1.5 Energetics of Life

The ability of a cell to move, to grow, and to reproduce require some input of energy. The cell in question must also extract this energy from the environment and store or use it in a manageable form.

Nevertheless, bioenergetics may be regarded as a special part of thermodyanmics: the general science of energy transformations.

1.5.1 Gibbs’ free energy

The change in Gibbs’ free energy \(\Delta G\)2 is denoted by:

\[\begin{equation} \Delta G = \Delta H - T \Delta S \tag{1.1} \end{equation}\]

Where:

  1. \(\Delta H\) represents the change in enthalpy (i.e., the heat content of the system) in the system
  2. \(T\) represents the temperature of the system in Kelvins
  3. \(\Delta S\) represents the change in entropy (i.e., how disordered the system is) in the system

Hence, the free energy change indicates whether a biological process will require energy or release energy (into its environment); if the system releases energy, the \(\Delta G\) will also indicate the amount of energy necessary for the process to perform useful work.

Gibbs' Free Energy Guidelines

Figure 1.20: Gibbs’ Free Energy Guidelines

Several rules and definitions have been laid for out differing values of \(\Delta G\) in figure 1.20. When a process has a negative \(\Delta G\), it is said to be exergonic. Otherwise, it is said to be endergonic.

Classical thermodynamics have also shown that the free energy of any component of the system from its standard value shares a logarithmic dependence on its activity.

Hence, we can define several new equations for \(\Delta G\) and for \(K\) (i.e., the equilibrium constant):

\[\begin{align} \Delta G &= \Delta G^{\omicron} + RT\ln(Q) \\ \Delta G^{\omicron} &= -RT\ln(K) \\ K &= e^{\frac{-\Delta G^\omicron}{RT}} \end{align}\]

Where:

  1. \(\Delta G^\omicron\) is the standard free energy change (i.e., the reference value).
  2. \(R\) is the gas constant (i.e., 8.314 J / K mol)
  3. \(T\) is the temperature in Kelvins
  4. \(Q\) is the ratio of concentrations
  5. \(K\) is the equilibrium constant

1.5.2 Free energy in Biological systems

Structure of ATP

Figure 1.21: Structure of ATP

Energetically unfavorable processes are generally coupled with reactions that have a large, negative free energy change (i.e., \(\Delta G^\omicron\)). Many of these “[e]nergetically unfavorable processes” are coupled with the dephosphorylation of ATP: a molecule that is capable of transferring a phosphoryl group to an acceptor molecule.

1.5.2.1 Some more examples

1.5.2.1.1 Mechanically…
Mechanical Example of Free Energy

Figure 1.22: Mechanical Example of Free Energy

In figure 1.22, the downward motion of an object releases potential energy that can do mechanical work. The potential energy made available by spontaneous downward motion, an exergonic process (i.e., the pink part of 1.22), can be coupled to the endergonic upward movement of another object (i.e., the blue part of 1.22).

1.5.2.1.2 Chemically…
Chemical Example of Free Energy

Figure 1.23: Chemical Example of Free Energy

Figure 1.23 can be broken down into two parts:

In reaction 1, the formation of glucose-6-phosphate from glucose and inorganic phosphate (i.e., Pi) is an endergonic reaction.

In the next reaction (i.e., reaction 2), the dephosphorylation of ATP is capable of driving an endergonic reaction. \(\Delta G_2\) represents the large, negative change in free energy of this reaction.

In the final reaction (i.e., reaction 3), the free energy change \(\Delta G_3\) is the sum of \(\Delta G_1\) and \(\Delta G_2\). The overall reaction is exergonic and proceeds spontaneously.

  1. This equation assumes a constant temperature and pressure!↩︎