Energy and enzymes

Learning Objectives

1. Explain how the 2nd Law of Thermodynamics applies to living organisms
2. Predict the direction of reactions from Gibbs free energy changes, and vice versa
3. Distinguish between steady-state (homeostasis) and chemical equilibrium
4. Use energy diagrams to explain how catalysts increase rates of reaction
5. Plot enzyme kinetics: initial velocity as a function of substrate concentration
6. Distinguish between competitive and noncompetitive inhibition
7. Distinguish between binding of substrate and binding of allosteric regulators to enzymes

How do the laws of thermodynamics apply to living organisms?

• The First Law says that energy cannot be created or destroyed.
• The Second Law says that in any energy conversion, some energy is wasted as heat; moreover, the entropy of any closed system always increases.

One way we can see the Second Law at work is in our daily diet. We eat food each day, without gaining that same amount of body weight! The food we eat is largely expended as carbon dioxide and heat energy, plus some work done in repairing and rebuilding bodily cells and tissues, physical movement, and neuronal activity.

Although living organisms appear to reduce entropy, by assembling small molecules into polymers and higher order structures, this work releases waste heat that increases the entropy of the environment.

Gibbs Free Energy

Gibbs free energy is a measure of the amount of work that is potentially obtainable. Instead of absolute quantities, what is usually measured is the change in free energy:

ΔG = ΔH – TΔS

where H = enthalpy (the heat energy content); T = absolute temperature (Kelvin), and S = entropy (sometimes called disorder, but a complicated and subtle concept that has more to do with degrees of freedom; 6 molecules of CO2 have greater entropy than a molecule of glucose, where the carbon atoms are linked together by covalent bonds).

If ΔG < 0, a chemical reaction is exergonic, releases free energy, and will progress spontaneously, with no input of additional energy (though this does not mean that the reaction will occur quickly – see the discussion about reaction rates below).

If ΔG > 0, a chemical reaction is endergonic, requires or absorbs an input of free energy, and will progress only if free energy is put into the system; else the reaction will go backwards.

Free energy and chemical equilibrium

If ΔG = 0, a chemical reaction is in equilibrium, meaning that the rates of forward and reverse reactions are equal, so there is no net change, or no potential for doing work.

This figure from Wikipedia illustrates that reactions will proceed spontaneously towards equilibrium, in either direction, and that the equilibrium point is the minimum free energy state of the reaction mixture. The x-axis (ξ) represents the ratio of products/reactants.

Cells couple exergonic reactions to endergonic reactions so that the net free energy change is negative

ATP is the primary energy currency of the cell; cells accomplish endergonic reactions such as active transport, cell movement or protein synthesis by tapping the energy of ATP hydrolysis:

ATP -> ADP + Pi (Pi = PO4, inorganic phosphate); ΔG = -7.3 kcal/mol

Over the next pages we’ll be looking at the cellular metabolic pathways that phosphorylate ADP to make ATP.

Reaction rates
Although the sign of ΔG (negative or positive) determines the direction that the reaction will go spontaneously, the magnitude of ΔG does not predict how fast the reaction will go.
The rate of the reaction is determined by the activation energy (the energy required to attain the transition state) barrier Ea:

The peak of this energy diagram represents the transition state: an intermediate stage in the reaction from which the reaction can go in either direction. Reactions with a high activation energy will proceed very slowly, because only a few molecules will obtain enough energy to reach the transition state – even if they are highly exergonic. In the figure above, the reaction from X->Y has a much greater activation energy than the reverse reaction Y->X. Starting with equal amounts of X and Y, the reaction will go in reverse.

The addition of a catalyst (definition: an agent that speeds up the rate of a reaction, but is not consumed or altered by the reaction) provides an alternative transition state with lower activation energy. What this means is that the catalyst physically ‘holds’ the substrates in a physical conformation that makes the reaction more likely to proceed. As a result, in the presence of the catalyst, a much higher percentage of molecules (X or Y) can acquire enough energy to attain the transition state, so the reaction can go faster, in either direction. Note that the catalyst does not affect the overall free energy change of the reaction. Starting with equal amounts of X and Y, the reaction diagrammed above will still go in reverse, only faster, in the presence of the catalyst.

Enzymes speed up reactions by lowering the activation energy barrier

Enzymes are biological catalysts, and therefore not consumed or altered by the reactions they catalyze. They repeatedly bind substrate, convert, and release product, for as long as substrate molecules are available and thermodynamic conditions are favorable (ΔG is negative; the product/substrate ratio is lower than the equilibrium ratio). Most enzymes are proteins, but several key enzymes are RNA molecules (ribozymes). Enzymes are highly specific for their substrates. Only molecules with a particular shape and chemical groups in the right positions can interact with amino acid side chains at the active site (the substrate-binding site) of the enzyme.

Enzyme-catalyzed reactions have saturation kinetics

The velocity of enzyme-catalyzed reactions increases with the concentration of substrate. However, at high substrate concentrations, the quantity of enzyme molecules becomes limiting as every enzyme molecule is working as fast as it can. At saturation, further increases in substrate concentrations have no effect; the only way to increase reaction rates is to increase the amount of enzyme.

The kinetic properties of enzymes are defined by their Vmax and Km

• The Vmax is the maximum rate at which enzymes can work, and represents work at saturating concentrations of substrate.
• The Km (Michaelis constant) is defined as the substrate concentration that produces 1/2 Vmax and is a measure of the affinity of the enzyme for its substrate.

Enzyme inhibitors
Enzymes are subject to regulation, and are the targets of many pharmaceutical drugs, such as non-steroidal pain relievers. Many enzymes are regulated by allosteric regulators which bind at a site distinct from the active site.

Noncompetitive inhibitors act allosterically (bind at a site different from the active site). When the noncompetitive inhibitor binds allosterically, it often changes the overall shape of the enzyme, including the active site, so that substrates can no longer bind to the active site.

Competitive inhibitors compete with the substrate for binding to the active site; the enzyme cannot carry out its normal reaction with the inhibitor, because the inhibitor physically blocks the substrate from binding the active site.

Below are lecture videos on thermodynamics and enzymes (with apologies for the have audio lag).

Powerpoint file used in the videos: free_energy

UN Sustainable Development Goal (SDG) 11: Sustainable Cities and Communities – The ability to catalyze and predict the direction of spontaneous reactions is useful in understanding the thermodynamics of energy conversion processes. Such processes can be optimized for efficiency and reduced waste/pollution, and can be engineered for resiliency in the face of natural disasters, rendering such technologies more sustainable and scalable in the long-term, particularly as cities expand. Furthermore, more nuanced understandings of activation sites and inhibition can be used to more effectively control disease-carrying pest populations in urban areas, making for more sustainable solutions to human-wildlife interactions as areas grow more populated.