CONCEPT OF FREE ENERGY AND THERMODYNAMICS PRINCIPLES
Living cells and organisms must perform work to stay alive, to grow, and to reproduce. The ability to harness energy and to channel it into biological work is a fundamental property of all living organisms; it must have been acquired very early in cellular evolution. Modern organisms carry out a remarkable variety of energy transductions, conversions of one form of energy to another.
They use the chemical energy in fuels to bring about the synthesis of complex, highly ordered macromolecules from simple precursors. They also convert the chemical energy of fuels into concentration gradients and electrical gradients, into motion and heat, and, in a few organisms such as fireflies and some deep-sea fish, into light. Photosynthetic organisms transduce light energy into all these other forms of energy.
The chemical mechanisms that underlie biological energy transductions have fascinated and challenged biologists for centuries. The French chemist Antoine Lavoisier recognized that animals somehow transform chemical fuels (foods) into heat and that this process of respiration is essential to life. He observed that in general, respiration is nothing but a slow combustion of carbon and hydrogen, which is entirely similar to that which occurs in a lighted lamp or candle, and that, from this point of view, animals that respire are true combustible bodies that burn and consume themselves.
Biological energy transductions obey the same chemical and physical laws that govern all other natural processes.
QUANTITIES OF THERMODYNAMICS
Gibbs free energy, G,- expresses the amount of energy capable of doing work during a reaction at constant temperature and pressure. When a reaction proceeds with the release of free energy (that is, when the system changes so as to possess less free energy), the free-energy change, ΔG, has a negative value and the reaction is said to be exergonic. In endergonic reactions, the system gains free energy and ΔG is positive.
Enthalpy, H,- is the heat content of the reacting system. It reflects the number and kinds of chemical bonds in the reactants and products. When a chemical reaction releases heat, it is said to be exothermic; the heat content of the products is less than that of the reactants, and the change in enthalpy, ΔH, has, by convention, a negative value. Reacting systems that take up heat from their surroundings are endothermic and have positive values of ΔH.
Entropy, S,- is a quantitative expression for the randomness or disorder in a system. When the products of a reaction are less complex and more disordered than the reactants, the reaction is said to proceed with a gain in entropy.
LAWS OF THERMODYNAMICS
1ST LAW
The first law is the principle of the conservation of energy: for any physical or chemical change, the total amount of energy in the universe remains constant; energy may change form or it may be transported from one region to another, but it cannot be created or destroyed.
2ND LAW
The second law of thermodynamics states that the entropy of the universe increases during all chemical and physical processes, but it does not require that the entropy increase take place in the reacting system itself. The order produced within cells as they grow and divide is more than compensated for by the disorder they create in their surroundings in the course of growth and division.
In short, living organisms preserve their internal order by taking from the surroundings free energy in the form of nutrients or sunlight, and returning to their surroundings an equal amount of energy as heat and entropy
CELLS REQUIRE SOURCES OF FREE ENERGY
Cells are isothermal systems—they function at essentially constant temperature (and also function at constant pressure). Heat flow is not a source of energy for cells, because heat can do work only as it passes to a zone or object at a lower temperature.
The energy that cells can and must use is free energy, described by the Gibbs free-energy function G, which allows prediction of the direction of chemical reactions, their exact equilibrium position, and the amount of work they can perform at constant temperature and pressure. Heterotrophic cells acquire free energy from nutrient molecules, and photosynthetic cells acquire it from absorbed solar radiation. Both kinds of cells transform this free energy into ATP and other energy-rich compounds capable of providing energy for biological work at constant temperature.
STANDARD FREE ENERGY
The composition of a reacting system (a mixture of chemical reactants and products) tends 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, Keq. In the general reaction
We must be careful to distinguish between two different quantities: the actual free-energy change, ΔG, and the standard free-energy change, ΔG′°. Each chemical reaction has a characteristic standard free-energy change, which may be positive, negative, or zero, depending on the equilibrium constant of the reaction. The standard free-energy change tells us in which direction and how far a given reaction must go to reach equilibrium when the initial concentration of each component is 1.0 M, the pH is 7.0, the temperature is 25 °C, and the pressure is 101.3 kPa (1 atm).
Thus ΔG′° is a constant: it has a characteristic, unchanging value for a given reaction. But the actual freeenergy change, ΔG, is a function of reactant and product concentrations and of the temperature prevailing during the reaction, none of which will necessarily match the standard conditions as defined above.
Moreover, the ΔG of any reaction proceeding spontaneously toward its equilibrium is always negative, becomes less negative as the reaction proceeds, and is zero at the point of equilibrium, indicating that no more work can be done by the reaction. ΔG and ΔG′° for any reaction aA + bB ⇌ cC + dD are related by the equation in which the terms in red are those actually prevailing in the system under observation.
The concentration terms in this equation express the effects commonly called mass action, and the term [C] c [D] d /[A] a [B] b is called the mass-action ratio, Q.
Notice that when a reaction is at equilibrium—when there is no force driving the reaction in either direction and ΔG is zero— Above Equation reduces to
which is the equation relating the standard free-energy change and equilibrium constant
For the Calculation of the standard free-energy change of the reaction catalyzed by the enzyme phosphoglucomutase,
given that, starting with 20 mM glucose 1-phosphate and no glucose 6- phosphate, the final equilibrium mixture at 25 °C and pH 7.0 contains 1.0 mM glucose 1-phosphate and 19 mM glucose 6-phosphate.
Does the reaction in the direction of glucose 6-phosphate formation proceed with a loss or a gain of free energy?
Solution: First we calculate the equilibrium constant
We can now calculate the standard free-energy change:
Because the standard free-energy change is negative, the conversion of glucose 1-phosphate to glucose 6-phosphate proceeds with a loss (release) of free energy. (For the reverse reaction, ΔG′° has the same magnitude but the opposite sign.)
ACTUAL FREE ENERGY CHANGES DEPENDS UPON REACTANT AND PRODUCT CONCENTRATION
The standard free-energy change tells us in which direction and how far a given reaction must go to reach equilibrium when the initial concentration of each component is 1.0 M, the pH is 7.0, the temperature is 25 °C, and the pressure is 101.3 kPa (1 atm). Thus ΔG′° is a constant: it has a characteristic, unchanging value for a given reaction. But the actual freeenergy change, ΔG, is a function of reactant and product concentrations and of the temperature prevailing during the reaction, none of which will necessarily match the standard conditions as defined above.
Moreover, the ΔG of any reaction proceeding spontaneously toward its equilibrium is always negative, becomes less negative as the reaction proceeds, and is zero at the point of equilibrium, indicating that no more work can be done by the reaction. ΔG and ΔG′° for any reaction aA + bB ⇌ cC + dD are related by the equation
The concentration terms in this equation express the effects commonly called mass action, and the term [C] c [D] d /[A] a [B] b is called the mass-action ratio, Q.
To determine the actual free-energy change, ΔG, under these nonstandard conditions of concentration as the reaction proceeds from left to right, we simply enter the actual concentrations of A, B, C, and D in Equation; the values of R, T, and ΔG′° are the standard values. ΔG is negative and approaches zero as the reaction proceeds, because the actual concentrations of A and B decrease and the concentrations of C and D increase. Notice that when a reaction is at equilibrium—when there is no force driving the reaction in either direction and ΔG is zero—Equation reduces to.
