# Principles of Bioenergetics

Bioenergetics is the quantitative study of the energy transductions that occur in living cells and of the nature and function of the chemical processes underlying these transductions. The first law of thermodynamics tells us that the total energy of an isolated system consisting of a cell (or organism) and its surroundings is the same before and after a series of events or chemical reactions has taken place. The second law of thermodynamics states that in all processes involving energy changes within a system, the entropy of the system increases until an equilibrium is attained. Entropy can be thought of as the energy of a system that is of no value for performing work (it is not useful energy per say). For example, the catabolism of sucrose or other sugars by a cell is accompanied by the formation of energy-rich ATP. The entropy change during a reaction may be quite small. For example, when sucrose undergoes hydrolysis to form the sugars glucose and fructose, much of the potential energy of the original sucrose is present in the resulting glucose and fructose molecules. Changes in entropy are extremely difficult to calculate but the difficulty can be circumvented by employing two other thermodynamic functions: enthalpy or heat content (H) and free energy (G). The change in a system’s enthalpy (∆H) is a measure of the total change in energy that has taken place, whereas the change in free energy (∆G) is the change in the amount of energy available to do work. Changes in entropy (∆S), enthalpy, and free energy are related by the equation in which T is the absolute temperature of the system.

∆G = ∆H – T∆

The change in free energy can also be defined as the total amount of free energy in the products of a reac­tion minus the total amount of free energy in the reactants. That is:

∆G = G products – Greactants

A reaction that has a negative ∆G value ( the sum of the free energy of the products is less than that of the reactants) will occur spontaneously and a reaction for which the ∆G is zero is at equilibrium. A reaction that has a positive ∆G value will not occur spontaneously and proceeds only when energy is supplied from some outside source. The composition of a reacting system (a mixture of chemical reactants and products) will tend to continue changing until equilibrium is reached. At the equilibrium concentration of reactants and products, the rates of the forward and reverse reactions are exactly equal and no further net change occurs in the system. The concentrations of reactants and products at equilibrium define the equilibrium constant. In the general reaction:

aA + bB  cC + dD,

where a, b, c, and d are the number of molecules of A, B, C, and D participating, the equilibrium constant is given by:

 Keq = [C]c[D]d [A]a[B]b

where [A], [B], [C], and [D] are the molar concentrations of the reaction components at the point of equilibrium. When a reacting system is not at equilibrium, the tendency to move toward equilibrium represents a driving force, the magnitude of which can be expressed as the free-energy change for the reaction, ΔG. Under standard conditions, when reactants and products are initially present at 1 M concentrations or, for gases, at partial pressures of 101.3 kPa (1 atm), the force driving the system toward equilibrium is defined as the standard free-energy change, ΔG° By this definition, the standard state for reactions that involve hydrogen ions is [H+] = 1 M, or pH is 0. Most biochemical reactions occur in well buffered aqueous solutions near pH 7 and both the pH and the concentration of water are essentially constant. For convenience of calculations, biochemists therefore define a slightly different standard state, in which the concentration of H+ is 10-7M (pH is 7) and that of water is 55.5 M. Physical constants based on this biochemical standard state are written with a prime (ΔG°’ and K’eq) to distinguish them from the constants used by chemists and physicists. Under this convention, when H2O or H+ are reactants or products, their concentrations are not included in the typical equations but are instead incorporated into the constants ΔG°’ and K’eq .Just as K’eq is a physical constant characteristic for each reaction, so too is ΔG°’ a constant. There is a simple relationship between K’eq and ΔG°’:

ΔG°’ = -RT ln K’eq

The standard free-energy change of a chemical reaction is simply an alternative mathematical way of expressing its equilibrium constant. If the equilibrium constant for a given chemical reaction is 1.0, the standard free energy change of that reaction is 0.0 (the natural logarithm of 1.0 is zero ). If K’eq of a reaction is greater than 1.0, its ΔG°’ is negative. If K’eq is less than 1.0, ΔG°’ is positive. Because the relationship between ΔG°’ and K’eq is exponential, relatively small changes in ΔG°’ correspond to large changes in K’eq.

