Introduction to Molecular Biology: From Cells to Atoms - Anthony Rees, Michael Sternberg 2002

Proteins
Energy and Forces

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Fig. 7.1.

Free energy is a quantity that can be defined as the portion of a chemical system's internal energy that can be harnessed to perform work on the surroundings. To determine whether a given process will occur spontaneously, one calculates The change in free energy (commonly denoted as ∆G) between the final and initial states of the system under consideration (∆G = G_final — G_initial). If ∆G is negative, the system will perform work spontaneously (much like a weight lifted to a certain height and ready to fall); conversely, if ∆G > 0, the system cannot perform work without an additional external energy input. When ∆G = 0, the system is in a state of thermodynamic equilibrium. AG is measured in joules (or kilojoules) per mole of substance (J/mol or kJ/mol).

∆G = ∆H — T∆S is an equation indicating that ∆G has two components at a constant Temperature T (measured on the absolute Kelvin temperature scale). One of these is the change in enthalpy (∆H), which can be equated to the change in potential energy of the system; this parameter is related to the energetic state of the molecules within the chemical system. The other parameter, the change in Entropy (∆S), multiplied by T, is a measure of the energy that cannot be used to perform useful work. Entropy itself (S) increases with the degree of disorder in the system and serves as a measure of its randomness. Thus, ∆S is positive if the system becomes less ordered (Chapter 44).

The Standard Free Energy change of a chemical reaction, designated as ∆G°, represents the value of ∆G when the concentration of each reactant is 1 mol ∙ L^-1 at THE START OF the reaction, with all reactants and products under standard conditions. For a reaction proceeding under standard conditions, ∆G° is related to the Equilibrium Constant K’ by the equation ∆G° = —RTlnK’, where R is the universal gas constant and T is the absolute temperature. Biochemists frequently use a slightly modified form of AG°, denoted by the symbol ∆G°' (Chapter 44).

A covalent bond is a chemical bond between atoms within a molecule. It is formed by the sharing of electrons belonging to one or more atoms. Covalent bonds are strong bonds: the AG of their formation is approximately —300 to —400 kJ/mol. To prevent such a large amount of energy from being wasted, any biochemical process is organized so that the Cleavage of a covalent bond is invariably energetically coupled with The formation of another covalent bond.

Adenosine triphosphate (ATP) serves as an energy source for a vast number of biochemical reactions.

Its Structure is described in Chapter 17. The —P—O—P— bonds store a significant amount of energy. The hydrolytic Cleavage of the terminal (in this case, γ-) phosphate group to yield adenosine diphosphate (ADP) and inorganic phosphate (P_i) is characterized by ∆G° = —30 kJ/mol:

ATP ↔ ADP + P_i

Approximately the same amount of energy is released upon the cleavage of the second (i.e., β-) phosphate. All of this energy can be used to drive a biochemical reaction, including one that is not spontaneous under standard conditions. Consider a reaction of the type X ↔ Y, for which ∆G° is, say, +20 kJ/mol. If The conversion of X to Y is coupled with ATP Hydrolysis, the overall reaction will be

ATP + X ↔ ADP + P_i + Y,

and its ∆G° will be approximately (—30 + 20) kJ/mol = —10 kJ/mol, meaning the reaction will proceed spontaneously under standard conditions.

A non-covalent bond refers to an interaction between atoms that are not covalently bound to each other. We will examine these interactions in more detail later using Cell/13.html">Protein Structure as an example, but they also occur in other biological molecules. Since non-covalent interactions take place in solution rather than in a vacuum, their evaluation requires taking the Influence of the solvent into account.

The stability of a folded protein molecule in solution relative to its unfolded state is typically about —40 kJ/mol (for example, in a Lysozyme molecule). This means that 40 kJ of energy is released for every mole of lysozyme transitioning from the unfolded to the folded state.

