Structural Biochemistry/Free energy

General Information

American scientist Josiah Willard Gibbs (1839-1903) had created the theory of available energy, known as Gibbs Free Energy in 1873. The theory relates the energy changes within the chemical reaction and how they depend upon the following quantities: enthalpy, temperature, reagents concentration and entropy of the system. In other words, these quantities will determine whether the reaction is favorable (exergonic) or not (endergonic).

The free energy change of a reaction (delta G) can tell us whether or not a reaction occurs spontaneously. Reactions that occur spontaneously have a negative delta G value, and such reactions are called exergonic. When delta G is positive, the reaction does not occur spontaneously, and the input of free energy is required for the reaction to proceed, thus it is called an endergonic reaction. When a system is at equilibrium where no net change occurs, then delta G is zero. The delta G of a reaction is the free energy of the final state minus the free energy of the initial state, making it is independent of the reaction pathway. However, the value of delta G provides no information on the rate of a reaction.

Gibbs Free Energy Equation

This is a Gibbs free energy graph by Josiah Willard Gibbs. it shows a plane perpendicular to the axis of v (volume) and passing through point A - represents the initial state of the body. MN is the section of the surface of dissipated energy. Qε and Qη are sections of the planes η = 0 and ε = 0, and therefore parallel to the axes of ε (internal energy) and η (entropy), respectively. AD and AE are the energy and entropy of the body in its initial state, AB and AC its Gibbs free energy and its capacity for entropy (the amount by which the entropy of the body can be increased without changing the energy of the body or increasing its volume) respectively.

We often focus on how to manipulate the use of Gibbs free energy equation instead of how to derives it and its derivation. The most commonly used equations for calculation are

$\Delta G = \Delta H - T \Delta S \,$ (for constant temperature) - equation(1)

$\Delta G = -R T \ln K \,$ (for equilibrium constant that depends on temperature) - equation(2)

Where ΔH is change in enthalpy, T is the temperature of the system (in kelvin (K)), ΔS is change in entropy of the system, R is gas constant, K is equilibrium constant.

Numerical Meaning of ΔG

If ΔG < 0 (negative), then the reaction will proceed spontaneously. Meaning the reaction is favorable (exergonic)

If ΔG > 0 (positive), then the reaction will not proceed spontaneously. Meaning the reaction is unfavorable (endergonic)

If ΔG = 0 (equal to zero), then the reaction is at equilibrium

In general, every system wants to achieve a minimum of free energy. Therefore, when Gibbs free energy is negative, the reaction is more favorable.

Standard Gibbs Free Energy of Formation

When we have to consider the relationship between Gibbs free energy and the standard-state free energy of a reaction, we use this equation:

$\Delta G = \Delta G^\circ + R T \ln Q \,$

to calculate Gibbs free energy at that of time under a specific circumstances. Where ΔG^o is the standard-states - reactants (or components) at 25^oC (degrees Celsius) and 1 atm (atmospheric pressure, 1 atm same as 100 kilopascals), Q is the reaction quotient. The motivation behind it is that these elements, reactants, and substances, are thermodynamically stable at such atmosphere.

Free Energy of Enzymes

Free energy determines whether a conversion of reactants to products will occur spontaneously. In the case of an enzyme, ΔG determines the rate of a reaction. Enzymes cannot affect thermodynamics of a reaction, and hence do not affect the equilibrium; Additionally, enzymes accelerate the attainment of equilibria but do not shift their positions. The equilibrium position is a function only of the free-energy difference between reactants and products. They are however, able to reach the equilibrium point at a far faster rate than without the presence of an enzyme.

For instance, in the presence of an enzyme, products could form within a second. On the other hand, products could take a as long as days to form without the presence of the catalyst. In both cases, concentration and amount of product formed remains entirely the same- it's equilibrium state. The amount of products it has formed has balanced with the amount of substrate.

Enzymes decrease only the free energy of activation- otherwise known as the activation energy. The Transition state between a substrate and the product is the point between a reaction where the substrates and products "meet in the middle". At this point, the highest free energy exists for the reaction. The activation energy is the energy it takes for a substrate to reach this transition state.

There are many competing theories of how enzymes actually bind their substrates, and each theory has a different graphic representation of the affect of the enzyme on the free energy of the reaction. In the lock and key mechanism theory, an enzyme has the pre-existing conformation to bind to a unique substrate. After binding and catalyzing the reaction, the enzyme will release the final products.

In the induced-fit mechanism theory, a similar approach is hypothesized. The only difference is that the pre-existing, unbound enzyme does not originally assume the exact conformation to bind the substrate; but rather assumes a slightly different structure prior to binding. Then, as the substrate binds to the enzyme, the structure of the active site conforms around the structure of the substrate to fit properly. Both of these mechanisms can be represented similarly in relation to their effect on the free energy of the reaction. Without really changing the pathway of the energy curve, these models serve to decrease the activation energy of a reaction, thereby increasing the rate of the reaction.

Another model has been suggested however, that appears slightly different on the free energy graph. This is the proposed transition-state model. This model suggests that an enzyme is not structurally adept to bind to the substrate itself, but that it is actually optimized to bind to the transition state of the reaction pathway. This produces a small stabilization of the transition state decreasing the overall activation energy as is characteristic of enzymes. The first increase in energy is due to the binding of the enzyme to the original substrate. The return to original free energy state is stabilization of the enzyme-substrate complex before reaction occurs. The next increase in energy comes from achieving the transition state, and the subsequent fall is the creation of the products. This theory is currently accepted as an alternative because the enzyme-substrate complex of the other theories acquires a very low free energy level due to stabilization. To achieve the transition state after this relatively low level of free energy is much more difficult than achieving the transition state from the relatively more energetically free enzyme-substrate complex suggested in this transition-state model. [1]

Bond Energies

How is energy being used? Is energy being consumed or absorbed in a reaction?

1) Bonds formed = Energy is released because it forms a more stable state. ΔH < 0 heat is released.

2) Bonds broken = Energy is absorbed because breaking a stable state and moving towards a less stable state. ΔH > 0 heat is absorbed.

Bond Energy products > Bond Energy reactants : spontaneous

Bond Energy products < Bond Energy reactants : non-spontaneous

Bond Energy Diagrams

ΔG = G products - G reactants

Note: You cannot switch the equation to be G reactants - G products.

The key is to understand if energy is being overall released or absorbed in a reaction. This will give you the correct sign for your ΔG.

Example of Gibbs Free Energy

References

Reece, Jane (2011). Biology. Pearson. ISBN 978-0-321-55823-7.