Biochemical Reactions and Enzyme Kinetics

Chemical Reactions

Consider the following single-stage chemical reaction

in which chemicals A and B react to form the product P, with reaction rate constant K. Equation (8.1) is known as a stoichiometric equation that lists the number of reactants on the left side necessary to form the product on the right side. Conservation of mass requires that the total quantity of reactant A must equal the quantity of A in the reactant and the product, and likewise, the same is true with reactant B. The stoichiometric equation does not describe the dynamics or kinetics of the chemical reaction—that is, the time course of the reaction that may be very fast or very slow. The kinetics of the reaction is written according to the law of mass action. The arrow in Eq. (8.1) shows the direction of the reaction that occurs spontaneously, and the reaction rate constant describes how quickly the reaction occurs. The reaction rate constant is a function of temperature, whereby an increase in temperature generally increases K. For our purposes, temperature is constant and so is K.

Chemical Bonds

Individual atoms rarely appear in nature, but they appear within a molecule. Molecules are collections of atoms that are held together by strong chemical bonds in which electron(s) are shared or electron(s) are transferred from one atom to another. Forces between molecules are relatively weak, allowing molecules to act independently of one another. A compound is a molecule that contains at least two different atoms, whereas a molecule can contain just one type of atom. Molecules such as hydrogen, H2, and oxygen, O2, are not compounds because they consist of a single type of atom. For simplicity in presentation, we will use the term molecules to describe both molecules and compounds.

An atom is an electrically neutral particle that consists of an equal number of protons and electrons. An atom with an unbalanced number of electrons or protons is called an ion, which makes it a positively or negatively charged particle. Examples of positively charged ions, called cations, include Na+, K+, and Ca+2; Na+ and K+ have each lost one electron, and Caþ2 has lost two electrons. An example of a negatively charged ion, called an anion, is Cl, which has gained an extra electron.

There are many types of chemical bonds that join atoms and molecules together. They vary in strength, with ionic and covalent bonds displaying the strongest bonds, and the hydrogen bond displaying the weakest bond.

Many molecules are composed of positively and negatively charged ions that are bound by an ionic bond. These bonds are extremely strong due to the electrostatic attraction between the oppositely charged ions. Ionic bonds usually involve an atom that has few electrons in the outer shell, with another atom that has an almost complete set of electrons in the outer shell. Ionic bonds involve a transfer of electrons from one atom to another atom. Consider sodium chloride, where sodium has one electron in the outer shell and chloride has seven electrons in its outer shell. The bond is formed by sodium transferring its electron to chloride, resulting in a molecule consisting of Na+ Cl-(usually written as NaCl) Consider magnesium and oxygen atoms forming an ionic bond. Magnesium has two electrons in its outer field that are transferred to oxygen, forming Mg+2 O-2 .

Covalent bonds involve two atoms sharing an electron pair that increases the stability of the molecule. The atoms do not have to be the same type, but they must be the same electronegativity. For instance, H2 is formed by a covalent bond. Consider carbon dioxide, a molecule that consists of one carbon and two oxygen atoms. These atoms share the electrons, with carbon having four electrons in its outer shell, and oxygen having six electrons in its outer shell. The four electrons in carbon are used in the outer shell of the two oxygen atoms.

A hydrogen bond involves the force between a hydrogen atom in one molecule and an electronegative atom in another molecule, typically with oxygen in H2O, nitrogen in NH3, and fluorine in HF: Note that the force experienced in a hydrogen bond is not within a molecule but between molecules. The small size of hydrogen allows it to become very close to another molecule with a small atomic radii like the ones previously mentioned.

An example of a hydrogen bond is found among water molecules. The oxygen in water, which is negatively charged, binds to two positively charged hydrogens from two other water molecules. These bonds connect the water molecules together and give it some unusual properties, such as high surface tension and viscosity. Keep in mind that this bond is a relatively weak bond compared to that holding the water molecule together. As water is heated to the boiling point, all of the hydrogen bonds are dissolved as it becomes a gas. When water freezes, the hydrogen bonds form a structured, less dense orientation. Between freezing and boiling, water is oriented in very dense, random configuration. Hydrogen also plays an important role within proteins and nucleic acids, which allows bonding within the molecule to achieve different shapes.