Sucrose + H2O → glucose + fructose

has a negative ∆G value, and therefore when sucrose is added to water, there is the spontaneous conversion of some of the sucrose molecules to glucose and fruc­tose. However, the reverse reaction

glucose + fructose →sucrose + H2O

has an equal but positive ∆G value and therefore does not occur without an input of energy. Hence, special attention must be paid to the direction in which the reaction is written and the sign of the ∆G value. Thus, ∆G values are dependent on the amounts and concentrations of reac­tants and products. More uniform standards of refer­ence that have been established by convention are the standard free energy changes, ∆G0 and ΔG°’ values. ∆G0 represents the change in free energy that takes place when the reactants and products are maintained at 1.0 molar concentrations during the course of the reaction and the reaction proceeds under standard conditions of temperature (25°C) and pressure (1 atmosphere) and at pH 0.0. The ΔG°’ value is a much more practical term for use with biological systems in which reactions take place in an aqueous environment and at a pH that usually is either equal or close to 7.0. The ΔG°’ value is defined as the standard free energy change that takes place at pH 7.0 when the reactants and products are main­tained at 1.0 molar concentration

ATP hydrolysis is the reaction by which chemical energy that has been stored in the high-energy phosphoanhydride bonds in adenosine triphosphate (ATP) is released, for example in muscles, by producing work in the form of mechanical energy. The product is adenosine diphosphate (ADP) and an inorganic phosphate(Pi). ADP can be further hydrolyzed to give energy, adenosine monophosphate (AMP), and another orthophosphate (Pi). ATP hydrolysis is the final link between the energy derived from food or sunlight and useful work such as muscle contraction, the establishment of electrochemical gradients across membranes, and biosynthetic processes necessary to maintain life. The hydrolytic cleavage of the terminal phosphoric acid anhydride (phosphoanhydride) bond in ATP separates off one of the three negatively charged phosphates and thus relieves some of the electrostatic repulsion in ATP. The Pi released by hydrolysis is stabilized by the formation of several resonance forms not possible in ATP and ADP2- , the other direct product of hydrolysis, immediately ionizes, releasing H+ into a medium of very low [H+](~10-7 M). The low concentration of the direct products favors, by mass action, the hydrolysis reaction. Although its hydrolysis is highly exergonic (ΔG°’ = -30.5 kJ/mol), ATP is kinetically stable toward non-enzymatic breakdown at pH 7 because the activation energy for ATP hydrolysis is relatively high. Rapid cleavage of the phosphoric acid anhydride bonds occurs only when catalyzed by an enzyme. Although the ΔG°’ for ATP hydrolysis is -30.5 kJ/mol under standard conditions, the actual free energy of hydrolysis (ΔG) of ATP in living cells is very different. This is because the concentrations of ATP, ADP, and Pi in living cells are not identical and are much lower than the standard 1.0 M concentrations. Furthermore, the cytosol contains Mg2+, which binds to ATP and ADP. In most enzymatic reactions that involve ATP as phosphoryl donor, the true substrate is MgATP2- and the relevant ΔG°’ is that for MgATP2- hydrolysis.

Direct hydrolysis of ATP consists of nucleophilic attack by H2O at the γ phosphate position of ATP and cleavage of the γ- β phosphoanhydride bond. Group transfer reactions involve the covalent transfer of a portion of the ATP molecule to a substrate (e.g. an enzyme active site), which in turn makes subsequent metabolic reactions involving this substrate more thermodynamically favorable. Table 1 classifies the three group transfer reactions that involve ATP by the phosphate position of ATP at which nucleophilic attack occurs.