Electrostatic effects constitute a significant portion of the enthalpy contribution of non-covalent interactions to AG. Opposite charges attract each other; thus, it is energetically favorable for them to approach one another. According to Coulomb's law, the interaction energy between two charges q₁ and q₂ separated by a distance r is directly proportional to the ratio

q₁q₂ / εr,

where ε is the Dielectric Constant of the medium (ε serves as a measure of the medium's ability to shield charged atoms). In a vacuum, ε = 1; inside a protein molecule, it is approximately 4; and in Water, ε = 80. Using Coulomb's law, it can be shown that bringing positive and inverse elementary charges from infinity to a distance of 0.3 nm is accompanied by a thermodynamically favorable free energy change of approximately —500 kJ/mol in a vacuum, —125 kJ/mol inside a protein molecule, and —6 kJ/mol in water.

An ionic bond (salt bridge) is formed when two oppositely charged atoms come into close proximity (0.3 nm). Within a protein molecule itself, the —COO^- group of a glutamate side chain and the —NH⁺₃ group of a Lysine side chain can interact much like low-molecular-weight salt ions, forming a salt bridge. If, however, such a bridge does not form, the side chains can interact with the solvent, which also decreases the Free energy of the system. Therefore, although salt bridge formation is thermodynamically favorable, it is characterized by a ∆G of only about —4 kJ/mol, which is much smaller than the value predicted by Coulomb's law.

Hydrogen Bonds. When a hydrogen atom is bound to an electronegative atom such as oxygen or nitrogen, a shift in electron density occurs, resulting in a partial positive charge (denoted as δ⁺) on the hydrogen atom and a partial negative charge (denoted as δ^-) on its partner. This creates an electric dipole that can interact with other dipoles. A bond of this type is called a Hydrogen bond. In protein molecules, the backbone >N—H and >C=O groups frequently participate in hydrogen bond formation. The ∆G of hydrogen bond formation in a vacuum is approximately —20 kJ/mol. However, these same >N—H and >C=O groups of a protein molecule could alternatively interact with surrounding water molecules—an interaction that is also thermodynamically favorable—making the actual ∆G of hydrogen bond formation within a protein molecule about —3 kJ/mol.

Van der Waals forces cause atoms to attract one another. Such attractive forces between atoms arise, in part, from interactions between fluctuating electric dipoles formed by the electron cloud and the positive Nucleus of each atom. However, two atoms can approach each other only until their electron clouds begin to overlap; further approach results in strong repulsion. The energy of this interaction is described by the expression

A/r¹² — B/r⁶

where A and B are constants that depend on the type of atoms involved. Thus, due to the competition between two opposing effects—the attractive effect (—B/r⁶) and the repulsive effect (A/r¹²)—it is logical to assume that an optimal (equilibrium) distance exists between any two atoms. This leads to METABOLISM/2.html">THE CONCEPT OF the effective atomic radius, commonly referred to as the van der Waals radius.

The structure of water surrounding a molecule significantly affects the entropy of the system. Normally, water molecules are in motion in solution, constantly forming and breaking hydrogen bonds with one another. When water molecules are forced into a rigid, ice-like configuration, however, the degree of order increases, which is thermodynamically unfavorable due to the decrease in entropy.

The hydrophobic effect is the tendency of non-polar groups to associate with one another to avoid contact with water. This association disrupts the water structure, resulting in an increase in the system's entropy. Examples of non-polar groups include the aliphatic and aromatic side chains of protein amino acid residues (Chapter 6) and nucleic acid bases (Chapter 17).

Thermal motion is the random movement of atoms and molecules that determines the temperature of a system. The fraction (f) of molecules whose thermal energy exceeds a certain arbitrarily chosen value E is given by the Boltzmann equation:

f = exp (-E/RT),

where R is the universal gas constant and T is the absolute temperature. Thus, the fraction of molecules with an energy greater than RT (= 2.5 kJ/mol at room temperature) is equal to exp(-1), or 0.37. Therefore, bond energies must exceed 2.5 kJ/mol; otherwise, they will be easily broken and reformed As a result of thermal motion. Consequently, bonds formed by van der Waals forces, and sometimes even Hydrogen bonds and salt bridges, are continually broken and re-formed.