A chemical reaction in which a molecule loses electrons is called oxidation, and a gain of electrons is called reduction. Some multistage chemical reactions involve both oxidation and reduction. Energy is released when a chemical bond is formed, which is the same amount of energy necessary to break that chemical bond. Thus, chemical bonds store energy. The first step in a chemical reaction requires energy to break the bonds holding the reactant molecules together so they can be rearranged to form an activated complex, an unstable high-energy intermediate. From the activated complex, the molecules join together to form the product and typically release energy. In chemical reactions, if the energy stored in the chemical bonds of the product is less than the total energy stored in the reactants, then net energy is released. The amount of energy required in a chemical reaction is inversely proportional to the reaction rate constant.

Enzyme Kinetics

As described earlier, catalysts are substances that accelerate reactions but are not consumed or changed by the reaction. Most chemical reactions in the body can occur without the presence of catalysts, but they occur at a very low rate. An enzyme is a large protein that catalyses biochemical reactions in the body. These reactions convert a reactant, now called a substrate because it involves an enzyme, into a product by lowering the free energy of activation. Enzymes can increase the rate of the reaction by an order of thousands to trillions. Each enzyme is highly specific and only allows a particular substrate to bind to its active site. Many enzymes are used in the control and regulation of functions of the body.

In general, an enzyme reaction involves a series of reactions. Binding the enzyme with the substrate is the first step in creating an intermediate complex, which increases the ability of the substrate to react with other molecules. The next step is when the substrate enzyme complex breaks down to form the free enzyme and product. Both the first step and the second step are reversible, but in the second step, the reverse reaction is so small that it is often omitted.

The overall rate of the enzyme catalysed reaction with a single substrate is a function of the amount of enzyme and substrate and is given as

where K2 and KM are reaction rate constants (KM is called the Michaelis constant). We will derive and discuss this equation in more detail later in this section.

In an enzyme catalysed reaction with much more substrate than enzyme, the reaction rate depends linearly on enzyme concentration according to Eq. (8.32), since the substrate concentration is essentially a constant. When there is much more enzyme than substrate, only a small portion of the enzyme is combined with the substrate, and the reaction rate is determined by both the enzyme and substrate levels. The typical enzyme catalysed reaction consists of a series of reactions, each step with its own reaction rate. As we will see, the overall reaction rate is determined by the slowest reaction in the chain of reactions. The slowest reaction is called the capacity-limited reaction.

Enzyme catalysed reactions serve a regulatory role, as well as accelerating biochemical reactions. Consider the relationship between adenosine diphosphate (ADP) and ATP inside the cell. ATP is created in the mitochondria where oxidation of nutrients (carbohydrates, proteins, and fats) produces carbon dioxide, water, and energy. The energy from the oxidation of nutrients converts ADP into ATP. ATP is used as fuel for almost all activities of the body, such as the Na K pump, action potentials, synthesis of molecules, creation of hormones, and contractions of muscles. At steady state, the concentration of ADP is very low in the cell, and thus the creation of ATP in the mitochondria is at a low rate. During periods of high cell activity, ATP is consumed, releasing energy through the loss of one phosphate radical, leaving ADP. The increased concentration of ADP causes an increase in the oxidation of nutrients in the mitochondria, producing more ATP. Thus, the ADP-ATP cycle is balanced and based on the needs of the cell.

Enzyme reactions do not appear to follow the law of mass action; that is, as the substrate increases, the reaction rate does not increase without bound but reaches a saturation level (that is, it is capacity-limited). Capacity-limited reactions are quite prevalent and describe most metabolic reactions and functions of the body, such as the movement of molecules across the cell membrane and how substrates are removed from the body through the kidneys.