Table 1. Group transfer reactions involving ATP

 Phosphate position of ATP Group transferred Phosphoryl transfer γ −PO​3​2−​​ Pyrophosphoryl transfer β −PO​3​​PO​3​3−​​ Adenylyl transfer α −PO​3​−​​Adenosine

Adenylyl transfer has the largest negative standard free energy change, and is commonly coupled to biological reactions that have a particularly large positive standard free energy change. One example is fatty acid adenylylation, in which exergonic adenylylation of fatty acid (initiating by nucleophilic attack by the carboxylate ion of the fatty acid) and pyrophosphatase-catalyzed pyrophosphate hydrolyzation is coupled to endergonic condensation of fatty acid and coenzyme A, yielding fatty acyl-coA, AMP, and two inorganic phosphate molecules:

fatty acid + CoA + ATP → fatty-acyl-CoA + AMP + P​i

​​ ΔG°’ = 34 kJ/mol

Many key enzymes in ATP synthesis and other biochemical pathways have oxidoreductase activity. Oxidation–reduction reactions can be broken into their half-reaction components to determine the number of electrons being transferred. For example, in lactic acid fermentation, pyruvate and NADH are converted to lactate and NAD+ by lactate dehydrogenase. This reaction can be broken down into half-reactions as follows:

Oxidation-reduction reactions (Redox reactions) must occur together. Electrons are transferred from the reducing agent to the oxidizing agent such that the reducing agent is oxidized and the oxidizing agent is reduced.2 It is convenient however to describe the electron transfer reaction as two half reactions, one for the oxidation of the reduced species and one for the reduction of the oxygen species. Oxidation–reduction reactions are characteristic of oxidoreductase enzymes. A half reaction consists of an electron donor and its conjugate electron acceptor. Take a moment to identify the oxidizing and reducing agents in the reaction catalyzed by lactate dehydrogenase.

In the cytoplasm, there are several molecules that act as high-energy electron carriers. These are all soluble and include NADH, NADPH, FADH2, ubiquinone, cytochromes, and glutathione. Some of these electron carriers are used by the mitochondrial electron transport chain, which leads to the oxidative phosphorylation of ADP to ATP. As electrons are passed down the electron transport chain, they give up their free energy to form the proton-motive force across the inner mitochondrial membrane. In addition to soluble electron carriers, there are membrane-bound electron carriers embedded within the inner mitochondrial membrane. One such carrier is flavin mononucleotide (FMN), which is bound to complex I of the electron transport chain and can also act as a soluble electron carrier. In general, proteins with prosthetic groups containing iron–sulfur clusters can act in the transport of electrons. Flavoproteins contain a modified vitamin B2, or riboflavin.3 They are nucleic acid derivatives, generally either flavin adenine dinucleotide (FAD) or flavin mononucleotide (FMN). Flavoproteins are most notable for their presence in the mitochondria and chloroplasts as electron carriers. Flavoproteins are also involved in the modification of other B vitamins to active forms. Finally, flavoproteins function as cofactors for enzymes in the oxidation of fatty acids, the decarboxylation of pyruvate, and the reduction of glutathione. Deficiency of riboflavin, a key component of flavoproteins, leads to a lack of growth, failure to thrive, and eventual death in experimental models. In humans, riboflavin deficiency is very rare, but may occur in severely malnourished individuals.3

References

1) Cermak, N. (2009, March 12). Fundamentals of Enzyme Kinetics: Michaelis-Menten and Deviations. Retrieved from http://cermak.scripts.mit.edu/papers/383final_cermak_enzymekinetics_20090312.pdf

2) Aboazma, S. M. (2014). Biological Oxidation. Retrieved from http://www1.mans.edu.eg/FacMed/english/dept/biochemistry/pdf/OXIDATION.pdf

3) Miles, B. (2003, January 17). Biological Redox Reactions. Retrieved from Texas A&M University: https://www.tamu.edu/faculty/bmiles/lectures/Biological%20Redox%20Reactions.pdf

4) Stephen J. Blanksby, G. B. (2002, August 6). Bond Dissociation Energies of Organic Molecules. Retrieved from Michigan State University: http://www2.chemistry.msu.edu/courses/cem850/handouts/Ellison_BDEs.pdf

5) Pearson. (2011). Thermodynamic versus Kinetic control reactions. Retrieved from http://www.chem.mun.ca/courseinfo/c2400/YZ/Chapter-7c.pdf

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