth factor and hormone receptors, as well as of proteins that regulate cell division, often leads to unregulated cell growth or cancer. The usual sites for phosphate addition to proteins are the serine, threonine and tyrosine R group hydroxyl residues.

Enzyme production (transcription and translation of enzyme genes) can be enhanced or diminished by a cell in response to changes in the cell's environment. This form of gene regulation is called enzyme induction and inhibition. For example, bacteria may become resistant to antibiotics such as penicillin because enzymes called beta-lactamases are induced that hydrolyse the crucial beta-lactam ring within the penicillin molecule. Another example are enzymes in the liver called cytochrome P450 oxidases, which are important in drug metabolism. Induction or inhibition of these enzymes can cause drug interactions.

Enzymes can be compartmentalized, with different metabolic pathways occurring in different cellular compartments. For example, fatty acids are synthesized by one set of enzymes in the cytosol, endoplasmic reticulum and the Golgi apparatus and used by a different set of enzymes as a source of energy in the mitochondrion, through β-oxidation.

Enzymes can be regulated by inhibitors and activators. For example, the end product(s) of a metabolic pathway are often inhibitors for one of the first enzymes of the pathway (usually the first irreversible step, called committed step), thus regulating the amount of end product made by the pathways. Such a regulatory mechanism is called a negative feedback mechanism, because the amount of the end product produced is regulated by its own concentration. Negative feedback mechanism can effectively adjust the rate of synthesis of intermediate metabolites according to the demands of the cells. This helps allocate materials and energy economically, and prevents the manufacture of excess end products. Like other homeostatic devices, the control of enzymatic action helps to maintain a stable internal environment in living organisms.

Enzymes can be regulated through post-translational modification. This can include phosphorylation, myristoylation and glycosylation. For example, in the response to insulin, the phosphorylation of multiple enzymes, including glycogen synthase, helps control the synthesis or degradation of glycogen and allows the cell to respond to changes in blood sugar. Another example of post-translational modification is the cleavage of the polypeptide chain. Chymotrypsin, a digestive protease, is produced in inactive form as chymotrypsinogen in the pancreas and transported in this form to the stomach where it is activated. This stops the enzyme from digesting the pancreas or other tissues before it enters the gut. This type of inactive precursor to an enzyme is known as a zymogen.

Some enzymes may become activated when localized to a different environment (eg. from a reducing (cytoplasm) to an oxidising (periplasm) environment, high pH to low pH etc). For example, hemagglutinin of the influenza virus undergoes a conformational change once it encounters the acidic environment of the host cell vesicle causing its activation.

Involvement in disease Phenylalanine hydroxylase. Created from PDB 1KW0Since the tight control of enzyme activity is essential for homeostasis, any malfunction (mutation, overproduction, underproduction or deletion) of a single critical enzyme can lead to a genetic disease. The importance of enzymes is shown by the fact that a lethal illness can be caused by the malfunction of just one type of enzyme out of the thousands of types present in our bodies.

One example is the most common type of phenylketonuria. A mutation of a single amino acid in the enzyme phenylalanine hydroxylase, which catalyzes the first step in the degradation of phenylalanine, results in build-up of phenylalanine and related products. This can lead to mental retardation if the disease is untreated.

Another example is when germline mutations in genes coding for DNA repair enzymes cause hereditary cancer syndromes such as xeroderma pigmentosum. Defects in these enzymes cause cancer since the body is less able to repair mutations in the genome. This causes a slow accumulation of mutations and results in the development of many types of cancer in the sufferer.

An enzyme's name is often derived from its substrate or the chemical reaction it catalyzes, with the word ending in -ase. Examples are lactase, alcohol dehydrogenase and DNA polymerase. This may result in different enzymes, called isoenzymes, with the same function having the same basic name. Isoenzymes have a different amino acid sequence and might be distinguished by their optimal pH, kinetic properties or immunologically. Furthermore, the normal physiological reaction an enzyme catalyzes may not be the same as under artifical conditions. This can result in the same enzyme being identified with two different names. E.g. Glucose isomerase, used industrially to convert glucose into the sweetener fructose, is a xylose isomerase in vivo.

Energy releasing processes, ones that "generate" energy, are termed exergonic reactions. Reactions that require energy to initiate the reaction are known as endergonic reactions. All natural processes tend to proceed in such a direction that the disorder or randomness of the universe increases (the second law of thermodynamics).

 Time-energy graphs of an exergonic reaction (top) and endergonic reaction (bottom). Images from Purves et al., Life: The Science of Biology, 4th Edition, by Sinauer Associates and WH Freeman, used with permission.